We have never directly sampled the mantle or cores, but based on how sound travels through them, the mantle is estimated to be about 1,000 ^oC nearest to the crust and 3,700 ^oC near the outer core.  The outer core varies from about 4,500 ^oC near the mantle to about 5,500 ^oC near the inner core.  The inner core is about 5,500 ^oC.  

The heat is thought to come from radioactive decay.  There are radioactive isotopes in the mantle and cores (much more than in the crust), and when radioactive decay occurs, heat is released. 

If you would like a copy of the periodic table to print out, you can find it here:

http://www.drwile.com/endsheet1.pdf

There are four sample laboratory notebook entries for Discovering Design with Chemistry:

Experiment 1.1

Experiment 1.2

Experiment 1.3

Experiment 2.1

There is a document on the course website that contains all the "Comprehension Check" and Review questions, with space between them so you can write in your answers.  You can get that document here:

http://www.bereanbuilders.com/olc/ddchem/dd_worksheets.pdf

Yes, you can use a weight scale instead of a mass scale for the experiments.  However, you will need to convert from the weight unit to grams.  If your scale reads the weight in ounces, multiply by 28.35 to convert to grams.  If it reads in pounds, multiply by 453.6 to convert to grams.  If it reads in Newtons, multiply  by 101.97 to get grams.

Weight and mass are two different things, but on the surface of the earth, the factors given above allow you to convert between them.

Please note that the scale needs to be fairly precise.  It needs to have an precision of 0.004 ounces (which is the same as 0.0002 pounds or 0.0009 Newtons).

It depends on what you are trying to cover.  If you want to cover a full year's worth of university-level chemistry in high school (this is typically referred to as an "AP course"), then yes, the student needs to take Advanced Chemistry in Creation after he or she takes Discovering Design with Chemistry.  However, if your goal is a solid, university-prep chemistry course, then Discovering Design with Chemistry is all the student needs.

Each semester final should be given twice the weight of an individual chapter test.  Since there are eight chapters for each semester, that means you should add the eight chapter test grades together and then add the semester test grade multiplied by 2.  Once you have that sum, divide by 10, and that will be the test average for the semester.

The grades on the lab reports shouldn't be based on the results, but instead on three criteria:

(1)  How well did the student follow instructions?

(2)  If there are calculations involved, did the student do the calculations properly (including with the proper number of significant figures)?

(3)  If you had never read the student text, could you understand what the student did and what was learned by simply reading the student’s notebook?
 

The third one is the most important.  If you want to assign point totals, I would say:

(1)  How well did the student follow instructions? (30 points)

(2)  If there are calculations involved, did the student do the calculations properly (including with the proper number of significant figures)?  (20 points)

(3)  If you had never read the student text, could you understand what the student did and what was learned by simply reading the student’s notebook?  (50 points)

This course will work well in a 32-week co-op.  Two weeks per chapter is a good pace.  The experiments are also well-suited to groups.  The pace of this book is very similar to the pace of the second edition of Exploring Creation with Chemistry, so if you have used that book in your co-op, this one will work nicely as well.

There really is no need for the Microchem kit with Discovering Design with Chemistry.  There are 45 experiments in the course, and many of them are more detailed than what is in the Microchem kit.  That was a great kit for supplementing Exploring Creation with Chemistry, but it just isn't necessary for Discovering Design with Chemistry.

Copper ions have similar solubility properties as silver ions.  Thus, copper iodide (and all copper + Group 7A ions) are only slightly soluble in water.  As a result, any significant concentration of it will result in a precipitate.  Here is an expanded list of solubility rules that includes copper:

http://www.ausetute.com.au/solrules.html

The actual solubility of copper iodide is 0.004 grams of copper iodide per 100 grams of water.  Thus, any reaction between copper nitrate and potassium iodide that makes more than 0.004 grams of copper iodide per 100 grams of water will produce a precipitate.

Yes, you could do this in a 24-26 week schedule.  There are two options.  I prefer the first one:

1) Encourage the students to work through the book at their own pace, not worrying about getting done when the co-op is done.  That way, they will be doing some experients ahead of the content, but that's fine.  If you do that, here are the experiments I would do: 1.3, 2.1, 2.3, 3.2, 4.2, 4.3, 5.2, 6.1, 6.3, 7.1, 7.3, 8.1, 9.1, 9.3, 10.3, 10.4, 11.2, 11.3, 12.2, 13.2, 13.3, 14.1, 15.1, 16.2, 16.3

2) Try to cover the content at the same pace as the co-op.  This will be tough for many students.  I would do the same experiments, but I would monitor the students carefully, because that is a short period over which to cover a dense course!

The course website, which is discussed in the introduction to the book is at:

http://www.bereanbuilders.com/olc/ddchem

On the website, you will find a link for each chapter.  When you click on the link, there will be several links that appear, all related to that chapter.  At the very bottom is a link to extra practice problems, with another link to the solutions.

Yes, there is.  The recording was completed in the middle of June (2016), and it is in the final editing stage.  It should be realeased in the third week of July, 2016.  It will be available from Berean Builders:

http://www.bereanbuilders.com

There is always error in the last significant figure.  As a result, when numbers differ by 1 or 2 in the last significant figure, they are treated by scientists as being the same.  If your student's answer differs from the book's answer by 1 or 2 in the last significant figure, you shouldn't take any points off.  

For example, 18.99 and 19.00 differ by only 1 in the last significant figure.  Thus, from a scientific point of view, they are the same.  Either is correct.  Answers such as 18.98, 19.01, and 19.02 would also receive full credit.  

There are alternate tests for the course.  To get them, email me at:

me@drwile.com

Just let me know that you are a teacher needing alternate tests, and I will send them to you.

You can get the list of elements that is on the inside cover of the book here:

http://www.drwile.com/elements_list.pdf

The only problems I have for the course are the ones in the book and the extra practice problems on the course website.  However, there are a few resources online that might help.  You can look at these websites and try to find the topics that you need more problems for:

http://www.chemteam.info/ChemTeamIndex.html

http://chemistry.about.com/od/workedchemistryproblems/a/workedproblems.htm

http://chemistry.about.com/od/testsquizzes/a/worksheets.htm

Any calculator that has the word "scientific" in its description will work for the chemistry course.  I personally prefer no-frills models, like this one:

https://www.amazon.com/Texas-Instruments-TI-30Xa-Scientific-Calculator/dp/B00000JBNS/ref=lp_172525_1_5?s=office-electronics&ie=UTF8&qid=1475026729&sr=1-5&th=1

The purpose of each experiment is discussed in the book itself, because I am using the experiment to illustrate something that the student is learning at the time.  For example, in Experiment 1.1, the student is determining the conversion factor between inches and centimeters.  Right before that experiment, I tell the student:

"Centimeters comes from a completely different unit system (the metric system), but since they also measure length, there should be some relationship between centimeters and inches. In the following experiment, you are going to figure out that relationship."

After the experiment, I discuss the result and what it means.  This is true for each experiment.

Strontium chloride comes with the kit that is included in the course.  However, if you are putting something together yourself, you can get strontium chloride from:

http://www.workshopplus.com/ProductCart/pc/viewPrd.asp?idproduct=4505&idcategory=0

You can also substitute lithium chloride for strontium chloride in Expeirment 3.4 and calcium chloride for strontium chloride in Experiment 9.4.

You can find denatured alcohol at most hardware stores as well as home-improvement stores. You can also find it in stores that sell catering materials (fondue and chaffing fuel), camping equipment (stove fuel), and marine supplies (marine stove fuel). It is sometimes called "denatured ethanol," "denatured ethyl alcohol," or "methylated spirits." Methanol and methyl hydrate are acceptable substitutes. Here are some brand names:
Kleen Strip Green
Bioflame
Blue Flame Fondue Fuel
Crown Alcohol Stove Fuel
Heet (NOT ISO Heet)

You may also use 70% isopropyl alcohol found in many stores. Make sure you don't use rubbing alcohol.

There are a few different consumer products in Canada that you can use for the experiments that require denatured alcohol.  Marine stores sell "Marine alcohol," which is denatured alcohol:

http://www.stevestonmarine.com/Captain-Phab-Marine-Stove-Fuel-Alcohol1L-CAP307?search=marine%20alcohol

Hardware stores sell "bioflame," which is also denatured alcohol:

http://www.homehardware.ca/en/rec/index.htm/Indoor-Living/Housewares/Giftware/Decorator-Lighting/Repl-Parts-Fuel/946ml-Ethanol-Fireplace-Fuel/_/N-ntkmmZ2pph/R-I4360521

You can also use methanol, which is sold as Methyl Hydrate

http://www.canadiantire.ca/en/pdp/methyl-hydrate-0497127p.html#srp

Finally, you may also use "Blue Flame Fondue Fuel".

It is important for a homeschooled student to document his or her experiments, because some universities require proof that a homeschooled student actually had a laboratory component for the course.  However, documentation doesn't mean a lab report.  In the introduction to the book (p. iv), I discuss how students should keep a lab notebook.  I think it would be good to have a lab notebook entry for each experiment.  That way, an evaluator can see exactly how much experimentation was done in the course.  The notebook entry isn't a report, however.  It is simply a record of the data (observations and measurments made in the expeirment) and a brief (NOT step-by-step) summary of what was done and what was learned.  There are samples of notebook entries on the course website, which is also discussed in the introduction to the book (pp. ix-x).

I do have an advanced chemistry book.  It is published by Apologia.  It's called Advanced Chemistry in Creation, and when added to Discovering Design with Chemistry, it covers all that is covered in the Advanced Placement Chemistry syllabus.

https://www.christianbook.com/advanced-chemistry-creation-2nd-edition-full/jay-wile/pd/236548?event=ESRCQ

Each student will use about 15 g of sodium hydroxide and 10 g of strontium chloride throughout the course.  If you are doing lab groups, each lab group will use those amounts.

Each student needs 30 grams of cupric sulfate to do all of the labs in the course.  If you are doing groups, each group needs 30 grams.

If you do your transcript by semester, just call the three semesters "Chemistry 1," Chemistry 2," and "Chemistry 3."  If this course is done in a year, it is an honors-level course.  Thus, it can be done over three semesters and count as a normal high-school-level course.

If you do your transcript by subject, list "Chemistry" with 1.5 years' worth of credit.  This is commonly done with honors courses, so it won't look odd for chemistry to have more than 1 year's worth of credit.

You can pour all of the chemicals used in this course down the drain.  It is best to use lots of water, just to make sure there isn't any residue left in the sink. 

Technically, it is done by hours.  Students need to spend 30 hours in lab.  That would translate to about 30-35 experiments, depending on the experiments you choose.  If you complete all 46 experiments and all the chapters, it is the equivalent of an high school honors chemistry course.

Skip the following:

Experiment 1.1: Determining the Relationship Between in and cm

Experiment 2.2: The Conservation of Mass

Experiment 3.1: The Wavelength of Microwaves

Experiment 4.2: Comparing a Metal and a Nonmetal

Experiment 6.2: In Between and All Around

Experiment 6.3: Copper-Plated Nails

Experiment 6.4: Burning Iron

Experiment 7.2: The Limiting Reactant

The SPARKlab links on the course website are for use with digital probes that have been made by PASCO.  These are for people who want to use computer-integrated technology in some of their labs.  The program that opens them is the program that controls and reads the probes:

https://www.pasco.com/prodMulti/sparkvue-software/index.cfm

This is a supplement that is not a part of the standard course.  

That is probably the most interesting question I have answered on this site!  The word "amphoteric" (can act as either an acid or a base) always makes me smile.

As I say on page v of the Answer Key and Tests book, I don't think semester tests are necessary.  Thus, if you are following the schedule in the Appendix, don't do them.   I just provide them in case parents want their students to have cumulative tests.

A product called methylated spirits in Australia and New Zealand is an acceptable denatured alcohol for use in the burner found in the lab kit.

https://www.bunnings.com.au/diggers-methylated-spirits-1l_p1560782

I do not require students to write formal lab reports.  I do not see any serious benefit to that.  They need to learn how to document their labs, and that's what the notebook is for.  There are sample notebook entries on the course website that help them see how a lab should be documented, but that's all they should be required to do.

It can only be used if it is 70% pure.  Most isopropyl alcohol has a lot of water in it, so it won't burn hot enough to boil water.  It is best to go to the hardware store and buy denatured alcohol.  

There aren't reviews for the semester exams.  The best review would be to go over each chapter test in the semester.

There is a PDF of the reading schedule on the course website.  It is the second link on this page:

https://bereanbuilders.com/ecomm/online-content/discovering-design-with-chemistry/ddc-omnibus/

The answers to the comprehension checks are near the end of the chapter, right before the sample experiment calculations (if the chapter has them) and the chapter review.  For Chapter 1, they start on page 27.

I wrote the tests to take an hour, but I don't necessarily think students should be required to get it done in that amount of time.  It is a good benchmark, however.

I am a strong proponent of doing the experiments before the students do the reading.  That's because I designed the course for the students to do the experiment and then read about what happened.  That way, they have the experience in mind as they read the explanation.  In a co-op setting, this is best acheived by having the students do the experiment before they do the reading.  Of course, this means they will not be able to write up the experiment until later, but that's fine.  You can always help them with questions they have about the write up the next time you meet for class.

The best way to watch the videos is to go here:

https://bereanbuilders.com/ecomm/vod/ddc/

"Syllabus" tells you what each class covers, and when you click on the class, you see the video that you rented at the top, and all the videos to which I refer directly below.

I wrote a blog article that details the answer to this question. You can find it here:

https://blog.drwile.com/what-are-the-differences-between-my-old-chemistry-course-and-my-new-chemistry-course/

The 2.0x10^3 g has only two significant figures, so the answer can have only two. The number is, indeed 44,400J, but you can only report that to two significant figures, which means 44,000J

Since the People's Republic of California is not allowing the sale of denatured alcohol, the best substitute is

99% isopropyl alcohol

It should be sold in pharmacies.

The AP exam covers a year of university-level chemistry.  Since Discovering Design with Chemistry is an honors-level high school course, it covers only 65-75% of what is covered in an AP course.  However, many students are very successful on the AP exam if they finish Discovering Design with Chemistry and then spend time in an AP chemistry review book, such as:

https://www.amazon.com/Princeton-Review-Chemistry-Premium-Prep/dp/0593516761/

There are three sample laboratory notebook entries for this chapter:

Experiment 1.1

Experiment 1.2

Experiment 1.3

It doesn't matter.  In the number 300.0002, all five zeroes are significant.  Remember, a significant figure represents a digit that has actually been measured.  If the instrument used was precise enough to measure the "2," it had to be able to measure all the decimal places in between as well.

If you are getting a "scale overload" error on your scale when you measure the filled graduated cylinder in Experiment 1.3, the scale is probably bad.  It is supposed to go from 0 to 500 g.  The graduated cylinder doesn't even weigh 100 g, and the water would only weigh 50, so there is no reason the scale should overload.  I guess one thing is to make sure you hit the "tare" button when there is nothing on the scale, to make sure it is reading 0 grams when nothing is on the scale.  If you have done that and it still reads an overload, your scale is not working.

If you bought it from Nature's Workshop Plus or Berean Builders, call 317-745-0443 to get it replaced.  If you bought it from another vendor call that vendor.  Make sure the vendor understands that the scale is supposed to have a range of at least 0 to 500 g.

The student is expected to recognize that the ruler is marked off in centimeters, since there are 10 marks between the numbers.  If the student reports the answer in inches, take off 1/4 of a point.

As a general rule of thumb, round at the end of every equation, unless there is a change of rules. So, if the equation is: (223.1)x (13.7)/12 Do all the multiplication and division and then round to two significant figures. However, if the equation is: 12.3x(4.5 - 4.22) You need to do the subtraction first, round to the tenths place, then do the multiplication and then round to one significant figure. If a problem's solution has multiple steps involving multiple equations, follow this rule for each equation.

The first answer in Example 1.3 doesn't need a unit because there isn't one.  When the centimeters cancel in the math, you are left with no unit.  Thus, you can't list one.  The answer isn't 0.151 inches or 0.151 centimeters, because there isn't any kind of unit.  The answer is just 0.151.  

There is actually a physical reason for this.  Suppose I measure the length of something to be 15.423 cm (the first number in the problem).  Then, suppose I measure its width to be 102 cm (the second number in the problem).  If I divide the length by the width, I get 0.151.  Now...suppose I take the same object and measure its length and width in inches instead of centimeters.  When I divide the two, I will still get 0.151.  This is why 0.151 has no units.  Regardless of the units you use, as long as you use the same unit in each measurement, you will always get 0.151 when you divide the two measurements.  Thus, 0.151 is independent of units.  That's why it has no units.

How do you know whether or not to list units?  You always list the unit, if there is one.  In the second part of Example 1.3, 7.0 in is mulitplied by 4.209 in.  The units don't cancel there.  They end up becoming in².  Since the units don't cancel, you must list the result: in².

Significant figures do not reduce accuracy.  They ensure that your answer is reported to the proper precision.  

In a calculation like 70 g x 4 g, the initial answer is 280 g², but that is too precise for the data you have.  A measurement of 70 means the measurement could be something like 68 g or 73 g.  If your measuring device can only be read to ten grams, then it cannot determine the ones position, so masses of 68 g and 73 g, for example, would both read as 70.  In the same way, a measurement like 4 g could be something like 3.8 g or 4.3 g.  Both of those masses would read as 4 g in a scale that can only read to the ones place.  So, when you multiply the two, the answer could something like:

68 g x 3.8 g = 258.4 g²

or it could be something like:

73 g x 4.3 g = 313.9 g²

Based on the precision to which you know each mass, those results would be possible as well.  Note how both of them round to 300 g².

By properly reporting the answer to one significant figure (300 g²), you are indicating just how well you know the result.  If you reported your answer as 280 g², it would indicate that you know the answer to a higher precision than you actually know the answer.

Remember that addition and subtraction use different rules from multiplication and division.  In addition and subtraction, you do not count significant figures.  Instead you report your answer to the same precision (decimal place) as the least precise number in the problem (see the pink box on page 6).

In this problem, the numbers are 3.1 and 8.991.  The first has its last significant figure in the tenths place.  The second has its last significant figure in the thousandths place.  The tenths place is less precise, so you must report your answer to the tenths place.  That's why the answer is 12.1 inches.

You might want to relook at Example 1.2, which shows you how to use significant figures in addition and subtraction.

On page 3, when explaining a ruler, I tell you, "As a general rule of thumb, when you are reading a measuring device that has a scale to read, you can read the scale to a division below what is marked off."  This is because you can estimate between the lines that are marked off.  

If you look at the graduated cylinder on page 16, there are 9 little marks between the numbers, and each number marks off 10's of mL.  That means each little mark represents 1 mL.  After all, if there are 9 marks between 90 and 100, the marks are 91, 92, 93,...99.

You can estimate where the meniscus is between those little marks, so that allows you to read to the tenths place.  So, as the discussion on that page tells you, you can see that the meniscus is a bit above 87, but still below 88.  That means it is something like 87.2.  The "87" is marked, and the "0.2" is your estimate between the lines.  That's the best you can do.  There is no way you can estimate hundreths, so a graduated cylinder can't be read to the hundredths place.

76000.0 g has 6 significant figures, because the last zero is significant, since it is at the end of the number and to the right of the decimal point.  That makes all the other zeroes significant as well.

76000 g has only 2 significant figures, because there is no decimal, so none of the zeroes at the end of the number are signficant.

The idea here is that the zeroes in 76000 g are not measured.  They are there because they have to be, to give the right value to the number.  However, the measuring device wasn't precise enough to measure them.  If you wanted to report 76000 g to a precision that indicated all those zeroes are significant, the only way you could do that is to put it in scientific notation:

7.6000x10⁴ g

With the decimal point there, now all the zeroes are significant.  So if you had measured the mass to a precision of 1 gram, that's how you would have to report it.

Think about the ruler for a moment.  You are determining the length of what you are measuring using the lines that are drawn on the ruler.  How thick is one of the lines that represents each 16th of an inch?  It is probably more than 1/100 of an inch wide.  Thus, if something ends up on the mark, it could be as much as 1/100 less than 1/16 or 1/100 more than 1/16.  There is simply no way to know what part of the line actually represents that exact 16th of an inch.  As a result, there is no way to know what is EXACTLY 1/16 of an inch, or 1/32 of an inch.  Because of this, there is no way to read the ruler to that kind of precision.  The width of the lines themselves limit how precise the ruler is.

Your experiment showed you that:

1mL = 1 cubic centimter

So...if you have liters, you need to convert to milliliters.  After that, whatever you have in mL is also the volume in cubic centimers. 

For example, if you have 0.456 liters, you first convert to mL:

(0.456 L/1) x (1 mL/0.001 L) = 456 mL

That means the volume is also 456 cubic centimeters.

Remember the rules of significant figures.  When multiplying, the answer has to have the same number of significant figures as the measurement with the least.  45.5 cm has three significant figures, but 9 cm has only one.  So the answer can have only one significant figure.  410 has two significant figures.  400 has only one significant figure, so that's the correct answer.

Since you can only have two significant figures in the answer, you have to drop th "4" and "9."  The problem is, that leaves you with "10," which has only one significant figure.  As discussed in the text, this is a situation in which you need to use scientific notation.  By putting the answer in scientific notation, you put in a decimal.  That makes the zero significant.  Thus, the answer has to be 1.0x10^1 g/mL, or 1.0x10 g/mL.  that way, the zero is at the end of the number and to the right of the decimal, making it significant.  As a result, that gives you two significant figures, which is what the rules say you need.

Mass tells you the total amount of matter in a substance, while density tells you how tightly-packed that matter is.  

Consider two objects, each of which has a mass of 1,000.0 grams.  The first object is the size of a golf ball, and the second object is the size of a basketball.  They each have the same total amount of matter in them (1,000.0 grams).  However, the first object has that matter packed in a small amount of space, while the second object has it packed in a much larger amount of space.  So while both have the same mass, the density of the first object is much higher than the density of the second object.

A conversion relationship tells you how two things relate to one another.  For example, the prefix "centi" means 0.01.  That means a centimeter is 0.01 meters.  We can write that as an equation:

1 cm = 0.01 m

That's a conversion relationship.  Now...since the to sides equal each other, multiplying by a fraction that has one side on the top and the other side on the bottom is like multiplying by 1.  It doesn't change the value, but it can change the unit.  So....if I have something that measured 15.1 cm, I could multiply it with a fraction made up by the conversion relationship.  If I take the "1 cm" side of the equation and put it on the bottom of the fraction that will allow the "cm" unit to cancel.  Thus:

(15.1 cm/1)x(0.01 m/1 cm)

will cancel the cm and leave m.  In other words, this is how we can convert between cm and m.  15.1 times 0.01 is 0.151, so 15.1 cm is the same as 0.151 m.  On the other hand, if I have something that measured 4.3 m, I could convert it to cm by multiplying with the fraction the other way around:

(4.3 m/1)x(1 cm / 0.01 m)

Now m cancels and we are left with cm.  Since 4.3 divided by 0.01 is 430, that means 4.3 m is the same as 430 cm.

Remember that you have to worry about significant figures.  The mass (55,670 g) has four.  That last zero is not significant, because it is not to the right of the decimal.  It needs to be BOTH at the end of the number AND to the right of the decimal.  The density (2.70 g/mL) has three.  That last zero is significant, because it is both at the end of the number and to the right of the decimal.  That means the lowest number of significant figures you have is three, so your answer can have only three.  20,600 mL has three.  The last two zeroes are not significant, because they are not to the right of the decimal.  They need to be BOTH at the end of the number AND to the right of the decimal.   The zero after the "2" is significant, since it is between two significant figures.

I stop between conversions in order to make the steps more clear.  However, students need not do that.  Their answers might not exactly match mine, but that's okay, because there is always error in the last significant figure.

The only time you should stop and worry about significant figures is when you change from addition/subtraction to multiplication/division or vice-versa.  When that happens, you also change the rules for significant figures, so you have to round with the rules of the process you are currently using and then continue with the next process and round that process with the new rules.  So in a situation like this:

(12.12)x(1.2) - (4.56)x(92.111)

You would do each multiplication and round based on the number of significant figures.  Then you would do the subtraction and round based on the precision of the numbers that you just determined.

When you round, you look at the first number you drop.  If it's 0-4, you do nothing, if it's 5-9, you round up.  Since you are dropping a "6" to make it three significant figures, you have to round up, so the final answer is 6.00x10³.  This is an example of an answer that MUST be in scientific notation, since that's the only way to give it three significant figures.

When you add and subtract, the errors affect each other in a specific way.  When you multiply and divide, they affect each other in a completely different way.  That's why there are two completely different rules.  One rule deals with how error is affected by adding and subtracting, while the other rule deals with how error is affected my multiplying and dividing. 

When you add 3.1 and 8.991, the second number is so very precise that there is no question about the value of the first three digits (8.99).  Only the last digit (the 1) has some error in it.  However, for 3.1, the 1 has error in it.  Thus, the 3 is the only number that is certain.  Both measurements are certain in the ones place, so your answer can be certain in the ones place.  However, the first number (3.1) has uncertainty in the tenths place, so adding it to anything will also produce uncertainty in the tenths place.  Thus, your answer must have uncertainty in the tenths place.  As a result, the answer is 12.1, because it is certain in all 12 of the ones, but it is not certain in the tenths place.  It doesn't matter that 12.1 has more significant figures than 3.1 and less than 8.991.  It only matters which decimal place is uncertain.

For multiplying and dividing, the decimal place doesn't play a role anymore, because you are making a much bigger change than adding or subtracting.  Counting significant figures takes that into account.

Remember that the "1" always goes with the unit that has the prefix.  The definition of the prefix always goes with the base.  So:

1 km = 1,0000 m

1 cL = 0.01 L

1 mg = 0.001 g

Notice that in all cases, the 1 is with the unit that has the prefix (km, cL, mg).  The definition of the prefix is then with the base unit (m, L, g).  When you multiply, you put the unit you want to cancel on the bottom of the fraction, along with its number.  So to convert from km to m, you want km to cancel, so you would multiply by (1,000 m/ 1 km).  If you want to convert from L to cL, you need L to cancel, so you would multiply by (1 cL / 0.01 L).

There are four.  The last zero is significant, because it is at the end of the number and to the right of the decimal.  That makes the other two zeroes in between significant figures.  800 has only one significant figure, but 800.0 has four.

You  can always use it if you want to use it, but the only time you MUST use it is when significant figures demand it.  For example, if you are solving this:

3.0x33.4

The answer is 100.2, but you can have only two significant figures because of the 3.0.  Thus, you have to report 100 to two significant figures.  The only way to do that is with scientific notation: 1.0x10².  However, if you have this equation:

3.000x33.40

The answer is 100.2 and you can keep all those significant figures.  Thus, you can call it 100.2 or 1.002x10².

It doesn't need to be.  The answer only requires two significant figures, and 740,000 cg has two significant figures.  You could put it in scientific notation if you want (7.4x10⁵ g), but you don't need to.  The only time you must use scientific notation is when it is required by the significant figures rules. Any other time, its use is optional.

Here is a sample laboratory notebook entry for this chapter:

Experiment 2.1

Using a proportion is fine.  If the student sets it up as:

11.2/75.0 = amount copper for new/29.86 g

11.2/75.0 = amount sulfur for new/15.06 g

11.2/75.0 = amount oxygen for new/30.1 g

he or she is using the same reasoning that I am using.  The answers the student gets might be a bit different from the ones in the book, but only by 1 or 2 digits in the last significant figure.  Since there is always error in the last significant figure, however, that is not a problem.

Multiplying by an exact number is the same as adding.  Thus, when "2" is exact, 2x6.4 is really 6.4 + 6.4.  Since that is an addition problem, we use the rules of addition and subtraction, which go by the decimal place.  Since 6.4 goes out to the tenths place, the answer must go out to the tenths place as well.  That's why the answer is 12.8 g.

However, the student might not understand that yet, so if the student gives the answer as 13 g, that's fine.  When the student starts adding atomic masses together, the fact that multiplying by an exact number is actually addition will be discussed explicitly.

In the plum pudding model, the electrons are in the pudding.  The alpha particles are repelled by the pudding, but they are attracted to the plums.  On average, then, the attraction and repulsion cancel, and the alpha particles travel pretty much straight.  This is different from the Rutherford model, because there, the electrons are away from the positive charges.  Thus, there is nothing to cancel the positive charge's repulsion, and the alpha particles are deflected.

When you have a situation where you add masses, like:

10.2 g + 98.1 g + 45.6 g = 153.9 g

You are gaining significant figures, but that's okay, because you are using the rule of addition and subtraction, which doesn't count significant figures. 

Remember, the rules are different because an operation like adding or subtracting is different from an operation like multiplying or dividing.  Addition and subtraction doesn't change the measurements nearly as much as multiplication and division, so the operations affect the precision of the measurements in different ways.  The different rules take that into account.

In this case, we want to make LESS than the known recipe, so we have to scale down.  That means the multiplication factor is less than one.  The way to remember it is ALWAYS divide the amount you want to make by the amount you know how to make.  That will always give you the right multiplication factor.

The frequency of a microwave is generally about 2,500 megaHertz, which is 2.5x10⁹ Hz.  If you see "60 Hz" on a label, that's for the power coming in from the power cord, not the microwaves.  Look for a frequency labeled in "MHz," which is megaHertz.  That stands for a million Hertz.

Let's suppose you have a wavelength of  3.95x10^-7 m.  To turn that into frequency, you would need to do:

f = (c) / (wavelength)

So you need to divide c (3.0 x 10^8 m/s) by 3.95x10^-7 m.  

When you divide 3.0 x 10^8 by  3.95 x 10^-7, you are dividing 3 by 3.95 and 10^8 by 10^-7.  3.0 divided by 3.95 is 0.76.  What's 10^8 divided by 10^-7?  When you divide numbers with exponents, you SUBTRACT the exponents.  So 10^8 divided by 10^-7 is 10^(8 - -7), which is 10^15.  Thus, the answer is 0.76 x 10^15, which is the same as 7.6 x 10 ^14.

Of course, it is much easier to do this on your calculator.  Most calculators have an "EE" or "EXP" key.  That key abbreviates "x 10^".  So, let's assume your calculator has an "EXP" key.  The calculator that comes on Windows computers is like that.  Here is how you would input the division:

3.0 EXP 8 divided by 3.95 EXP 7 +/- =

That should give you the proper answer, 7.6 x 10^14.

Try doing it without the juice glasses, sitting the pan on the bottom of the microwave oven.  Different microwaves are set up differently.  For most, the upper part of the oven is sensitive to the crests and troughs of the waves.  For some, it is the lower part.  If nothing else, you can watch this video:

https://www.youtube.com/watch?v=eVw1EPvdFDE

The important thing is to learn how to put scientific notation in your calculator.  Most calculators have an "EE" or an "EXP" button.  That abbreviates "x10^"  Thus, when you put in

3.00 x 10^8

You must input it as 3.00 EE (or EXP) 8.  Your calculator will then show 3.00 with a little "08" on the right.  That means 3.00 x 10^8.  To continue, you would hit the divide button, and then to input

2.31 x 10^-7

you would hit 2.31 EE (or EXP) 7 +/-.  Your calculator will then show 2.31 with a little "-07" on the right.  That means 2.31 x 10^-7.  When you hit the equal sign, you should see a 1.2987 with a little "15" on the right.  That means 1.2987x10^15.

If your calculator doesn't have an EE or EXP button, you need to look at the manual and learn the proper way to input scientific notation.

Strontium chloride comes with the kit that is included in the course.  However, if you are putting something together yourself, you can get strontium chloride from:

http://www.workshopplus.com/ProductCart/pc/viewPrd.asp?idproduct=4505&idcategory=0

You can also substitute lithium chloride for strontium chloride in this experiment.

You don't see color from the chlorine ion in NaCl and SrCl₂ or the sulfate ion in cupric sulfate because those substances do not emit light in the visible spectrum.  The electron energy levels of negative ions tend to be very far apart, so the light they emit when excited is very high energy (ultraviolet).  As a result, the light is there, but you don't see it.

It is best to use a scientific calculator in these problems.  Most calculators have an "EE" or an "EXP" key, which abbreviates "x10^"  Thus, for the first equation:

(475/1) x(10^-9/1)

you would enter:

475

x

1 EXP 9 +/-

=

The calculator should display 4.75 with a small -7 at the top right, indicating the answer is 4.75x10^-7

For the next equation:

(3.00 x 10⁸)  / (4.75x10^-7)

you would enter

3.00 EXP 8

divided by

4.75 EXP 7 +/-

That will give you 6.32 with a little 14 on the top right, indicating 6.32x10¹⁴

You can do the equations longhand, remebering that when you multiply numbers with exponents, the exponents add and when you divide, they subtract.  Thus:

(3.00 x 10⁸)  / (4.75x10^-7)

becomes 

3.00/4.75 x 10⁸/10^-7

3.00 divide by 4.75 is 0.632

10⁸ divided by 10^-7 is 10 raised to the 8 - -7, which is 15.  Thus, you have:

0.632 x 10¹⁵

To put this in scientific notation, you have to move the decimal to the right one place.  That makes the number bigger, so to compensate for that, you make the exponent smaller:

6.32 x 10¹⁴

When an electron moves to a lower orbital (closer to the nucleus), it has to emit light because it has too much energy to be in the lower orbital.  So, it gets rid of that excess energy by emitting light.  When an electron moves to a higher orbital (away from the nucleus), it needs to gain energy, because it doesn't have enough energy to get to the higher orbital.  It gains that energy by absorbing light.

Remember, energy can't be created or destroyed.  So, when an electron does something that requires more energy than it has, it needs to gain that energy.  The energy can't be created, so it must be taken from something.  The electron absorbs light, taking the light's energy.  When it does something that requires less energy than what it has, it needs to lose that energy.  It does that by emitting light, and the light takes that energy away.

Any "oven safe" saucer will work great.  If it shouldn't be placed under a broiler, it probably shouldn't be used.  You also don't have to use a saucer.  If you have a metal pie pan or something like that which will fit in your sink, that will work as well.  It just needs to be something that can get hot without melting or catching on fire and can also fit in a sink.

If you are getting a number that is way off for your answer, you are not entering the scientific notation properly in your calculator.  If you do the math longhand, you can come up with the proper answer:

(2.49 x 10^-23) / (1.66 x 10^-24)

You can do the numbers and exponents separately:

(2.49/1.66)x(10^-23/10^-24)

2.49 divided by 1.66 is 1.50

When dividing numbers with exponents, you subtract, so:

(10^-23/10^-24) = 10^{-23 - -24} = 10¹

So the answer is 1.50x10¹, or 15.0.

You need to find out how to properly put scientific notation into your calculator.  It depends on the calculator, but you should be able to google instructions, if you use your calculator's make and modle.

It's an attempt to label the most common charges for the last two transition metal groups.  In most ionic compounds, copper, silver, and gold usually take on the 1+ charge, while zinc, cadmium, and mercury usually take on the 2+ charge.  However, that doesn't really apply to the numbers of the other B groups, so it's not clear why it's still in use.

We have the equation

f = (c) / (wavelength)

Doing algebra to solve for wavelength tells us:

wavelength = (c) / (f)

So you need to divide c (3.00 x 10⁸ m/s) by 7.89x10¹² 1/s.  

It is best to do this on your calculator.  Most calculators have an "EE" or "EXP" key.  That key abbreviates "x 10^".  So, let's assume your calculator has an "EXP" key.  The calculator that comes on Windows computers is like that.  Here is how you would input the division:

3.00 EXP 8 divided by 7.89 EXP 12 =

That should give you the proper answer, 3.80 x 10^-7 m.

To get to nanometers, you use the fact that 1 nm = 10^-9 m.

(3.80 x 10^-5 m / 1) * (1 nm / 10^-9 m)

Once again, it is best to do this on your calculator.  Remember that 10^-9 can also be expressed as 1x10^-9.  In the calculator, then, you would put:

3.80 EXP 5 +/- divided by 1 EXP 9 +/- =

That should give you 380 nm.  You need three significant figures, however, so the only proper way to express the answer is 3.80x10² nm.

Yes, there really are 98 naturally-occurring elements.  Most websites and texts list 92, but that's just not true.  Elements 1-92 are stable (with the exception of technetium), so some texts and websites say there are 91 naturally-occurring elements.  However, both of those numbers are wrong.  Some of the unstable elements are made by natural processes and exist in trace quantities in nature.  In uranium-rich pitchblende, you can find traces of technetium, neptunium, plutonium, americium, curium, berkelium, and californium.  They are all produced in small quantities by the breakdown of uranium-235 and uranium-238.  Now, it was once thought that all seven of those elements can only be artificially produced (indeed, that's how they were discovered), but we now know differently. 

https://www.thoughtco.com/how-many-elements-found-naturally-606636

Thus, the current number of naturally-occurring elements is 98.

For #9, remember that the energy of light that is emitted is equal to the difference in energy between the orbits.  Orbit 2 is farther from the nucleus than orbit 1, so it has a higher energy than orbit 1.  However, orbit 5 is even farther away, so it has an even higher energy.  When the electron moves from 5 to 1, then, it must emit more energy than when it moves from 2 to 1.  Remember that energy is determined by frequency, so the higher the energy, the higher the frequency.  However, frequency are wavelength are inversely related, so the higher the frequency, the SHORTER the wavelenth.  

For #10, you have to think about every possible way the electron can move from n=4 to n=1 (which is always the ground state).  It can jump directly from 4 to 1.  That will result in one wavelength of light.  However, it can go from 4 to 3 and then 3 to 1.  That will result in 2 more wavelengths.  Continue that reasoning to figure out the answer.

Remember, an electron has many choices as to how it releases its energy, but it must make it to the n=1 orbit.  Each jump from one orbit to another requires a specific energy and thus a specific wavelength. 

It starts in n=4.  It could jump straight down to n=1.  That would be one amount of energy to release, and therefore one wavelength of light that must be emitted.  However, it could also go first to n=3 and then to n=1.  The first jump requires a specific energy, as does the second.  That's two more wavelengths of light.  It could also go first to n=2 and then n=1.  That's two more energies and thus two more wavelengths.  It could also go to n=3, then n=2, then n=1.  However, we already considered it going from n=2 to n=1, so that doesn't count as a new energy and thus it is not a new wavelength.  We also already considered it going first to n=3, so that is also not a new energy and not a new wavelength.  We have not considered it going from n=3 to n=2, so that IS a new energy and thus a new wavelength.  That makes a total of six.

Hydrogen's ideal electron configuration exists when it has two electrons, because then it is like the nearest noble gas, helium.  As a nonmetal, it will gain an electron to get its ideal configuration. 

If bubbles appear on one tack and not the other, your battery is fine.  The only way bubbles could form on either tack is if electricity is being conducted.

The tack touching the positive terminal of the battery might not have looked like it was bubbling, but it probably was.  The oxygen that is forming there tends to make tiny bubbles that can be hard to see through the water.  One thing you might try to do is add significantly less salt (1/2 of a teaspoon instead of a tablespoon).  When the concentration of salt is high, other reactions can occur, which might obscure the oxygen being formed.

On page 119, just below the definition of electrolysis, the text says, "So the only chemical in the experiment that was actually changing was the water.  The salt didn’t change, nor did the sugar."  However, they both dissolved in the water.  Isn't that a change?

As you will learn in an upcoming chapter, when a chemical dissolves, the chemical itself does not change.  Salt water tastes salty because the dissolved salt is still salt.  Sugar water tastes sweet because the dissolved sugar is still sugar.  So the only chemical that changed in the experiment was water.  It stopped being water and became hydrogen and oxygen instead.  The salt stayed salt, and the sugar stayed sugar.

The quantum mechanical model of the atom is one in which the electrons are treated as waves rather than particles.  As the text discusses, electrons can act as either particles or waves.  The Bohr model treats the electrons as particles that orbit the nucleus.  The quantum mechanical model treats them as waves that occupy orbitals.  As the book says:

"[Schrodinger] thought that perhaps the problem with the Bohr model was that it forced electrons to behave like particles. Of course, it makes sense that they are particles, but it also made sense that light is a wave. If light (which should be a wave) can act like a particle, perhaps electrons (which should be particles) can act like waves. As a result, he analyzed the electrons in the atom as if they behaved like waves instead of particles...because he analyzed the electrons as waves instead of particles, they weren’t constrained to circular orbits. Instead, they were constrained to specific shapes called orbitals."

To determine the charge from the periodic table, look at the column the element is in, and think about what it needs to do to reach group 8A.  Those in group 1A (with the exception of hydrogen), for example, must lose one electron.  That makes them have the same valence electron configuration as the elements in group 8A.  Since they lose one electron, they are 1+.  For those in group 2A, they must lose two electrons, so they become 2+.  The elements in Group 7A need to gain one electron to become like the elements in Group 8A, so they become 1-.  The elements in Group 6A need to gain two electrons to become like the elements in Group 8A, so they become 2-.

A compact flourescent light bulb will work for this experiment. A white LED bulb will also work.

Pd is an exception to the rules we have been discussing.  It probably wasn't the best example to give because of that.  Based on our rules, the ground state configuration is what I give in the book:

The number of valence electrons in an element in one of the B columns is the number of s and d electrons, which is equal to the number of boxes from the left side of the periodic table.  For example, zircon (Zr) has four valence electrons.  Its electron configuration is [Kr]5s²4d², so it has two "s" electrons and two "d" electrons for a total of four.  It is also the fourth box from the left.  Silver has 11 because it is the eleventh from the left and its electron configuration is [Kr]5s²4d⁹.

It's important to note, however, that the valence electrons in the B-column elements doesn't tell you much about their charges in ionic compounds.  Silver, for example, has 11 valence electron, but its main charge in ionic compounds is 1+.  These are the "rule-breakers," so it is hard to determine their charge from their valence electrons.

We don't include the 1s orbital in the  number of orbitals in the 2nd energy level, because the number right before the letter indicates the energy level.  The 1s orbital is in the first energy level, while the 2s and 2p orbitals are in the second energy level.  It is true that the 1s orbital must fill up before the 2s orbital can start filling, but the energy of the 2s orbital is much higher than the energy of the 1s orbital, because it is on a different energy level.  You might want to review page 101, right under the illustration of the various s orbitals.

Electrons fill orbitals based on the energy of the orbital.  1s has the lowest energy, so it fills first.  2s has the next lowest energy, so it fills next.  2p has lower energy than 3s but higher energy than 2s.  So it fills after the 2s but before the 3s.  In the same way, 3p is higher in energy than 4s, so after 2p and 3s fill, then the 3p orbitals fill.  However, 3d orbitals are higher in energy than 4s, so after 3p fills, the 4s fills and then the 3d fills.  This can be hard to remember, so that's why I have you walk through the periodic table.  It is arranged so that you know the order in which the orbitals fill.

You use the one that has the closest atomic number that is LOWER than the atomic number of the element whose electron configuration you want to abbreviate.  So, if you want to do Se (atomic number 34), you would use Ar, because its atomic number is lower than 34 but closer than the other two Group 8A elements with lower atomic numbers.  In the same way, for iodine (atomic number 53), you would use Kr (atomic number 36).  It the group 8A element with the closest atomic number that is lower than iodine's.

The Lanthanides and Actinides have pretty complex electron configurations, due to their access to f orbitals.  This page discusses them.

You should start as far from the light as you can get and still be in the same room.  You will eventually walk closer and then back again, so you will end up exploring a wide range of distances.

Most thumbtacks are made of steel with a nickel or bronze coating.  It sounds like yours had a bronze coating.  The bronze is not very reactive, but the steel likes to react with the oxygen made from the breakdown of water.  The coating does not make a perfect seal, so some of the oxygen got under the coating and reacted with the steel.  That made rust, which does not adhere to the bronze coating, so the coating came off.

This happens only at the postive side of the battery, because that's where oxygen is made.  In order to make oxygen from water, electrons have to be pulled from the oxygen.  That can only happen at the positive terminal.  The hydrogen is made by forcing electrons only hydrogen, and therefore the hydrogen is made at the negative terminal.  Hydrogen doesn't react with eigther bronze or steel, so nothing happened there.

In this experiment, there are other reactions happening besides the breakdown of water.  The metal touching the positive terminal is reacting with the oxygen produced there, and that tend to make a metal oxide, which is the black solid.  Most thumbtacks have a lot of nickel, so it is nickel (II) oxide.  The yellow is caused by the small amount of metal oxide that dissolves.

I am sorry that the names were left off.  They are:

a.  Rubidium oxide

b.  Strontium sulfide

c.  Calcium nitride

d.  Magnesium iodide

Any color will work, but if you can't see through the side of the cup, you will need to look into the cup from the top, and that might make it harder to see what is going on.

A single orbital can hold only two electrons.  The reason is that each electron in an orbital must have its own spin state, which reduces the repulsion that the electrons feel.  As a result, each orbital can hold only two.  However, remember that there are multiple p and d orbitals for every energy level.  There are three p orbitals in every energy level, and each of them can hold two electrons, so there can be up to six electrons in the p orbitals of a given energy level.  There are five d orbitals, and each can hold two electrons, so there can be up to ten electrons in the d orbitals of a given energy level.

You do not need an incandescent light bulb.  You will get better rainbows with an incandescent light bulb, but a fluorescent or LCD light bulb will work as well.  

In the second edition of Exploring Creation with Chemistry (which I wrote), Astatine (At) is listed as a homonuclear diatomic.  However, in Discovering Design with Chemistry, it is not.  The reason is that astatine is only theoretically a homonuclear diatomic.  All its isotopes are radioactive, and they decay fairly quickly.  Thus, it is hard for two astatine atoms to live long enough to encounter one another and form a bond.  If they did, however, they would form a bond and become a homonuclear diatomic molecule.  That means you can think of it as a homonuclear diatomic, even though you will probably never encounter it in that form.

CF4 is a purely covalent molecule, but it does not have purely covalent bonds. A purely covalent bond is one in which the electrons are shared equally. CF4 doesn't have those bonds, because F is much more electronegative than C. It is a purely covalent molecule because its polar covalent bonds cancel each other out. So the question is asking specifically about the bonds,not the molecule as a whole.

This is a three-step process:

1.  Determine if the molecule is covalent.  It must have only nonmetals in it to be covalent.  If there are metals in the molecule, it is ionic.

2.  If the molecule is covalent, draw its Lewis structure.  If there are bonds between different elements, then the electrons are shared unevenly, and the molecule has polar BONDS.  It might not be a polar molecule, however.  If the bonds are between idental atoms (or atoms with the same electronegativity), then the molecule is nonpolar, which is the same as purely covalent.

3.  If there are polar bonds in the molecule, determine its geometry.  If the molecule is tetrahedral with the same elements surrounding the central atom (like CH₄), then the polar bonds cancel each other out, and the molecule is nonpolar, which is the same as purely covalent.  If the molecule is linear with the same elements on either side of the central atom (like CO₂), then the polar bonds cancel out, and the molecule is once again nonpolar, which is the same as purely covalent.  If the geometry is pyramidal (like NH₃), bent (like H₂O), or linear with only two atoms in the molecule (like HCl), then it is polar.

You might want to check out the videos on the course website (which is given in the introduction to the course).  There are several vidoes that discusse drawing Lewis structures, determing shapes, and determining polarity.

There are some countries where a comma has been traditionally used instead of a decimal point.  While most countries now accept that the decimal point is an international standard, some still use the traditions of their country.  The layout person who put together the chart on page 138 is from France, where the comma was traditional.  In case you are interested, here is a map that shows you the places in the world where a comma has been traditionally used in place of a decimal point:

http://www.statisticalconsultants.co.nz/blog/how-the-world-separates-its-decimals.html

Have you taken a look at the course website, which is discussed in the introduction to the book?  

http://www.bereanbuilders.com/olc/ddchem/

The section on Chapter 5 has two very good videos that might help:

http://www.bereanbuilders.com/olc/ddchem/ddc05.html

The links are labelled "VSPER theory" and "More on VSEPR Theory."  They may help.

The real key in figuring the shapes out is to figure out how many GROUPS of electrons are around the central atom and how many of those groups are bonds.  In the first molecule of Example 5.4, there is a triple bond and a single bond on the carbon, which is the central atom.  Each bond is a group, so there are two groups of electrons around it.  How can two groups get as far apart as possible?  By forming a line, as discussion on the bottom of page 145.  Thus, this molecule is linear.

In the second molecule, there are three bonds on the N and one lone pair of electrons.  That's 4 groups.  How can 4 groups get as far away from each other as possible?  By forming a tetrahedron, as discussed on page 143.  A real tetrahedron, however, has 4 bonds, with each bond being a leg on the tetrahedron.  This molecule has only 3.  So this molecule is a tetrahedron with one leg removed.  As discussed on page 144, that's pyramidal.

For the last molecule in the example, there are three bonds.  One is a double bond, and the other two are single bonds.  Each bond is a group, so there are three groups.  How can three groups get as far away from each other as possible?  By forming a triangle, as discussed on page 146. Thus, this is triangular.

Notice that the last two molecules each have three BONDS around the central atom, but they have different shapes.  Why?  Because the NH₃ has four GROUPS of electrons, and the number of GROUPS form the basic shape.  4 groups form the basic shape of a tetrahedron.  For each group that is not a bond, you remove a leg from the tetrahedron.  So when one group isn't a bond, it's a tetrahedron with one leg removed, which is pyramidal.  When 2 groups aren't bonds, it is a tetrahedron with two legs removed, which is bent.  3 groups make the basic shape of a triangle.  If one of the groups isn't a bond, it is a triangle with one leg removed, which is bent.  2 groups form the linear shape.

A moveable group of electrons is either a bond or a pair of electrons that don't form a bond.  Remember that a bond counts as a single group, regardless of whether it is a single, double, or triple bond.  So, in a molecule like CH₂O (shown on the bottom of p. 133, there are two single bonds and a double bond on the C.  That means three moveable groups.  In HCN (shown on the bottom of p. 134), there is a single bond and a triple bond on the C.  That means two moveable groups.  In H₂O (shown in the middle of page 140), there are two single bonds and two pairs of electrons that don't form a bond on the O.  That means there are four moveable groups.

Remember that there are a total of four pairs of electrons around the central atom.  All of those electron pairs repel each other, so they all want to get as far apart from one another as possible.  If the bonds were 180 degrees apart, they would be farther from each other than in the bent configuration, but the lone pairs would be only 90 degrees away from the bonds.  So the bonds would be farther from one another, but the lone pairs would be closer to the bonds.  Those lone pairs repel as well, so they won't want to get that close.  So...all four pairs of electrons get as far apart as possible.  Thus, they form a tetrahedron.  However, two of the pairs are not bonds, so they don't make "legs" on the tetrahedron.  That means you have a tetrahedron with two legs missing, which is a bent structure.

There are many countries in which a comma is used in numbers instead of a decimal point.  One of those countries is Sweden.  The chemist who first came up with the idea of electronegativity was Jöns Jacob Berzelius, who was from Sweden.  In addition, the man who came up with today's scale (Wolfgang Pauli) was Austrian.  Austria is another country that uses commas instead of decimal points.  Since the two main people associated with electronegativity come from countries that use commas instead of decimal points, most electronegativity tables do that.

Here is a page that goes through the geometric proof to show that a tetrahedral molecule has bond angles of 109.5 degrees.

http://www.ctralie.com/Teaching/Tetrahedron/

The electrons definitely are moving in a polar compound.  They move in orbitals around both atoms that share them.  However, there is no NET motion.  In a polar molecule, the electrons move around one of the atoms more than they move around the other.  Thus, there is net motion that favors one atom.  That atom is the one with the partial negative charge.  The atom that is not favored in the net motion has the partial positive charge.  In nonpolar molecules, the atoms are moving, but they move around both atoms equally, so there is no net motion.

Yes. As log as you have all Fs and Cls attached to the Si with single bonds. The order is not important. 

There are two ways to think about this problem.  The first is to remember that a projectile that is landing at the height from which it was launched reaches its maximum height halfway through its journey.  Thus, if it reaches its maximum height at 0.29 seconds, it takes twice that long (0.58 seconds) to do the entire journey.

If you don't remember that, it's fine.  All you have to do is realize that this question is asking about height, so it's dealing with the y-dimension.  Thus, you can use the speed and angle to get the y-component of the velocity:

voy = (5.2 m/s)(sin[33]) = 2.8 m/s

Now, when it reaches the height from which it is launched, what is the new y-component of the velocity? Well, in the y-dimension, it rises up until its y-velocity is zero, and then it falls.  When it reaches the same height, it will get all that velocity back, but in the opposite direction.  Thus, vy = -2.8 m/s.

Now we can solve for time:

vy = voy + at

-2.8 m/s = 2.8 m/s + (-9.81 m/s²)(t)

t = (-5.6 m/s) / (-9.81 m/s²) = 0.57 seconds

Since there is always error in the last significant figure, 0.57 seconds and 0.58 seconds  are the same.

You do need to repeat steps 24 and 25 once you have poured the two liquids together.  You measured the mass of the first graduated cylinder plus its 25 mL of liquid.  You then measured the mass of the second graduated cylinder plus its 25 mL of liquid.  When you add the two, you get the total mass of the system, which includes both graduated cylinders and both samples of liquid.  To see that the mass doesn't change, then, you need the compare it to the final mass of both graduated cylinders and both samples of liquid. 

Both samples of liquid are in only one graduated cylinder in step 28, so when you put that on the scale, you are measuring the mass of one graduated cylinder and the mass of both samples together.  However, to get the total mass of the system at step 28, you still have to measure the mass of the empty graduated cylinder.  That way, the total mass still includes both graduated cylinders and both samples of liquid. 

15a  asks  for an equation for the formation of CaCO3.  As discussed on pp. 182-183 in the book, a formation reaction has reactants that are all elements, and the only product is what is being formed (CaCO₃, in this case).

Now, if you look at the elements, you have Ca, C, and O.  From chapter 5 (p. 128), students were told to memorize seven homonuclear diatomic elements.  O is on that list.  This means the element O exists as O₂.  Since Ca and C are not on that list, those elements exist just as Ca and C.  Thus, the unbalanced equation becomes:

Ca  +  C  +  O₂  --> CaCO₃

15b asks for a decomposition equation.  Those reactions start with the chemical given (K₂CrO₄), but the products are all elements.  Thus, the products involve K, Cr, and O.  Once again, O is a homonuclear diatomic, so it is O₂.  K and Cr are not, so they are just K and Cr.  That means the unbalanced equation is:

K₂CrO₄  -->  K  +  Cr +  O₂

I strongly recommend using a scientific calculator in this course.  They are very inexpensive, and they help you do this kind of math more efficiently.  This is the calculator I recommend:

https://www.amazon.com/Texas-Instruments-TI-30Xa-Scientific-Calculator/dp/B00000JBNS/ref=sr_1_3?ie=UTF8&qid=1477589928&sr=8-3&keywords=ti-30x

However, if you want to do it longhand, you need to remember that a fraction means multiply by the number in the numerator and divide by the number in the denominator.  Thus, you first multiply by the 5:

5x-108 = -540

Then, you divide by the 9:

-540 ÷ 9 = -60

Since 108 has three significant figures and 9/5 is exact, the answer should have three.  That's why it is -60.0 degrees C.

What was the temperature of the water and alcohol compared to the temperature of the room?  If the water and alcohol were a lot colder than the room,  the thermometer might be increasing in temperature because the room is warming it more than the evaporation is cooling it.  Even if that's the case, the thermometer should never reach room temperature again, because the evaporation should keep it cooler than room temperature.

Let the water and alcohol sit for a while so they come to room temperature, then try it again.  

While it is copper that is formed on the nail, it might not look "coppery" in color because of contaminants in the water and on the nail.  Those contaminants get incorporated into the copper and can turn it black.

If you can't find liquid food coloring, you could use something like flavored drink mix that has a definite color.  Add very little water to a lot of the drink mix to make a concentrated liquid that has a deep color.  You could also go the other way.  Take something like coffee or tea and then boil lots of the water away to make a concentrated, dark liquid.

Number 12 asks, "Give the balanced chemical equation for the formation of HNO₃."  Remember that formation equations start with elements and make the compound of interest, as given in the definition on page 182.  Thus, we need to start with the elements in the molecule: hydrogen, nitrogen, and oxygen.  All three of those are homonuclear diatomics, so they exist as H₂, N₂, and O₂.  That means the unbalanced equation is:

H₂ + N₂ + O₂  -->  HNO₃

Notice that on the reactants side, we have only elements, and on the products side, we have the compound being made.  That's the definition of a formation reaction.

Remember from Chapter 4 that the Roman numeral after the metal in an ionic compound indicates the metal's positive charge.  Metals give up electrons, so they are always positive.  The name iron (III) oxide tells you that in this ionic compound, the iron has a charge of 3+.  Since oxygen is in group 6A, it has a charge of 2-.  To get the chemical formula, you drop the signs and switch the numbers, meaning the "2" in "2-" goes with the iron, and the "3" in "3+" goes with the oxygen, making it Fe₂O₃.

If you don't like the "switch the numbers" shortcut, think about the charges.  They have to cancel one another out.  Since Fe is 3+ and iron is 2-, you will need two iron atoms (which total 6+) to cancel out the charge of three oxygens (which total 6-).  That makes Fe₂O₃.

Remember from chapter 4 that atoms want to get to the ideal electron configuration: that of a Noble Gas.  Nonmetals do that by gaining electrons.  As indicated on the periodic table in the book, all elements in Group 7A are nonmetals, so they all need to gain electrons to get the electron configuration of a Noble Gas.  Well, any element in 7A can gain one electron, and they will end up having the electron configuration of the Noble Gas that is right next to them.  Thus, Group 7A elements gain one electron and therefore become 1- in ionic compounds.  Elements in Group 6A can gain two electrons to get the Noble Gas electron configuration, so they are 2- in ionic compounds.  Nonmetals in group 5A gain three electrons and become 3-.  Nonmetals in group 4A gain four electrons and become 4-.

Metals, on the other hand, do not gain electrons.  They lose electrons.  They get the Noble Gas configuration by losing all their valence electrons.  That gives them the electron configuration of the Noble Gas that is ABOVE them in the periodic table.  Aluminum is in group 3A, so it has three valence electrons.  It must lose all of them, which makes it 3+.  Elements in group 2A lose their two valence electrons to become 2+, and elements in group 1A lose their only valance electron to become 1+

You might want to review pages 114-117, where this is covered.

Remember that when you add liquids, the volumes do not add.  As Experiment 6.2 showed, the final volume is LESS than the sum of the individual volumes, because the molecules get in between each other.  So, the sum of the volumes is 23, but we know the actual volume is less than that.  22 is the only number on the list that is less than 23.

You don't need to do this for the course, but if you are interested in figuring out which reactant is the limiting reactant, here's how: 

You just have to start the stoichiometry with each reactant in the equation.  Convert each reactant to moles (if it isn't in moles already), and then use it to calculate the moles of one of the products.  When you have the moles of product for each separate reactant, choose the SMALLEST result.  After all, the limiting reactant runs out first, so it will make the smallest amount of product.  Use that result in the rest of the stoichiometry. 

Here's an example:

Determine the number of grams of hydrogen gas made when 50.0 grams of magnesium and 50.0 grams of HCl react according to the following equation:

Mg(s)  +  2HCl (aq)  -->  H₂ (g)  +  MgCl₂ (aq)

First, use Mg:

(50.0 grams Mg/1)x(1 mole Mg/24.31 g Mg) = 2.06 moles Mg

(2.06 moles Mg/1)x(1 mole H₂/1 mole Mg) = 2.06 moles H₂

Next, use HCl:

(50.0 grams HCl)x(1 mole HCl/36.46 g HCl) = 1.37 moles HCl

(1.37 moles HCl)x(1 mole H₂/2 moles HCl) = 0.685 moles H₂

So, 50.0 g of Mg could make 2.06 moles of H₂, but 50.0 g of HCl can make only 0.685 moles H₂.  That means HCl is the limiting reactant, since it produces the smaller amount of product.  That means we use the number of moles of H₂ calculated from HCl to finish the problem.

(0.685 moles H₂/1)x(2.02 grams H₂/1 mole H₂) = 1.38 grams H₂
 

The numbers in front of molecules in a chemical equation represent BOTH moles and molecules.  So, in a chemical equation like:

2Al +  6HBr  -->  2AlBr₃  +  3H₂ 

You can say:

Two atoms of Al react with six molecules of HBr to make two molecules of AlBr₃ and three molecules of hydrogen 

or you can say:

Two moles of Al react with six moles of HBr to make two moles of AlBr₃ and three moles of hydrogen 

Remember, a mole is simply a certain number of molecules.  So any relationship that works with molecules will work with moles as well.  If I run the reaction just one time, two atoms of Al react with 6 molecules of HBr to make two molecules of AlBr₃ and three molecules of hydrogen.  If I run it a dozen times, two dozen Al react with six dozen HBr to make two dozen AlBr₃ and three dozen hydrogen.  If I run it 6.02x10²³ times, two moles of Al react with six moles of HBr to make two moles of AlBr₃ and three moles of hydrogen.

If you got more than 5 molecules of water for every molecule of CuSO₄, that's not really a problem.  Most likely, some of the solid popped out of the beaker during your experiment (or you lost some in another way), causing you to read too much mass loss between the hydrated and non-hydrated form.  Just check your calculations against the ones at the end of the chapter to make sure you didn't make a mistake.

Remember, the chemical equation gives you the relationship in moles.  Thus, since the chemical equation is:

2Al (s) + 3Br₂ → 2AlBr₃

You know that

2 moles of Al = 2 moles of AlBr₃

You can use that conversion relationship to convert 0.407 moles of AlBr₃ into moles of Al.  In the same way, the equation tells you:

3 moles Br₂ = 2 moles of AlBr₃

Once again, that's a conversion relationship which allows you to convert 0.407 moles AlBr₃ into moles of Br₂.

In the end, we only know how many molecules of water can be absorbed for each molecule of magnesium sulfate.  We know that every molecule of MgSO4 can absorb 7 molecules of water.  Thus, if we have 10 molecules of MgSO₄, they can absorb 7x10 = 70 molecules of water.  

Now remember, since a mole is just a bunch of molecules we can also say that for if we have 10 moles of MgSO₄, they can absorb 7x10 = 70 moles of water.  Of course, we don't have 10 moles of MgS0₄.  Instead, we have 0.8308 moles.  That means they can absorb 7x0.8308 moles of water.  

We keep the answer in moles (rather than molecules) because the question asks for the mass of water.  Thus, we need to convert to grams.  Well, the mass of the molecule allows us to easily convert from moles of water into grams of water, so it is best to keep the answer in moles.

If you are trying to calculate the moles of acetic acid in the experiment to see how close they are to the moles of sodium bicarbonate, you need to take into account the fact that vinegar is only about 5% (by mass) acetic acid.  Thus, you must multiply the mass of the vinegar by 0.05 to get the mass of acetic acid.  If you then convert that to moles, you will have the moles of acetic acid.

Remember that when you are determining the mass of a molecule, you are really adding, not multiplying, because the numbers of atoms are exact.  Thus, it's not really:

2×22.99 amu + 12.01 amu + 3×16.00 amu

Instead, it's:

22.99 amu + 22.99 amu + 12.01 amu + 16.00 amu + 16.00 amu + 16.00 amu

When you add, you don't count significant figures.  Instead, you report your answer to the same decimal place as the least precise number in the problem.  Since all the numbers go out to the hundreths place, you report your answer to the hundredths place.  That's why it is 105.99.

This is discussed in Example 7.1 on pp 199-200.

The significant figures are correct as given in the solution.  In the first conversion, 1.0x10²² has two significant figures, 6.02x10²² has three significant figures, and the 1's are exact.  Thus, the lowest number of significant figures is two, so the answer should have two.  That's why it is 0.017.  Remember that a zero is significant only if it is between two significant figures or at the end of the number AND to the right of the decimal.  Thus, neither zero in 0.017 is significant.

It's important to stress that "significant" doesn't mean "important."  It means "measured."  The second zero in 0.017 is very important, but it is not significant, because there is no way to measure it.  That's what the rules for zeroes tell you.  If a zero is between two significant figures, it was measured.  If it is at the end of the number and to the right of the decimal, it was measured.

As long as all the balloons are the same, the shape doesn't matter.  You will just be looking at how much they inflate.

You can certainly put the answer in scientific notation if you wish.  However, you don't have to, since the significant figures don't require it.  Remember, you can usually choose whether or not to use scientific notation (see page 15, right below the Comprehension Check box).  However, if the significant figures require it, you have no choice.  Since the "169" in this problem limits you to three significant figures, 14,900 grams is a good answer.  So is 1.49x10⁴ grams.  They are identical, since they both refer to the same value, and they both have three significant figures.

The water is attracted to the CuSO₄, which is why it becomes a part of the solid.  When things move towards the things they are attracted to, they reach a lower-energy state.  So when the water joins the CuSO₄, it goes to a lower-energy state than when it was not part of the solid.  Energy cannot be created or destroyed, so it has to go somewhere.  The energy that the water lost gets released into the surroundings, heating the surroundings.

If you are converting from one chemical to another, you must use the chemical equation, which can only be used with moles.  Thus, before you do that, the amount must be in moles.  In Example 7.7, you are given grams of PCl₅ and are asked for grams of Cl₂.  To go from PCl₅ to Cl₂, you must use the chemical equation.  Thus, your amount of PCl₅ must be in moles.  It is not, so you have to convert it to moles before you can use the chemical equation.  Since the chemical equation uses only moles, the answer will be in moles of Cl₂.  Since the problem asked for grams of Cl₂, you must convert to grams.

Compare that with Example 7.6.  There, you are given moles of Fe and are asked for moles of Fe₂O₃.  To go from Fe to Fe₂O₃, you must use the chemical equation, which uses moles.  However, you already have moles of Fe, so you can just go straight to the chemical equation and convert from Fe to Fe₂O₃.  That will give you moles of Fe₂O₃, which is what the problem asks for, so there is no reason to convert back to grams.

So it depends on what you are given and what you are asked for.  If you are given moles, you go straight to the chemical equation and use it to calculate the moles of what is being asked for.  If you are given grams, then you must first convert to moles before using the chemical equation.  Once you have used the chemical equation, your answer will be in moles.  If that's what the problem asks for, you are done.  If not, it must be asking for grams, so you must convert to grams.

Remember that the chemical equation gives you the conversion relationship between two chemicals, but only in moles.  So:

1) You will be given the amount of one chemical. Is it in moles? If not, you must convert it to moles. If it already is in moles, go to step 2.

2) Use the chemical equation to convert the moles of the chemical you were given to the moles of the chemical you need to find out.

3) Does the question ask for the moles of the chemical you need to find out?  If so, you have the answer. If not, convert it to the units the question asks for (usually grams).

This question asks for the molecular formula, but in the first printing of the book, the solution doesn't supply it.  I am sorry that was overlooked.  In the end, to get the correct molar mass, you need to multiply the molar mass of the empirical formula by 3.  Thus, the molecular formula is the empirical formula times 3:

C₉H₂₄O₃

The final answer is incorrect.  Unfortunately, the "3" was accidentally dropped.  The proper answer is

C₂H₅O₃

I am very sorry for the mistake!

In Chapter 4 (p. 116, Example 4.4) you learned how to determine the chemical formula of an ionic compound.  First, you determined the charge of each ion.  Then, you dropped the signs on the charges, switched the numbers on the charges, and then turned those numbers into subscripts.  In this example, you are using that same method again, but this time, with polyatomic ions.

For sodium carbonate, then, you know that sodium becomes Na⁺ because it is in group 1A.  That means its charge is +1.  Carbonate is CO₃^2-, so its charge is -2.  Dropping the signs means you have a 1 with Na and a 2 with CO₃.  Now you switch the numbers, so the 2 goes with Na and the 1 goes with CO₃.  That's how you get the formula Na₂CO₃.

It might be helpful to review Example 4.4 on page 116 to refamiliarize yourself with the process.

Think about where the carbon dioxide comes from.  There are only two reactants: the fuel and oxygen.  Oxygen has no carbon in it, so every carbon atom in CO₂ must come from the fuel.  So, supose you burned the fuel completely and got 5 molecules of CO₂.  How many atoms of carbon are in 5 molecules of CO₂?  Each molecule has one carbon atom, so if there are 5 CO₂ molecules, there are 5 carbon atoms.  Where did those atoms come from?  They all came from the fuel.  So, how many atoms of carbon must have been in the fuel?  If there are 5 carbon atoms, and they came from the fuel, that must means there were 5 carbon atoms in the fuel.  Since the fuel is the only source of carbon atoms, every carbon atom in CO₂ must have been in the fuel.

Now remember, moles are just a way of counting atoms and molecules, so anything that works for atoms and molecules also works for moles.  So, supose you burned the fuel completely and got 5 moles of CO₂.  How many moles of carbon are in 5 moles of CO₂?  Each molecule has one carbon atom, so each mole of CO₂ has one mole of C.  If there are 5 moles of CO₂, there are 5 moles of C.  Where did those moles come from?  They came from the fuel.  So, how many moles of carbon must be in the fuel?  If there are 5 moles of carbon, and they came from the fuel, that must means there were 5 moles of carbon in the fuel.  Since the fuel is the only source of carbon atoms, every mole of carbon in CO₂ must have been in the fuel.

The same reasoning applies to hydrogen.  The only source of hydrogen is the fuel.  So any hydrogen in the water produced must come from the fuel.  Since every mole of water has 2 moles of hydrogen, then the number of moles of hydrogen in the fuel is twice the number of moles of water produced.

Oxygen is a homonuclear diatomic, but that only applies when it is by itself, not part of a compound.  So you never see O as the product in a chemical reaction.  You see O₂.  However, when you put O with any other element, it doesn't have to be O₂.  In carbon monoxide, for example, it is CO.  In calcium carbonate, it is CaCO₃.  So when O is not with any other element, it is O₂.  When it is with any other element, it can be anything.

C₅H₁₀O is not a carbohydrate.  There must be twice as many H's as O's.  C₆H₁₂O₆ is a carbohydrate, because there are 12 H's and 6 O's.  Thus, it reduces to CH₂O.   C₅H₁₀O cannot be reduced, because there is only one O, so you can't divide it by anything.  If you divided by 5, you would have CH₂O_1/5.

The mass of CaCO₃ (100.09) has 5 significant figures, 500.0 g has 4, and the mass of Ca₃(PO4) (310.18) has 5.  Thus, the answer should have 4. 

This goes back to something you learned in Chapter 4. 

When you figure out the charge of an ion, there is a number and a sign. Mg ions, for example, are Mg²⁺, while nitride ions are N^3-. The number is what comes in front of the charge, so for Mg²⁺ the number is 2 and the charge is +. For N^3-, the number is 3 and the charge is -. If Mg and N make an ionic compound it is Mg₃N₂, because you dropped the charges (+ and -), and you switched the numbers (Mg's 2 went to N, while N's 3 went to Mg).

You determine the value for "i" by figuring out how many particles the solute splits into when dissolving. 

For covalent compounds (compounds made of only nonmetals), i = 1, because they never split up into multiple particles, since all their elements are chemically bonded to one another.  Thus, even though there are a lot of atoms in C₆H₁₂O₆, i = 1, because all the atoms are nonmetals, so the compound is covalent and doesn't split up into multiple particles when it dissolves.

For ionic compounds, "i" equals the number of ions in the compound.  If the ionic compound contains only single-atom ions, it is fairly easy, because each atom in the chemical formula becomes an ion.  Thus, for Na₂S, i = 3, because the compound has two Na⁺ ions and one S^2- ions.

If the ionic compound contains polyatomic ions, you need to be able to recognize the polyatomic ions, which is why it is so important to keep the bold polyatomic ions in the table on page 245 memorized.  For example, if you look at Na₂CO₃ and have those polyatomic ions memorized, you should recognize CO₃ as representing the carbonate ion.  Thus, this compound has two Na⁺ ions and one CO₃^2- ion, so i = 3.

You might have forgotten a rule that was mentioned on the top of page 115 (in the pink box).  It says that ionic compounds are formed between metals and nonmetals.  If you look at the Periodic Table, Sr is in a box whose color indicates it is a standard metal.  Cl is in a box whose color indicates it is a nonmetal.  Thus, SrCl2 is a compound between a metal and a nonmetal.  As a result, it is ionic.

Remember, metals like to give away electrons, and nonmetals like to gain them.  Thus, when there is a metal and a nonmetal in a compound, the metal will give its electrons away, forming a positive ion, and the nonmetal will take them, forming a negative ion.  Thus, all compounds that contain at least one metal and one nonmetal are ionic.

Strontium chloride comes with the kit that is included in the course.  However, if you are putting something together yourself, you can get strontium chloride from:

http://www.workshopplus.com/ProductCart/pc/viewPrd.asp?idproduct=4505&idcategory=0

You can also substitute calcium chloride for strontium chloride in this experiment.

You might want to go back to Chapter 4 (pp. 114-117), where you learned how to determine the charge of ions in ionic compounds and how to use charge to determine the chemical formual of an ionic compound.  As you learned there, the column in the periodic table tells you the charge of the element.  Na is 1+ in ionic compounds because it is in group 1A and therefore must lose an electron to become like the nearest noble gas.  As another example, O takes on a charge of 2- in ionic compounds, because it is in group 6A and must gain two electrons to become like the nearest noble gas.

In Chapter 8 on page 245, there is a table of polyatomic ions.  The ones in bold need to be memorized.  Notice that OH- is one of the bolded ones.  Thus, when you see OH in an ionic compound, you should immediately recognize that it is the OH- ion.

As you learned in Chapter 4, once you have the charges, you drop the signs and switch the numbers to get the chemical formula.  So, since Sr is in group 2A of the periodic table, it must lose two electrons to become like the nearest noble gas, so it is 2+.  You are supposed to have OH- memorized.  You drop the signs and switch the numbers, so the "2" in "2+" goes with the OH, and the "1" in "1-" goes with the Sr.  Since the 2 goes with OH, that means you need to put the OH in parentheses and have the 2 on the outside, which is why it is Sr(OH)₂.

In this problem, 102.0 degrees C has four significant figures, and 100 degrees C is exact.  However, you are subtracting them to get the change in boiling point (Delta T)

Delta T = solution boiling point - solvent boiling point

Delta T = 102.0 degrees C - 100 degrees C 

Remember that when subtracting (or adding), you don't count significant figures.  As explained on page 6 (that was a long time ago!), you report your answer to the same precision (decimal place) as the least precise number in the problem.  100 is exact, so it is infinitely precise.  102.0 has its last significant figure in the tenths place, so your answer must have its last significant figure in the tenths place.  That means

Delta T = 2.0 degrees C 

In this problem, the solvent is ethanol, and the solute is water.  That's why ethanol's boiling point and K_b are given.  In addition, the solution determines i for water, because it is the solute.  I know we usually think of water as a solvent, but it is often a solute in alcohols.  For example, distilled ethanol is about 95% ethanol and 5% water.  Thus, it is a solution in which ethanol is the solvent and water is the solute.  The rubbing alcohol you get at the drugstore is usually 70% isopropyl alcohol and 30% water.  Once again, then, alcohol is the sovent, and water is the solute.

The oxygen that the alcohol is reacting with comes from the air.  The oxygen atoms in the water molecules will not react with alcohol, since they are in a lower-energy state inside the water molecule.  If the oxygen in the water molecules did react with the alcohol, water could not be used to put out fires!

You know that N₂H₂ is a covalent solute because it is composed of only nonmetals.  Remember, ionic compounds have at least one nonmetal and one metal.  Covalent compounds are made of only nonmetals.  As shown on the periodic table, H and N are both nonmetals (the legend on the periodic table tells you that all blue boxes are nonmetals), so N₂H₂ is covalent.  All covalent molecules have i = 1, because they do not split up into particle when they dissolve.  They dissolve as an entire molecule.

Carbon dioxide doesn't really dissolve in water.  It reacts with water to make carbonic acid:

H₂O + CO₂ --> H₂CO₃

This reaction is reversible, however, so it's like carbon dioxide has dissolved.  This is covered in Chapter 11.

The ions in salt have full electrical charges, and the water has only partial electrical charges.  However, there are A LOT of water molecules, and they can surround the salt ions.  Lots of slight charges add up to more charge than the full charge on the oppositely-charged ion, so the ions are more attracted to the water molecules than they are to one another.

The volume is given as 200.0 mL.  That's four significant figures.  The zero at the end is significant, since it is both at the end of the number and right of the decimal.  That makes the other two zeroes significant, since they are between two significant figures.  The metric conversion factors are exact, so the 0.001 has an infinite number of signficant figures.  Thus, the answer needs to have four significant figures.  0.2000 has four.   The zero at the end is significant, since it is both at the end of the number and right of the decimal.  That makes the two zeroes between it and the 2 significant, since they are between two significant figures.  The first zero is not significant.  It is not at the end of the number and right of the decimal, and it is not between two significant figures. 

The same reasoning can be used for moles.  15.67 has four, 96.11 has four, so the answer must have four.  That's why it is 0.1630.  Then, in the final step, you have four significant figures in both 0.2000 and 0.1630, so the answer must have four, which is why it is 0.8150 M.

In this case, they are.  For many reactions, it doesn't matter.  However, this is a reaction that forms a precipitate.  You need the phase symbols so it is clear what the precipitate is.

The problem tells you the solution is not saturated.  Thus, you could dissolve more sodium bromide in it.  However, you don't have any more sodium bromide to add.  A saturated solution would not allow you to dissolve more sodium bromide.  So how do you turn this into a solution that cannot dissolve any more sodium bromide? 

Well, since sodium bromide is a solid, its solubility decreases with decreasing temperature.  If you decrease the temperature, then, less sodium bromide can dissolve.  That means the amount which is already dissolved in solution is closer to the maximum amount that can be dissolved.  If you lower the temperature enough, the amount that is already in solution will be the maximum amount that can be dissolved.  At that point, no more sodium bromide can be dissolved, so the solution is saturated.

Warming the solution will increase the solubiluty of sodium bromide, which means even more can be dissolved.  In that case, you are making the solution even less saturated.

Think about putting something in the oven to cook.  If the recipe says that the meal will take 30 minutes to cook at 400 degrees, how long will it take to cook at 300 degrees?  It will take longer than 30 minutes.  After all, the hotter the oven, the more quickly the food cooks.  Conversely, the cooler the oven, the longer it takes to cook.  Crock pots take a long time to cook specifically because they cook at a low temperature. 

If you are boiling something in water, you are using the temperature of the water to cook the food.  Sure, the water might reach boiling more quickly because it doesn't have to be heated to as high a temperature.  However, that lower temperature will take longer to cook the food.

Remember what Avagadro's Law tells us.  At the bottom of p. 305, the pink box has the following:

"When all substances of interest are gases, as long as pressure and temperature remain the same, the chemical equation gives you the relationship between the volumes of those gases."

The only two substances of interest in this equation are H₂ and CH₄.  Carbon is there as a solid, but it is not mentioned at all.  You are given the volume of CH₄ and asked to determine the voume of H₂.  Thus, the only two substances of interest are gases.  That means the chemical equation tells you the relationship between the two gases: 2 liters of H₂ make 1 liter of CH₄.  Thus, you can use that as a relationship to convert between the two.

If you don't get exactly the answer that the book has, that's not necessarily a problem.  Remember, the last signficnt figure has error in it (see the box on p. 9).  Thus, when you solve the combined gas law equation and get T2 = 286 K, that's fine.  Even though the book's answer is 285 K, that "5" has error in it.  It could be 4, 6, 3, even 7.  From a scientific point of view, 286 K and 285 K are the same (see the discussion under the box on p. 9).  That's why it is so important to report your answer with the proper number of significant figures.  That way, everyone knows which digit has error in it.

However, if you want to get exactly what the book gets, you should only round for significant figures at the end of the equation or when you are forced to change the rules.  In this problem, for example, I multiply all the top numbers, then divide by all the bottom numbers, and then round.  That gives me 285 K as the answer for T2 in the combined gas law.  

If the problem had been something like this one:

q = (1.00g) (1.0000 J/gC)(14.6 C - 14.3 C)

You would have to do the subtraction and then round to 0.3 C, since subtraction uses different rules from multiplication.  Thus, the equation becomes:

q = (1.00g) (1.0000 J/gC)(0.3 C) = 0.3 J

The only time I round in the middle of an equation, then, is when it changes from addition/subtraction to multiplication/division.

You can use the Ideal Gas Law to determine this.  After all, standard temperature is 0 C, which is 273.15 K.  Standard pressure is 1 atm.  R = 0.0821 (l atm)/(mole K), and if there is 1 mole, n = 1.  So, the Ideal Gas Law says:

PV = nRT

(1 atm)(V) = (1 mole)(0.0821 [l atm]/[mole k])(273.15 K)

V = (1 mole)(0.0821 [l atm]/[mole k])(273.15 K) / 1 atm = 22.4 liters

The 1's are exact, since they are coming from definitions, so you are limited to three significant figures by 0.0821.

Remember what I say on page 301:

"In this course, you can assume gases will behave ideally if their temperature is near or above 0 ºC and their pressure is near or below 1 atm."

I can say this because the lower the pressure and the higher the temperature, the more ideally a gas behaves.  Thus, I don't have to be at STP for the Ideal Gas Law to work.  I simply need to be near or below 1 atm and near or above 0 ^oC.  So consider Example 10.4.  The pressure is 1.02 atm, which is very near 1 atm.  The temperature is not near 0 ^oC, but it is ABOVE 0 ^oC.  That means the gas behaves even more ideally than it would at 0 ^oC.  Thus, I can use the Ideal Gas Law.  In the end, the Ideal Gas Law works well in most situations with which we are familiar, as the pressures we usually encounter are right around 1 atm, and the temperatures are usually higher than 0 0 ^oC.

The hydrogen peroxide you use in the lab is a solution made by dissolving hydrogen peroxide in water.  It is actually a pretty weak solution, because concentrated hydrogen peroxide can be very dangerous.  The mass that you measured at the beginning was the total mass of the solution, which is the mass of hydrogen peroxide plus the mass of water.  The mass you got from the moles of oxygen is the mass of only the hydrogen peroxide.  So dividing the two gives you the fraction of hydrogen peroxide in the solution.  Multiplying by 100 turns that into a percent.

The Na₂C₂H₃O₂ produced in the reaction is a solid that dissolves in the water.  Since it is a dissolved solid, it doesn't exert pressure.  Only liquids can evaporate, so a substance must be in its liquid phase to exert a vapor pressure.  A dissolved solid is not a liquid. 

Gases become more ideal the warmer the temperature.  After all, the warmer they are, the more space they occupy, so the less important the volume of their molecules is.  So STP is a benchmark.  0 ^oC is a good estimate for the minimum temperature to consider it an ideal gas, but the higher the temperature, the more ideal the gas. In the same way, 1 atm is also a benchmark.  It is a good estimate for the maximum pressure.  The lower the pressure, the more ideal the gas.

Remember that when you add and subtract, you don't count significant figures.  You look at the decimal place, and you report your answer to the same decimal place as the least precise number in the problem.  285 has its last significant figure in the ones place, while 273.15 has its last significant figure in the hundredths place.  The ones place is less precise, so the answer can only be reported to the ones place.  Thus, 11.85 has to become 12.

A round balloon is what most people think of when they think of balloons.  However, there are tublular balloons, which are much longer than they are wide.  There are also heart-shaped balloons, etc.  You just want one that is fairly round when it is inflated, like these:

https://cdn.shopify.com/s/files/1/1051/1098/products/BLN_LG_01.jpg?v=1454621505

When you boil the water in the microwave, it is so hot that its vapor pressure is equal to atmospheric pressure.  Thus, it boils.  As a result, the empty space above the water in the jar is filled with water vapor at atmospheric pressure.  When you put the lid on and turn it upside down, that space is still filled with water vapor at atmospheric pressure.  That's what I mean by the "pressure in the jar."  However, when you put the ice on the jar, that water vapor in the empty space gets cooled.  So some of it condenses.  When the water vapor that was in the empty space condences, the pressure in that empty space (the pressure in the jar) reduces.  

The vapor pressure is the pressure of water vapor that evaporates from the water.  That is determined only by the temperature of the water.  Since the water cooled a bit while you were closing the lid and turning the jar upside down, the vapor pressure was lower than atmospheric pressure.  That' why it stopped boiling as you were pulling the jar out of the microwave and putting the lid on.  At that point, the pressure in the empty space (the pressure in the jar) was greater than the water's vapor pressure.  As the pressure in the empty space (the pressure in the jar) reduced, it eventually reached the vapor pressure of the water, which is why the water started to boil again.

In this problem, you are being asked to  determine the liters of one chemical in a reaction using the liters of another chemical.  Remember that the numbers in a chemical equation always refer to the MOLES of each chemical.  However, when the chemicals you are analyzing are all gases, they also refer to the VOLUMES of each chemical.  So the chemical equation tells you that:

1 mole of C₃H8 = 3 moles CO₂

However, since both are gases, you also know that:

1 liter of C₃H8 = 3 liters of CO₂

This is now a conversion relationship between liters of C₃H8 , which you were given, and liters of CO2, which you want to know.  Thus, it is much like Example 10.5, except that the volume unit is liters, not mL.

When you have a sample of liquid at any temperature, some portion of it evaporates.  Thus, there is always some gas right over the surface of the liquid.  The warmer it is, the more gas there is above the liquid.  Vapor pressure is a measure of how much of the gas phase exists right above the liquid phase.  The higher the vapor pressure, the more the lquid has evaporated, so the more gas there is above the liquid.

When both blue and red litmus papers retain their color for the same substance, that substance is neutral.  Purple is actually an ambiguous color.  It could mean the substance is slightly basic or slightly acidic.  You can sometimes figure out which it is by comparing the color change it causes on both red and blue litmus paper.  If the red litmus paper doesn't change much but the blue does, then it is probably slightly acidic.  If the blue litmus paper doesn't change much but the red does, then it is probably slightly basic.

While you would think the endpoint should be purple to indicate a neutral solution, the high base content of the sodium hydroxide solution actually causes a small structural change in the anthocyanins.  The change is small, but it affects the colors in the red region and blue regions of the spectrum, making them much paler.  As a result, the solution ends up being clear (not purple) when it first turns neutral. 

Remember, there are two different kinds of bases - covalent bases and ionic bases.  As you already learned, if a compound has a metal and a nonmetal, it is ionic.  If it has only nonmetals it is covalent.  So, when a base has a metal in it, like Al(OH)₃, it is an ionic base.  When it has no metals in it, like NH₃, it is a covalent base.

When you are doing an acid/base reaction with an ionic base, you use the fact that an acid reacts with an ionic base to make water and a salt.  Since the salt's ions come together, the opposite charges cancel one another out.  That's why there are no positive and negatuve signs in Comprehension Check #7.  It is a reaction between an acid and an ionic base.

For #6, however, the base is covalent.  At that point, you don't make water and a salt.  You have to rely on the definition of an acid and the definition of a base.  An acid donates an H⁺, and a base accepts an H+.  So, whatever is left after you pull the "H" of the acid has lost a positive charge.  HClO₃, then, becomes ClO₃^-.  Since NH₃ gains an H⁺, it gains an H and a positive charge.  That makes it NH₄⁺.  The charges have to be left in there, because there is no such thing as ClO₃ or NH₄.  Those chemicals can't exist.  However, ClO₃^-  and NH₄⁺ do exist, because the charges make them stable.

In general, then, when you are dealing with covalent bases, you will have charges in your products.  When you are dealing with ionic bases, there will be no charges in your products.  There are actually charged things produced, because a salt is made of ions.  However, the chemical formula of the salt cancels out those charges.

If you use more than 50 mL in your titration, it could be that your vinegar is stronger than most vinegar. However, you don't need to worry.  If you use the entire graduated cylinder and reached the endpoint, then your volume was 50.0 mL.  If you need more, just refill the graduated cylinder and use vinegar again until you reach the endpoint.  Then add 50.0 to the volume that you took from the second filling, and you have the volume of vinegar used.

Remember, an ionic compound needs at least one metal (to give away electrons) and one nonmetal (to take electrons).  H, N, S, and O are all nonmetals.  You can see that by looking at the periodic table and following the color coding.  Because there are no metals among them, HNO₃ and H₂SO₄ are not ionic.

Solid sodium hydroxide is caustic, because you have only a little moisture on your hands, and there is plenty of sodium hydroxide, so it forms a concentrated solution.  In Experiment 11.2, there is a lot more water, and so the concentration of the solution is low. As a result, it is not caustic.  However, if you don't want to touch the solution, just put some plastic wrap over the top of the test tube before covering it with your thumb.

Electroplating is the opposite of a Galvanic cell.  In a Galvanic cell, you are using the chemicals to make a battery.  In electroplating, you are using a battery to make a chemical.  So, in a Galvanic cell, the reduced metal is at the cathode, because it wants electrons.  Thus, it is attracting electrons towards it.  In electroplating, you are forcing the reduced metal to take electrons.  Thus, you have to shove the electrons onto it, and that requires a battery (or other power source).  Since the anode is where electrons are forced off, that's where the reduced metal goes in electroplating.  This is what you saw in the experiment.  The copper plated on only one side of the battery: the negative side (anode).

You don't actually have to know why in order to answer the question.  At the bottom of page 379, the student is told how gold is treated in order to be used for electroplating.  The student is specifically told that a strong acid is used. 

To see why you add an acid, look at the chemical equation at the bottom of page 379.  The gold is getting oxidized, because it is going from an oxidation state of 0 to an oxidation state of 3+.  Thus, the acid oxidizes the gold.  Why is that important?  In electroplating, the metal ion is reduced.  If I have gold that I want to plate onto something, then, I will first have to oxidize it so that it can then be reduced in the electroplating process.

As discussed on page 369, the reaction between the copper ions in solution and the aluminum in the foil is:

2Al (s) + 3Cu²⁺ (aq) --> 3Cu (s) + 2Al³⁺ (aq)

Notice what is happening.  The dissolved copper ions are becoming solid copper, and the solid aluminum is becoming aluminum ions, which are dissolved in solution.  So the holes that you saw in the aluminum were the result of aluminum changing to Al³⁺ and dissolving in solution.  There still should have been "dirt" in the solution and on the foil.  That's the copper.

On page 361, I discuss the rule about oxygen and say, "The sixth “rule” is that in most compounds, oxygen has the oxidation state of 2-. This is true in both ionic compounds (like MgO) and in most covalent compounds (like CO2). However, there are a few covalent compounds in which oxygen’s oxidation state is 1-, such as in H2O2. You won’t have to worry about those kinds of compounds, however."

Since you don't have to worry about the compounds where O has an oxidation state of 1-, you can always assume that the rule for oxygen is true.  It is a last resort, but it is more likely to be true than the rule for all Group 7A elements except for flourine.  If you are ever presented with a molecule that has F and O, you know that F is 1-.  However, if you have any other Group 7A element in a molecule along with O, assume that O is 2-.

In Chapter 11, you learned that acids donate H+ ions.  In the experiment, you added vinegar, which contains acetic acid.  The acetic acid donated those H+ ions.

Think about what happens in a Galvanic cell.  Electrons are lost by the chemicals at the anode.  What do those electrons do?  They travel to the cathode, where the chemicals gain them.  So in a Galvanic cell, electrons from from the anode to the cathode. 

Think about how electrons react to charge.  They are repelled by a negative charge, and they are attracted to a positive charge.  If I look at how electrons are traveling in a Galvanic cell, then, it looks like the anode is negative, because electrons are traveling away from it, as if they are repelled by it.  In the same way, it looks like the cathode is positive, because electrons are traveling towards it, as if they are attracted to it.

In electroplating, the positive ions in the solution absorb electrons.  Where are those electrons coming from?  They are coming from the anode.  That's where the positive ions in solution first "see" them. so they are attracted to the anode, so they can absorb the electrons coming from it.

It does not have to be shiny.  In fact, the difference you are supposed to see will probably be easier to see if the penny is not shiny. 

Remember that the always true rules beat the usually true rules.  This is a covalent compound (no metals), so H must be +1.  Thus, you have to choose between rule #6 and rule #7 to get the rest of the molecule.  When I discuss Rule #6, I tell the student he won't have to worry about compounds in which O is not 2-.  Thus, for the student, rule #6 is more reliable.  Also, in discussing rule #7, I give an example of ClO₂, and I tell the student that O is more electronegative than Cl.  That's another reason to choose rule #6 over rule #7.  So O is 2-, which makes Cl 5+.

The mass of the metal object can be greater than 15 grams.  Even something like 50 grams will work.  My main concern is that the metal piece can't be so big that it is difficult to stir the water and evenly distribute the heat.  So as long as the object isn't too big, then, the larger the mass, the better. 

I can't verify this, but I think the reason a food Calorie is 1,000 calories is really just for convenience.  If nutritionists used regular calories, there would be a lot more zeroes to write.

The question asks, "A student says that because a chemical reaction has a negative ∆S, it cannot be spontaneous.  Is he correct?  Why or why not?"

Students often think that the Second Law of Thermodynamics says that Delta S can never be negative, since entropy cannot decrease.  Thus, a chemical reaction with a negative Delta S can never be spontaneous.  However, the Second Law doesn't say that.  It says that the TOTAL entropy of the UNIVERSE can never decrease.  As a result, the Delta S of a chemical reaciton CAN be negative, as long as the resulting Delta S of the surroundings is so positive that the total entropy change of the universe (Delta S of the reaction + Delta S of the surroundings) is positive or zero. 
 

When electrons return to their ground state, the entropy of the atom itself decreases.  However, in order to do that, the electrons must release energy, usually in the form of light.  That energy increases the entropy of the surroundings.  The entropy increase in the surroundings is always greater than or equal to the entropy decrease of the atom, so that the total entropy of the universe always increases or stays the same, in accordance with the Second Law of Thermodynamics.

When you are determining Delta_H, in this problem, you end up with the following result:

Delta_H = 1000 kJ + (1 mole)(triple CN bond energy)

However, because the bond energy of the CN single bond is 300 kJ/mole, you need to report that "1000 kJ" to the hundreds place.  In other words, the first zero after the 1 needs to be significant, but the other cannot be.  Since the rules say that none of the zeros in 1000 are significant, we have to make one of them significant using scientific notation.  Thus, we convert it to:

Delta_H = 1.0x10³ kJ + (1 mole)(triple CN bond energy)

Think about what this means.  The number 1.0x10³ has two significant figures: the 1, and the zero right after the 1 (because it is at the end of the number and to the right of the decimal).  Now...the numerical value of  1.0x10³ is 1000, and since only the first zero after the 1 is significant, that means the 0 in the hundreds place is significant.  Thus, 1.0x10³ has its last significant figure in the hundreds place.  If it were 1.00x10³, the second zero after the 1 would be significant.  That would be the zero in the tens place of 1000, so the number has its last significant figure in the tens place.  If it were 1.000x10³, the third zero after the 1 would be significant.  That would be the zero in the ones place of 1000,  so the number has its last significant figure in the ones place.  

Gaseous carbon isn't stable at 25 C.  The main reason it is on the table is that we often assume that the absolute entropy of a substance doesn't change a lot with temperature.  Thus, even though it is an approximation, we can use it for higher temperatures, where gaseous carbon is stable.

In Chapter 5, Comprehension Check 3a asks for that Lewis structure.  The solution in on page 155.  Look at the drawings there as you read this explanation.  You put carbon's 4 valence electrons around it and oxygen's 6 valence electrons around it.  When you link one of the lone electrons on carbon with one of the lone electrons on oxygen, the carbon has 5 and the oxygen has 7.  That doesn't give either atom 8.  However, if you put the other lone electron from oxygen in between the two atoms as well as one of the lone electrons on carbon between the two atoms, you now have a double bond between carbon and oxygen.  The oxygen has 8, but the carbon only has six.  To fix this, you take a pair of electrons on oxygen and put them in between the two atoms.  That makes a triple bond, and now both carbon and oxygen have 8.  To make things tidy, it is best to pair up the two lone electrons left on carbon.

If you used a paper cup, the specific heat is just a bit higher.  It's 1.4 J/gC.

Whenever you use Hess's Law for delta H, delta S, or delta G, you always add each product and subtract each reactant.  For determining the delta S in Comprehension Check #11, for example, you would add 2 times the absolute entropy of NH₃ (g), then you would subtract the absolute energy of N₂ (g), and then you would subtract three times the absolute entropy of H₂ (g).

In step 2, you were supposed to measure the mass of the top cup in the calorimeter.  That's the part of the calorimeter that absorbed heat.  In step 13, the lab tells you to multiply the mass of the top cup by 1.3 J/gC to get the heat capacity of your calorimeter.  When you multiply mass by 1.3 J/gC, the unit will be J/C, which is the proper unit for heat capacity.  That's what you use when calculating the heat absorbed by the calorimeter.

Yes.  Once you measure the mass of the cup, then put it back into the other one.  The idea here is that only the cup you measured the mass of will be in contact with the water, so it's the only thing that will heat up.  However, putting it back into the other cup will help make the system more insulated so that less heat leaaks out.

Remember that Delta_H_f is Delta_H of the formation reaction for any chemical.  So the Delta_H_f of CH₄ (g) is the Delta_H of the formation reaction:

C (s) + 2H₂ (g) --> CH₄ (g)

What is the formation reaction for H₂ (g)?  A formation reaction is the reaction that takes elements and makes the molecule of interest, so it's

H₂ (g)  -->  H₂ (g)

The Delta_H of that reaction is obviously zero.  Now, the Delta_H_f of H2 (l) is not zero, because the elemental form of hydrogen is H₂ (g), so you have to take energy away from the elemental form to make it a liquid.  That means the Delta_H_f of H2 (l) is negative.  However, you don't have to make H₂ (g).  It is the simplest form of H₂.  That means there is no energy involved in making it.

These are measured quantities, and remember that in measured quantities, there is always error in the last significant figure.  The book says the H-H bond energy is 436 kJ/mole.  However, others say 432 kJ/mole.  The variance in the last significant figure reflects the error associated in measuring the bond energy. 

Remember that when you add or subtract, you report your answer to the same DECIMAL PLACE as the least precise number in the problem. When you just do the math, you get:

-137 + 1.0x10³= 863

However, you now have to take significant figures into account. 137's last significant figure is the 7, and it's in the ones place. 1.0x10³'s last significant figure is in the hundreds place, because 1.0x10³ is 1,000 with the first zero significant. Well, that first zero is in the hundreds place. The hundreds place is less precise than the ones place, so the answer must have its last significant figure in the hundreds place. Thus, you must drop the 6 (which is in the tens place) and the 3, which is in the ones place. However, since you are dropping a 6, you round up, so the answer is 900.

There are two ways to think about this.  I will give you the easy way first:  An equilibrium will shift so as to reduce the stress.  If you add more reactant, it shifts to the product so as to reduce the amount of reactant that you just added.  In other words, an equilibrium shifts to counteract the way it was stressed.  If I increase pressure, then, it will shift so that the total pressure is lowered.  Thus, it will shift to the side with the fewest gas molecules.  On the other hand, if I lower the pressure, it will shift so the pressure increases.  That can be accomplished by shifting to make more gas molecules.

However, it really is all about reaction rates, and that brings us to the harder way to think about this:  Think about how reaction rates change with changing pressure.  If I lower the pressure, BOTH the forward AND reverse reaction rates will decrease, because the molecules aren't being pushed together as hard.  As a result, there won't be as many effective collisions.

Now...think about which side will experience the most drastic reduction in rate.  If I have only two molecules on one side of the equation, and they are suddently not forced together as hard, they wll have fewer effective collisions.  So their reaction rate will be lower.  However, if I have four molecules on the other side, and they all have to collide to make their reaction work, they will experience a GREATER DECREASE in rate, because their four-molecule collision is much less likely than a two-molecule collision.  As a result, their successful collision is more dependent on pressure.  When you reduce the pressure, then, the reaction that has to have more molecules colliding will have a greater reduction in its rate.

So BOTH sides of the equilibrium experience a decrease in rate, but the one that has the most gas molecules experiences the largest decrease in rate.  Thus, it slows down more than the other reaction.  That means the reaction that uses fewer gas molecules slows down less.  As a result, the reaction that uses fewer gas molecules becomes faster, so the equilibrium will shift away from it and towards the side with more gas molecules.

Remember that for the Second Law to be followed, the total disorder in the universe must increase.  Well, when a reaction is at equilibrium, there is more disorder than when it is all products or all reactants.  After all, if it is a complete reaction that becomes nothing but products, all the mass is concentrated in a few chemicals (the products).  If it is a reaction that never starts, all the mass is also concentrated in a few chemical (the reactants).  When both the reactants and products are present, there is more disorder, as the mass is spread out over more chemicals (both the reactants and the products).

At the same time, however, some chemicals are more disordered than others.  So, if I have all the mass concentrated in a few chemicals that are really disordered, that may be a more disordered situation than spreading the mass over the really disordered chemicals and some really ordered chemicals.  The value for Delta_G takes all this into account.  When Delta_G is zero, the reactants and products have similar disorder, so the universe is most disordered when things are spread evenly over reactants and products.  When Delta_G is small and positive, the reactants are a bit more disordered than the products, but you still gain a bit of disorder by having some of the mass spread out over all the chemicals.  However, that only gains you a bit of disorder, so the reaction only makes a few products.  When the value of Delta_G is large and positive, the reactants are much more disordered than the products, so you don't gain any disorder by making products.

In the end, then, the state of the equilbirium contributes to the disorder of the universe, and that's why Delta_G really determines the equilibrium constant.

Respiration is a part of the metabolism characteristic. Organisms use oxygen to burn the molecules they get from food, while others (anaerobic organisms) use a different process to get energy. Thus, respiration is a part of metabolism. Movement is one of the ways organisms respond to stimulus, so it is a part of that characteristic.

Other fruits will work, but the amount of DNA extracted will be different, because of the chemical nature of the fruits themselves and the amount of DNA in them. Strawberries and bananas give the best results for this particular procedure, but other fruits will work. It just might be harder to see the DNA.

Think about a rock like this one:

https://www.coueswhitetail.com/forums/uploads/monthly_2019_02/20190219_181903.jpg.b9bbd342716dd34cf7ef9dacfe71896a.jpg

It's got a complex shape (lots of bumps, valleys, and points) but the complexity doesn't serve any purpose. It's not specified or specific.  It's just complex.  Now consider this rock:

https://upload.wikimedia.org/wikipedia/commons/a/af/Mousterian_tool_4_form_Syria_%28University_of_Zurich%29.JPG

It also has a complex shape (pointed at one end, round at the other, sides sharpened). The difference is that this shape serves a purpose - it can be used to cut and scrape. In many ways, this rock is less complex than the first one, but the complexity of this rock is specific, so you know it was designed to be a tool.

Complexity can occur via random processes, but complexity that is specified or specific always originates in design.

Specific complexity (design) is the recognition that the system is complicated, but it is complicated in order to serve a function. So...if you see this rock:

https://upload.wikimedia.org/wikipedia/commons/9/9a/Roccia_dell%27Elefante_2010.jpg

You can recognize it is a complex shape, but that complexity doesn't serve any purpose. Thus, it is complex, but it does not have specified complexity.  If you see this statue:

https://5.imimg.com/data5/ANDROID/Default/2022/8/RR/RI/ZN/80694218/product-jpeg-500x500.jpg

You see that it is complex, but you know the complexity has a purpose - to show the viewer what an elephant looks like. The first rock was not designed, because its complexity is not specified. The statue was designed, because its complexity is specified.

Irreducible complexity is complexity that comes from a bunch of components that must already exist in their current form and cannot come about by modifying something else. In both cases above, the complexity is not irreducible, because both come from modifying rocks, and many different kinds of rocks could be used in the process.

Compare both of those to this elephant robot:

https://media.leisureliving.com/media/49c0f92827e873870ca3aa15fc9fd10d.jpg

Some of its electronic components might work in other robots, but some of them only work in this model of elephant robot. Those components cannot be the result of modifying other components. That means the elephant robot has irreducible complexity.

On page 85, we tell you that in aerobic respiration the final electron receptor molecule is oxygen. It receives the electrons at the end of the electron transport chain.  Then, on page 87, we tell you that this kind of respiration can also happen without oxygen, if the organism has another final electron receptor molecule. For example, methanogens use carbon dioxide as the final electron receptor.

If the organism has no final electron receptor molecule, all it can do is glycolysis, so it must do glycolysis and fermentation, as discussed on pp. 80-83.

Remember that mitosis starts with a diploid cell and ends with two duplicates of it. If the cell has a haploid number of 11, then its diploid number is 22. Thus, mitosis would start with a cell that has 22 chromosomes and will end with two duplicates, so each daughter cell will have 22.  

When mitosis starts, the DNA is duplicated. So after the duplication, the cell will have 22 chromosomes, each of which is attached to its duplicate. Those 22 chromosomes with their duplicates attached line up at metaphase, and then anaphase separates the chromosomes from their duplicates. The original 22 chromosomes go into one daughter, and the duplicates go into the other daughter. Thus, each daughter has 22 chromosomes.

To do the microscope experiments in the biology course, you need a microscope with two main features:

1) At least three magnifications, from 40x to at least 400x.  Note that for most scopes, the eyepiece is x10, so whatever the lens says, you multiply it by 10 to get the total magnficiation.  Most student scopes have three lenses that are 4x, 10x, and 40x, which results in magnifications of 40x, 100x, and 400x.

2) Separate coarse and fine focus knobs.  When you turn the coarse focus knob, you see the microscope move.  When you turn the fine focus knob, you don't see it move, because it is moving on a microscopic scale.

To weight the grades the way I suggest, calculate a percentage for each test, and give each lab report grade as a percent as well.  Then, add all the regular tests' percents together, then add each quarterly test percent twice, and then divide all that by the total number of points, which should be 2,400 (1600 from the 16 module tests and 800 from the four quarterly tests added twice).  That will give you a decimal number that represents the tests' average.  Separately, add all the lab report percents and divide by the total possible points (100 for each lab), and that will give you a decimal for the lab reports' average.  The final grade is then:

(0.65)x(decimal from the tests) + (0.35)x(decimal from the labs)

Here is an example:

Test 1: 87
Test 2: 91
Test 3: 93
Test 4: 88
Qtst 1: 95
Qtst 1: 95
Test 5: 87
Test 6: 89
Test 7: 96
Test 8: 95
Qtst 2: 89
Qtst 2: 89
Test 9: 91
Test 10: 99
Test 11: 100
Test 12: 97
Qtst 3: 92
Qtst 3: 92
Test 13: 99
Test 14: 88
Test 15 : 85
Test 16: 87
Qtst 4: 91
Qtst 4: 91

sum: 2,206

decimal: 2,206/2,400 = 0.919167

Do the same things for labs.  Add up the percentages and divide by the number of labs times 100.  You will get another decimal.  Let's say it is 0.965143

The final grade is:

(0.65)x(0.919167) + (0.35)x(0.965143) = 0.933959

So the student's final grade is 93.4%

You can diffuse the light by placing a piece of tissue (Kleenex) over the LED aperature.  If that isn’t sufficient try a strip of paper towel.

Exoskeletons are not shells.  Think of a clam, snail, or oyster.  They have shells.  Shells are typically very hard, thick, and jointed in at most one place.  A snail shell, for example, doesn't open, so it has no joints.  A clam shell has one joint between the two halves.  Now think of ants, lobsters, and crabs.  They have exoskeletons.  Exoskeletons are typically thinner (you can crush an ant easily, you can't crust a clam easily) and jointed in many places so the occupant can move its legs, arms, etc.  Insects all have exoskeletons, as do spiders, millipedes, lobsters, crabs, etc.

The cell wall and capsule don't interfere with the plasma membrane's job of bringing chemicals into the cell, because both the cell wall and capsule are permeable.  The cell wall has large holes in it so that chemicals can easily pass through.  The capsule isn't solid.  It is more like a gel.  So chemicals can easily pass through it as well.  Thus, even when there is a cell wall and/or capsule, the plasma membrane has access to all the chemicals in the surroundings.

You can preserve fungi that you find early in the school year, but drying them out is the key.  Ideally, you would use a food dehydrator.  However, if you don't have one, there are some alternative methods:

http://www.mushroomexpert.com/pinch_drying.html

As long as you get them dry, you should not refrigerate or freeze them.  Just store them in a Ziploc bag and keep the bag in a cool, dry place.

Yes.  It's a lot, but it is necessary.  Biology is a vocabularly-driven science.

The key difference between neo-Darwinism and Darwinism is the recognization that information must be added to the genome.  Nevertheless, the way that is assumed to be accomplished is through mutation.  If the student mentions information being added but not mutatons (or vice-versa), I would give the student 1/2 of a point.

Convergent evolution is the idea that macroevolution produced similar structures in two organisms that are not closely related.  As a result, the similar structures were not inherited from a common ancestor.  The similarity is simply a coincidence.

Homologous structures are similar structures in two organisms that are closely related.  As a result, they were inherited from a common ancestor.

Convergent evolution is a purely macroevolutionist idea made up to explain the problem that some creatures have similar structures even though they are distantly related to one another.  In other words, it is simply an attempt to explain around evidence so as to preserve macroevolutionary theory.

Homologous structures apply to both macroevolution and microevolution.  A macroevolutionist would believe that a penguin flipper and human arm are homologous.  However, the term can apply to microevolution as well.  All dogs have essentially the same set of teeth, so their teeth are homologous structures, because they are all related by microevolution.

You can kill insects without destroying them by using a kill jar.  Here are instructions on how to make one:

http://www.extension.umn.edu/garden/insects/collecting/

It is lobed.  Technically, we say it is "irregularly lobed," but lobed is good enough.

There is a set of daily lesson plans available here:

https://www.christianbook.com/lesson-plans-exploring-creation-advanced-physics/lynn-ericson/pd/427128?en=google&event=SHOP&kw=homeschool-0-20%7C427128&p=1179710&dv=c&gclid=Cj0KCQjwkK_qBRD8ARIsAOteukAyNQLdRZ1UlqGqxsf6_9wVGy7jOopHdvOlUhWmTD2Kt6HpuOilRMgaAmBEEALw_wcB

There are no other problems than what you see in the book.  There are a couple of good websites that do a lot of things like that, however:

https://www.chemteam.info/ChemTeamIndex.html

https://general.chemistrysteps.com/general-chemistry-practice-problems/

http://chemistrysky.com/Practice%20Problems.html

https://www.wiredchemist.com/chemistry/instructional/general-chemistry-problems

You may have forgotten this from your first-year course, but enthalpies follow the rules for addition.  That's because even though you are multiplying sometimes, the numbers you are multiplying by are exact.  When you multiply a Delta_H by 3, for example, it is really just adding the Delta_H three times, since the three is exact.  So you are really just adding Delta_H's and should therefore follow the addition rules, reporting your answer to the same precision as the least precise Delta_H.

The signs are really arbitrary.  They depend on how you define the three-dimensional space.  Thus, whether you use positive or negative magnetic and spin quantum numbers first doesn't matter.  If you have l = 2 (for p orbitals), then you can use m_l = -1 first or m_l = 1 first.  If you have l=3 (d orbitals), you can use  m_l = -2 first or m_l = 2 first. In the same way, if there is only one electron in an orbital, you can give it an ms of -1/2 or an m_s of 1/2.  It doesn't matter.

There should be four significant figures in the exponent of "e" in both of those problems, which means the answers should have four as well.

The phrase, "When raising a number to a power that has error in it..." refers to a situation when the exponent isn't an exact number.  Think about a rate equation like:

R = k[A]²

The exponent (the square) is exact, because rate equations have integer or half-integer exponent.  Thus, it can't be

R = k[A]^1.9 or R = k[A]^2.1

It is exactly R = k[A]²

In these thermodynamics problems, the values for Delta_G are not exact.  They have error in them.  Thus, in Example 6.2a, the equation:

e^0.485

could actually be

e^0.483 or e^0.487

In other words, the exponent itself has error in it.  You need to know how that affects the error in your answer.  That's where the significant figure rule comes into play. It tells you that in this case, your answer needs to have three significant figures.

You use the standard rules for multiplication and division to get the exponent.  So you are dividing a number with three significant figures by two numbers, each with four significant figures.  That means you can have only three significant figures in your answer, which is why the exponent is 67.4.

The method works because of the nature of an equilibrium reaction.  Remember, for a given set of reactants at a given temperature, there is only one equilibrium position.  If I start with a certain concentration of NO and a certain concentration of Cl₂, the reaction will reach an equilibrium position.  If I somehow then force it out of equilibrium without changing the amounts of anything, the reaction will strive to get back to that same equilibrium point.  So, in this method, I am starting with a certain amount of NO and a certain concentration of Cl₂, and then I am artificially forcing the reaction to go as far to the right as possible.  That's okay, though, because the reaction will strive to get back to equilibrium.  So all I have to do is figure out what the concentrations of all the chemicals are once the reaction is artificially forced to the right, and then I can track how it gets back to equilibrium.
 

Why do I use the K as it's set up for the forward reaction if I am tracking the reverse reaction?  Because it doesn't matter.  If you wanted to use the K for the reverse reaction, you could.  What would it be?  It would be [NO]²[Cl₂]/[NOCl]².  What's the value of that equilibrium constant?  Since it is the inverse of the K as given, the value is the inverse of the given K's value, or 1/(2.5x10³).  In the end, if you use that K to set up the equilibrium, you just get the inverse of the first equation on page 251.  That will end up giving you the same value for x, which will lead to the same answer. 


Now there is an error in the solution, which I didn't notice until this question was asked.  In the solution, I failed to square the concentration of NOCl.  Thus, the top term on the right-hand side of the equation on page 251 should be (3.80-x)².  That leads to a MUCH longer set of approximations, and x = 0.11 instead of 0.049.

You ignore water when you know it is a liquid or solid. Since the phases aren’t given in the problem, you don’t know that it is a liquid or solid, so you can’t ignore it.

Also, on a more technical note, you ignore liquid water only in aqueous solutions. When water is the solvent, you have enough of it to keep the concentration constant. However, if it is not a solvent and is either being used or made, the concentration does change under certain conditions. As a result, it needs to be kept in the equilibrium constant.

You can use either, because they are really the same thing.  There are no free H+ ions in solution.  They are always added to a water molecule.  Thus, you can use either one.  The only thing that changes is the number of water molecules on the other side.  So a reaction like

ClO₃¯ + 3H₂O + 3SO₂ ---> 3SO₄²¯ + Cl¯ + 6H⁺

would become

ClO₃¯ + 9H₂O + 3SO₂ ---> 3SO₄²¯ + Cl¯ + 6H₃O⁺

Both equatons are equivalent.

Remember that A is the maximum distance from equilibrium. So....let's assume it is pulled all the way to the right and let go. When it travels left to the equilibrium position, it has traveled A. Then it travels left through the equilibrium position to the left side, traveling another A. That's only half the trip back, however. It must now travel A to the right so it gets back to the equilibrium position and another A to get back to the A on the right. That's a total round trip, and it is 4A. 

Isotope is a relative term.  It means in relation to something else. So you have to compare two atoms. It's like the term "brother." A single male child cannot be a brother. There must be at least two siblings. If so, the male siblings are the brothers. In the same way, you must compare two atoms to determine if there are isotopes. The isotopes will be the atoms that BOTH have the same number of protons but a different number of neutrons. So A and C are isotopes since they both have six protons (they have the same number of protons) but they have different numbers of neutrons (one has six neutrons, and the other has eight).

Speed and time are not the same thing. Let's suppose a substance moves at the same speed in all cells, no matter the size. In a small cell, that substance would get to its destination in less time, because it had less surface area to cover. However, if a substance is supposed to get to its destination in a set time, it must move faster in a larger cell, because it has more surface area to cover.

Think about it this way - It's 7:00 AM, and you have to get to an appointment by 7:30. If the appointment is 5 miles away, you wouldn't have to travel very fast to get there on time. If it is 25 miles away, you would have to travel faster to get there on time. So...if a substance in a cell must make it to a destination, it must travel faster the farther away that destination is.

I have heard from parents whose 5th graders have done the course successfully.  In my opinion, there are two things to consider:

1.  What is the child's math level?  If he or she will be doing 7th-grade math at the same time (that means the student will be one year before pre-algebra), then he or she is also at the 7th-grade level when it comes to science.

2.  Does the student have experience with studying for and then taking tests?  That's a big adjustment for some students.  If the student has already learned how to study for and take tests, that will help a lot.

A student could easily get tired after scrubbing 2 or 3 tiles.  It all depends on how much force he or she uses and how fast he or she scrubs.  I can tire after just a minute of exerting a lot of force quickly. 

The problem doesn't say that there are different amounts of heel marks, but it also doesn't say that there are the same amounts of heel marks.  Thus, that could be a variable.  Think about heel marks on a floor.  Do they happen uniformly everywhere?  No.  Most likely, then, the amount of heel marks varies.

If you are having trouble finding alum in the UK, try Amazon:

https://www.amazon.co.uk/Anti-Bacterial-Deodorant-Fatakdi-Potassium-Sulphate/dp/B00C77ZSSS/279-1060947-6666120?ie=UTF8&*Version*=1&*entries*=0

You can also try Oxford ChemServe

http://oxfordchemserve.com/alum-potassium-aluminium-sulphate-recrystallised-200-g/

I don't have a scope and sequence of the math in Exploring Creation with Physical Science, but I can tell you what the student needs to know to understand what's in the course:

1)  The student needs to be able to multiply fractions, recognizing that like terms in the numerator and denominator cancel.

2)  The student needs to be able to square numbers, like  3² = 9.

3)  The student needs to be able to plug numbers into equations and evaluate them.  For example, if distance  = (1/2)(a)(t)², and a = 9.8 m/sec and t = 1.0 sec, what is the distance?

4)  The student needs to understand proportional and inversely proportional, including squares.  For example, the force of gravity is proportional to the mass.  So...if mass is multiplied by 2, the force of gravity is multiplied by 2.  However, it is inversely proportional to the square of the distance.  So, if distance is multiplied by 2, the force of gravity is divided by 4.

In order to get the water to break down into hydrogen and oxygen, you have to add energy.  In Experiment 4.1, you are adding that energy with electricity.  However, for electricity to add energy to the water, it must flow through the water.  Pure water cannot conduct electricity.  Thus, this experiment wouldn't work in pure water, because electricity could not flow through it.  As a result, you must dissove something in the water that will allow it to conduct electricity.

There are lots of things you could have added, including normal table salt.  However, normal table salt will cause a side reaction to occur that will take oxygen away.  You don't want that, so you need to add something that both makes the water conduct electricity and doesn't promote a lot of side reactions.  Epsom salts fit that bill, so that's why they are used.

The idea is that the equation

F = ma

only works when F is the total of all the forces acting in the problem.  Friction always acts against motion, so if you have a man pushing something:

F = F_man - F-friction

For example, if a man applues 100 N of force, but there is a 35 N frictional force:

F = 100 N - 35 N = 65 N

That means

65 N = ma

Alternatively, lets say a man is using a 50 N force, and a 10-kg object is accelerating at 3 m/sec².  We can calculate the total force:

F = ma

F = 10 kg x 3 m/sec² = 30 N

However, that's the TOTAL force, which include both the man pushing and friction.  So:

F = F_man - F_friction

Since F is 30 N and the man is pushing with a 50 N force:

30 N = 50 N - F_friction

The only way this works is for the frictional force to be 20 N.

It is quite possible that the ice cube will slide down the rough board faster than the smooth board.  That's because the ice cube is melting, and therefore there is water coming off it.  That water can fill up the pits in the rough board, making a thin layer of water that the ice cube can slide on.  This can't happen as well on the smooth board, because the water just rolls down it.  In this case, then, the WATER is sliding down the rough board more slowly, but that allows the ice cube to slide down more quickly,

In the General Theory of Relativity, mass bends space and time together.  In this view of physics, space and time are not separate.  They are connected together in a four-dimensional matrix called "spacetime."  Mass bends spacetime because it interacts with the matrix.  We have no idea exactly how this happens.  However, if we assume it does, we can explain several observations that otherwise could not be explained.

Because of this effect, mass affects the passage of time.  In the presence of a lot of mass, time moves slowly.  In the presence of less mass, time moves more quickly.  This sounds odd, but it is has been experimentally confirmed.  For example, time moves more quickly on the global positioning system satellites than it does on the surface of the earth, since the satellites are farther away from the mass of the earth.  If this difference in the way time behaves were not taken into account, the global positioning system would not work.  Since the moon has less mass than the earth, time moves more quickly on the surface of the moon than it does here on earth.  As a result, a person would age more quickly on the moon than he would on earth.

Yes, but you won't hear them.  However, some animals can.  A level of 0 decibels means you are at a volume where human ears can barely hear.  So, if a sound has such a low volume that a human can't hear it, the sound would have a negative decibel measurement.  Dogs, for example, can hear certain sounds that have volumes of up to -4 decibels.  However, this is frequency dependent.  Typically, the higher the frequency, the more decibels of volume it needs to have for the dog to hear it.

In the situation where the season is wrong for outdoor experiments, I would just skip the experiment.  I would go ahead and do the lesson, since some lessons build on previous lessons.  However, I would mark the lesson in some way so that you can do the experiment later when the season changes.  One other thing to consider is that you could do a YouTube search for a video of a similar experiment.  For example, if it is just too overcast and cloudy  to do the experiment where you burn paper with a magnifying glass, just go on YouTube and search "burning paper with a magnifying glass," and you can watch a video of it.

I think the ideal notebook for Science in the Beginning would be a spiral-bound notebook that has blank pages.  There is a lot of drawing in the course, and lined paper makes that just a little harder.  Also, I like spiral-bound for elementary because it lays flat.  In high school, the student will need a bound notebook that makes it difficult to tear paper out.  However, for elementary science, that's not necessary.  If you can't find a spiral-bound notebook with blank pages, use a 3-ring binder and punch holes in blank, white paper.

I did design the course assuming that the student starts at day 1 and goes through the days in order.  For example, in Day 1, I define certain kinds of energy (mechanical energy, chemical energy, radiant energy, etc.).  In later days I simply refer to those kinds of energy, assuming the student will know what they are.  Of course, they are defined in the glossary, so by looking at the glossary more often, etc., you probably could do the days out of order.

Two mothers who used Science in the Beginning have made a notebook that is free to download:

https://www.bereanbuilders.com/mkt/res/nb/9780989042406nb.pdf

A few typos were found in the first printing of the course.  The corrections are listed here.

I think it would be hard to teach this as a one-hour-per-week class.  If you skip the challenge lessons, you still need to do two lessons per week to cover the book in a year.  In a class setting, that means two experiments per class.  I would think doing two experments and explaining their meaning would be difficult in one hour.

You could do one lesson in class and then suggest that they do the other lesson at home.  Alternatively, you might be able to do two lessons if you had 90 minutes instead of just an hour.

One other thought, which I am not a big fan of but could work, is to do the expeirments as demonstrations.  I want the students to do the experiments themselves, but if you did them as demonstrations, they would go faster, and you could probably do two in an hour.

I would say that the "youngest" students are those who aren't able to write much. They have two questions to answer orally. Once the students are comfortable writing, they should do the "older" student exercises. The "oldest" student exercises should be done by fifth and sixth grade students.

They are the pads you use to hold on to hot things.  When you pull a casserole dish out of the oven, you use hot pads to protect your hands from being burnt.

The moon is like a mirror in the sense that it reflects light, but a mirror reflects light differently than the moon.  You will learn the difference between the way a mirror reflects light and the way things like the moon or a sheet of white paper reflect light in Lesson 5. 

Stars do make their own light.  They are too far away to reflect light from the sun.

We know that the moon reflects light from the sun for at least three reasons.  The most important one is that it goes through phases.  At times, some parts of the moon are dark, while other parts are light.  When you compare where the moon is to where the sun is, you see that the light parts of the moon are the parts that can reflect light from the sun to the earth.  The dark parts are not in the right place to reflect the sun's light back to earth.  Thus, the light from the moon is the sun's reflected light.

Another reason is what we call "earth shine," and it was figured out by Da Vinci in the 1500s.  When the moon is a thin crescent, you can often see the rest of the moon, but it is dim.  That's because the earth is reflecting the sun's light to the moon, and then the moon is reflecting that light back to the earth.  It is dimmer than the sun's light, so those parts of the moon are dimmer.

Nowadays, we can actually measure precisely how much light is coming from the moon.  We can do the same thing for the sun.  We see that when the sun gets a bit brighter, the moon does as well.  When the sun gets a bit dimmer, the moon does as well.  Thus, the moon's light is actually the sun's light.

Actually, there is pink in a rainbow.  However, it is difficult for us to see, since our eyes see the red more vividly.  If you are fortunate enough to see a wide rainbow where the colors are more streched out, you might be able to find pink in it.

All objects are made up of either atoms or molecules.  These molecules are able to absorb certain colors, and they reflect other colors.  Two shirts made from the same material can be different colors because dyes are added to the fabric.  Those dyes are chosen so that they absorb the colors you don't want to see and reflect the colors you do want to see.  A red shirt, for example, is dyed with a chemical that absorbs all colors except red.  A blue shirt made of the same material is dyed with a chemical that absorbs all colors except blue.

Black is the absence of all color.  We see it because we are comparing it to other things that send light to our eyes.  You see a black box sitting on a table, for example, because the table is reflecting light, sending it to your eyes.  The black box is not reflecting any light, so it is sending nothing to your eyes.  As a result, your eyes see light coming from the table, and then this box-shaped area from which no light is coming.  That lack of light surrounded by light from the table defines the box.

Suppose you had a box that was open on the top but completely black inside.  Now suppose you put a red ball in it.  You would see the ball because light comes in through the open top, hits the ball, and the ball reflects red light into your eyes.  Now suppose you replaced the red ball with a black ball.  The inside of the box isn't sending any light to your eyes, and neither is the ball.  Thus, you wouldn't see the ball. 

Artificial light can be used in lesson 4, but it has to be from an incandescent light bulb (the kind with a filament - not a compact flourescent light bulb or an LED light bulb) that is around 100 Watts or more.  You need to get the light bulb directly above the plastic in some way, either by using a lamp with a movable head or by laying the lamp on its side on books so the bare light bulb is hanging above the plastic.  Also, you have to play a bit with the distance between the light and the plastic.  If you get the light too close, it will heat both of them up so much that you won't notice a difference.  If you have it too far away, it won't heat either of them enough to notice.

When you use mechanical energy to move, you are using your muscles.  As you walk, for example, your muscles contract and relax to move the bones in your skeleton.  As the muscles are doing that, the fibers that make them up are rubbing against each other, causing friction.  Your muscles expend energy fighting that friction.  When you want to stop, your muscles stop fighting the friction, and the friction between the muscle fibers quickly causes the muscles to stop contracting, which causes you to stop your motion. 

Friction converts mechanical energy into heat energy.  If you rub your palms together vigorously, for example, you will feel them heat up.  That's because friction is converting some of that mechanical energy into heat energy.

Most mechanical energy, then, gets converted into heat energy via friction.  That's where most of the energy in motion goes to when you stop moving.  Some of it is also absorbed by the molecules in the air, and they end up moving more quickly as a result.  If you could really account for it, you would find that all the energy you used for motion was converted into some other kind of energy (heat via friction, motion of air molecules, etc.)

[Names are never published with the answers.  Only the answers are published.]

All colors are present in white light.  However, when they hit an object, the object refects only certain colors, giving the object the color you see.  The darker colors don't overpower the lighter colors because an object reflects light based on the ENERGY of the light, and each color of light has a different energy.  Thus, the colors don't overlap.  This is different from when you draw with a ight-colored crayon and then draw over it with a darker-colored crayon.  When you do that, the light hits BOTH colors, and they each reflect the light that corresponds to their color.  However, they both absord the OTHER COLOR'S light.  In the end, the darker color absorbs a lot more light, so most of the lighter color's light is taken away.  As a result, you see mostly the darker color.  In white light, the colors don't overlap.  They each have a different energy, and since an object reflects light based on its energy, the colors don't interfere with one another.

All objects are made of atoms or molecules.  Even molecules are made up of atoms, so essentially, all objects are made of atoms.  An atom has tiny particles called electrons that orbit its center.  The center of the atom is made up of other tiny particles called protons and neutrons.  When light hits an atom, if it has the right energy, the atom's electrons can absorb the light.  This usually results in the light's energy being converted into thermal energy, which heats up the object.  The key is that when this happens, the light is gone.  Any light that has energy which cannot be absorbed is typically reflected, and it becomes the light you see coming off the object.  Well, each color of light has its own energy, so when certain energies are absorbed, certain colors are taken away.  Whatever is not abosorbed is reflected, and those colors mix to form what you see as the color of the object.  So when I want to paint an object red, I will use a paint whose molecules have atoms that absorb energies corresponding to all colors except the shade of red that I want. That way, the paint gets rid of all the colors in the white light except the shade of red I want, and it reflects that color.

This experiment does work better when the sun is higher in the sky.  If it is fall or winter, it doesn't work as well.  Nevertheless, you should still be able to get it to work.  First, try a single sheet of newspaper and wad it up very loosely.  The paper is thin and will burn more easily.  Second, play with the tilt of the magnifyinng glass so that the circle of light is as tight as possible.  It's not just the distance between the magnifying glass and the paper that is important.  It is also how the magnifying glass is tilted.  Play with both the distance and the tilt to get as tight a circle of light as possible.

You can make energy by converting it from one form to another.  For example, we make electricity by burning something (like coal).  The heat is used to boil water, and the motion of the steam is used to turn turbines, which generate electrical energy.  Throughout that process, no energy is created.  Instead, the energy that is stored in the chemical bonds of the wood and the oxygen in the air gets released in the form of heat.  So chemical energy has been converted into heat energy.  That heat energy then boils the water, and that causes the steam to move.  Boiling the water, then, converts the heat energy into mechanical energy.  The motion of the steam is used to move the turbines that generate the electricity.  This means the mechanical motion of the steam is converted into electrical energy.

In science, when something is "conserved," it means that it is kept intact.  The Law of Mass Conservation, for example, says that in chemical processes the total amount of mass cannot change.  The chemicals can change, but the total mass of all the chemicals after a reaction have to add up to the total mass of the chemicals before the reaction.  Since all the mass is kept intact, the mass is "conserved."  In the same way, the Law of Energy Conservation says that even though the energy changes form, the total amount has to remain intact.

Now, of course, the Law of Energy Conservation is important when we do energy conversions.  When a black sheet of paper absorbs light, the radiant energy is converted to thermal energy, and the Law of Energy Conservation says that the total amount of energy before has to equal the total amount of energy after.  However, the law of Energy Conservation applies to things other than energy conversions.  For example, when sunlight is split into its many colors by drops of water in the air (forming a rainbow), the total amount of energy in the white light must be the same as the total amount of energy in all the colors of the rainbow.  In this case, energy isn't converted.  It is radiant energy when it is white, and it is still radiant energy when it is in the rainbow.  Even though energy isn't converted, it is still conserved. 

That's the long answer to your question.  The shorter answer is that The Law of Energy Conservation applies to situations other than just energy conversion.

Unfortunately, an LED light will not work.  The only kind of light that works in this experiment is a fluorescent light.

Microwave ovens use microwave radiation, which is light waves that have wavelengths between 0.001 meters and 1 meter.  Most microwave ovens today use microwaves with wavelengths of around 0.12 meters.

Radio waves are also light waves.  They comprise a broad range of light waves that have wavelengths between 0.001 meters and 100,000,000 meters.  In other words, microwaves are a subset of radio waves. 

So you can say that microwave ovens use radio waves - they just use the radio waves with the smallest wavelengths.  However, radio waves are just another form of light.  The light waves have longer wavelengths than the light waves we can see with our eyes, so your eyes can't detect the light.  Nevertheless, they are just a form of light.

Click here fore an excellent video that explains why light slows down when it travels through a substance like glass:

Yes, it does.  You need 12-ounce cans, because they have the right density.

You need to use standard, 12-ounce cans.  Smaller cans will be less dense than water, regardless of what is inside.

Water is more attracted to itself than many surfaces, which causes the water molecules to move more closely to one another than to those surfaces.  You might think this would cause water to form big globs, because the water molecules would just keep getting closer and closer together.  Remember, however, that gravity is working on everything as well.  If the water molecules got as close as they wanted to get, they would end up forming a big sphere.  However, gravity keeps that from happening, because it pulls down on the water molecules, "squishing" the sphere that would form.  The result is a water droplet.  This happens all over the surface, so there are lots of little water droplets instead of just one big glob of water.

When salt dissolves in water, the sodium and chloride ions move about in the solution.  As a result, they "loose track" of the ions that were right next to them.  When the water evaporates, they recombine with the nearest ions, which probably aren't the ones they were originally next to.  If you want to add this to the story, you could have the ions looking for each other as the water evaporates, wondering if they can find each other before it's "too late."

Any size bottle will produce a fountain, but any bottle smaller than 2 liters will be much more likely to tip over, spraying soda everywhere!

Plastic is made from long molecules that chemists call "polymers."  In order to reduce the cost of making the bottle, it is common these days to use polymers that are not stable at high temperatures in bottles that aren't supposed to reach high temperatures.  Since soda bottles are never supposed to reach the temperature of boiling water, many soda manufacturers use a cheaper polymer that breaks down at those temperatures.  When the polymers break down, the structural integrity of the bottle is reduced, and this causes the bottle to collapse a bit.  The only result is that the balloon in the experiment won't deflate as much, but it stil should have deflated noticeably.

In general, the size of the bits of rock that make up the soil determines the size of the pores in the soil.  The larger the bits of rock, the larger the pores, and the smaller the bits of rock, the smaller the pores.  Sand, for example, is made up of fairly large particles.  As a result, it has very large pores and doesn't hold water very well.  Clay, on the other hand, is made of very tiny particles, so it has very small pores and holds onto water really well.  The ideal growing soil has a mixture of different sized particles so that the pores are small, but not too small.

If sedimentary rock is subject to enough heat to become magma, it will first become metamorphic rock.  So in the end, sedimentary rock cannot become magma directly.  It must first pass through a stage where it is metamorphic rock.
 

Atoms are the basic building blocks of molecules.  If you have two or more atoms linked together in some way, you have a molecule.  Atoms are made of smaller particles called protons, neutrons, and electrons.  So...molecules are bigger than atoms, which are bigger than protons, neutrons and electrons.

An ion is an atom that has an imbalance of protons or electrons and therefore has an electrical charge.  Protons are positive, and electrons are negative.  If an atom ends up with more electrons than protons, it is a negatively-charged ion.  If it ends up with more protons than electrons, it is a positively-charged ion.  Whereas ions have electrical charge, molecules do not.

So sugar is made of a bunch of atoms linked together in a molecule.  There is no charge on a molecule of sugar.  When it dissolves, the water simply pulls the molecules of sugar away from each other, spreading them out in the solution.  

Salt, on the other hand, is made of two IONS.  When it dissolves, it splits up into its positively-charged ion (sodium) and its negatively-charged ion (chloride).  Because of its ions, salt can conduct electricity when dissolved in water.  Sugar cannot, because it has no charge.

Roots, like all parts of a plant, are made of cells.  Most of the absorption in roots come from the tiny "hairs" that grow off them.  Those root hairs are very thin - only one cell or a few cells thick.  Those cells are covered in a cell wall that has large holes in it.  Under the cell wall is a plasma membrane that has channels in it.  For something to get into the plant, it has to go through one of those channels.  There are some channels that have specific shapes to allow in only specific molecules.  However, many of the channels are less discriminating.  They are typically the smaller channels, and they allow many different small molecules to get inside the plant.  If a plant absorbs poison through its roots, for example, it usually comes through one of these smaller, less discriminating channels. 

Unfortunately, I don't know of anything you can use to replace the iodine in that experiment.  Since that lesson is a challenge lesson, I think you should just skip it if you think your daughter will be allergic to the iodine.

That's a great question!  When you look at the sun when it is higher in the sky, you see it is white.  That's where the "ROY" colors are.  They are adding to the other colors to make white light.  However, the light isn't perfectly white, since  some of the "BIV" colors have been removed because they are bouncing off the dust particles in the sky.  The ROY colors don't bounce off the dust particles, so they travel straight to your eyes, along with the BIV parts.  Because of the bouncing, though, there is slightly more ROY in the light coming straight from the sun, and all the light coming from the rest of the sky is BIV.

The earth spins so that it makes a complete rotation every 24 hours.  The speed at which a person on the surface of the earth moves in order to make that rotation depends on where you are on the earth.  If you are on the equator (the imaginary line that runs all the way around the center of the earth), you move at just over 1,000 miles per hour.  In the U.S., you move at about 850 miles per hour. 

Of course, you don't notice this, because the entire surface of the earth is spinning with you.  Think about being in an airplane.  It doesn't seem like you are moving at several hundred miles per hour when you are in an airplane, because the entire airplane and everyone in it is moving right along with you.

Think about tying a toy plane to a string and then twirling it around in the air above your head.  The plane is revolving around you, because the string you are holding is keeping the plane from flying away.  You are much heavier than the plane, so you can stay in one place while the the plane moves.

It's similar for the earth and sun.  The sun holds the earth in orbit with its gravity, much like the string holds the plane in orbit around you.  The sun is much, much heavier than the earth, so it stays in one place while the earth revolves around it.

The distance between the moon and earth changes a bit.  The closest the moon gets to the earth is 226,000 miles (363,000 kilometers).  The farthest it is from the earth is 252,000 miles (406,000 km).  The average distance between the two is about 239,000 miles (384,000 km).

The light we see coming from the moon is reflected light from the sun.  The light comes from the sun, hits the moon, reflects off the moon, and hits our eyes.  The surface of the moon reflects all colors of light.  Remember that white light contains all colors of light, so since the moon reflects all colors, the light coming from it is white.

The sun's temperature is definitely not responsible for the shift from summer to winter.  Remember, when the Northern Hemisphere of the earth is experiencing summer, the Southern Hemisphere is experiencing winter, and the temperature of the sun is the same for each of them!  The changing of the seasons is caused by the tilting of the earth.  Because the earth is tilted, one hemisphere is pointed directly towards the sun, and the other is pointed away from the sun.  The one pointed directly towards the sun is heated more efficiently, so it experiences summer.  The other one is heated less efficiently, so it experiences winter.

The temperature of the sun doesn't affect weather on a day-to-day basis, because the changes in temperature due to weather patterns are much stronger than the changes in temperature due to the temperature fluctuations in the sun.  However, a given seaon (winter or summer) might be a bit warmer when there are a lot of sunspots and a bit cooler when there are few sunspots.  This is a small effect, however, and it isn't noticeable in any meaningful way.

Most plants must have green in them, because green is the color of chlorophyll, which is the main pigment used for photosynthesis.  Thus, while a plant can have other colors (especially a flowering plant), it must have green on it.  That's why the diagram says, "Have a lot of green in them."  It's not that they are exclusively green, but the green parts give them the ability to make food for themselves, so the gree parts are necessary. 

When the diagram says that animals "Can be many different colors," it just means that animals don't need green in them.

The dye in the experiment for Lesson 63 operates under diffusion, not osmosis.  The dye is moving from the water (where there is a lot of dye) into the egg (where there is little dye).  This happens because the dye can travel through the membrane, and it does so in order to spread out as evenly as possible.  That's diffusion. 

Water is being pulled in the egg because of osmosis.  There are a lot of solutes inside the egg, but the membrane holds them in, so they can't travel into the water.  As a result, they pull the water inside the egg.  Thus, the solvent (water) gets pulled into the egg because of osmosis.  However, the dye (a solute) moves into the egg because of diffusion. 

Yes.  However, you need to make sure it goes in a consistent direction.  To do that, cut the ends out of a long, narrow bottle (like a water bottle) and blow the balloon up inside the cut-up bottle. That way, the bottle will force the balloon to take on the shape of a tube.

I am sorry that you are having trouble with that experiment.  The best thing to do is use a longer piece of straw.  It sounds like you aren't losing enough volume when you squeeze the bottle.  To get more volume variation, cut a 15-cm section of straw rather than an 10-cm section.  You could also try a variation on the experiment, like this one:

sciencebob.com/make-a-cartesian-diver/

Yes, fat does protect animals from the heat.  It can prevent heat from coming into an animal's body, which is good if it's too hot.  However, SOME animals want heat to come into their bodies.  Reptiles, for example, love to live in hot places and soak up the warmth, because they can't keep themselves warm.  So those animals that live in hot places only use fat to store excess energy.  However, there are animals (especially mammals) that live in hot places that do use their fat to protect them from the heat.

You can use Science in the Ancient World for all students ages 6-12.  It has three different levels of review at the end of each lesson, so you can determine how much each child should retain by choosing the level of review appropriate for each student.  There are 90 lessons in the course.  If you do science every other day, it will last the full year with 10 extra days so you can be a bit flexible with the schedule.

This is not the final table of contents, but it is close:

http://www.drwile.com/as_toc.pdf

There are a few resources that would work really well as supplemental reading.    An excellent web series can be found here:

http://creationsafaris.com/wgcs_1.htm

It starts at AD 1000, so it relates to the later parts of the book, but it is very good.

There is a list of famous scientists here:

http://www.famousscientists.org/list/

Clicking on the name will lead you to a biography.

There are also two books you might consider.  The first is

Scientists of Faith by Dan Graves

Once again, it deals with scientists from the later parts of the course.  For the more ancient natural philosophers, you could use

Scientists of the Ancient World by Margaret J. Anderson and Karen F. Stephenson

Currently, there is no workbook for Science in the Ancient World.  There is, however, a lapbook for the course:

http://www.ajourneythroughlearning.net/jaywiinanwol.html

While we don't plan to produce one, it is quite possible an independent person will.  If so, we will work to make it available for free or for a very low cost.  Two such workbooks have been made for Science in the Beginning already.

https://www.bereanbuilders.com/cgi-bin/commerce.cgi?preadd=action&key=SIBSET

(Click on "Downloads" and "Printable Notebook")

http://allthelittlemonkeys.blogspot.com/search/label/science%20in%20the%20beginning

A few typos were found in the first printing of the course.  The corrections are listed here.

When I say middle of the tree, I am talking about the middle of the tree's trunk.  In other words, I am not talking about the middle of its height.  I am talking about the middle of its width.  Perhaps the better word is "center" of the tree.

Actually, depending on where you live and what time of day you did the experiment, it's possible that the shadow is longer. When the sun is low in the sky, the shadows increase in length, so if it's low enough, the shadows can be longer than the objects. However, the math still works. Just do the math as shown in the Helps&Hints book.  Your factors will be less than one, but they should still give you the correct height for the tree or whatever you ended up measuring.

The sounds that you make when you talk are produced by your vocal cords vibrating and making waves.  That's what determines the number of clumps of air that hit your ear every second, and that's what determines the pitch.  The speed at which you speak affects how quickly the waves change.  

When you speak in a low tone, for example, you are using your vocal cords to produce waves that have low frequencies, and therefore not many crests hit your ears per second.  Speaking quickly simply makes each sound wave you are making change quickly. It does not affect the pitch.

Most people think that the ancients thought the earth was flat, but in fact, no one of any repute believed that, even in BC times.  In fact, even uneducated people who lived by the sea knew the earth isn't flat, because they saw a departing ship's hull disappear before its mast, at least on a really clear day.  As a result, they understood that the earth is curved.  Here is a good discussion of this fact and why even Christopher Columbus's detractors didn't think the earth was flat.

The answer to the "Oldest Student" review question says, "As you mature, the body's need for nutrients drops, so you don't pump as much blood."  The phrase "As you mature" refers to children maturing into adults.  The more you mature, the less nutrients you need, because your body isn't growing and developing as much.  Thus, the answer is more over the course of a child's life, not the course of an entire life.

As an adult gets older, other things happen, including the blood vessels becoming more stiff.  This reduces the pulse rate even more.  

Numbers are, indeed, infinite.  No matter how large a number you say, I can add one to it and make a larger number.  Therefore, numbers are infinite.  However, there is no way for a single number to be infinite, because I can always add one to it, making a larger number.  So numbers go on without end (which means they are infinite), which is why there is no single number that can actually be infinite.

Usually, this kind of gelatin comes in a box that has several packets in it.  You need only one packet.

You should ignore any "extras" like sugar, fruit, etc.  Those are to make the gelatin flavored in some way, and you want plain, unflavored gelatin.  Just use the water and the gelatin mix.  Nothing else.

I have not tested the experiment with nonfat, dry milk, but it should work.  The important component is the protein part, and once you mix it with water, the proteins in dry milk should be similar enough to get the job done.  

When scientists want to know what's inside an animal, they typically do a dissection, where they cut open a dead animal and see what's inside.  However, that doesn't work for microscopic creatures.  Instead, scientists use microscopes.  Many details of microscopic creatures can be seen with really good microscopes that use light, but light microscopes aren't strong enough to allow us to see the details of what's inside a bacterium.  For that, scientists use electron microscopes.  They shoot beams of electrons at the bacteria, and the way the electrons bounce off the bacteria allow scientists to make an image of the bacteria.  High-energy electrons can pass through the outer layers of the bacteria and bounce of the structures inside, so by varying the electron energy, scientists can see both the outside and the inside of the bacterium.

If you wanted to cover the book in 27 weeks, you would be skipping the challenge lessons and covering 3 lessons each week.  I am not sure how you would do that in a co-op, since most co-ops concentrate on the experiments, which means doing three experiments each week.  You could choose the two most interesting of the three lessons to do in co-op, and have the students do the other one at home. 

Alternatively, you could just do two lessons per week, skipping the challenge lessons, and have the students finish the book at home when the co-op is over.

Here are some more illustrations from Micrographia:

https://scolarcardiff.wordpress.com/2012/08/30/life-through-a-lens-exploring-the-miniature-world-with-robert-hookes-micrographia/

Newton's First Law does apply, since the coin was at rest and then started to move. However, what would have happened had the other coin been moving slowly when it hit the stack? The bottom coin wouldn't have slid out, right? So the force with which the bottom coin gets hit must produce enough acceleration to make the coin on the bottom of the stack move quickly enough to slide out. So...while both laws apply, the second law is more important, since it determines whether or not the coin slides out from under the stack.

Here is a video of a man making paper from old jeans.  It is similar to what you do in the experiment:

http://viewpure.com/TPdZPvMVMZk

Rusting does release heat, so it's possible that the balloon inflated because the rusting heated up the interior, increasing the volume of the gas inside.  However, I wouldn't expect that, because the heat releases pretty slowly, so I would expect that it wouldn't get significantly warmer.  I suppose that the temperature of the room could change enough to inflate the baloon, but you would certainly have noticed that.  

It's also possible that there was something contaminating the steel on the steel wool, and it reacted to produce a gas.