Apologia Advanced Chemistry Sample
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Apologia Advanced Chemistry Sample
Module #1: Units, Chemical Equations, and Stoichiometry Revisited
Introduction
There are probably no concepts more important in chemistry than the three listed in the title of this module. In your first-year chemistry course, I am sure that you learned quite a lot about each of these concepts. You certainly did not learn everything, however. Whether we are talking about units, chemicals equations, or stoichiometry, there is simply too much information to possibly learn in just one year. As a result, we will take another look at each of these concepts in this first module. This will help you “warm up” to the task of recalling all of the things you learned in your first year chemistry course, and it will help to learn each of these valuable concepts at a much deeper level.
Units Revisited
Almost regardless of the chemistry course, units are always covered first, because a great deal of chemistry is based on properly analyzing units. In your first year course, you were taught how to solve problems such as the one in the following example:
EXAMPLE 1.1
A sample of iron has a mass of 254.1 mg. How many kg is that?
In this problem, we are asked to convert from milligrams to kilograms. We cannot do this directly, because we have no relationship between mg and kg. However, we do know that a milligram is the same thing as 0.001 grams and that a kilogram is the same thing as 1,000 grams. Thus, we can convert mg into g, and then convert g into kilograms. To save space, we can do that all on one line:
The sample of iron has a mass of 2.541 x 10 -4 kg .
Did this example help dust the cobwebs out of your mind when it comes to units? This should all be review for you. I converted the units using the factor-label method. Because this is a conversion, I had to have the same number of significant figures as I had in the beginning, and even though it was not necessary, I reported the answer in scientific notation. If you are having trouble remembering these techniques, then go back to your first-year chemistry book and review them.
There are a couple of additional things I want you to learn about units now. I am not going to show you any new techniques; I am just going to show you new ways of applying the techniques that you should already know. Do you remember the concept of molarity? Molarity is a concentration unit that you learned in first year chemistry. It is expressed in moles per liter. There are other ways of expressing concentration, however. For example, you can express concentration in grams per milliliter instead. Well, if you have concentration in one unit, you should be able to convert it to another unit, right? Study the next example.
EXAMPLE 1.2
The concentration of HCl in a solution of muriatic acid is about 0.35 g per mL. What is the molarity of the HCl in muriatic acid?
Now remember, molarity is a concentration unit, just like grams per milliliter, so all we need to do is make a conversion. Hopefully, you remember how to convert grams into moles. You find the mass of HCl from the periodic chart and realize that the mass tells you the number of grams it takes to make a mole of HCl. The mass of HCl is 36.5 amu, so this tells us that it takes 36.5 grams of HCl to make one mole. We also know that a mL is the same as 0.001 L. Now that we know both of the relationships between what we have and what we know, we can set up the conversion:
Although there is nothing new here, you probably haven't seen a conversion done in this way. Despite the fact that the unit is a derived unit (g/mL), you can still do conversions on it. I could have just converted grams to moles and gotten the unit moles/mL. I could have just converted mL to L and gotten g/L. In this case I did both. When working with derived units, remember that you can convert any unit that makes up the derived unit. Thus, 0.35 g/mL is the same thing as 9.6 M .
Okay, we are almost done reviewing units. There is just one more thing that you need to remember. Sometimes, units have exponents in them. You were probably taught how to deal with this fact in your first year chemistry course, but we need to review it so that you really know how to deal with it.
EXAMPLE 1.3
One commonly-used unit for volume is the cubic meter. After all, length is measured in meters, and volume is length times width times height. The more familiar unit, however, is cubic centimeters (cc) which is often used in medicine. If a doctor administers 512 cc of medicine to a patient, how many cubic meters is that?
Once again, this is a simple conversion. If, however, you do not think as you go through it, you can mess yourself up. We need to convert cubic centimeters to cubic meters. Now remember, a cubic centimeter is just a cm 3 and a cubic meter is just a m 3 . Now we have no relationship between these units, but we do know that 1cm = 0.01 m. That's all we need to know, as long as we think about it. Right now, I have the following relationship:
1 cm = 0.01 m
This is an equation. I am allowed to do something to one side of the equation as long as I do the exact same thing to the other side of the equation. Okay, then, let's cube both sides of the equation:
Now look what we have. We have a relationship between cm 3 and m 3 , exactly what we need to convert between!
So 512 cc's is the same as 5.12 x 10 -4 m 3 .
Now when most students do a conversion like the example without thinking, they simply use the relationship between cm and m to do the conversion. That, of course does not work, because the cm 3 unit does not cancel out, and you certainly don't get the m 3 unit in the end:
Do you see what happened? The cm unit canceled one of the cm out of cm 3 , but that still left cm 2 . Also, since m is the unit that survives from the conversion relationship, you get the weird unit of m × cm 2 ! When you are working with units that have exponents in them, you need to be very careful about how you convert them. Make sure you are using a conversion relationship that will definitely give you the unit you want in the end.
ON YOUR OWN
1.1 The speed limit on many highways in the United States is 65 miles per hour. What is the speed limit in meters per second? (There are 1609 meters in a mile.)
1.2 The instantaneous rate of disappearance of NaOH in a chemical reaction is 1.02 . What is the rate in ?
1.3 The size of a house is 1600 square feet. What is the square yardage of the house?
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