Lesson 2: Moles
In dealing with atomic weights, chemists were faced with a problem of sorts. They needed to be able to measure elements but could not measure individual atoms, because the atoms were much too small. Consequently, chemists invented a quantity called a mole. (The international spelling and accepted abbreviation is mol; don't abbreviate moles as "m" -- "m" means meter not mole!) A mole is the amount of an element, measured in grams, that corresponds to its atomic weight. It is a very simple relationship and it's a very useful concept (for chemists).
In this section we deal with the mole concept, calculations relating moles and grams, and application of the concept and calculations to compounds and molecular elements.
Mole Concept | Mole-Gram Calculations
Moles of Compounds & Molecular Elements | Additional Calculations
Mole Concept
One of the values of the mole is that every mole of any element has the same number of atoms in it. We have not yet discussed what that number is in this course (we will deal with that later when we consider the size of atoms), but we do know that it is the same amount for each element.
If you were to weigh out an equal number of oxygen and hydrogen atoms, the amount of oxygen that you have would weigh 16 times the weight of the amount of hydrogen you have because each oxygen atom weighs 16 times more than each hydrogen atom. Conversely, if you weigh out 16 times more oxygen (by weight) than hydrogen, you will have equal amounts (by atoms) of each. As long as the weight of the oxygen measured was 16 times heavier than that of the hydrogen used, we would have the same number of atoms. Pause for a moment to make sure that makes sense to you. If not, talk with an instructor about this relationship. (You can use e-mail if you are not in the lab.)
We can focus on one particular combination of numbers and units to define the quantity that we call a mole. We use the number given by the relative atomic weight for each element and we use the mass unit gram. Thus, if we weigh out 1 gram of hydrogen, we have 1 mole of hydrogen atoms. If we weigh out 16 g of oxygen, we have 1 mole of oxygen atoms.
This gives us a new perspective on the units that can be used with atomic weights. Atomic weights can be used as unitless quantities that give the relative weights of atoms (as we saw in the previous section). Atomic mass units were defined so that the atomic weights would represent the weights of individual atoms. Moles were defined so that atomic weights in grams would represent that particular quantity of an element. This is why, when you calculate formula weights, the units as most often given as g/mole or g/mol.
Mole-Gram Calculations
One of the things you will do throughout this course is to work back and forth between mass in grams and the amount of material in moles. In order to convert back and forth between mass and moles, you simply need to use the same kind of conversion calculations that you have done before. I'll work through two examples (these are also shown in your workbook as Example 15), then you can practice the calculations yourself in Exercise 16 in your workbook.
The task is to express 45 grams of carbon in moles. There are different ways of accomplishing that task. We'll use the conversion factor approach. |
45 g C | = ? moles C | ||
We start with 45 grams of carbon. We want to find out how many moles we have, so we need a relationship between the number of grams of carbon and the number of moles. |
45 g C |
x? moles C ? g C |
= ? moles C | |
That relationship is simply that 12.0 grams of carbon is one mole. So we set up the calculation with 45 grams of carbon times the conversion factor of one mole over 12.0 grams of carbon. |
45 g C |
x 1 mole C 12.0 g C |
= ? moles C | |
Carry out the calculations and we get 3.8 moles. In this case we round off the answer to two significant digits, 3.8, because the initial value of 45 g has just two significant digits. |
45 g C |
x 1 mole C 12.0 g C |
= 3.8 moles C | |
If we had known that there were 45.0 grams of carbon, then we would have given the answer as 3.75 moles. You still have to remember to keep working with significant digits. |
45. 0 g C |
x 1 mole C 12.0 g C |
= 3.75 moles C | |
Along that same line, if we had started with 45.00 grams of carbon, and we wanted our answer to be more precise than 3.75, we wouldn't be able to use 12.0 grams of carbon in the conversion factor. The precision of the atomic weights is in the weight value rather than the mole value. When we say that one mole of carbon weighs 12.0 grams, we mean that exactly one mole of carbon weighs 12.0 grams when measured to three significant digits. So the answer is rounded off to the number of digits shown in the atomic weight or in the starting value, not in the 1 mole. |
45. 00 g C |
x 1 mole C 12.0 g C |
= 3.75 moles C | |
To get four digits of precision in the answer, we would have to look up a more precise atomic weight in order to get the 4th digit there, which is 12.01. So any time that you want to work with numbers that are more precise than 3 digits, you will have to look up an atomic weight that is more precise than just 3 digits. Remember that these atomic weights are measured values. They are not exact, except for that one particular isotope of carbon called carbon-12. |
45. 00 g C |
x 1 mole C 12.01 g C |
= 3.747 moles C |
Next, consider the question "How much would 3.53 moles of iron weigh?" Here we are trying to change from moles to grams, so 3.53 moles of iron is out in front. |
3.53 moles Fe | = ? g Fe | ||
The relationship between moles of iron and grams of iron is 1 mole for every 55.8 grams of iron. So that's what goes in the conversion factor with the grams on top and the moles on the bottom, so that the moles cancel out. |
3.53 moles Fe |
x 55.8 g Fe 1 mole Fe |
= ? g Fe | |
When you multiply that through, you get 197 grams of iron. |
3.53 moles Fe |
x 55.8 g Fe 1 mole Fe |
= 197 g Fe |
These conversion calculations relating moles and grams are the same kind of calculations that you have worked with before. It is just that now you are dealing with another unit--a mole--that you may have never heard of before.
As you know from lesson 1, many units can be abbreviated; so "gram" becomes "g", "liter" becomes "l" or "L", and so on. Many students want to abbreviate "mole" as "m", forgetting that we use "m" to stand for "meter". The abbreviation for "mole" is "mol" - not much of an abbreviation at all!
Practice with Mole-Gram Calculations
Before you continue with the lesson, work through the 4 problems in exercise 16. Check your answers below before continuing. If you have any trouble, check with the instructor.
Answers
OK, here are the answers that you should have for the problems in Exercise 16. "A" is 3.6 grams of carbon. "B" is 2.2 x 102 gram of potassium. My calculations came out to 215, but since 5.5 is only good to 2 digits, I rounded the answer off to 220. Then to show that the zero was not significant I converted the answer to scientific notation. "C" is 1.58 moles of fluorine. "D" is 2.4 moles of nitrogen. So, you should have those values. If you did not come up with those answers, you should take some time now to work with the instructor and find out what kinds of problems are keeping you from getting those answers.
Moles of Compounds & Molecular Elements
The concept of a mole can be applied to compounds as well as elements. A mole of a compound is what you have when you weigh out, in grams, the formula weight of that compound. (Use the molecular weight if the compound is a molecular material.) For example, the formula weight for HF is 20.0. That means that one mole of HF weighs 20.0 grams, and you can use that relationship to convert back and forth between grams and moles.
If you needed to change 15.0 g of HF to moles, you would simply multiply by the conversion factor that changes from g HF to moles HF. The relationship we just figured out is that 1 mole of HF weighs 20.0 g. Carrying out the calculations, we get 0.750 moles of HF. |
15.0 g HF |
x 1 mole HF 20.0 g HF |
= 0.750 mole HF |
To emphasize that this is the weight of one mole of that chemical, some chemists call it the molar formula weight or the mole weight or even the molar mass.
Special care must be taken when dealing with moles of a molecular element. If someone talks about "so many moles of hydrogen," it is necessary to find out whether they mean moles of atomic hydrogen (H, 1.0 g/mole) or moles of molecular hydrogen (H2, 2.0 g/mole). To avoid mistakes, look for a formula or consider the context.
Additional Calculations
Additional Practice with Mole-Gram Calculations
I'd like you to use formula weights as conversion factors to answer the four questions in Exercise 17. The answers follow.
Answers
The answers you should have come up with are 68 grams of HF, 0.53 moles of CH4, 166 grams of O2, and 0.0452 moles of Fe2(CO3)3. If you didn't get all of those correct, please take some time to check with the instructor to find out why. Note that the answers were rounded off to the correct number of significant digits based on each problem.