Moles

In dealing with atomic masses, 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 mass. It is a very simple relationship and it's a very useful concept for chemists.

The 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 mass 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 mass) than hydrogen, you will have equal amounts (by atoms) of each. As long as the mass 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.

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 mass 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 masses. Atomic masses can be used as unitless quantities that give the relative masses of atoms (as we saw in the previous section). Atomic mass units were defined so that the atomic masses would represent the masses of individual atoms. Moles were defined so that atomic masses in grams would represent that particular quantity of an element. This is why, when you calculate formula masses, the units as most often given as 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, and there are many more you can do for practice in your lab workbook.

To start, lets say we have 45.0 g of carbon, and we want to know how many moles this is. The atomic mass of carbon is 12.011 amu (from the periodic table), so using the mole concept we know that the molar mass of carbon is 12.011 g/mol. We will use this molar mass in the conversion factor approach to solve for the moles of carbon.

This dimensional analysis setup simplifies to 45.0/12.011, which gives a value of 3.7466 mol C; because our starting value has three significant figures, we simplify this to 3.75 mol.

As a second example, let's say we want to know the mass of iron present in 0.084 moles of iron. This is the reverse of the type of calculation we did above, where we started with grams and went to moles.

This dimensional analysis setup simplifies to 0.084*55.845, which gives a value of 4.69 g. Simplifying to two significant figures (to match our initial value) gives 4.7 g.

Moles of Compounds and 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 mass of that compound. (Use the molecular mass if the compound is a molecular material.) For example, the formula mass for HF is 20.006 amu. That means that one mole of HF weighs 20.006 grams, and you can use that relationship to convert back and forth between grams and moles.

Try finding the mass of 1.45 moles of HF now. Hopefully, you get a value of 29.0 g.

Take some time now to work through practice problems in your lab workbook until you feel confident about your ability to convert between moles and grams (in both directions).