The Mole Concept
Use Avogadro number, molar mass, and mole conversions to connect particles, mass, and amounts of substance.
A lesson of Chemistry, in Chemical Reactions and Stoichiometry, about 35 minutes.
By the end of this lesson, you will be able to say why chemistry needs a counting unit at all, convert between mass, moles and particles in any direction, compute a molar mass, and use molar volume for gases.
Counting Things You Cannot Count
Reactions happen between individual particles in whole-number ratios. Two hydrogen molecules react with one oxygen molecule, never with $1.7$ of one.
$$2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$$
But nobody can count out two hydrogen molecules. A laboratory measures mass, and the reaction cares about number, and those two are not proportional across different substances because atoms have different masses.
The mole is the bridge. It is a counting unit, exactly like "dozen", chosen so that the number in one mole is convenient for chemistry.
$$1 \text{ mol} = 6.022 \times 10^{23} \text{ particles}$$
That is Avogadro's number, and its size is not arbitrary. It is defined so that one mole of an element has a mass in grams equal to its atomic mass in amu.
$$\text{carbon: } 12 \text{ amu per atom} \quad \Rightarrow \quad 12 \text{ g per mole}$$
That correspondence is the whole design. It means the periodic table doubles as a table of grams-per-mole, with no conversion required.
A mole is enormous. A mole of sand grains would bury the entire United States a kilometer deep. It has to be, because atoms are that small: one teaspoon of water holds about $6 \times 10^{23}$ molecules.
Molar Mass: Add Up the Table
Molar mass is the mass of one mole, in g/mol, and you get it by adding the atomic masses in the formula.
$$\mathrm{H_2O}: \quad 2(1.01) + 16.00 = 18.02 \text{ g/mol}$$
$$\mathrm{CO_2}: \quad 12.01 + 2(16.00) = 44.01 \text{ g/mol}$$
Multiply each atomic mass by its subscript, then add. The commonest error is forgetting a subscript, and it is worth reading the formula out loud: "two hydrogens and one oxygen".
Brackets multiply everything inside:
$$\mathrm{Ca(NO_3)_2}: \quad 40.08 + 2[14.01 + 3(16.00)] = 164.10 \text{ g/mol}$$
The subscript $2$ applies to the nitrogen AND all three oxygens, giving two nitrogens and six oxygens.
Example 1: Computing a Molar Mass
Here is every step, worked all the way through. $$\mathrm{H_2SO_4}$$
- How many hydrogen atoms are there? 2
- Hydrogen is 1.01 g/mol. What do the hydrogens contribute? 2.02 g/mol
- Sulfur is 32.07. How many sulfur atoms are there? 1
- Oxygen is 16.00 and there are four. What do they contribute? 64.00 g/mol