The Mole Concept

Atoms are impossibly small. A single carbon atom has a mass of about $2 \times 10^{-23}$ grams. You cannot weigh one atom on any balance in any lab. But you can weigh $6.022 \times 10^{23}$ of them - and that clump happens to weigh exactly 12.01 grams, a number you can read right off the periodic table.

That number - $6.022 \times 10^{23}$ - is Avogadro’s number (Nₐ), and it defines the mole.

The Mole - Chemistry’s Counting Word

A “dozen” means 12. A “mole” means $6.022 \times 10^{23}$. That is all it is - a counting word for an absurdly large number.

One mole of any element contains exactly $6.022 \times 10^{23}$ atoms. One mole of any compound contains $6.022 \times 10^{23}$ molecules (or formula units for ionic compounds).

Molar Mass - The Bridge Between Grams and Moles

The molar mass (also called molecular weight or formula weight) is the mass of one mole of a substance, expressed in grams per mole (g/mol). For elements, it is the atomic mass from the periodic table. For compounds, it is the sum of all the atomic masses in the formula.

Examples:

• Molar mass of O₂ = 2(16.00) = 32.00 g/mol
• Molar mass of H₂O = 2(1.01) + 16.00 = 18.02 g/mol
• Molar mass of NaCl = 22.99 + 35.45 = 58.44 g/mol
• Molar mass of CaCO₃ = 40.08 + 12.01 + 3(16.00) = 100.09 g/mol

The Mole Map - Your Navigation Tool

Every stoichiometry problem boils down to moving between three quantities: grams, moles, and number of particles. The mole sits at the center of this map.

The key insight: you must always pass through moles. You cannot go directly from grams of one substance to grams of another. The route is always grams → moles → ratio → moles → grams.

Working with Avogadro’s Number

Avogadro’s number connects the macroscopic (grams) to the microscopic (atoms, molecules). Here is how it works in practice:

Example: How many water molecules are in 36.04 g of water?

1. Convert to moles: 36.04 g / 18.02 g/mol = 2.00 mol
2. Convert to molecules: $2.00 \text{ mol} \times 6.022 \times 10^{23} = 1.204 \times 10^{24}$ molecules

Example: How many oxygen atoms are in 36.04 g of water?

Each water molecule (H₂O) contains 1 oxygen atom. So the number of oxygen atoms equals the number of molecules: $1.204 \times 10^{24}$.

But each molecule also has 2 hydrogen atoms: $2 \times 1.204 \times 10^{24} = 2.409 \times 10^{24}$ hydrogen atoms.

Molar Volume at STP

For gases at standard temperature and pressure (STP: 0°C, 1 atm), one mole of any ideal gas occupies 22.4 liters. This gives you a third conversion pathway:

• Liters (at STP) → divide by 22.4 → moles
• Moles → multiply by 22.4 → liters (at STP)

This only applies to gases at STP. At other conditions, use the ideal gas law (PV = nRT) from Chapter 8.