Unit 1 · Topic 1.1

1.1 Moles and Molar Mass

A mole is a counting unit, like a dozen, but for 6.022 × 10²³ particles. Molar mass lets you turn a mass you can weigh into a number of moles, and Avogadro's number turns moles into particles. Almost every calculation in AP Chemistry passes through moles.

Key terms

mole
Avogadro's number
molar mass
atomic mass unit (amu)
dimensional analysis

Why chemists count in moles

Atoms and molecules are far too small to count one at a time. In the lab you can only measure mass or volume. But reactions happen particle by particle, so you need a bridge between grams and particles. The mole is that bridge.

One mole of anything is 6.022 × 10²³ of those things. This number is Avogadro's number, written as 6.022 × 10²³ mol⁻¹. A mole of carbon atoms, a mole of water molecules and a mole of NaCl formula units each contain 6.022 × 10²³ particles. A formula unit is the smallest repeating ratio of ions in an ionic compound, such as one Na⁺ and one Cl⁻ in NaCl.

Molar mass and the amu link

The mass of a single atom or molecule is measured in atomic mass units (amu). One water molecule has an average mass of about 18.02 amu. Here is the useful part: one mole of water has a mass of 18.02 grams. The number is the same; only the unit changes. That's true for every substance, which is why the periodic table's atomic masses work in both amu per atom and grams per mole.

Molar mass (M) is the mass of one mole of a substance, in g/mol. You find it by adding the atomic masses of every atom in the formula. For CaCl₂: 40.08 + 2(35.45) = 110.98 g/mol.

The three conversions

Every problem in this topic is some chain of these three steps. The equation sheet gives the first one as n = m/M, where n is moles, m is mass in grams and M is molar mass.

To go from	To	Do this
grams	moles	divide by molar mass (g/mol)
moles	particles	multiply by 6.022 × 10²³
moles of a compound	moles of one kind of atom or ion	multiply by its subscript in the formula

Dimensional analysis keeps you honest

Dimensional analysis means writing every number with its unit and multiplying by conversion factors so unwanted units cancel. If you set up 9.00 g H₂O × (1 mol / 18.02 g), the grams cancel and you're left with moles. If the units don't cancel to what the question asks for, the setup is wrong, even before you touch a calculator.

Watch the particle you are counting. One mole of H₂O contains 6.022 × 10²³ molecules but 2 × 6.022 × 10²³ hydrogen atoms. One mole of CaCl₂ contains 6.022 × 10²³ formula units but 3 × 6.022 × 10²³ ions.

Significant figures

Report a final answer with about as many significant figures as the least precise measurement you were given. Keep extra digits while you work and round only at the end.

Worked examples

Try each one yourself first, then open the solution.

Example 1Calculator allowed
Grams to molecules and atoms
How many water molecules are in 9.00 g of H₂O? How many hydrogen atoms is that?
Show the solutionHide the solution
1. Step 1: Find the molar mass: 2(1.008) + 16.00 = 18.02 g/mol.
2. Step 2: Convert grams to moles: 9.00 g × (1 mol / 18.02 g) = 0.4996 mol H₂O.
3. Step 3: Convert moles to molecules: 0.4996 mol × 6.022 × 10²³ molecules/mol = 3.01 × 10²³ molecules.
4. Step 4: Each molecule has 2 H atoms, so multiply by 2: 6.02 × 10²³ H atoms.
Answer: 3.01 × 10²³ H₂O molecules, containing 6.02 × 10²³ H atoms
Example 2Calculator allowed
Counting ions in an ionic compound (classic trap)
How many chloride ions are present in 5.55 g of CaCl₂?
Show the solutionHide the solution
1. Step 1: Molar mass of CaCl₂ = 40.08 + 2(35.45) = 110.98 g/mol.
2. Step 2: Moles of CaCl₂ = 5.55 g ÷ 110.98 g/mol = 0.05001 mol.
3. Step 3: Each formula unit contains 2 Cl⁻ ions, so moles of Cl⁻ = 2 × 0.05001 = 0.1000 mol.
4. Step 4: Number of Cl⁻ ions = 0.1000 mol × 6.022 × 10²³ = 6.02 × 10²² ions.
5. Step 5: The trap: stopping at 0.05001 mol × 6.022 × 10²³ = 3.01 × 10²² counts formula units, not chloride ions.
Answer: 6.02 × 10²² Cl⁻ ions
Example 3Calculator allowed
Particles to grams
What is the mass of a sample containing 2.50 × 10²² copper atoms?
Show the solutionHide the solution
1. Step 1: Particles to moles: 2.50 × 10²² ÷ 6.022 × 10²³ per mol = 0.04151 mol Cu.
2. Step 2: Moles to grams: 0.04151 mol × 63.55 g/mol = 2.64 g.
Answer: 2.64 g Cu

Common mistakes

Using the molar mass of an element instead of the whole compound. For CaCl₂, add Ca once and Cl twice; don't use 35.45 alone.
Forgetting subscripts when counting atoms or ions. Moles of formula units times the subscript gives moles of that atom or ion.
Multiplying by Avogadro's number when you should divide. If you start with particles and want moles, the particle count must get smaller.
Rounding in the middle of a problem. Rounding 0.4996 mol to 0.5 mol partway through can shift your final answer; keep the extra digits until the end.

On the exam

Mole conversions rarely appear alone on the exam; they are the first step inside stoichiometry, gas, solution and titration problems. Write the units on every line so a reader can follow your setup.
Expect conceptual multiple-choice questions such as which sample contains the most atoms. Convert each to moles of atoms before comparing; the heaviest sample isn't always the one with the most particles.

Connected topics

Videos

An Introduction to Moles and Molar Mass - AP Chem Unit 1, Topic 1a
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Unit 1.1 - Moles and Molar Mass
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The mole and Avogadro's number | Atomic structure and properties | AP Chemistry | Khan Academy
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How big is a mole? (Not the animal, the other one.) - Daniel Dulek
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The Mole
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