AP Chemistry Mole Conversions

Grams, moles, and particles, with three full worked examples.

Almost every quantitative AP Chemistry problem starts by turning a mass you can measure into a number of moles. The relationship is short, but the habits that go with it (computing molar mass correctly, keeping units visible, and knowing which conversion factor to use) are what the worked examples below practice.

The Mole Conversion Map: Grams, Moles, and Particles

The mole is the bridge between mass and particle count (see the Unit 1 review for why it works). Every conversion follows the same three steps:

Find the molar mass (g/mol) by adding the atomic masses from the periodic table for every atom in the formula, multiplying each by its subscript.
Convert between grams and moles with the molar mass: n = m/M, or m = n × M.
Convert between moles and particles with Avogadro's number: particles = n × 6.022 × 10²³.

Grams and particles never convert directly. The path is always grams ↔ moles ↔ particles. The atomic masses on the periodic table are weighted averages across isotopes, the same calculation practiced in mass spectrometry problems.

Worked Example 1: Converting Grams of Glucose to Moles

How many moles are in 25.0 g of glucose, C₆H₁₂O₆?

Molar mass = 6(12.01) + 12(1.008) + 6(16.00) = 72.06 + 12.10 + 96.00 = 180.16 g/mol
n = m/M = 25.0 g ÷ 180.16 g/mol = 0.139 mol

Worked Example 2: Converting Moles of Aluminum Sulfate to Grams

What mass of aluminum sulfate, Al₂(SO₄)₃, is 0.250 mol?

The subscript 3 outside the parentheses multiplies everything inside, giving 2 Al, 3 S, and 12 O:
Molar mass = 2(26.98) + 3(32.07) + 12(16.00) = 53.96 + 96.21 + 192.00 = 342.17 g/mol
m = n × M = 0.250 mol × 342.17 g/mol = 85.5 g

Worked Example 3: Counting Hydrogen Atoms in a Mass of Water

How many hydrogen atoms are in 9.00 g of water, H₂O?

Molar mass of H₂O = 2(1.008) + 16.00 = 18.02 g/mol
Moles of water: 9.00 g ÷ 18.02 g/mol = 0.4996 mol
Molecules: 0.4996 mol × 6.022 × 10²³ molecules/mol = 3.008 × 10²³ molecules
Each molecule has 2 hydrogen atoms: 3.008 × 10²³ × 2 = 6.02 × 10²³ hydrogen atoms

Final answers keep the number of significant figures of the least precise given value, here 3.

Common Mole Conversion Mistakes

Skipping the subscript or the parentheses when finding molar mass. In Al₂(SO₄)₃ there are 12 oxygens, not 4.
Dividing when you should multiply. Write the units: grams ÷ (g/mol) gives mol, while mol × (g/mol) gives grams. If the units don't cancel to what you want, flip the factor.
Stopping at molecules when the question asks for atoms. Multiply by the number of atoms of that element in each molecule, as in Example 3.
Using atomic number instead of atomic mass. Molar mass comes from the atomic mass (the decimal number), not the whole-number atomic number.

This same mole-first habit starts almost every calculation in AP Chemistry, from stoichiometry onward -- for every other free tool and guide on this site, start from the AP Chem Score Calculator.

Frequently Asked Questions

How do you convert grams to moles?

Divide the mass in grams by the substance's molar mass in g/mol: n = m/M. The molar mass is the sum of the atomic masses from the periodic table for every atom in the formula.

How do you convert moles to grams?

Multiply the number of moles by the molar mass: m = n × M. It is the same relationship as grams to moles, rearranged.

How do you convert moles to number of particles?

Multiply by Avogadro's number, 6.022 × 10^23 particles per mole. To go from particles back to moles, divide by it.

How do you find the molar mass of a compound?

Add up the atomic mass of every atom in one formula unit, multiplying each element's atomic mass by its subscript. For a formula with parentheses, such as Al2(SO4)3, multiply the subscript outside the parentheses through everything inside first.

Why can't you convert grams directly to particles?

Because the two are connected only through the mole. The molar mass links grams to moles, and Avogadro's number links moles to particles, so the conversion always passes through moles.

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