How to Convert Grams to Moles (and Moles to Grams)

Almost every quantitative problem in chemistry has the same hidden first step: turn the mass you were given into moles. Balanced equations speak in moles. Balances speak in grams. Until you can move between the two without thinking, stoichiometry will feel harder than it really is.

The good news is that there’s only one idea involved.

The one conversion factor you need

The bridge between grams and moles is molar mass — the mass of one mole of a substance, in grams per mole (g/mol). You find it by adding up the atomic weights of every atom in the formula. (If that part is new, start with what molar mass is and how to calculate it.)

Once you have it, the two conversions are mirror images:

• grams → moles: divide by molar mass
• moles → grams: multiply by molar mass

That’s genuinely it. The units tell you which way to go: grams ÷ (grams per mole) leaves moles, and moles × (grams per mole) leaves grams.

Worked example 1: grams of an element to moles

How many moles are in 50.0 g of iron?

Iron’s atomic weight is 55.845, so its molar mass is 55.845 g/mol.

50.0 g ÷ 55.845 g/mol = 0.895 mol

Notice the answer is less than one mole. That makes sense: a full mole of iron would weigh almost 56 g, and we only have 50.

Worked example 2: grams of a compound to moles

How many moles of water are in 100 g of water?

First the molar mass of H₂O: 2 × 1.008 + 15.999 = 18.015 g/mol.

100 g ÷ 18.015 g/mol = 5.55 mol

A single glass of water (about 250 g) is roughly 14 moles — around 8 × 10²⁴ molecules. Numbers like that are exactly why chemists count in moles instead of molecules.

Worked example 3: moles to grams

A reaction needs 0.250 mol of sodium chloride. How much do you weigh out?

NaCl: 22.990 + 35.45 = 58.44 g/mol.

0.250 mol × 58.44 g/mol = 14.6 g

Worked example 4: a hydrate

How many moles are in 10.0 g of copper(II) sulfate pentahydrate, CuSO₄·5H₂O?

The five waters of crystallization are part of the solid you’re weighing, so they count toward the molar mass:

• CuSO₄: 63.546 + 32.06 + 4 × 15.999 = 159.60 g/mol
• 5 H₂O: 5 × 18.015 = 90.08 g/mol
• Total: 249.68 g/mol

10.0 g ÷ 249.68 g/mol = 0.0401 mol

If you’d forgotten the water and used 159.60, you’d get 0.0627 mol — an error of more than 50%. Hydrates are the single most common trap in these problems.

Going one step further: moles to particles

Sometimes a question asks for atoms or molecules rather than moles. That’s one more multiplication, by the Avogadro constant, 6.022 × 10²³ per mole (more on where that number comes from).

How many molecules are in 5.55 mol of water?

5.55 × 6.022 × 10²³ = 3.34 × 10²⁵ molecules

And because each water molecule contains three atoms, the same sample holds three times as many atoms: about 1.00 × 10²⁶.

So the full chain looks like this:

grams ⇄ moles ⇄ particles (÷ or × molar mass) (× or ÷ 6.022 × 10²³)

You can never jump straight from grams to particles. You always go through moles.

Where this shows up

Grams-to-moles is the opening move in nearly every calculation that follows it in a chemistry course:

• Stoichiometry: convert the given mass to moles, use the equation’s ratio, convert back to grams.
• Limiting reagent problems: convert every reactant to moles before comparing them.
• Molarity: moles of solute divided by litres of solution.
• Empirical formulas: convert each element’s mass to moles to find the ratio.
• Gas law problems: the n in PV = nRT is moles.

Common mistakes

• Dividing the wrong way. If your answer for “moles in 5 g of something heavy” comes out larger than 5, check your units — you’ve probably multiplied.
• Using atomic mass for a diatomic gas. Oxygen gas is O₂, so its molar mass is 32.00 g/mol, not 16.00. The same goes for H₂, N₂, F₂, Cl₂, Br₂ and I₂.
• Forgetting parentheses. Ca(NO₃)₂ has two nitrogens and six oxygens. Its molar mass is 164.09 g/mol, not 102.
• Ignoring waters of hydration, as in example 4.
• Rounding atomic masses too hard. Using 1 for hydrogen and 16 for oxygen gives water as 18 g/mol, which is usually fine, but for large molecules or multi-step problems those small errors add up. Keep at least two decimal places until the end.

Quick answers

What is the formula for grams to moles? n = m ÷ M, where n is moles, m is mass in grams, and M is molar mass in g/mol.

Is one mole always the same mass? No. One mole is always the same number of particles, but different substances have different masses per mole. A mole of hydrogen gas weighs about 2 g; a mole of gold weighs about 197 g.

Can you convert grams to moles without the formula? Not for a compound — you need the formula to calculate the molar mass. For a pure element you just need its atomic weight from the periodic table.

Check your work instantly

Once you’re comfortable doing these by hand, the grams to moles converter does the whole chain — molar mass, moles and particle count — for any formula, and shows each step so you can compare it with your own working.