Molar Mass Calculator

Molar mass $\mathcal{M}$ is the mass of one mole of a substance, in grams per mole. It is the sum of the atomic masses in the chemical formula, each multiplied by its subscript:

$\mathcal{M} = \sum_i \nu_i A_i$

where $A_i$ is the standard atomic mass of element $i$ and $\nu_i$ is how many of that atom the formula unit contains. Numerically it equals the formula mass in atomic mass units, because the mole is defined so that the two coincide.

Molar mass is the bridge between what a balance measures and what a chemical equation counts:

$n = \frac{m}{\mathcal{M}} \qquad\qquad m = n\,\mathcal{M} \qquad\qquad N = n N_A$

with $N_A = 6.02214 \times 10^{23}$ particles per mole.

Molar concentration then follows by dividing by the volume of solution:

$c = \frac{n}{V} = \frac{m}{\mathcal{M}\,V}$

What this assumes. Atomic masses are the standard terrestrial averages over natural isotopes, so a sample with an unusual isotope ratio has a different molar mass. Concentration is defined by the total volume of solution and refers to the temperature at which that volume was measured.

Step by step

1. Parse the formula. Expand every bracket first: $\mathrm{Ca(NO_3)_2}$ is one Ca, two N and six O.
2. Look up each atomic mass and multiply by its count.
3. Add the contributions to get g/mol.
4. Keep the decimals consistent. Molar masses are added, so the result is limited by the decimal places of the least precise atomic mass, not by significant figures.

Then convert

Hydrates and formula units

The water in a hydrate counts: $\mathrm{CuSO_4 \cdot 5H_2O}$ has a molar mass of 249.68 g/mol, not the 159.61 g/mol of the anhydrous salt. Using the wrong one shifts every downstream number by more than 50%.

Significant figures

The measured mass almost always has fewer figures than the molar mass, so the mass sets the precision of the final answer. Carry extra digits through intermediate steps and round only once, at the end.

• Missing a bracket subscript. In $\mathrm{Al_2(SO_4)_3}$ there are three sulfurs and twelve oxygens. Expanding the formula before adding is the reliable fix.
• Using the atomic mass of an atom where the element is diatomic. Elemental oxygen gas is $\mathrm{O_2}$, 32.00 g/mol, not 16.00 g/mol.
• Dividing by the molar mass in the wrong direction. Grams to moles divides; moles to grams multiplies. A quick check: a few grams of a light molecule should give a fraction of a mole, not thousands.
• Ignoring water of hydration when the bottle's formula includes it.
• Dividing by the solvent volume rather than the final solution volume when computing concentration.
• Rounding atomic masses too early. Using 12 instead of 12.011 for carbon costs about 0.1% per carbon atom, which shows up quickly in a large organic molecule.