Molar Mass Calculator

How a molar mass is assembled

Molar mass is the mass of one mole of a substance in grams, and for a compound it is nothing more than a weighted sum. Take each element in the formula, multiply its standard atomic weight by how many times that element appears, and add the terms together: M = Σ (count × atomic weight). There is no chemistry in the arithmetic, only bookkeeping, so the errors that occur are almost always errors of counting rather than errors of multiplication.

The atomic weights themselves are not integers because most elements occur as a mixture of isotopes. Chlorine is quoted as 35.45 rather than 35 because natural chlorine is roughly three parts chlorine-35 to one part chlorine-37. This calculator uses the IUPAC CIAAW abridged atomic weights, given to five significant figures, which is more than enough for any balance found in a teaching or production laboratory.

Worked example: the molar mass of glucose

Glucose, C₆H₁₂O₆, has three elements and three terms:

• Carbon: 6 × 12.011 = 72.066
• Hydrogen: 12 × 1.008 = 12.096
• Oxygen: 6 × 15.999 = 95.994
• Total: 72.066 + 12.096 + 95.994 = 180.156 g/mol

Textbooks often round this to 180.16 g/mol, which is the same figure to five significant figures. Rounding the individual atomic weights before multiplying is what introduces drift, so keep the full values until the final addition.

How to convert grams to moles

To convert grams to moles, divide the mass by the molar mass: n = m / M. Going the other way, moles to grams, multiply instead: m = n × M. To count the particles in the sample, multiply the moles by the Avogadro constant, N = n × N_A, where N_A = 6.02214076 × 10²³ mol⁻¹ exactly; to go from a number of particles back to moles, divide by it. The calculator does all three from whichever quantity you give it: choose Mass → moles, Moles → mass or Particles → moles under Convert, and the panel under it lists the whole sample as a mass, an amount in moles, a number of formula units and a number of atoms, then splits the atoms and the mass by element.

A formula unit is one copy of the formula as written. For a molecular substance such as water it is one molecule, and for a lone element such as iron it is one atom. An ionic solid such as sodium chloride has no molecules, so its particles are counted as formula units of NaCl, each one sodium ion and one chloride ion. A count of atoms is shared out first: 2 × 10²⁴ atoms of NaCl are 10²⁴ formula units, because each unit holds two.

Worked example: 10 g of water to moles and molecules

Water, H₂O, has a molar mass of 2 × 1.008 + 15.999 = 18.015 g/mol. Then:

• Moles: n = 10 g / 18.015 g/mol = 0.55509 mol, which the calculator shows as 555.09 mmol
• Molecules: N = 0.55509 mol × 6.02214076 × 10²³ mol⁻¹ = 3.3428 × 10²³
• Atoms of hydrogen: 2 × N = 6.6857 × 10²³, and of oxygen 1 × N = 3.3428 × 10²³
• Atoms in total: 3 × N = 1.0029 × 10²⁴

The reverse runs the same equations backwards: 1.0 × 10²⁴ molecules of water are 10²⁴ / (6.02214076 × 10²³) = 1.6605 mol, and 1.66054 mol × 18.015 g/mol = 29.915 g. Carry the unrounded moles into the second step, as the calculator does: 1.6605 × 18.015 gives 29.914, and the last figure drifts.

Percent composition by mass

The percent composition of a compound is each element’s share of the molar mass: its count times its atomic weight, divided by the molar mass, times 100, or % = count × A_r / M × 100. The Percent composition table above prints it for every element in the formula, with a bar for each, and the shares add up to 100%, give or take rounding in the last figure.

For water, hydrogen is 2.016 / 18.015 × 100 = 11.19% and oxygen is 15.999 / 18.015 × 100 = 88.81%. Because the share is the same in any amount of the compound, the 10 g sample above holds 1.1191 g of hydrogen and 8.8809 g of oxygen, the masses the whole-sample table lists. To go the other way, from measured percentages back to a formula, use the empirical formula calculator, which divides each percentage by its atomic weight and finds the whole-number ratio. For an amount in solution rather than a weighed solid, the molarity calculator takes the molar mass and a volume instead.

How much precision to carry

The molar mass is rarely the limiting source of uncertainty. A balance reading 2.922 g to the nearest milligram already carries about one part in three thousand, which is looser than the atomic weights being used. Carrying molar mass to two decimal places is therefore sufficient for solution preparation, and quoting more digits does not make a weighing more accurate.

Elements with wide isotopic variability are the exception. Sulfur, boron and lead differ measurably between geological sources, and CIAAW quotes intervals rather than single values for them. For high-accuracy isotope work, use the value appropriate to the material rather than the conventional average.

Common mistakes

• Using the anhydrous mass for a hydrate. CuSO₄ is 159.60 g/mol, but CuSO₄·5H₂O is 249.68 g/mol. The waters of crystallisation are part of the solid being weighed, so omitting them makes you weigh about 36% too little.
• Misreading capitalisation. Co is cobalt at 58.933 g/mol while CO is carbon monoxide at 28.010 g/mol. A single case error changes the answer by more than a factor of two.
• Not distributing a bracketed group. Ca(OH)₂ contains two oxygens and two hydrogens, giving 74.092 g/mol. Counting one of each gives 57.085 and is a common slip in hydroxides and nitrates.
• Ignoring reagent purity. Molar mass assumes the pure compound. For a reagent supplied at 97%, divide the calculated mass by 0.97 to get the amount actually to weigh out.

Converting units first? Use the mass and amount of substance conversion tables.