How to Calculate Molar Mass

What molar mass actually means

A mole is a fixed count of particles - 6.02214076 × 10²³ of them - in the same way that a dozen is a fixed count of twelve. Molar mass is simply the mass of one mole of whatever you are counting, quoted in grams per mole. One mole of carbon atoms weighs 12.011 g, so carbon's molar mass is 12.011 g/mol.

The convenient part is that the number is already familiar. An element's molar mass in grams per mole is numerically equal to its relative atomic mass, the figure printed under every symbol on the table. That correspondence is deliberate rather than lucky - the size of the mole was chosen so it would hold - and it means the periodic table doubles as a molar-mass lookup table for all 118 elements.

Where the numbers come from

Open any element on ChemTable and its atomic mass sits directly under the symbol. These are standard atomic weights: averages taken across the isotopes found in ordinary terrestrial samples, weighted by how common each isotope is. That is why they are so rarely whole numbers. Chlorine reads 35.45 rather than 35 because natural chlorine is a mixture of roughly three parts chlorine-35 to one part chlorine-37.

For molar-mass work, four significant figures is almost always plenty, and you should carry the value your data sheet gives rather than rounding early. These are the ones you will reach for constantly:

• Hydrogen 1.008, carbon 12.011, nitrogen 14.007 and oxygen 15.999 cover most of organic and biological chemistry.
• Sodium 22.990, sulfur 32.06, chlorine 35.45 and calcium 40.078 cover most common salts and acids.
• Iron 55.845 and copper 63.546 are the transition metals you will meet earliest.
• Round only at the end, not at each step - rounding early is the usual reason two people get different answers.

The method, step by step

Calculating a molar mass is the same three moves every time: read the formula, look up each element, then add. Work through calcium carbonate, CaCO₃, the main component of limestone, chalk and seashells.

1. Count the atoms of each element in the formula. CaCO₃ has one calcium, one carbon and three oxygens.
2. Look up each atomic mass: calcium 40.078, carbon 12.011, oxygen 15.999.
3. Multiply each mass by its atom count. Calcium contributes 40.078, carbon contributes 12.011, and oxygen contributes 3 × 15.999 = 47.997.
4. Add the contributions: 40.078 + 12.011 + 47.997 = 100.086.
5. Write the answer with its unit: the molar mass of CaCO₃ is 100.09 g/mol.

Worked examples

The same three moves handle anything. Water is the smallest useful case: two hydrogens at 1.008 give 2.016, the single oxygen gives 15.999, and the total is 18.015 g/mol. That number is worth committing to memory, because water appears in more calculations than any other compound.

Glucose looks intimidating and is not. C₆H₁₂O₆ needs 6 × 12.011 = 72.066 for carbon, 12 × 1.008 = 12.096 for hydrogen and 6 × 15.999 = 95.994 for oxygen, which sum to 180.156 g/mol. A long formula means longer arithmetic, never harder arithmetic.

• H₂O: 2(1.008) + 15.999 = 18.015 g/mol
• CO₂: 12.011 + 2(15.999) = 44.009 g/mol
• NaCl: 22.990 + 35.45 = 58.44 g/mol
• H₂SO₄: 2(1.008) + 32.06 + 4(15.999) = 98.07 g/mol
• C₆H₁₂O₆: 72.066 + 12.096 + 95.994 = 180.156 g/mol

Parentheses, hydrates and other traps

Parentheses multiply everything inside them. Calcium hydroxide, Ca(OH)₂, contains two complete hydroxide groups, so it has two oxygens and two hydrogens rather than one of each: 40.078 + 2(15.999 + 1.008) = 40.078 + 34.014 = 74.092 g/mol. Distribute the outside subscript before you start adding and this error simply cannot happen.

Hydrates carry water of crystallisation, written after a centred dot. Copper(II) sulfate pentahydrate, CuSO₄·5H₂O, is the anhydrous salt at 63.546 + 32.06 + 63.996 = 159.602 g/mol plus five waters at 5 × 18.015 = 90.075 g/mol, giving 249.677 g/mol. Forgetting the water is one of the most common ways to lose marks in a gravimetric question.

• A subscript outside a bracket multiplies every atom inside the bracket.
• Diatomic elements are molecules: O₂ is 31.998 g/mol, not 15.999 g/mol.
• The dot in a hydrate means 'plus', not 'times' - add the water in.
• Charge makes no practical difference to mass: treat Na⁺ as 22.990 g/mol.

From molar mass to moles and grams

Molar mass earns its keep as a conversion factor. Moles equal mass divided by molar mass, and mass equals moles multiplied by molar mass. Weigh out 36.03 g of water and you are holding 36.03 ÷ 18.015 = 2.000 mol. Need 0.250 mol of sodium chloride and you weigh 0.250 × 58.44 = 14.61 g.

It also turns a balanced equation into something you can actually put on a balance. When propane burns, C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O, the coefficients say one mole of propane consumes five moles of oxygen - which is 44.097 g of propane reacting with 5 × 31.998 = 159.99 g of oxygen. Add the totals: 204.087 g on the left, and 3(44.009) + 4(18.015) = 204.087 g on the right. Mass is conserved, and molar mass is what lets you see it.

When you want to check your own answers, the molar-mass calculator in ChemTable's tools runs entirely in your browser and parses subscripts and brackets for you. Use it to verify rather than to replace the practice, because the method above is what an exam will ask you to show.

Frequently asked questions

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