Chemistry
How To Calculate Molar Mass
Molar mass is the mass of one mole of a substance, and it converts between the grams you weigh on a balance and the moles every chemistry formula expects.
Quick Answer
M = m / n
- M
- Molar mass in grams per mole
- m
- Mass of the sample in grams
- n
- Amount of substance in moles
- c
- Concentration in moles per litre, from moles over volume
Divide the mass in grams by the number of moles. Sodium chloride has a molar mass of 58.44 grams per mole, so one mole dissolved in two litres gives a concentration of 0.5 moles per litre. The same molar mass turns a 29.22 gram sample into 0.5 moles and a solution strength of 29.22 grams per litre.
What Is Molar Mass?
Molar mass is the mass of one mole of a substance, expressed in grams per mole. It is the bridge between the macroscopic world of balances and the microscopic world of particles, because a mole is a fixed count of particles while a balance measures mass. Dividing the mass in grams by the amount in moles returns the molar mass directly.
The numerical value of the molar mass of an element is the same as its relative atomic mass, which is why the numbers on a periodic table can be read either as atomic mass units per atom or as grams per mole. Sodium has a relative atomic mass of 22.99, so one mole of sodium weighs 22.99 grams. This coincidence is not an accident; it is the historical definition of the mole.
For a compound the molar mass is the sum of the atomic masses of every atom in its formula. Water is two hydrogens at 1.008 each plus one oxygen at 15.999, giving 18.015 grams per mole. Glucose is six carbons, twelve hydrogens and six oxygens, which comes to 180.156 grams per mole. Adding the contributions is the whole method.
The relationship rearranges in two useful directions. Given a mass and a molar mass you can find the number of moles by dividing, and given moles and a molar mass you can find the mass by multiplying. Almost every stoichiometry problem starts with one of those two conversions, which is why the molar mass sits at the centre of introductory chemistry.
Dividing the number of moles by the volume of the solution in litres gives the molarity, the concentration that pH, titration and equilibrium calculations all depend on. The chain from a weighed sample to a concentration is therefore two divisions: mass by molar mass gives moles, and moles by volume gives molarity.
Multiplying the molarity by the molar mass returns the concentration in grams per litre. This is the same information written in the units a stockroom uses, and it is a quick way to check that a solution recipe makes sense. A 0.5 mole per litre solution of a compound with a molar mass of 58.44 is 29.22 grams per litre.
The distinction between molar mass and molecular mass matters. Molecular mass is the mass of a single molecule in atomic mass units, while molar mass is the mass of a whole mole in grams. The numbers are identical, but the units are not, and mixing them up is a common source of confusion in written work.
For substances that do not exist as discrete molecules the term formula mass is often preferred. Sodium chloride forms a lattice rather than molecules, so its molar mass is really the mass of one mole of formula units. The arithmetic is unchanged; only the language differs.
Hydrated salts carry water molecules within their crystal structure, and that water contributes to the molar mass. Copper sulfate pentahydrate has five waters added on, which raises its molar mass from 159.609 to 249.685 grams per mole. Weighing the anhydrous form when the recipe expects the hydrate introduces an error of more than fifty percent.
Because molar mass is a ratio of mass to amount, it is independent of how much substance you happen to have. Ten grams and a hundred grams of the same compound share the same molar mass, which is what makes it a useful constant. Only a change in the substance itself, not in the quantity, changes the value.
Formula
M = m / n
The definition. Divide the mass of a sample in grams by the amount of substance in moles to get grams per mole.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| m | Mass of the sample | grams | Measured on a balance, in grams. |
| n | Amount of substance | moles | The number of moles in that sample. |
| M | Molar mass | grams per mole | A constant for the substance, in grams per mole. |
n = m / M
The rearrangement used most often in practice: convert a weighed mass into moles before any stoichiometry can be done.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| m | Mass of the sample | grams | What the balance reads, in grams. |
| M | Molar mass | grams per mole | Looked up or computed from the formula. |
| n | Amount of substance | moles | The moles the sample contains. |
c = n / V
Moles divided by volume in litres gives molarity. It is the last step from a weighed sample to a usable solution concentration.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| n | Amount of substance | moles | Moles obtained from the mass and molar mass. |
| V | Volume of solution | litres | The final volume, not the volume of water added. |
| c | Concentration | moles per litre | Molarity, in moles per litre. |
How To Calculate Molar Mass
- 1
Find the molar mass of the substance
For an element, read the relative atomic mass off the periodic table. For a compound, add the atomic masses of every atom in the formula; water is two hydrogens plus one oxygen, which is 18.015 grams per mole.
- 2
Weigh the sample in grams
The molar mass is defined against the gram, so any mass in milligrams or kilograms must be converted first. A mass in the wrong unit produces moles that are out by the same factor of a thousand.
- 3
Divide the mass by the molar mass
29.22 grams of a substance with a molar mass of 58.44 grams per mole is 0.5 moles. This single division is the conversion every stoichiometry calculation begins with.
- 4
Divide the moles by the volume for molarity
One mole in two litres gives 0.5 moles per litre. The volume is the final volume of the solution, not the volume of solvent added, because dissolving changes the total volume.
- 5
Cross-check in grams per litre
Multiplying the molarity by the molar mass gives 29.22 grams per litre for the example above. If that figure does not match the recipe, one of the earlier steps has gone wrong.
Examples
Example 1: Sodium chloride dissolved in water
- Mass
- 58.44 grams
- Moles
- 1 mole
- Volume
- 2 litres
- Second sample
- 29.22 grams
| Step | Calculation | Result |
|---|---|---|
| Molar mass | 58.44 / 1 | 58.44 |
| Concentration | 1 / 2 | 0.5 |
| Moles in the second sample | 29.22 / 58.44 | 0.5 |
| Strength in grams per litre | 0.5 x 58.44 | 29.22 |
Result: Sodium chloride has a molar mass of 58.44 grams per mole, so one mole in two litres is a 0.5 mol/L solution, 29.22 grams is 0.5 moles, and the strength is 29.22 grams per litre.
Example 2: Building the molar mass of water
- Hydrogen atoms
- 2 at 1.008
- Oxygen atoms
- 1 at 15.999
| Step | Calculation | Result |
|---|---|---|
| Contribution from hydrogen | 2 x 1.008 | 2.016 |
| Contribution from oxygen | 1 x 15.999 | 15.999 |
| Molar mass of water | 2.016 + 15.999 | 18.015 |
Result: Water has a molar mass of 18.015 grams per mole, made up of 2.016 for the two hydrogens and 15.999 for the oxygen.
Example 3: Glucose from its formula
- Carbon
- 6 at 12.011
- Hydrogen
- 12 at 1.008
- Oxygen
- 6 at 15.999
| Step | Calculation | Result |
|---|---|---|
| Contribution from carbon | 6 x 12.011 | 72.066 |
| Contribution from hydrogen | 12 x 1.008 | 12.096 |
| Contribution from oxygen | 6 x 15.999 | 95.994 |
| Molar mass of glucose | 72.066 + 12.096 + 95.994 | 180.156 |
Result: Glucose comes to 180.156 grams per mole, summing 72.066 for carbon, 12.096 for hydrogen and 95.994 for oxygen.
Calculator
Molar mass in grams per mole
58.44
- Concentration in moles per litre
- 0.5
- Moles in the second sample
- 0.5
- Strength in grams per litre
- 29.22
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the Molar Mass calculator page.
Common Mistakes
Using the volume of solvent instead of the final volume
Molarity divides moles by the total volume of the solution, which changes when a solute dissolves. Measuring out a litre of water and adding a solute does not produce a litre of solution, and the concentration is slightly off.
Mixing up molar mass and molecular mass
Molecular mass is the mass of one molecule in atomic mass units; molar mass is the mass of a mole in grams. The numbers match but the units do not, and quoting the wrong one loses marks and can lead to a real unit error.
Forgetting the water in a hydrated salt
A hydrate carries water within its crystals, and that water counts towards the molar mass. Ignoring it makes the calculated moles too large, sometimes by more than fifty percent for a pentahydrate.
Adding the formula subscripts incorrectly
The molar mass of a compound is the sum of each element's atomic mass multiplied by how many times it appears. Treating the subscripts as a single count, rather than a multiplier, understates the total.
Substituting a mass in the wrong unit
The molar mass is defined against the gram. A mass given in milligrams or kilograms must be converted first, or the moles come out wrong by a factor of a thousand.
Rounding the molar mass too early
Rounding atomic masses heavily before adding them compounds the error. Keep at least three decimal places through the addition and round only the final figure to the precision the inputs justify.
FAQ
What is the difference between molar mass and molecular mass?
Molar mass is the mass of one mole of a substance in grams per mole. Molecular mass is the mass of one molecule in atomic mass units. The two numbers are numerically equal, which is convenient, but they are different quantities with different units.
How do I find the molar mass of a compound?
Add the relative atomic masses of every atom in the formula, multiplying each element's mass by how many times it appears. Water is two hydrogens at 1.008 plus one oxygen at 15.999, giving 18.015 grams per mole.
Why is the molar mass of an element the same number as its atomic mass?
Because the mole was defined so that a mole of carbon twelve weighs exactly twelve grams. That choice makes the gram-per-mole value of any element equal to its atomic mass in atomic mass units, which is what lets a periodic table serve both purposes.
Does molar mass change with temperature?
No. Molar mass is a ratio of mass to amount of substance and is a property of the material, not of its conditions. Temperature changes volume and therefore concentration, but the molar mass itself is unaffected.
What if the substance does not form molecules?
Then the term formula mass is used instead, and it refers to one mole of formula units. Ionic solids such as sodium chloride fall into this group, and the arithmetic for adding atomic masses is identical.
How do I get from a weighed sample to a concentration?
Divide the mass by the molar mass to get moles, then divide the moles by the final volume in litres. A 29.22 gram sample of a substance with a molar mass of 58.44 is 0.5 moles, which in two litres is 0.5 moles per litre.
References
- [1]Wikipedia, Molar mass — https://en.wikipedia.org/wiki/Molar_mass
- [2]Wikipedia, Mole (unit) — https://en.wikipedia.org/wiki/Mole_(unit)
- [3]Wikipedia, Concentration — https://en.wikipedia.org/wiki/Concentration