Introduction
By now you know what a mole is — a counting unit for 6.02 × 10²³ particles. But in the lab, you can't weigh out "particles" directly; you weigh out grams. Molar mass is the bridge that connects the mass you measure on a balance to the amount (in moles) you need for chemical calculations. Without it, none of the stoichiometry problems you'll meet later in this unit (mass–mass, mass–gas volume, concentration problems) would be possible (Talbot, p. 424).
What is molar mass?
Molar mass (M) is the mass of one mole of a substance, expressed in grams per mole (g mol⁻¹). Numerically, it is equal to the relative atomic mass (Ar) of an element or the relative formula mass (Mr) of a compound — you just add the unit g mol⁻¹.
- Relative atomic mass values come straight from the periodic table.
- Relative formula mass is the sum of the atomic masses of every atom in the formula (Talbot, p. 86).
So:
- M(C) = 12.01 g mol⁻¹
- M(O₂) = 2 × 16.00 = 32.00 g mol⁻¹
- M(CaCO₃) = 40.08 + 12.01 + (3 × 16.00) = 100.09 g mol⁻¹
The key formula
The relationship between mass, moles, and molar mass is:
n = m / M
where:
- n = amount of substance (mol)
- m = mass (g)
- M = molar mass (g mol⁻¹)
Rearranged, this also gives you m = n × M and M = m / n, depending on what you're solving for.
Worked Example 1 – Finding molar mass
Question: Calculate the molar mass of magnesium hydroxide, Mg(OH)₂.
Answer:
- Mg: 24.31
- O: 16.00 × 2 = 32.00
- H: 1.01 × 2 = 2.02
M(Mg(OH)₂) = 24.31 + 32.00 + 2.02 = 58.33 g mol⁻¹
Worked Example 2 – Mass to moles
Question: How many moles are in 9.00 g of water, H₂O?
Answer: M(H₂O) = (2 × 1.01) + 16.00 = 18.02 g mol⁻¹
n = m / M = 9.00 / 18.02 = 0.499 mol
Worked Example 3 – Moles to mass
Question: What is the mass of 0.250 mol of sodium carbonate, Na₂CO₃?
Answer: M(Na₂CO₃) = (2 × 22.99) + 12.01 + (3 × 16.00) = 105.99 g mol⁻¹
m = n × M = 0.250 × 105.99 = 26.5 g
Why this matters
Molar mass is the first conversion step in almost every stoichiometry problem you'll tackle in this unit. For example, in mass–mass problems, you first convert a given mass to moles using molar mass, then use the mole ratio from a balanced equation, then convert back to mass using the molar mass of the product (Talbot, p. 424–425). The same logic applies when the "required substance" turns out to be a gas, except the final step uses the molar gas volume instead of molar mass (Talbot, p. 425).
Key takeaways
- Molar mass (M) is the mass of one mole of a substance, in g mol⁻¹, numerically equal to Ar or Mr.
- Use the periodic table to find atomic masses, then add them up for compounds (relative formula mass).
- The core formula is n = m / M — rearrange it to find mass or molar mass as needed.
- Molar mass is the essential first (and often last) conversion step in mass-based stoichiometry problems.
- Always double-check you've multiplied atomic masses by the correct number of atoms in the formula.