The formula
- Molar mass of a compound
M = Σ (atoms of each element × atomic mass)- Moles from mass
n = m / M- Mass from moles
m = n × M- Particles from moles
N = n × N_A
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
M | Molar mass of the substance | g/mol |
m | Mass of the sample | g |
n | Amount of substance | mol |
N | Number of atoms, molecules or formula units | count |
N_A | Avogadro constant, the number of entities in one mole | 6.022 × 10²³ mol⁻¹ |
atomic mass | Standard atomic weight from the periodic table, read as grams per mole | g/mol |
When it applies
- Any conversion between the mass of a sample and the moles the balanced equation works in, in either direction.
- The subscripts multiply everything inside their group. In Ca(NO₃)₂ the subscript 2 applies to the whole nitrate group, giving two nitrogens and six oxygens.
- Molar mass, molecular mass and formula mass are the same number here; formula mass is the term used for ionic compounds, which have no discrete molecules.
- Carry the periodic table values to at least two decimal places through the calculation, and round only the final answer.
Worked example
Problem. Find the molar mass of calcium nitrate, Ca(NO₃)₂, then the number of moles and the number of formula units in a 50.0 g sample.
- Read off the atom counts. The subscript 2 applies to the whole nitrate group, so the formula holds 1 Ca, 2 N and 6 O.
- Work out the nitrate group first: N + 3O = 14.007 + 3(15.999) = 62.004 g/mol.
- Add the calcium and two nitrates: M = 40.078 + 2(62.004) = 164.086 g/mol, which is 164.09 g/mol.
- Convert the sample to moles: n = 50.0 / 164.086 = 0.30472 mol, which is 0.305 mol.
- Multiply by the Avogadro constant for the particle count: N = 0.30472 × 6.022 × 10²³ = 1.84 × 10²³ formula units.
Answer. 164.09 g/mol, giving 0.305 mol and 1.84 × 10²³ formula units in 50.0 g.
Common mistakes
- Applying a subscript outside a bracket to only the first atom inside it. Ca(NO₃)₂ has six oxygens, not three.
- Using the atomic number from the periodic table instead of the atomic mass, which is the other number in the same box.
- Multiplying by molar mass when the problem calls for dividing. Grams to moles divides; moles to grams multiplies, and a quick size check catches the slip.
- Treating a diatomic element as a single atom. Nitrogen gas is N₂ at 28.014 g/mol, not 14.007 g/mol.
Related formulas
- Empirical formula:
%X = (mass X / mass compound) × 100% - Limiting reactant:
compare n(X) / coefficient(X) across reactants; the smallest value is limiting - Molarity formula:
M = mol solute / L solution