The formula
- Whole-number multiplier
n = molar mass / empirical formula mass- Building the molecular formula
molecular formula = (empirical formula) × n- Empirical formula mass
EFM = Σ (atoms in the empirical formula × atomic mass)
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
n | Whole-number multiplier relating the two formulas | dimensionless integer |
molar mass | Measured molar mass of the compound | g/mol |
EFM | Empirical formula mass, the molar mass of one empirical formula unit | g/mol |
atomic mass | Standard atomic weight from the periodic table | g/mol |
When it applies
- You already have the empirical formula and an experimentally measured molar mass. Composition data alone can never reach the molecular formula.
- The multiplier has to come out as a whole number within rounding. A value like 2.5 means the empirical formula was wrong, not that the molecule has half an atom.
- Ionic compounds have formula units rather than molecules, so sodium chloride is written NaCl and stops at the empirical formula.
- Different compounds can share one empirical formula. CH₂O covers formaldehyde, acetic acid and glucose, and only the molar mass separates them.
Worked example
Problem. A compound has the empirical formula CH₂O and a measured molar mass of 180.16 g/mol. What is its molecular formula?
- Work out the empirical formula mass: C + 2H + O = 12.011 + 2(1.008) + 15.999 = 30.026 g/mol.
- Divide the measured molar mass by it: n = 180.16 / 30.026 = 6.000.
- That is a whole number, so multiply every subscript in CH₂O by 6: C₆H₁₂O₆.
- Check the result: 6(12.011) + 12(1.008) + 6(15.999) = 180.16 g/mol, which matches the measured value.
Answer. C₆H₁₂O₆, six times the empirical formula, which is the formula of glucose.
Common mistakes
- Dividing the empirical formula mass by the molar mass. The measured molar mass is the larger number and belongs on top.
- Rounding a multiplier of 2.5 to 3 to force a whole number, instead of going back and rechecking the empirical formula.
- Multiplying only the first subscript. Every subscript in the empirical formula is multiplied by n.
- Assuming the molecular formula is always different. When n comes out as 1 the two formulas are identical, as they are for water and for ammonia.
Related formulas
- Empirical formula:
%X = (mass X / mass compound) × 100% - Molar mass:
M = Σ (atoms of each element × atomic mass)