Empirical and molecular formulas: from percentage composition to molecules

From mass percentages to moles

Treat the percentages as masses in a 100 g sample: 40.0% carbon means 40.0 g of carbon, 6.7% hydrogen means 6.7 g, and 53.3% oxygen means 53.3 g. Divide each mass by the element's standard atomic mass to get moles: carbon 40.0 / 12.011 = 3.330 mol, hydrogen 6.7 / 1.008 = 6.646 mol, oxygen 53.3 / 15.999 = 3.331 mol.

If the percentages do not sum to 100%, first normalize them: divide each by the total and multiply by 100, then convert. The element ratios are what matter, so a small rounding difference in the percentages changes the moles slightly but not the final integer ratio. Keep a few decimal places through the division instead of rounding to whole moles early.

From moles to the empirical formula

Divide every mole amount by the smallest one. The smallest is carbon and oxygen at about 3.330, so carbon becomes 3.330 / 3.330 = 1, hydrogen becomes 6.646 / 3.330 = 1.996, and oxygen becomes 1.000. A ratio of 1 : 1.996 : 1 rounds to 1 : 2 : 1, giving the empirical formula CH2O.

If the ratios are not close to whole numbers, multiply all of them by the same small integer until they are: a 1 : 1.5 ratio becomes 2 : 3 with a multiplier of 2. The empirical formula mass is then the sum of the atomic masses in that formula; for CH2O it is 12.011 + 2 × 1.008 + 15.999 = 30.026 g/mol, about 30.03.

Rounding is a judgement call. A ratio of 1 : 1.996 is sensibly treated as 1 : 2, while 1 : 1.8 should not be forced to 2 without checking the data or trying a multiplier. The tolerance is there to absorb small analytical errors, not to disguise a genuinely different ratio.

From empirical to molecular formula

The molecular formula is the empirical formula multiplied by a whole number n, where n = molar mass / empirical formula mass. For glucose with a molar mass of 180.16 g/mol, n = 180.16 / 30.026 = 6.00, so every subscript is multiplied by 6: C6H12O6.

If n comes out far from a whole number, do not round it without thinking. The molar mass may belong to a different compound, the percentage data may contain an error, or the sample may be a mixture. A value of 3.4, for example, is not a meaningful multiple and should send you back to the data rather than to a formula.

The quality of the molar mass matters: a molecular ion mass from a mass spectrum usually resolves n much more clearly than a rough value estimated from boiling point elevation. The more accurate the molar mass, the more confidently the multiplier can be called a whole number.

Empirical versus molecular formulas in practice

The same empirical formula can describe very different compounds: CH2O is the empirical formula of formaldehyde (CH2O), acetic acid (C2H4O2) and glucose (C6H12O6). All three have the same element ratio, but their properties differ because their molecules contain different numbers of atoms.

For ionic solids such as sodium chloride, the empirical formula is the formula unit and there is no separate molecular formula to find. Molecular formulas are meaningful for molecular compounds, which is why the molar mass measurement matters so much in identifying an unknown compound.

Common mistakes and checks

Most errors come from treating percentages as moles directly, dividing by the wrong smallest value, or rounding intermediate mole amounts so aggressively that the ratio distorts. Another common mistake is forgetting to multiply when a ratio lands near a half or a third instead of within tolerance of a whole number.

• Convert every percentage or mass to moles before comparing.
• Divide all moles by the smallest amount, then scale the ratios.
• Use a small tolerance before rounding; do not force 1.9 into 2 without checking the data.
• Compute the empirical formula mass from the formula you found, not from the percentages.
• Multiply by n only when n is close to a whole number.