How to Derive an Empirical Formula from Mass Percentages

An empirical formula is a mole ratio

An empirical formula gives the smallest whole-number ratio of atoms in a compound. Mass percentages cannot be used directly as subscripts because atoms combine by numbers of particles, represented in calculations by moles, not by equal masses.

Use a repeatable four-step method

1. Assume a 100 g sample so each percentage becomes the same numerical mass in grams.
2. Divide each element's mass by its molar mass to convert grams to moles.
3. Divide every mole amount by the smallest mole amount.
4. If the ratios are not close to whole numbers, multiply all ratios by the same small integer until they are.

Do not round a value such as 1.50 straight to 2. A ratio near 1.5 indicates halves, so multiply every ratio by 2. Ratios near 1.33 or 1.67 often call for multiplying by 3, while ratios near 1.25 or 1.75 often call for multiplying by 4.

Work a fresh example

Suppose a compound is 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. In a 100 g sample:

Dividing by the smallest amount gives approximately $1:2:1$, so the empirical formula is $\mathrm{CH_2O}$.

Check the result and its limits

Recalculate the mass percentages from the proposed formula to see whether they agree with the measured composition within the stated precision. Small deviations are expected when the input percentages and atomic masses have been rounded.

The empirical formula does not necessarily give the actual number of atoms in one molecule. To find a molecular formula, divide the compound's measured molar mass by the empirical-formula mass. That quotient must be close to a positive integer, which multiplies every empirical subscript.