Why Percent Composition Alone Cannot Fix a Molecular Formula

Percent composition determines a ratio, not molecule size

Mass percentages tell how much of each element is present relative to the whole sample. After each mass is converted to moles, the result can be reduced to the smallest whole-number atom ratio. That ratio is the empirical formula.

Reducing a ratio deliberately removes scale. A $1:2:1$ ratio and a $6:12:6$ ratio describe the same relative composition, so percentage data alone cannot tell which set of subscripts belongs to one molecule.

One empirical formula can represent different molecular formulas

Consider compounds whose empirical formula is $\mathrm{CH_2O}$. The empirical-formula mass is approximately

$$12.01+2(1.008)+16.00=30.03\,\mathrm{g\,mol^{-1}}.$$

Different measured molar masses imply different integer multipliers:

These formulas have the same elemental mass percentages even though their molecules contain different numbers of atoms.

Molar mass supplies the missing scale

Use the measured molar mass, $M$, to find the multiplier:

$$n=\frac{M}{\text{empirical-formula mass}}.$$

For a valid molecular formula, $n$ should be close to a positive integer within the precision of the measurements. Multiply every empirical subscript by $n$. If the quotient is not near an integer, recheck the mole ratios, atomic weights, rounding, sample purity, and molar-mass measurement instead of forcing a convenient result.

The method identifies composition, not structure. $\mathrm{C_2H_4O_2}$, for example, can describe more than one structural isomer.