two compounds a and b have the formula \(\mathrm{CH_2}\) is a standard cue that the written formula is an empirical formula, meaning the simplest whole-number ratio of atoms. A molecular formula describes the actual numbers of atoms in one molecule and is an integer multiple of the empirical formula.
Empirical-formula unit mass
Atomic masses \(\mathrm{C} \approx 12.01\ \mathrm{g\ mol^{-1}}\) and \(\mathrm{H} \approx 1.008\ \mathrm{g\ mol^{-1}}\) give an empirical-formula mass for \(\mathrm{CH_2}\):
Scaling relationship
A molecular formula has the form \((\mathrm{CH_2})_n = \mathrm{C}_n\mathrm{H}_{2n}\) where \(n\) is a positive integer given by \(n = \dfrac{M_{\text{molecule}}}{M(\mathrm{CH_2})}\).
Molecular formulas of A and B from molar mass
The molar mass of compound A is \(42.0\ \mathrm{g\ mol^{-1}}\) and the molar mass of compound B is \(84.0\ \mathrm{g\ mol^{-1}}\). Each is compared to the empirical-formula mass \(14.03\ \mathrm{g\ mol^{-1}}\).
Summary table
| Compound | Empirical formula | Molar mass (g/mol) | Multiple \(n\) | Molecular formula |
|---|---|---|---|---|
| A | \(\mathrm{CH_2}\) | \(42.0\) | \(3\) | \(\mathrm{C_3H_6}\) |
| B | \(\mathrm{CH_2}\) | \(84.0\) | \(6\) | \(\mathrm{C_6H_{12}}\) |
Visualization of empirical-unit stacking
Consistency checks
The ratios \(42.0/14.03\) and \(84.0/14.03\) land very close to integers because the given molar masses are rounded while atomic masses are not exact integers. Integer \(n\) values are the chemically meaningful outcome, since molecular formulas require whole-number subscripts.