Question

What is the molecular formula of each of the following compounds? (a) empirical formula ${\mathrm{CH}}_2$, molar mass $=84\mathrm{g}/\mathrm{mol}$ (b) empirical formula ${\mathrm{NH}}_2\mathrm{Cl}$, molar mass $=51.5\mathrm{g}/\mathrm{mol}$

Short answer

The molecular formulas of the two compounds are: (a) ${\mathrm{C}}_6{\mathrm{H}}_{12}$ (b) ${\mathrm{NH}}_2\mathrm{Cl}$

Step-by-step solution

Calculate the molar mass of the empirical formula

We will find the molar mass of the empirical formula ${\mathrm{CH}}_2$: C: 1 atom × 12.01 g/mol = 12.01 g/mol H: 2 atoms × 1.01 g/mol = 2.02 g/mol ----------------------------------------- Total: 14.03 g/mol The molar mass of ${\mathrm{CH}}_2$ is 14.03 g/mol.

Calculate the multiple

To find the multiple, we will divide the molar mass of the molecular formula (84 g/mol) by the molar mass of the empirical formula (14.03 g/mol): Multiple = $\frac{84}{14.03}$ ≈ 6

Determine the molecular formula

Now, multiply the empirical formula by the multiple: ${\mathrm{CH}}_2$ × 6 = ${\mathrm{C}}_6{\mathrm{H}}_{12}$ The molecular formula of the compound is ${\mathrm{C}}_6{\mathrm{H}}_{12}$. (b) empirical formula ${\mathrm{NH}}_2\mathrm{Cl}$, molar mass $=51.5\mathrm{g}/\mathrm{mol}$

Calculate the molar mass of the empirical formula

We will find the molar mass of the empirical formula ${\mathrm{NH}}_2\mathrm{Cl}$: N: 1 atom × 14.01 g/mol = 14.01 g/mol H: 2 atoms × 1.01 g/mol = 2.02 g/mol Cl: 1 atom × 35.45 g/mol = 35.45 g/mol ----------------------------------------- Total: 51.48 g/mol The molar mass of ${\mathrm{NH}}_2\mathrm{Cl}$ is 51.48 g/mol.

Calculate the multiple

To find the multiple, we will divide the molar mass of the molecular formula (51.5 g/mol) by the molar mass of the empirical formula (51.48 g/mol): Multiple = $\frac{51.5}{51.48}$ ≈ 1

Determine the molecular formula

Now, multiply the empirical formula by the multiple: ${\mathrm{NH}}_2\mathrm{Cl}$ × 1 = ${\mathrm{NH}}_2\mathrm{Cl}$ The molecular formula of the compound is ${\mathrm{NH}}_2\mathrm{Cl}$.