Question

A hydrocarbon $X$ contains $85.7\%$ carbon by mass. If the relative molecular mass of $X$ is $28$ , find the molecular formula of $X$.

Answer 1

Empirical formula

• We know that the hydrocarbon is $85.7\%$ by mass Carbon.
• So, we address the empirical formula by assuming an $100\mathrm{gm}$ mass of the unknown compound.

Mass of Carbon = $85.7\mathrm{gm}$

Mass of Hydrogen = $14.3\mathrm{gm}$

$\mathrm{number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}$

Number of moles of Carbon $\left(\mathrm{C}\right)$

$\mathrm{number}\mathrm{of}\mathrm{moles}=\frac{85.7\mathrm{gm}}{12.02\mathrm{gm}}=7.10$

Number of moles of Hydrogen $\left(\mathrm{H}\right)$

$\mathrm{number}\mathrm{of}\mathrm{moles}=\frac{14.3\mathrm{gm}}{1.0002\mathrm{gm}}=14.20$

Ratio of Carbon $\left(\mathrm{C}\right)$ & Hydrogen $\left(\mathrm{H}\right)$ = $\frac{\mathrm{C}}{\mathrm{H}}=\frac{7.10}{14.20}=\frac{1}{2}$

So, the empirical formula will be ${\mathrm{CH}}_2$.

Relative molecular mass of $\mathrm{X}=28$

Molecular formula of $\mathrm{X}$

$$\begin{gathered} {\left({\mathrm{CH}}_2\right)}_{\mathrm{n}}=28 \\ \mathrm{n}\times (12+2\times 1)=28 \\ \mathrm{n}\times (14)=28 \\ \mathrm{n}=\frac{28}{14} \\ \mathrm{n}=2 \end{gathered}$$

So molecular formula = ${\mathrm{C}}_{\mathrm{n}}{\mathrm{H}}_{2\mathrm{n}}$ = ${\mathrm{C}}_2{\mathrm{H}}_4$.