States of Matter - Result Question 93
####93. A hydrocarbon contains $10.5 g$ of carbon per gram of hydrogen. $1 L$ of the vapour of the hydrocarbon at $127^{\circ} C$ and $1 atm$ pressure weighs $2.8 g$. Find the molecular formula of the hydrocarbon.
(1980, 3M)
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Solution:
- First we determine empirical formula as
| $C$ | $H$ | |
|---|---|---|
| Weight | 10.5 | 1 |
| Mole | $\frac{10.5}{12}=0.875$ | 1 |
| Simple ratio | 1 | $1 / 0.875=1.14$ |
| Whole no. | 7 | 8 |
$\Rightarrow$ Empirical formula $=C _7 H _8$
From gas equation : $p V=\left(\frac{w}{M}\right) R T$
$$ M=\frac{w R T}{p V}=\frac{2.8 \times 0.082 \times 400}{1 \times 1}=91.84 \approx 92 $$
$\because \quad$ Molar mass $(M)$ is same as empirical formula weight.
Molecular formula $=$ Empirical formula $=C _7 H _8$
