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:

  1. 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 $=C _7 H _8$



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