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Q.

A gaseous compound is composed of 85.7% by mass carbon and 14.3% by mass hydrogen. It's density is 2.28 g/litre at 300 K and 1.0 atm pressure. Determine the molecular formula of the compound :

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a

$C_{2} H_{2}$

b

$C_{2} H_{4}$

c

$C_{4} H_{8}$

d

$C_{4} H_{10}$

answer is C.

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Detailed Solution

$\begin{array}{l} d = \frac{PM}{RT} \Rightarrow M = \frac{dRT}{P} \\ = \frac{2 .28 \times 0 .0821 \times 300}{1} = 56 .15 g / mol \\ E . F . = \frac{85 .7}{12} : \frac{14 .3}{1} = 7 .14 : 14 .3 = 1 : 2; \end{array}$
$∴ E . F . is {CH}_{2}; M . F . = {({CH}_{2})}_{n}$
Where $n = \frac{56 .15}{12 + 2} ≃ 4$
$∴ M . F . is C_{4} H_{8}$

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