Ncert Exercises & Solutions

5.18 2.9 g of a gas at 95 °C occupied the same volume as 0.184 g of dihydrogen at 17 °C, at the same pressure. What is the molar mass of the gas?

Volume (v) occupied by dihydrogen is given by,

$V = \frac{m}{M} \frac{R T}{p}$
$= \frac{0.184}{2} \times \frac{R \times 290}{p}$

Let M be the molar mass of the unknown gas. Volume (V) occupied by the unknown can be calculated as:

V = \frac{m}{M} \frac{R T}{p}

= \frac{2.9}{M} \times \frac{R \times 368}{p}

According to the question,

\frac{0.184}{2} \times \frac{R \times 290}{p} = \frac{2.9}{M} \times \frac{R \times 368}{p}

\Rightarrow \frac{0.184 \times 290}{2} = \frac{2.9 \times 368}{M}

\Rightarrow M = \frac{2.9 \times 369 \times 2}{0.184 \times 290}

= 40 g m o l^{- 1}

Hence, the molar mass of the gas is 40 g

m o l^{- 1}