Question

A and B are two identical vessels. A contains 15 g of ethane at 298 K and 1 atm. The vessel B contains 75 g gas ${{X}_{2}}$ at the same temperature and pressure. The vapour density of ${{X}_{2}}$ is:

• A. 300
• B. 375
• C. 150
• D. 75

Answer 1

Answer: (D)

75

Answer 2

From gas equation, ${{P}_{1}}{{V}_{1}}={{n}_{1}}\cdot R{{T}_{1}}=\frac{{{w}_{1}}}{{{m}_{1}}}\cdot R{{T}_{1}}$ ?(i) ${{P}_{2}}{{V}_{2}}=\frac{{{w}_{2}}}{{{m}_{2}}}\cdot R{{T}_{2}}$ ?(ii) As, ${{P}_{1}}={{P}_{2}},$ ${{V}_{1}}={{V}_{2}}$ hence, ${{T}_{1}}={{T}_{2}}$ Hence, $\frac{{{w}_{1}}}{{{m}_{1}}}=\frac{{{w}_{2}}}{{{m}_{2}}}$ $\therefore$ $\frac{15}{30}=\frac{75}{{{m}_{2}}}$ ( $\because$ molecular weight of ethane = 30) $\therefore$ ${{m}_{2}}=150$ Hence, vapour density of ${{X}_{2}}$ gas is $=\frac{M}{2}=\frac{150}{2}=75$