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Q.

A $0.5 d m^{3}$ flask contains gas A and $1 d m^{3}$ flask contains gas B at the same temperature. If density of A = 3 $g / d m^{3}$ and that of B = 1.5 $g / d m^{3}$ and the molar mass of A = 1/2 of B, the ratio of pressure exerted by gases is

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a

$\frac{P_{A}}{P_{B}} = 2$

b

$\frac{P_{A}}{P_{B}} = 1$

c

$\frac{P_{A}}{P_{B}} = 4$

d

$\frac{P_{A}}{P_{B}} = 3$

answer is C.

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Detailed Solution

$\begin{array}{l} V_{A} = 0 .5 {dm}^{3}, V_{B} = 1 {dm}^{3} \\ d_{A} = 3 g / {dm}^{3}, d_{B} = 1 .5 {dm}^{3} \\ M_{A} = \frac{1}{2} M_{B}; P_{A} = \frac{d_{A} RT}{M_{A}}; P_{B} = \frac{d_{B} RT}{M_{B}} \\ \frac{P_{A}}{P_{B}} = \frac{d_{A}}{d_{b}} \times \frac{M_{B}}{M_{A}} \Rightarrow \frac{3}{1 .5} \times 2 = 4 \end{array}$

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