Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is?? [2013]

Question

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is [2013]

Smart Achievers · Accepted Answer

(4)

$P_{1} M_{1} = P_{1} R T and P_{2} M_{2} = P_{2} R T$

$∴$ $\frac{P_{1}}{P_{2}} \times \frac{M_{1}}{M_{2}} = \frac{P_{1}}{P_{2}}$

$\frac{4}{3} \times \frac{2}{3} = \frac{P_{1}}{P_{2}}$

$∴$ $\frac{P_{1}}{P_{2}} = \frac{8}{9}$

Solution

Q.
Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is [2013]

1 1 : 4

2 1 : 2

3 6 : 9

4 8 : 9

Ans.
(4)

$P_{1} M_{1} = P_{1} R T and P_{2} M_{2} = P_{2} R T$

$∴$ $\frac{P_{1}}{P_{2}} \times \frac{M_{1}}{M_{2}} = \frac{P_{1}}{P_{2}}$

$\frac{4}{3} \times \frac{2}{3} = \frac{P_{1}}{P_{2}}$

$∴$ $\frac{P_{1}}{P_{2}} = \frac{8}{9}$

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