Q142 / 160 · TS EAMCET 2021 (05 Aug Shift 2) · Physics

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

A
$1.1$
B
$2.0$
C
$0.9$
Correct answer
D
$0.5$

Solution

From ideal gas equation, we have

P V = n R T

\Rightarrow P V = \frac{m}{M} R T

\Rightarrow P = \frac{ρ R T}{M}

Taking the corresponding ration, we have

\Rightarrow \frac{P_{A}}{P_{B}} = \frac{\frac{ρ_{A} R T_{A}}{M_{A}}}{\frac{ρ_{B} R T_{B}}{M_{B}}}

\Rightarrow \frac{P_{A}}{P_{B}} = \frac{ρ_{A}}{M_{A}} \times \frac{M_{B}}{ρ_{B}}, (∵ T_{A} = T_{B})

\Rightarrow \frac{ρ_{A}}{ρ_{B}} = \frac{P_{A}}{P_{B}} \times \frac{M_{A}}{M_{B}}

\Rightarrow \frac{ρ_{A}}{ρ_{B}} = \frac{3}{4} \times \frac{2}{3} = 0.5

Hence, the correct answer is option: 'D'.

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