First slide

Kinetic theory of ideal gases

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

Moderate

A

1:4
B

1:2
C

6:9
D

8:9

Solution

$\begin{array}{l} PV = nRT = \frac{m}{M} RT \\ \Rightarrow PM = ρ RT \\ \Rightarrow \frac{ρ_{1}}{ρ_{2}} = (\frac{P_{1}}{P_{2}}) (\frac{M_{1}}{M_{2}}) = (\frac{4}{3}) (\frac{2}{3}) = \frac{8}{9} . \end{array}$

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