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Question
A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is 27°C. The ratio of root mean square speed of the molecules of the two gases $\left( \frac{V_{\text{rms}\text{~}}^{Ar}}{V_{\text{rms}\text{~}}^{Cl}} \right)$ is:
(Atomic mass of argon $= 40.0u$ and molecular mass of chlorine $= 70.0u$ )
Options
A.$\frac{\sqrt{7}}{2}$
B.$\frac{7}{4}$
C.$\frac{7}{2}$
D.$\frac{2}{\sqrt{7}}$
Solution
Sol. [Key Concept: Kinetic theory — molecules ∝ mass/molar mass] $v_{\text{rms}\text{~}} = \sqrt{\frac{3RT}{M}}$
For same temperature, $v_{\text{rms}\text{~}} \propto \frac{1}{\sqrt{M}}$
$$\frac{V_{rms}^{Ar}}{V_{rms}^{Cl}} = \sqrt{\frac{M_{Cl}}{M_{Ar}}} = \sqrt{\frac{70}{40}} = \frac{\sqrt{7}}{2}$$
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