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Kinetic Theory
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A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is $27^\circ C$. The ratio of root mean square speed of the molecules of the two gases $\left(\frac{v_{rms}^{Ar}}{v_{rms}^{Cl}}\right)$ is: (Atomic mass of argon = 40.0 u and molecular mass of chlorine = 70.0 u)$v_{rms} = \sqrt{\frac{3RT}{M_w}}$ At constant temperature, $v_{rms} \propto \frac{1}{\sqrt{M_w}}$ (independent of the mass ratio in the mixture) $\frac{v_{rms}^{Ar}}{v_{rms}^{Cl}} = \sqrt{\frac{M_{w,Cl}}{M_{w,Ar}}} = \sqrt{\frac{70}{40}} = \frac{\sqrt{7}}{2}$