2026 Kinetic TheoryRoot mean square speed of gas molecules Medium Question 1 of 34 in Kinetic Theory

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)

A $\frac{\sqrt{7}}{2}$
B $\frac{7}{2}$
C $\frac{7}{4}$
D $\frac{2}{\sqrt{7}}$

The answer is A.

Solution

$v_{rms} = \sqrt{\frac{3RT}{M_w}}$ At constant temperature, $v_{rms} \propto \frac{1}{\sqrt{M_w}}$ (independent of the mass ratio in the mixture) $\frac{v_{rms}^{Ar}}{v_{rms}^{Cl}} = \sqrt{\frac{M_{w,Cl}}{M_{w,Ar}}} = \sqrt{\frac{70}{40}} = \frac{\sqrt{7}}{2}$

Kinetic Theory in past papers

34 questions from this chapter have appeared across 19 exam years.