A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is 2 7 ∘ C. The ratio of root mean square speed of the molecules of the two gases ( v r m s Cl v r m

Question

A flask contains argon and chlorine in the ratio of $2 : 1$ by mass. The temperature of the mixture is $2 7^{\circ}$ C. The ratio of root mean square speed of the molecules of the two gases $(\frac{v _{r m s}^{A r}}{v _{r m s}^{Cl}})$ is :
(Atomic mass of argon $= 40.0$ u and molecular mass of chlorine $= 70.0$ u)NEET 2026 (Cancelled)

TestHub · Accepted Answer

The root mean square speed of a gas molecule is given by $v_{r m s} = \frac{3 RT}{M}$ , where $T$ is the absolute temperature and $M$ is the molar mass.

For argon and chlorine in the same flask, the temperature $T$ is the same.

Therefore, the ratio of their rms speeds is inversely proportional to the square root of their molar masses:

$\frac{v _{r m s}^{A r}}{v _{r m s}^{Cl}} = \frac{M _{Cl}}{M _{A r}}$

Given the molecular mass of chlorine $M_{Cl} = 70.0$ u and atomic mass of argon $M_{A r} = 40.0$ u:

$\frac{v _{r m s}^{A r}}{v _{r m s}^{Cl}} = \frac{70.0}{40.0} = \frac{7}{4} = \frac{7}{2}$

The mass ratio of the gases in the mixture is extra information and not required for this calculation.

Answer: $\frac{7}{2}$

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