A flask contains argon and chlorine in the ratio of 2:1$2:1$ by mass. The temperature of the mixture is 27°C$27^{\circ}\mathrm{C}$. The ratio of root mean square speed of the molecules of the two gases ( VrmsArVrmsCl)$\left(\frac{\mathrm{V}_{\mathrm{rms}}^{\mathrm{Ar}}}{\mathrm{V}_{\mathrm{rms}}^{\mathrm{Cl}}}\right)$ is: (Atomic mass of argon = 40.0u$40.0\mathrm{u}$ and molecular mass of chlorine = 70.0u$70.0\mathrm{u}$)

Related Formula

Core Logic

The root mean square speed of a gas relies entirely on its temperature (T$T$) and its molecular mass (M$M$). The mass ratio of the gases in the container (2:1$2:1$) is a distractor and does not affect the average kinetic energy or RMS speed of the individual molecules.

Since both gases are perfectly mixed in the same flask, they are in thermal equilibrium, meaning TAr = TCl = 27°C = 300~K$T_{\text{Ar}} = T_{\text{Cl}} = 27^{\circ}\mathrm{C} = 300\mathrm{~K}$.

Because T$T$ is constant, vrms ∝ 1√(M)$v_{\text{rms}} \propto \frac{1}{\sqrt{M}}$.

Step 1: Calculate RMS Ratio

Pattern Recognition

For gas mixtures, vrms$v_{\text{rms}}$ ratio depends exclusively on the inverse square root of the molar mass ratio. Mixture masses or mole fractions are irrelevant distractors.

Chapter Mix

Class 11 Physics: Kinetic Theory