Q45 (2024)
A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is $27^{\circ}\mathrm{C}$ . The ratio of root mean square speed of the molecules of the two gases $\left(\frac{\mathrm{V}_{\mathrm{rms}}^{\mathrm{Ar}}}{\mathrm{V}_{\mathrm{rms}}^{\mathrm{Cl}}}\right)$ is:
(Atomic mass of argon = 40.0u and molecular mass of chlorine = 70.0u)
- $\frac{\sqrt{7}}{2}$
- $\frac{7}{2}$
- $\frac{7}{4}$
- $\frac{2}{\sqrt{7}}$
### Related Formula
$$v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$$
### Core Logic
At a constant temperature $T$, $v_{\text{rms}} \propto \frac{1}{\sqrt{M}}$.
$$\frac{v_{\text{rms}}^{\text{Ar}}}{v_{\text{rms}}^{\text{Cl}}} = \sqrt{\frac{M_{\text{Cl}}}{M_{\text{Ar}}}} = \sqrt{\frac{70}{40}} = \frac{\sqrt{7}}{2}$$
### Pattern Recognition
RMS speed ratio depends inversely on the square root of molar mass.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 11 Physics: Kinetic Theory
