Q114 / 180 · NEET 2026 (Cancelled) · Physics
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 $\left(\dfrac{v_{rms}^{Ar}}{v_{rms}^{Cl}}\right)$ is :
(Atomic mass of argon $= 40.0$ u and molecular mass of chlorine $= 70.0$ u)
(Atomic mass of argon $= 40.0$ u and molecular mass of chlorine $= 70.0$ u)
- Correct answerA$\dfrac{\sqrt{7}}{2}$
- B$\dfrac{7}{4}$
- C$\dfrac{7}{2}$
- D$\dfrac{2}{\sqrt{7}}$
Solution
The root mean square speed of a gas molecule is given by $v_{rms} = \sqrt{\dfrac{3RT}{M}}$, 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:
$\dfrac{v_{rms}^{Ar}}{v_{rms}^{Cl}} = \sqrt{\dfrac{M_{Cl}}{M_{Ar}}}$
Given the molecular mass of chlorine $M_{Cl} = 70.0$ u and atomic mass of argon $M_{Ar} = 40.0$ u:
$\dfrac{v_{rms}^{Ar}}{v_{rms}^{Cl}} = \sqrt{\dfrac{70.0}{40.0}} = \sqrt{\dfrac{7}{4}} = \dfrac{\sqrt{7}}{2}$
The mass ratio of the gases in the mixture is extra information and not required for this calculation.
Answer: $\dfrac{\sqrt{7}}{2}$
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:
$\dfrac{v_{rms}^{Ar}}{v_{rms}^{Cl}} = \sqrt{\dfrac{M_{Cl}}{M_{Ar}}}$
Given the molecular mass of chlorine $M_{Cl} = 70.0$ u and atomic mass of argon $M_{Ar} = 40.0$ u:
$\dfrac{v_{rms}^{Ar}}{v_{rms}^{Cl}} = \sqrt{\dfrac{70.0}{40.0}} = \sqrt{\dfrac{7}{4}} = \dfrac{\sqrt{7}}{2}$
The mass ratio of the gases in the mixture is extra information and not required for this calculation.
Answer: $\dfrac{\sqrt{7}}{2}$
Hence, the correct answer is option: 'A'.