Question

Three gases A, B and C are at same temperature if their r.m.s speed are in the ratio $1:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}$ then their molar masses will be in the ratio:

• A. $1:2:3$
• B. $3:2:1$
• C. $1:\sqrt{2}:\sqrt{3}$
• D. $\sqrt{3}:\sqrt{2}:1$

Answer 1

The correct option is A $1:2:3$

The expression for the root mean square velocities is $V_{rms}^2=\frac{3RT}{M}$.

The ratio of the root mean square velocities is $V_A:V_B:V_C=1:1/\sqrt{2}:1/\sqrt{3}$.

The ratio of the square of root mean square velocities is $V_A^2:V_B^2:V_C^2=1:1/2:1/3$.

Hence, $\frac{1}{M_A}:\frac{1}{M_B}:\frac{1}{M_C}=1:\frac{1}{2}:\frac{1}{3}$ or $M_A:M_B:M_C=1:2:3$.

Option A is correct.