Question

Three gases A, B and C are at the same temperature. If their r.m.s. speeds are in the ratio of $1:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}$, 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

Answer: (A)

$1:2:3$

${V_{rms}}^2=\frac{3RT}{M}$
$V_a:V_b:V_c=1:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}$
${V_A}^2:{V_B}^2:{V_C}^2=1:\frac{1}{2}:\frac{1}{3}$
$\frac{1}{M_A}:\frac{1}{M_B}:\frac{1}{M_C}=1:\frac{1}{2}:\frac{1}{3}$
$M_A:M_B:M_C=1:2:3$

Hence, the correct answer is option $\text{A}$.