Question

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

• A. $6:3:2$
• B. $1:2:3$
• C. $1:\sqrt{2}:\sqrt{3}$
• D. $\sqrt{3}:\sqrt{2}:1$

Answer 1

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

$u_{\text{rms}}^2=\frac{3RT}{M}$
$u_A:u_B:u_C=1:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}$
$u_A^2:u_B^2:u_C^2=1:\frac{1}{2}:\frac{1}{3}$
$\frac{1}{M_A}:\frac{1}{M_B}:\frac{1}{M_C}=1:\frac{1}{2}:\frac{1}{3}$
Since RMS velocity and Molecular mass are inversely related.
$M_A:M_B:M_C=1:2:3$