Question

If $U_{RMS}$ of a gas is 30$R^{1/2}$ ${ms}^{-1}$ at ${27}^{\circ }C$ then the molar mass of gas is :

• A. $0.001$ $kg/mol$
• B. $0.02$ $kg/mol$
• C. $0.003$ $kg/mol$
• D. $1$ $kg/mol$

Answer 1

Answer: (D)

$U_{rms}=\sqrt{\frac{3RT}{M}}$

Given, $U_{rms}=30R^{1/2}$

$⟹30R^{1/2}=\sqrt{\frac{3R\left(300\right)}{M}}$

$⟹$ M = 1kg/mol

Hence, Option "D" is the correct answer.