Question

If the $V_{rms}$ is $30R^{1/2}$ at $27^{\circ }C$ then calculate the molar mass of gas in kilogram :

• A. 1
• B. 2
• C. 4
• D. 0.001

Answer 1

Answer: (D)

$v_{rms}=\sqrt{\frac{3PV}{M}}=\sqrt{\frac{3RT}{M}}$
Given, $T=27^{\circ }C=273+27=300K$
$M=$ molar mass
$=v_{rms}=30R^{1/2}$ On substituting the values we get
$30R^{1/2}=\sqrt{\frac{3R\times 300}{M}}$
On squaring both sides, we get
$30\times 30\times R=\frac{3\times R\times 300}{M}$
or $M=\frac{3\times R\times 300}{30\times 30\times R}$