Question

If the $V_{rms}$ is $30\,R^{1/2}$ 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)

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