Question

The rate of effusion of two gasesa a and b under identical condition of temperature and pressure are in ratio of $2:1$. What is the ratio of rms velocity of their molecules if $T_a$ and $T_b$ are in ratio of $2:1$?

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

Answer 1

Answer: (C)

$2\sqrt{2}:1$

$\frac{rat{e}_a}{rat{e}_b}=\sqrt{\frac{M_b}{M_a}}$ & ${}^{\nu }rms=\sqrt{\frac{3RT}{M}}$

$\Rightarrow \frac{{}^{\nu }rm{s}_a}{{}^{\nu }rm{s}_b}=\sqrt{\frac{T_a/M_a}{T_b/M_b}}$

$=\sqrt{\frac{T_a}{T_b}\times \frac{M_b}{M_a}}$

$=\sqrt{\frac{T_a}{T_b}\times \frac{rat{e}_a}{rat{e}_b}}$

$=\sqrt{\frac{2}{1}\times \frac{2}{1}}$

$=2\sqrt{2}:1$