The rate of effusion of two gases 'A' and 'B' under identical conditions of temperature and pressure are in the ratio of 2 : 1. What is the ratio of rms velocity of their molecules if temperature of A and B are in ratio 2: 1?

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$2 \sqrt{2} : 1$

$2 : 1$

$1 : \sqrt{2}$

$\sqrt{2} : 1$

answer is D.

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Detailed Solution

$\begin{array}{l} \frac{2}{1} = \sqrt{\frac{M_{B}}{M_{A}}} \Rightarrow \frac{M_{B}}{M_{A}} = \frac{4}{1} \\ U_{rms} \propto \sqrt{\frac{T}{M}} \\ \frac{U_{A}}{U_{B}} = \sqrt{\frac{T_{A}}{T_{B}} \times \frac{M_{B}}{M_{A}}} = \frac{2 \sqrt{2}}{1} \end{array}$

Thus, the rate of effusion of two gases 'A' and 'B' is $2 \sqrt{2} : 1$ .

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