States of Matter 1 Question 67
67. At $400 \mathrm{~K}$, the root mean square (rms) speed of a gas $X$ (molecular weight $=40$ ) is equal to the most probable speed of gas $Y$ at $60 \mathrm{~K}$. The molecular weight of the gas $Y$ is
(2009)
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Answer:
Correct Answer: 67. (4)
Solution:
- Given,
$$ \begin{array}{llrl} \text { Given, } & u_{\mathrm{rms}} & =u_{\mathrm{mps}} \ \Rightarrow & & \sqrt{\frac{3 R T}{M(X)}}=\sqrt{\frac{2 R T}{M(Y)}} \ \Rightarrow & \frac{3 R \times 400}{40} & =\frac{2 R \times 60}{M(Y)} \ \Rightarrow & & M(Y) & =4 \end{array} $$
