Question

At 400 K, the root mean square (r.m.s) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is:

• A. 3
• B. 4
• C. 10
• D. 2

Answer 1

The correct option is B 4

$V_{rms}=V_{mp}$

$\sqrt{\frac{3RT}{M_X}}=\sqrt{\frac{2RT}{M_Y}}$

$M_Y=\frac{2\times 60}{3\times 400}\times M_X$

$M_Y=\frac{2\times 60\times 40}{3\times 400}$

$M_Y=4$

Hence, the correct answer is option $\text{B}$.