Question

The rms velocities of molecules of two gases of equal volume are 2 ms${}^{-1}$ and 3 ms${}^{-1}$ respectively. The ratio of their pressure will be

• A. 3 : 2
• B. 2 : 3
• C. 9 : 4
• D. 4 : 9

Answer 1

The correct option is D 4 : 9

$V_{rms}$(root mean square vgelocity)=$\sqrt{\frac{3PV}{M}}$

Given that volumes of the gases are equal

then ratio of rms velocity becomes $\sqrt{\frac{3P}{M}}$

Assuming the molecular weight of the gases to be equal,we get

$\sqrt{\frac{P_1}{p_2}}=\frac{2}{3}$

$\Rightarrow \frac{P_1}{p_2}=\frac{4}{9}$