States of Matter - Result Question 27
####27. The root mean square speeds at STP for the gases $H_2, N_2, O_2$ and $HBr$ are in the order: [1991]
(a) $H_2<N_2<O_2<HBr$
(b) $HBr<O_2<N_2<H_2$
(c) $H_2<N_2=O_2<HBr$
(d) $HBr<O_2<H_2<N_2$.
Show Answer
Solution:
(b) $P V=\frac{1}{3} m N u^{2}=\frac{1}{3} M u^{2}$
or $u=\sqrt{3 P V / M}$.
At STP, $u \propto \sqrt{\frac{1}{M}}$
i.e. higher will be the molar mass, lower will be the value of $u _{r m s}$.
Molecular masses of $H_2, N_2, O_2$ and $HBr$ are 2, 28, 32 and 81. Hence the correct order of $u _{r m s}$ will be $HBr<O_2<N_2<H_2$
