Question

The root mean square speeds at STP for the gases $H_2,N_2,O_2$ and $HBr$ are in the order:

• 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. $HBr<O_2<H_2<N_2$

Answer 1

Answer: (A)

$H_2<N_2<O_2<HBr$

We know,

$U_{RMS}=\sqrt{\frac{3RT}{M}}$

So on seeing the equation we can make out that $U_{RMS}$ is directly proportional to temperature and inversely proportional to Molar mass.

In the given options the increasing order of Molar mass is,

$H_2<N_2<O_2<HBr$

So,more the molar mass lesser then $U_{RMS}$

Hence the order of $U_{RMS}$ is,

$HBr<O_2<N_2<H_2$