Consider ideal and real gases.

One or more options correct

Consider ideal and real gases. Choose the correct statement(s).

A. An equimolar mixture of $\mathrm{H_2}$ and $\mathrm{O_2}$ effuses through a pin-hole into vacuum; the first effusate has mole ratio $\mathrm{H_2}:\mathrm{O_2}=4:1$ .
B. At the same temperature, the average translational kinetic energy per molecule of $\mathrm{He}$ is twice that of $\mathrm{H_2}$ .
C. At the same temperature and pressure, the density of $\mathrm{CH_4}$ is half that of $\mathrm{O_2}$ (both treated as ideal).
D. For a van der Waals gas at low pressure where attractive forces dominate, the compression factor $Z$ is greater than $1$ .

Show answer and solution

Answer: A, C

(A) True. Effusion rate is inversely proportional to

\sqrt{M}

, so the rate ratio is

\sqrt{32/2}=4

. In an equimolar mixture the first effusate is therefore enriched in

\mathrm{H_2}

in the ratio

4:1

.
(B) False. Average translational kinetic energy per molecule is

\tfrac32k_BT

, independent of the gas, so

\mathrm{He}

and

\mathrm{H_2}

have equal values.
(C) True.

\rho=PM/RT

, so at fixed

T,P

the ratio is

16/32=0.5

.
(D) False. When attraction dominates, the gas is more compressible than ideal and

Z=1-\dfrac{a}{RTV_m}+\ldots<1

;

Z>1

arises when repulsion (the

b

term) dominates at high pressure.
Correct options: (A) and (C). Numerical check:

\sqrt{32/2}=4.0

and

16/32=0.5

Original question written in the JEE Advanced 2022 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake