JEE Advanced 2022 Paper 1 · Chemistry · Chemical Kinetics · hard

(s) about gases (all gases at the same temperature T unless stated).

One or more options correct

Choose the correct statement(s) about gases (all gases at the same temperature

T

unless stated).

A. The ratio of the most probable speed of $\mathrm{CH_4}$ to the root-mean-square speed of $\mathrm{SO_2}$ is about $1.63$
B. A van der Waals gas has $Z=1$ at all pressures when it is at its Boyle temperature
C. The Boyle temperature of a van der Waals gas is $T_B=\dfrac{2a}{Rb}$
D. At the critical point the compressibility factor of a van der Waals gas is $0.375$ , and its value depends on the constants $a$ and $b$

Show answer and solution

Answer: A

A is correct:

u_{mp}=\sqrt{2RT/M}

and

u_{rms}=\sqrt{3RT/M}

, so the ratio is

\sqrt{\dfrac{2/16}{3/64}}=\sqrt{8/3}=1.633

(computed numerically). B is incorrect: at

T_B

the second virial coefficient vanishes, so

Z\to1

only in the limit of low pressure; at finite pressure higher-order terms (and the repulsive volume term) make

Z

differ from

1

. C is incorrect: from

Z\approx1+\dfrac{1}{V_m}\left(b-\dfrac{a}{RT}\right)

the second virial coefficient vanishes at

T_B=\dfrac{a}{Rb}

; the expression

2a/Rb

is not correct (note

T_c=\tfrac{8a}{27Rb}

). D is incorrect: at the critical point

Z_c=\dfrac{P_cV_c}{RT_c}=\dfrac38=0.375

, a pure number independent of

a

and

b

. Only A is correct.

Original question written in the JEE Advanced 2022 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake