Consider the van der Waals constants, $a$ and $b$, for the following gases. | Gas | Ar | Ne | Kr | Xe | |-----|----|----|----|----|----| | $\mathrm{a} /\left(\mathrm{atm} \mathrm{dm}^{6} \mathrm{~mol}^{-2}\right)$ | 1.3 | 0.2 | 5.1 | 4.1 | | $\mathrm{~b} /\left(10^{-2} \mathrm{dm}^{3} \mathrm{~mol}^{-1}\right)$ | 3.2 | 1.7 | 1.0 | 5.0 | Which gas is expected to have the highest critical temperature?

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · States of Matter

Consider the van der Waals constants,

a

and

b

, for the following gases.

Gas	Ar	Ne	Kr	Xe
$a / (atm dm^{6} mol^{- 2})$	1.3	0.2	5.1	4.1
$b / (1 0^{- 2} dm^{3} mol^{- 1})$	3.2	1.7	1.0	5.0

Which gas is expected to have the highest critical temperature?

(A)Ar
(B)Xe
(C)Kr✓ Correct
(D)Ne

Answer: (C)

Solution

The critical temperature goes as

T_{c} = \frac{8 a}{27 R b}

, so the gas with the largest

\frac{a}{b}

wins. The ratios are

\frac{1.3}{3.2} \approx 0.41

for Ar,

\frac{0.2}{1.7} \approx 0.12

for Ne,

\frac{5.1}{1.0} = 5.1

for Kr and

\frac{4.1}{5.0} \approx 0.82

for Xe. Krypton's ratio is far the largest, so it has the highest critical temperature.

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option

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