Question

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
$b/(10^{-2}\,dm^{3}\,mol^{-1}$	3.2	1.7	1.0	5.0

Which gas is expected to have the highest critical temperature?

• A. Kr
• B. Ne
• C. Ar
• D. Xe

Answer 1

Answer: (A)

$T_c \, = \, \frac{8a}{27Rb}$
Greater value of $\frac{a}{b} \, \Rightarrow $ higher is 'T$_c$'
Gas $ \, \, \, \, \, \, \, \, \, \, a/b$
Ar $ \, \, \, \, \, \, \, \, \, \, \frac{1.3}{3.2} \, = \, 0.406$
Ne $ \, \, \, \, \, \, \, \, \, \, \, \, \frac{0.2}{1.7} \, = \, 0.118$
Kr $ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac{5.1}{1} \, = \, 5.1$
Xe $ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac{4.1}{5} \, = \, 0.82$
$\therefore \, T_c$ has order : $Kr > Xe > Ar > Ne$