States of Matter 1 Question 4
4. Consider the van der Waals’ constants, $a$ and $b$, for the following gases.
| Gas | $\mathbf{A r}$ | $\mathbf{N e}$ | $\mathbf{K r}$ | $\mathbf{X e}$ |
|---|---|---|---|---|
| $a /\left(\mathrm{atm} \mathrm{dm}^{6} \mathrm{~mol}^{-2}\right)$ | 1.3 | 0.2 | 5.1 | 4.1 |
| $b /\left(10^{-2} \mathrm{dm}^{3} \mathrm{~mol}^{-1}\right)$ | 3.2 | 1.7 | 1.0 | 5.0 |
Which gas is expected to have the highest critical temperature?
(2019 Main, 9 April I)
(a) $\mathrm{Kr}$
(b) $\mathrm{Xe}$
(c) $\mathrm{Ar}$
(d) $\mathrm{Ne}$
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Solution:
- Critical temperature is the temperature of a gas above which it cannot be liquefied what ever high the pressure may be. The kinetic energy of gas molecules above this temperature is sufficient enough to overcome the attractive forces. It is represented as $T_{c}$.
$$ T_{c}=\frac{8 a}{27 R b} $$
For Ar,
$$ T_{c}=\frac{8 \times 1.3}{27 \times 8.314 \times 3.2}=0.0144 $$
For $\mathrm{Ne}$,
$$ T_{c}=\frac{8 \times 0.2}{27 \times 8.314 \times 1.7}=0.0041 $$
For $\mathrm{Kr}$,
$$ T_{c}=\frac{8 \times 5.1}{27 \times 8.314 \times 1.0}=0.18 $$
For Xe,
$$ T_{c}=\frac{8 \times 4.1}{27 \times 8.314 \times 5.0}=0.02 $$
The value of $T_{c}$ is highest for $\mathrm{Kr}$ (Krypton).
