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Liquefaction of Gases and Critical Constants

The value of ...

Question

The value of $\frac{P_{c} V_{c}}{R T_{c}}$ is

A

\frac{P_{c} V_{c}}{R T_{c}} = \frac{3}{8}

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B

\frac{P_{c} V_{c}}{R T_{c}} = \frac{5}{8}

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C

\frac{P_{c} V_{c}}{R T_{c}} = \frac{1}{2}

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D

None of these

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Solution

The correct option is A $\frac{P_{c} V_{c}}{R T_{c}} = \frac{3}{8}$
$V_{c} = 3 b, P_{c} = \frac{a}{27 b^{a}} a n d T_{c} = \frac{8 a}{27 R b}$
$\frac{P_{c} V_{c}}{R T_{c}} = \frac{\frac{a}{27 b^{2}} \times 3 b}{R \times \frac{8 b}{27 R b}} = \frac{\frac{a}{9 b}}{\frac{8 a}{27 R b}} = \frac{\frac{a}{9 b}}{\frac{8 R a}{27 b}}$
$\frac{P_{c} V_{c}}{R T_{c}} = \frac{a}{9 b} \times \frac{27 b}{8 a} = \frac{3}{8} = 0.375$

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