If $Z$ is a compressibility factor, van der Waals equation at low pressure can be written as :

Z = 1 - \frac{P b}{R T}

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Z = 1 + \frac{P b}{R T}

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Z = 1 + \frac{R T}{P b}

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Z = 1 - \frac{a}{V R T}

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Solution

The correct option is B $Z = 1 - \frac{a}{V R T}$
For one mol gas :

$[P + \frac{a}{V^{2}}] [V - b] = R T$

At low pressure, the volume will be high $∴ (V - b) \approx V$

$P V + \frac{a}{V} = R T$

$\frac{P V}{R T} = 1 - \frac{a}{V R T}$

$Z = 1 - \frac{a}{V R T}$

Hence, the correct option is D.

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[p + \frac{a}{V^{2}}] V = R T

At low pressure, van der Waal’s equation for 1 mol can be represented as

[p + \frac{a}{v^{2}}] V = R T

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