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Question

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


A
Z=1PbRT
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B
Z=1+PbRT
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C
Z=1+RTPb
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D
Z=1aVRT
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Solution

The correct option is B $$Z = 1 - \dfrac {a}{VRT}$$
For one mol gas :

$$\left [P + \dfrac {a}{V^{2}}\right ] [V - b] = RT$$

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

$$PV + \dfrac {a}{V} = RT$$

$$\dfrac {PV}{RT} = 1 - \dfrac {a}{VRT}$$

$$Z = 1 -\dfrac {a}{VRT}$$

Hence, the correct option is D.

Chemistry

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