Question

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

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

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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