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

Engineering

Chemistry

Vander Waal Gas and compressibility Factor

Question

$Z = 1 + \frac{Pb}{RT}$

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

$Z = 1 + \frac{RT}{Pb}$

$Z = 1 - \frac{Pb}{RT}$

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$(P + \frac{a}{V^{2}}) (v - b) = RT$

at low pressure

V will be very high.

$∴$ Volume correction can be neglected.

${(P + \frac{a}{V^{2}})}^{V} = RT$

$∴ PV = RT - \frac{a}{V}$

$∴ Z = 1 - \frac{a}{VRT}$