If Z is the compressibility factor,then for 1 | vedclass

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(D) The van der Waals equation for $n \, 	ext{moles}$ of a gas is $\left(P + \frac{n^2 a}{V^2}ight)(V - nb) = nRT$.For $1 \, 	ext{mole}$ $(n=1)$,t

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

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(D) The van der Waals equation for $n \, 	ext{moles}$ of a gas is $\left(P + \frac{n^2 a}{V^2}ight)(V - nb) = nRT$.For $1 \, 	ext{mole}$ $(n=1)$,the equation is $\left(P + \frac{a}{V^2}ight)(V - b) = RT$.Expanding this,we get $PV - Pb + \frac{a}{V} - \frac{ab}{V^2} = RT$.At low pressure,the volume $V$ is very large,so the terms $\frac{b}{V}$ and $\frac{ab}{V^2}$ are negligible.The equation simplifies to $PV + \frac{a}{V} = RT$.Dividing the entire equation by $RT$,we get $\frac{PV}{RT} + \frac{a}{VRT} = 1$.Since the compressibility factor $Z = \frac{PV}{RT}$,we can write $Z + \frac{a}{VRT} = 1$.Therefore,$Z = 1 - \frac{a}{VRT}$.

If $Z$ is the compressibility factor,then for $1 \, \text{mole}$ of a real gas,the van der Waals equation at low pressure can be written as:

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