If Z is a compressibility factor,the van der | vedclass

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(B) The van der Waals equation for $1 \ mol$ of a gas is given by:$(P + \frac{a}{V^2})(V - b) = RT$At low pressure,the volume $V$ is very large,so $V

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

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(B) The van der Waals equation for $1 \ mol$ of a gas is given by:$(P + \frac{a}{V^2})(V - b) = RT$At low pressure,the volume $V$ is very large,so $V >> b$. Therefore,the term $(V - b)$ can be approximated as $V$.The equation simplifies to:$(P + \frac{a}{V^2})V = RT$Expanding the equation:$PV + \frac{a}{V} = RT$Rearranging to solve for $PV$:$PV = RT - \frac{a}{V}$Dividing both sides by $RT$ to express in terms of the compressibility factor $Z = \frac{PV}{RT}$:$\frac{PV}{RT} = 1 - \frac{a}{VRT}$Thus,$Z = 1 - \frac{a}{VRT}$.

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

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