At high pressure,the van der Waals equation f | vedclass

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Question

(C) The van der Waals equation for $n$ moles of a gas is: $(P + \frac{an^2}{V^2})(V - nb) = nRT$. For $1$ mole of gas $(n=1)$,the equation becomes: $(

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$PV = RT + Pb$

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(C) The van der Waals equation for $n$ moles of a gas is: $(P + \frac{an^2}{V^2})(V - nb) = nRT$. For $1$ mole of gas $(n=1)$,the equation becomes: $(P + \frac{a}{V^2})(V - b) = RT$. Expanding this,we get: $PV - Pb + \frac{a}{V} - \frac{ab}{V^2} = RT$. At high pressure,the volume $V$ is very small,so the term $\frac{a}{V}$ is negligible compared to $P$. Also,the term $\frac{ab}{V^2}$ is very small and can be neglected. Thus,the equation simplifies to: $PV - Pb = RT$,which rearranges to $PV = RT + Pb$.

At high pressure,the van der Waals equation for a real gas reduces to:

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