At relatively high pressure, vander waals' equation reduces to:

P V = R T

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P V = R T + \frac{a}{V}

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P V = R T + P b

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P V = R T - \frac{a}{V^{2}}

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Solution

The correct option is A $P V = R T + P b$
Van der waal equation is,
$(P + \frac{a n^{2}}{V}) (V - n b) = n R T$ .... for n moles of gas
For 1 mole, the equation becomes,
$(P + \frac{a}{V}) (V - b) = n R T$
At highpressure, the $P_{c o r r e c t i o n}$ = negligible but volume correction cannot be regarded as negligible
$P (V - b) = R T$ or $P V - P b = R T$
or $P V = R T + P b$
So, option $C$ is correct.

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Similar questions

Column A	Column B
(A) High pressure	(i) $P V = R T + P b$
(B) Low pressure	(ii) $P V = R T - \frac{a}{V}$
(C) $P \to 0$	(iii) $P V = R T$
(D) Neither $a$ nor $b$ is negligible	(iv) $(P + \frac{a}{V^{2}}) (V - b) = R T$

\frac{R T}{P V}

\frac{R T}{P V}

In a gas equation, PV = RT, V refers to the volume of:

P V = R T

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