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NEET levelSingle correct optionDifficulty 1 of 3rg122

The van der Waals equation for $n$ moles of a gas is

A $(P + \frac{a}{V ^{2}}) (V - b) = n RT$
B $(P + \frac{a n ^{2}}{V ^{2}}) (V - nb) = n RT$
C $(P - \frac{a n ^{2}}{V ^{2}}) (V + nb) = n RT$
D $(P + \frac{an}{V}) (V - b) = n RT$

Answer: B

The pressure correction scales with the square of the number density, giving

a n^{2} / V^{2}

, and the excluded volume scales with

n

, giving

nb

. Both corrections are added or subtracted so as to recover the ideal pressure and free volume.

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