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(D) The Van der Waals equation for $1$ mole of a real gas is given by $\left( P + \frac{a}{V_m^2} \right) (V_m - b) = RT$,where $V_m$ is the molar vol

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$\left( P + \frac{n^2 a}{V^2} \right) (V - nb) = nRT$

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(D) The Van der Waals equation for $1$ mole of a real gas is given by $\left( P + \frac{a}{V_m^2} \right) (V_m - b) = RT$,where $V_m$ is the molar volume $(V_m = V/n)$.Substituting $V_m = V/n$ into the equation:$\left( P + \frac{a}{(V/n)^2} \right) (V/n - b) = RT$$\left( P + \frac{n^2 a}{V^2} \right) \left( \frac{V - nb}{n} \right) = RT$Multiplying both sides by $n$ gives the expression for $n$ moles:$\left( P + \frac{n^2 a}{V^2} \right) (V - nb) = nRT$

Van der Waals equation of state is obeyed by real gases. For $n$ moles of a real gas,the expression will be

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