Correction Term for Attractive Forces in Real Gas Van der Waals Equation

The van der Waals equation of state for $n$ moles of a real gas is written as:
$\left( P + \frac{an^2}{V^2} \right)(V - nb) = nRT$

In this equation:

1. Pressure Correction: Due to intermolecular attractive forces between gas molecules, the molecules striking the walls of the container experience an inward pull from neighboring molecules in the bulk. Consequently, the actual measured pressure ($P$) of a real gas is lower than the ideal pressure ($P_{\text{ideal}}$) that the gas would exert in the absence of attractive forces.

   To account for this reduction in pressure, a correction term (often called the internal pressure) is added to the measured pressure:
   $P_{\text{ideal}} = P + p_{\text{corr}}$

   The magnitude of this inward pull depends on:

   • The number of molecules striking the container walls per unit volume ($\propto \frac{n}{V}$)
   • The number of attracting molecules in the interior per unit volume ($\propto \frac{n}{V}$)

   Therefore, the pressure correction term is proportional to the square of the molar density:
   $p_{\text{corr}} \propto \left(\frac{n}{V}\right)^2 \implies p_{\text{corr}} = \frac{an^2}{V^2}$
   where $a$ is the van der Waals constant that measures the magnitude of the intermolecular attractive forces.

2. Volume Correction: The term $nb$ accounts for the finite volume occupied by the gas molecules (co-volume or excluded volume), correcting the effective free volume available for molecular motion to $(V - nb)$.

Thus, the term that corrects for the attractive forces present in a real gas is $\frac{an^2}{V^2}$.

Therefore, the correct option is B.