Describe the van der Waals equation and explain why it corrects the ideal gas law for real gases.

• A. (P + a(n/V)^2)(V - nb) = nRT
• B. (P + a(n/V^2))(V - nb) = nRT
• C. (P - a(n/V)^2)(V - nb) = nRT
• D. The van der Waals equation is PV = nRT.

Answer: (A)

Real gases don’t follow the ideal gas law exactly because molecules have finite size and exert intermolecular attractions. The van der Waals approach introduces corrections to account for these effects: the pressure term is increased by a(n/V)^2 to reflect the reduction in effective pressure due to attractions, and the volume term is reduced to V − nb to account for the space taken up by the molecules themselves. Putting these together gives (P + a(n/V)^2)(V − nb) = nRT. If you solve for P, you get P = nRT/(V − nb) − a(n/V)^2, showing how the first part drives pressure up as free volume decreases, while the second part subtracts pressure due to attractive forces.

The other forms either misuse the dependence on n and V, flip the sign of the correction, or revert to the ideal gas law entirely, which is why this equation is the correct one.