Question

Wonderwall equation including correction for pressure and volume unit of wonderwall forces

Answer 1

The van der Waals equation for real gases is stated as follows:

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

For the coefficient b, we can reason out that more the number of molecules, the more volume will be occupied by the molecules (in turn reducing the free space available for the motion of the molecules). It must be linearly proportional to nbecause b represents the sum of the excluded volume of each molecule in a mole. Therefore, we must multiply it by n to obtain the total excluded volume.

The coefficient a is said to represent the strength of the intermolecular attractive forces. Intuitively, we can say that it must be proportional to the number of molecules per unit volume. The more the number of molecules around a molecule, the more attractive forces it shall feel.

Therefore, the correction term for pressure must be proportional to \frac{n}{V}. But we know that in reality, it is proportional to the square of \frac{n}{V}.

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