# Anomaly in van der Waals constants of noble gases

In van der Waals equation for a real gas, the equation is

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

where $$P$$ is the pressure of the real gas, $$n$$ is the number of moles of the gas, $$R$$ is the ideal gas constant, $$T$$ is the temperature, $$a$$ is a constant to correct for the intermolecular forces of attraction, and $$b$$ is a constant to correct for the size of the molecules.

It follows that gases with large intermolecular forces have large $$a$$ values and gases with large molecular size have large $$b$$ values.

Below is a table of the $$a$$ and $$b$$ values of the ideal gases:

$$\begin{array}{ccc} \hline \text{gas} & a & b \\ \hline \ce{He} & 0.0341 & 0.0237 \\ \ce{Ne} & 0.211 & 0.0171 \\ \ce{Ar} & 1.35 & 0.0322 \\ \ce{Kr} & 2.32 & 0.0398 \\ \ce{Xe} & 4.19 & 0.0511 \\ \hline \end{array}$$

Why is the $$b$$ value for helium larger than the $$b$$ value for neon even though helium's atomic radius is smaller than that of neon? Does it maybe have to do with helium's small size, and thus higher electron density surrounding the nucleus, creating more repulsions with other helium atoms?