The compressibility factor for a real gas at high pressure is :

The compressibility factor $$Z$$ is defined as $$Z = \frac{PV}{RT}$$ for one mole of a gas.

For a real gas we use the van der Waals equation
$$(P + \frac{a}{V^{2}})(V - b) = RT$$

At very high pressure the molar volume $$V$$ becomes very small, so the term $$\frac{a}{V^{2}}$$ (which accounts for intermolecular attractions) is negligible compared with $$P$$. Retaining only the finite-size correction, the equation simplifies to
$$P(V - b) \approx RT$$

Expanding: $$PV - Pb = RT$$ which gives
$$PV = RT + Pb$$

Divide by $$RT$$ to obtain the compressibility factor:
$$Z = \frac{PV}{RT} = 1 + \frac{Pb}{RT}$$

Thus, at high pressure the compressibility factor of a real gas exceeds unity by the amount $$\frac{Pb}{RT}$$.

Option C which is: $$1 + \frac{pb}{RT}$$