For a real gas, the chemical potential is given by

We know the property relation $$dG=VdP-sdT$$     for constant temperature $$dT=0$$
For an ideal gas
$$\eqalign{ & dG = VdP \cr & dG = \frac{{RT}}{P}dP \cr & \Rightarrow dG = RTdlnP \cr} $$
For a real gas also if we want to describe the relation in the same functional form we express it as $$dG = RTd \,ln\, f \Rightarrow d\mu = RTd \,ln\, f$$       where $$f=$$ fugacity, that means we buried the entire non ideality in this term fugacity. The term fugacity is also called as effective pressure.