Regarding reversible phase transition of a real gas According to change in entropy for a reversible phase transition, say from liquid to gas at constant pressure $p$ and temperature $T$
: $\Delta S =\frac{\int dq_p}{T} $  which comes out to be $\Delta S =\frac{\Delta H_{vap}}{T_b}$. This means that this process is spontaneous since Entropy change is positive. But the Gibb's Energy change for this process is $0$. Why is that?
Change in entropy for this process suggests that this is a spontaneous process but Gibb's Energy change suggests it is not. Why does irregularity occur?
$$\Delta S_\mathrm{sys} =\frac{\Delta H_\mathrm{vap}}{T_b}$$
is the entropy change of the system.
$$\frac {\Delta G}{T_\mathrm{b}} = \Delta S_\mathrm{tot} = \Delta S_\mathrm{ext} + \Delta S_\mathrm{sys} = \Delta S_\mathrm{ext} + \frac{\Delta H_\mathrm{vap}}{T_b} = 0$$
is proportional to the total entropy change.