Question

What can you comment on the chemical potentials when the plane surface of the liquid lies in equilibrium with the vapor.

Please answer in detail.

Answer 1

When the liquid is in thermal equilibrium with its vapor, the molecules may evaporate or condense at a constant temperature and pressure.

we know that

now if the external work done by a body in a reversible isothermal process is equal to the decrease in helmoholtz free energy.

now the only external work done duering evaporation is work of expansion so da=0 which implies that dg=0.

when dG is =0 ==> G is constant which implies that the chemical potential of the two phases must be equal.