 # Gibbs Pressure Dependence (Review)

Another recent exam problem asking what happens
if you have an isothermal compression – what happens to the Gibbs free energy of a non-ideal
gas? And so we can use a simple relation for the Gibbs free energy, which says that the
Gibbs free energy is equal to VdP minus SdT. If we have an isothermal system, then dT is
equal to zero, therefore dG will just be equal to VdP at constant temperature. Alright, and
so what this basically says is that, because there’s a positive correlation here – the
volume has always got to be a positive number – that if the change in pressure is positive (which
it is in this problem), then the change in Gibbs free energy will also be positive. Alright,
and so the Gibbs free energy will therefore increase. This makes sense intuitively that
the Gibbs free energy we end up relating to the chemical potential of the system, and
as the pressure is increased at constant temperature, we increase the chemical potential so the
likelihood that mass will be transferred from the system is higher when that system is under
high pressure.