# Given the enthalpy and entropy change of a natural phase transition, derive an expression for the normal boiling point of any substance? Hint: consider that the change in Gibbs' free energy is zero for two phases in equilibrium.

##### 1 Answer

Jul 13, 2017

The hint tells you exactly what to do. Consider the relationship between the Gibbs' free energy, enthalpy, and entropy:

#DeltaG = DeltaH - TDeltaS#

At **equilibrium** (more specifically, *phase equilibrium* at constant temperature and pressure!),

#DeltaG_(vap) = 0 = DeltaH_(vap) - T_bDeltaS_(vap)#

#=> color(blue)(T_b = (DeltaH_(vap))/(DeltaS_(vap)))# ,where

#T_b# is the boiling point.

That is, you are somewhere on the green curved dotted line on a phase diagram:

Once you obtain the temperature in