Question

Predict whether the changes in enthalpy, entropy, and free energy will be positive or negative for the boiling of water, and explain your predictions. How does temperature affect the spontaneity of this process?

Answer 1

You are ripping water molecules away from the attractive forces between them, and furthermore you know you need to supply heat to boil water, so clearly dH > 0. You know the process is spontaneous at the boiling point, but only just (meaning if you were removing heat instead of adding it the water would be condensing at the boiling point), so dG = 0. That alone tells you dS > 0, but you can also deduce that from first principles, by realizing you are taking a number of water molecules and greatly increasing the volume in which they have to move around. They used to be tightly packed in the liquid state, now they are free to roam the entire room. Clearly there are a lot more ways to arrange the water molecules in the much bigger volume of the room than the pot of boiling water, so dS > 0.

Given that dG = dH - T dS, and that the facts that make dH > 0 and dS > 0 are not very sensitive to modest changes in temperature, and that when T = Tb we know dG = 0, we can conclude that if T > Tb then dG < 0, so boiling will be spontaneous, and that if T < Tb then dG > 0, so that condensation will be spontaneous.