Equilibria and entropy changes at boiling temperature

There seem to be two ways of defining boiling temperature.

(1) temperature at which saturated vapor pressure equals external pressure (considering the equilibrium between liquid and its vapor).

(2) temperature at which increase in entropy of the system just balances the decrease in entropy of the surroundings or vice versa (considering thermodynamics). T = enthalpy change / (entropy change of system)

How are these two concepts related so that they give the same temperature? I can see that if saturated vapor pressure equals external pressure and temperature is increased further no equilibrium is possible unless external pressure is also increased and liquid would continue to boil over since Qp = p(liquid(g)) < Kp. I just don’t understand how it so happens that two entropy changes also balance out at this very same temperature.

I see the same issue in other equilibria like decomposition of CaCO3 / Kp = p(CO2)

Thanks.

Reply 1

Arctic Kitten

Because (2) is simply not true? Where have you read that statement? Entropy of vaporisation always increase because the increase in disorder from liquid to gas. Beside, entropy is NOT conserved in an isolated system. So there is no "balance between system entropy and surrounding entropy"

Reply 2

thomas.rhett

Original post by Arctic Kitten

What I wrote I did not quote verbatim from a text. During vaporization, at the boiling temperature, the entropy of the system increases by the same amount as decrease in entropy of the surroundings due to change being endothermic. It has to be that way because when a system is at equilibrium change in total entropy is zero (neither forward nor backward change/reaction is spontaneous), which means change in entropy of the system and surroundings are equal an opposite whichever direction you consider i.e. vaporization or condensation. Given the enthalpy change (latent heat of vaporization in this case) and entropy change of the system you can find the temperature at which water will boil or steam will condense. You can see the calculation in Chemistry: Silberberg & Amateis.