A state function that includes both system and surroundings
We have seen that entropy can describe all types of processes only if we include both the entropy chenage in the system and the sourroundings. The point is that changes in the system may actually have an entropy change Delta Ssys less than zero, but only if there is a compensating entropy change in the surroundings, for which Delta Ssurr greater than zero. In such a case the netropy change in the surroundings must also be greater than that in the system. How can combine these two requirements into one state function? This is the question that led to the definition of the free energy. The free energy contains that reversible entropy change in the system combined with the entropy change in the surroundings described as the heat dissapated by the process taking place in the system. That heat is an enthalpy since processes at the surface of earth take place at constant pressure. Thus, when we combine the two aspects we obtain a function, which can predict the directoin of spontaneous change in a chemical reaction and can also quantify that spontaneous change in the form of an equilibrium constant. The derivation is described in the video below.
The starting point for our derivation of state functions is a constant volume state function. For example, we began with the First Law by defining the internal energy, which is a constant volume state function. Then in the process of examining reversible and less than reverssible paths we obtained a second state function at constant pressure called enthalpy. We actually use enthalpy much more than internal energy in chemistry since most processes take place at constant pressure. The same holds for the Helmholtz free energy that was our start point for the derivation of the free energy. The Helmholtz free energy s the constant volume state function that describes free energy. We can add a work term to the Helmholtz free energy to obtain a constant pressure state function of free energy, the Gibbs free energy. This is descrbied in the next videao.
