Reaction Equilibrium

Author: John Hutchinson

Having developed a thermodynamic understanding of phase equilibrium, it proves to be even more useful to examine the thermodynamic description of reaction equilibrium to understand why the reactants and products come to equilibrium at the specific values that are observed.

Recall that DG=DH-TDS<0 for a spontaneous process, and DG=DH-TDS=0 at equilibrium. From these relations, we would predict that most (but not all) exothermic processes with DH<0 are spontaneous, because all such processes increase the entropy of the surroundings when they occur. Similarly, we would predict that most (but not all) processes with DS>0 are spontaneous.

We try applying these conclusions to synthesis of ammonia

N2(g)+3 H2(g) 2 NH3 (g)

[6]

at 298K, for which we find that DS° = -198 J/molK. Note that DS°<0 because the reaction reduces the total number of gas molecules during ammonia synthesis, thus reducing W, the number of ways of arranging the atoms in these molecules. DS°<0 suggests that equation 6 should not occur at all. However, DH° = -92.2 kJ/mol. Overall, we find that DG° = -33.0 kJ/mol at 298K, which according to equation 3 suggests that equation 6 is spontaneous.

Given this analysis, we are now pressed to ask, if equation 6 is predicted to be spontaneous, why does the reaction come to equilibrium without fully consuming all of the reactants? The answer lies in a more careful examination of the values given: DS°, DH°, and DG° are the values for this reaction at standard conditions, which means that all of the gases in the reactants and products are taken to be at 1 atm pressure. Thus, the fact that DG°<0 for equation 6 at standard conditions means that, if all three gases are present at 1 atm pressure, the reaction will spontaneously produce an increase in the amount of NH₃. Note that this will reduce the pressure of the N₂ and H₂ and increase the pressure of the NH₃. This changes the value of DS and thus of DG, because as we already know the entropies of all three gases depend on their pressures. As the pressure of NH₃ increases, its entropy decreases, and as the pressures of the reactants gases decrease, their entropies increase. The result is that DS becomes increasingly negative. The reaction creates more NH₃ until the value of DS is sufficiently negative that DG = DH-TDS = 0.

From this analysis, we can say by looking at DS°, DH°, and DG° that, since DG°<0 for equation 6, reaction equilibrium results in production of more product and less reactant than at standard conditions. Moreover, the more negative DG° is, the more strongly favored are the products over the reactants at equilibrium. By contrast, the more positive DG° is, the more strongly favored are the reactants over the products at equilibrium.