However, it is not the comparison between reaction quotients, Q, and equilibrium constants, K, but the consideration of the rates of reaction that is regarded in the paper as the best way of understanding the effects. This is illustrated with the increase of concentration of one of the reactants. For the effect of temperature, a comparison of the activation energies for the forward and reverse reactions and the knowledge of the quantitative dependence of the (microscopic) rate constants on temperature and activation energy would be needed. But if students must master this knowledge, then certainly they could master the essentials of the second law of thermodynamics--and then the quantitative comparison of Q and K acquires real meaning. In particular, an answer is found to "why chemical systems do not 'like' to have reaction quotients different from K". We feel that it is a pity that students practice calculations based on this comparison without being aware that the evolution of a disturbed system (Q Æ K) is such that the total entropy of system plus surroundings increases until a new maximum (a new equilibrium state) is attained, or, alternatively, that the free energy of the system decreases until a new minimum is reached. This is a fourth level of interpretation for the alterations of equilibrium states, which is at the same time quantitative and closest to full understanding. In line with our defending the inclusion of the entropy concept (and the second law) in secondary school, we propose that this fourth level should not be ignored at that stage.

A minimum approach consists in analyzing the information given for the total entropy variation on going from an equilibrium state 1 to an equilibrium state 2, due to some disturbance. For example, for a reaction A(g) + 3B(g) 2C(g), assumed for convenience to have DH° = 0, and considering the following values for the standard molar entropies

S_A° = 120 J K^-1 mol^-1
S_B° = 100 J K^-1 mol^-1
and
S_C° = 200 J K^-1 mol^-1
(K = 0.090 at 298 K) we have:

1. S°_total = 220 J K^-1 for an initial state with unit partial pressures, p, for both A and B (Q < K);
2. S°_total = 228.5 J K^-1 for the equilibrium state 1 (Q = K);
3. S°_total = 217.8 J K^-1 for a state with the same composition as 1 except that the volume is ¹/₂ (Q < K);
4. S°_total = 218.7 J K^-1 for the equilibrium state 2 (Q = K);
5. S°_total < 218.7 J K^-1 for any system composition beyond equilibrium state 2 (Q > K).

An additional step is to understand how these values are calculated. This means mastering the expression S_i = S_i°- Rln(p_i) for an ideal gas. It is this same expression that enables both an interpretation of Q Æ K and a qualitative prediction of the direction in which the system composition is changed. In fact, maximum total entropy, or minimum free energy, G, occurs when the free energy difference DG = DG° + RTlnQ is zero (that is, Q = K, with DG° = -RT ln K), DG being 2G_C - (G_A + 3G_B) calculated for the partial pressures being considered. If DG becomes negative or positive, Q must increase or decrease (a shift according to Æ or ¨). Instead of DG > 0 or DG < 0, we can consider DS_total < 0 or DS_total > 0, respectively. Qualitatively, we can see that a decrease in volume leads to an identical decrease in the molar entropies of all the (gaseous) components of the system, with a larger effect on S_A + 3S_B than on 2S_C (that is, DS_total < 0). The only way of DS_total becoming zero (total entropy maximum) is a change in the sense Æ.

This approach requires a little more discussion when temperature effects are dealt with and DH° ≠ 0.

Literature Cited

1. Tyson, L.; Treagust, D. F.; Bucat, R. B. J. Chem. Educ. 1999, 76, 554.

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