Chemical Education Today
Letters The Complexity of Teaching and Learning Chemical Equilibrium In their interesting paper, Tyson et al. (1) discuss the “three levels of explanation” that can be used at the secondary school level to predict what will occur when reaction mixtures that are equilibrium are disturbed: Le Châtelier’s principle, the equilibrium law (reaction quotient versus equilibrium constant), and the changes in the (microscopic) rates for the forward and reverse reactions. The first and the last are of a qualitative nature, whereas the second one enables quantitative predictions and interpretations. 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 → 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 ∆H ° = 0, and considering the following values for the standard molar entropies SA° = 120 J K᎑1 mol ᎑1 and
SB° = 100 J K᎑1 mol ᎑1
SC° = 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 t°otal < 218.7 J K᎑1 for any system composition beyond equilibrium state 2 (Q > K ). 1560
An additional step is to understand how these values are calculated. This means mastering the expression S i = Si° – R ln(pi) for an ideal gas. It is this same expression that enables both an interpretation of Q → 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 ∆G = ∆G ° + RT ln Q is zero (that is, Q = K, with ∆G ° = ᎑RT ln K ), ∆G being 2GC – (GA + 3GB) calculated for the partial pressures being considered. If ∆G becomes negative or positive, Q must increase or decrease (a shift according to → or ←). Instead of ∆G > 0 or ∆G < 0, we can consider ∆Stotal < 0 or ∆Stotal > 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 SA + 3SB than on 2SC (that is, ∆Stotal < 0). The only way of ∆Stotal becoming zero (total entropy maximum) is a change in the sense →. This approach requires a little more discussion when temperature effects are dealt with and ∆H ° ≠ 0. Literature Cited 1. Tyson, L.; Treagust, D. F.; Bucat, R. B. J. Chem. Educ. 1999, 76, 554. João C. M. Paiva Secondary School Penacova, Portugal
[email protected] Victor M. S. Gil Department of Chemistry University of Coimbra, Portugal
[email protected] The author replies: We appreciate the interest shown in our article by colleagues Paiva and Gil and accept their comments that a fourth level of interpretation for the alterations of equilibrium states provides a valid thermodynamic approach to the study of chemical equilibrium. We also acknowledge that this thermodynamic approach may encourage a deeper understanding of the topic. However, the considerations of Paiva and Gil are beyond the scope of Australian high school chemistry syllabuses and we could not imagine this thermodynamic approach being used in secondary school. The concern of our paper was an investigation into existing secondary school chemistry teaching and learning practices. Consequently, our article referred to the syllabuses used in local schools and also throughout Australia; it did not examine all possible approaches to this important topic in the chemistry curriculum. David Treagust (On behalf of Louise Tyson and Bob Bucat) Science and Mathematics Education Centre Curtin University of Technology Perth, WA 6845, Australia
Journal of Chemical Education • Vol. 77 No. 12 December 2000 • JChemEd.chem.wisc.edu
