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Chap09 solutions

Physical Chemistry

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9 Chemical equilibrium Solutions to exercises Discussion questions E9.1(b) The thermodynamic equilibrium constant involves activities rather than pressures. See eqn 9.18 and Example 9.1. For systems involving gases, the activities are the dimensionless fugacities. At low pressures, the fugacity may be replaced with pressures with little error, but at high pressures that is not a good approximation. The difference between the equilibrium constant expressed in activities and the constant expressed in pressures is dependent upon two factors: the stoichiometry of the reaction and the magnitude of the partial pressures. Thus there is no one answer to this question. For the example of the ammonia synthesis reaction, in a range of pressures where the fugacity coefficients are greater than one, an increase in pressure results in a greater shift to the product side than would be predicted by the constant expressed in partial pressures. For an exothermic reaction, such as the ammonia synthesis, an increase in temperature will shift the reaction to the reactant side, but the relative shift is independent of the fugacity coefficients. The ratio ln( K 2 /K 1 ) depends only on r H . See eqn 6.26. E9.2(b) The physical basis of the dependence of the equilibrium constant on temperature as predicted by the van’t Hoff equation can be seen when the expression r G = r H T r S is written in the form R ln K = − r H /T + r S . When the reaction is exothermic and the temperature is raised, ln K and hence K decrease, since T occurs in the denominator, and the reaction shifts to favor the reactants. When the reaction is endothermic, increasing T makes ln K less negative, or K more positive, and products are favored. Another factor of importance when the reaction is endothermic is the increasing entropy of the reacting system resulting in a more positive ln K , favoring products. E9.3(b) A typical pH curve for the titration of a weak base with a strong acid is shown in Figure 9.1. The stoichiometric point S occurs on the acidic side of pH = 7 because the salt formed by the neutralization reaction has an acid cation. E9.4(b) Buffers work best when S A , that is when the concentrations of the salt and acid are not widely different. An abundant supply of A ions can remove by reaction any H 3 O + supplied by the addition of an acid; likewise an abundant supply of HA can remove by reaction any OH supplied by addition of base. Indicators are weak acids which in their undissociated acid form have one colour, and in their dissociated anion form, another. In acidic solution, the indicator exists in the predominantly acid form (one colour), in basic solution in the predominantly anion form (the other colour). The ratio of the two forms is very pH sensitive because of the small value of p K a of the indicator, so the colour change can occur very rapidly with change in pH.
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