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Example: Two moles of an ideal equimolar A-B gas mixture (designated No. 1) are mixed with three moles of a similar mixture containing 20 mole percent of A (No. 2). Both are at the same temperature. What is the entropy change when these two mixtures are combined to form mixture

The method is to start from the pure components (1.6 moles of A and 3.4 moles of B) and prepare solutions 1, 2, and 3 from them. The difference in the mixing entropies is the desired result.

The pure components are shown in the middle two boxes; the final mixture is the large top box. At the bottom are the two starting mixtures.

The entropy gains in preparing the two initial solutions from the pure components are: ASmix1 = -R[(1.0)ln(0.5) + (1.0)ln(0.5)] = 1.39R ASmix2 = -R[(0.6)ln(0.2) + (2.4)ln(0.8)] = 1.50R The mole fraction of A in mixture 3 is 0.32 and its mixing entropy is:

ASmix3 = -R[(1.6)ln(0.32) + (3.4)ln(0.68)] = 3.13R The entropy change due to combining mixture 1 and 2 to form mixture3 is: ASmix = ASmix3 - ASmix1 - ASmix2 = 0.24R = 2.0 J/K

Inclusion of the entropy of mixing in situations with components at different initial conditions (pressure and/or temperature) is the topic of problem 7.1.

Although the mixing-entropy formula was derived for ideal solutions, it is also present in mixtures of species that behave nonideally (see problems 7.11 and 7.17). Other exercises in mixing entropy are problems 7.5/7.6 and 7.18/7.19.