HW Sol#8

HW Sol#8 - Chemistry 131 Fall 2007 Solutions to Homework No...

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Chemistry 131, Fall 2007 Solutions to Homework No. 8 Problem 1. See Levine, problem 9.33. (a) True. Since x i < 1 for each component i in solution and since ln x i < 0 when x i < 1, then Δ mix G = RT i n i ln x i < 0, at constant T and P (Levine eq. 9.44). (b) True. The formation of a solution is an irreversible process, for which Δ S univ > 0 (Levine eq. 3.39). Since Δ G = - Δ S univ /T at constant T and P (Levine eq. 4.21), then Δ mix G < 0 for the formation of any solution. (c) False. For an ideal solution, Δ mix H = 0 (Levine eq. 9.47) and Δ mix S = - R i n i ln x i (Levine eq. 9.46). Therefore, Δ mix S 6 = Δ mix H/T . (d) False. The condition for phase equilibrium (Levine eq. 4.88) pertains to each individual component i in the system, e.g., a solution, not to the system as a whole. Therefore, for equilibrium between a solution and its vapor, the chemical potential of each substance in the solution must equal (or be less than, if the substance is non-volatile) the chemical potential of the vapor of that substance. (e) False. The relation between x v i and x l i for an ideal solution is given by Raoult’s law, x v i P = x l i P * i (Levine eq. 9.52). Therefore, in general x v i 6 = x l i . (f) True (Levine eq. 9.55). Follows from V i = ± ∂μ i ∂P ² T,n j (Levine eq. 9.31) and from μ i = μ * i + RT ln x i (Levine eq. 9.41). Problem 3. See Levine, problem 9.40. V = X i n i V i (Levine eq. 9.16) = X i n i V * m ,i (Levine eq. 9.55) = X i V i (Levine eq. 1.4) = X i w i ρ i (Levine eq. 1.2) , w = X i w i , ρ = w V = i w i i w i i , where w i and w represent the masses of component i and of the whole solution, respectively. Note that equal masses of benzene and toluene are in used in this problem, so the last expression simplifies to: ρ = 2 ³ X i 1 ρ i ! - 1 = 2 ´ (0 . 8790 g / cm 3 ) - 1 + (0 . 8668 g / cm 3 ) - 1 µ - 1 = 0 . 8729 g / cm 3 . Problem 5.
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This note was uploaded on 05/22/2008 for the course CHEM 131 taught by Professor Lindenberg during the Fall '08 term at UCSD.

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HW Sol#8 - Chemistry 131 Fall 2007 Solutions to Homework No...

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