Exam3 2009 - UNIT 4 - PHYSICAL CHEMISTRY 158B Unit 3...

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PHYSICAL CHEMISTRY 158B: Unit 3 mid-term SAMPLE exam This exam will last approximately 1 hour. Answer all the questions. Useful constants: N A = 6.0221367 × 10 23 mol -1 , R = 8.314510 J K -1 mol -1 = 0.0820578 dm 3 atm K -1 mol -1 , 0.0831451 dm 3 bar K -1 mol -1 , 1 Pa = 10 -5 bar = 9.86923 × 10 -6 = 7.50062 × 10 -3 . 1 L = 1000 cm 3 = 10 -3 m 3 . 1.Consider a binary solution in which the vapor pressure of the components is given by: 2 2 x * 1 1 1 e P x P α = and 2 1 x * 2 2 2 e P x P α = For a regular solution, statistical thermodynamics provides an interpretation for α : RT ϖ = α , and ( 29 12 22 11 A 2 N ε - ε + ε = ϖ , where ε ij is the interaction energy between molecules of component i and j. (a) Derive expressions for the activity coefficients of components 1 and 2. (b) Write down the relationship for the Gibbs energy of mixing. Sketch a graph showing how ϖ / G mix varies with x 1 . Show two distinct curves in your graph: one representing the case in which RT/ ϖ = 0.6, and the other curve with RT/ ϖ = 0.4.
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