PS5Solutions

PS5Solutions - Chemistry 120B SP11 Problem Set 5 Solutions...

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Chemistry 120B SP11 Problem Set 5 Solutions Total: 50 points 1. (20 points) See MQS Solutions Manual. 2. (i) (5 points) W ( V 1 ,V 2 ) = V 1 N 1 × V 2 N 2 × (stuff independent of V ) Neglecting volume-independent terms, S = k B ln W = k B ln ( V 1 N 1 V 2 N 2 ) = k B ( ln V 1 N 1 + ln V 2 N 2 ) = k B ( N 1 ln V 1 + N 2 ln V 2 ) (ii) (5 points) W ( V 1 ,V 2 ) = ( V 1 + V 2 ) ( N 1 + N 2 ) S = k B ln W = k B ln h ( V 1 + V 2 ) ( N 1 + N 2 ) i = k B ( N 1 + N 2 )ln( V 1 + V 2 ) = k B N 1 ln( V 1 + V 2 ) + k B N 2 ln( V 1 + V 2 ) (iii) (5 points) Δ S mix = S final - S initial = k B N 1 ln( V 1 + V 2 ) + k B N 2 ln( V 1 + V 2 ) - k B ( N 1 ln V 1 + N 2 ln V 2 ) = k B ± N 1 [ln( V 1 + V 2 ) - ln V 1 ] + N 2 [ln( V 1 + V 2 ) - ln V 2 ] ² = - k B ± N 1 ln ³ V 1 V 1 + V 2 ´ + N 2 ln ³ V 2 V 1 + V 2 ´² Δ S mix N 1 + N 2 = - k B " ³ N 1 N 1 + N 2 ´ ln ³ V 1 V 1 + V 2 ´ + ³ N 2 N 1 + N 2 ´ ln ³ V 2 V 1 + V 2 ´ # = - k B " x 1 ln ³ V 1 V 1 + V 2 ´ + x 2 ln ³ V 2 V 1 + V 2 ´ # Since the initial densities are equal, V 1 / ( V 1 + V 2 ) = N 1
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PS5Solutions - Chemistry 120B SP11 Problem Set 5 Solutions...

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