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PS9Solutions

# PS9Solutions - Chemistry 120B SP11 Problem Set 9 Solutions...

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Chemistry 120B SP11 Problem Set 9 Solutions Total: 50 points 1. See MQS Solutions Manual. 2. (i) Use the ideal gas law to write the mole fraction in terms of partial pressures. p j = N j V k B T p = p 1 + p 2 = N 1 + N 2 V k B T p j p = N j N 1 + N 2 = x j Equate the two expressions for μ (v) j . μ (0) j + k B T ln x (v) j = ¯ μ (0) j + k B T ln p j p 0 μ (0) j = ¯ μ (0) j + k B T ln p j p 0 - k B T ln x (v) j = ¯ μ (0) j + k B T ln p j p 0 - k B T ln p j p μ (0) j = ¯ μ (0) j + k B T ln p p 0 (ii) At coexistence (boiling point), μ ( ) j = μ (v) j . μ (0) 1 ( T b ) + k B T b ln x (v) 1 = μ * 1 ( T b ) + k B T b ln x ( ) 1 μ (0) 2 ( T b ) + k B T b ln x (v) 2 = μ * 2 ( T b ) + k B T b ln x ( ) 2 (iii) μ * j ( T ) μ * j ( T j ) + ∂μ * ∂T p T j ( T - T j ) From the Gibbs-Duhem equation, we know that ∂μ * ∂T p = - S ( ) j /N j . We get four equations because there are two components and two phases: μ * 1 ( T ) = μ * 1 ( T 1 ) - S ( ) 1 N 1 ( T - T 1 ) μ * 2 ( T ) = μ * 2 ( T 2 ) - S ( ) 2 N 2 ( T - T 2 ) μ (0) 1 ( T ) = μ (0) 1 ( T 1 ) - S (v) 1 N 1 ( T - T 1 ) μ (0) 2 ( T ) = μ (0) 2 ( T 2 ) - S (v) 2 N 2 ( T - T 2 ) 1

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(iv) Plugging in the expressions from part (iii) into the result from part (ii): μ (0) 1
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PS9Solutions - Chemistry 120B SP11 Problem Set 9 Solutions...

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