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PS7Solutions

# PS7Solutions - Chemistry 120B SP11 Problem Set 7 Solutions...

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Chemistry 120B SP11 Problem Set 7 Solutions Total: 50 points 1. (i) See handout on bspace. (ii) Δ μ (0) is the change in free energy associated with moving one solute from octanol to water in the standard state. (iii) dG = - SdT + V dp + Σ i μ i dN i The Maxwell relation we want is ∂μ i ∂T p, { N j } = - ∂S ∂N i T,p,N j 6 = i The RHS of this equation is just - ¯ S i . ∂μ i ∂T p, { N j } = - ¯ S i For the second part, use the chain rule to get ∂μ i /T 1 /T p, { N j } = μ i + 1 T ∂μ i 1 /T p, { N j } Switching derivatives, d 1 T = - 1 T 2 dT ∂μ i /T 1 /T p, { N j } = μ i - T 2 T ∂μ i ∂T p, { N j } Use the relation you got in the first part of the problem to write ∂μ i /T 1 /T p, { N j } = μ i + T ¯ S i There are two ways to differentiate G corresponding to these two expressions G = H - TS G = X i μ i N i Differentiating these w.r.t. N i at fixed T , p , and N j 6 = i ∂G ∂N i T,p,N j 6 = i = μ i = ∂H ∂N i T,p,N j 6 = i - T ∂S ∂N i T,p,N j 6 = i Using the definitions of ¯ H and ¯ S , μ i = ¯ H i - T ¯ S i Plug this expression for μ i ∂μ

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PS7Solutions - Chemistry 120B SP11 Problem Set 7 Solutions...

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