HW1 solutions

# HW1 solutions - Solutions to Unit 1 Homework No 1 1(a K Z=...

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Solutions to Unit 1 Homework No. 1 1. (a) ( 29 RT R K RT Z σ α - β - σ σ = σ Π = A plot of Z versus : The two partial derivatives are: β - σ = Π σ K T , and ( 29 3 2 T 2 K σ α + β - σ - = σ Π ( 29 σ σ α + β - σ - β - σ = Π d 2 K dT K d 3 2 2. The total differential of P is: dn n P dT T P dV V P dP T V V n T n , , , + + = We can determine each partial derivative. The total differential is then: dn V RT dT V nR dV V nRT dP + + - = 2 , which can then be approximated as: n V RT T V nR V V nRT P + + - 2 1 Z Π A very slight dip due to very weak hydrophobic attractive interactions at low surface pressure A sharp increase in Z at higher surface pressures when the inter- headgroup repulsions become significant

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( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 3 3 1 1 3 1 1 3 3 2 3 1 1 10 779 1 0015 0 020000 0 15 298 3144 8 0000 1 85 0 020000 0 15 298 3144 8 0000 1 10 200 0 020000 0 15 298 3144 8 0000 1 - - - - - - - - × + + × - - Nm . mol . m . K . mol JK . mol . K . m . K . mol JK . mol .
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