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# Physical Chemistry for the Chemical and Biological Sciences

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Outline of the Course 1) Review and Definitions 2) Molecules and their Energies 3) 1 st Law of Thermodynamics 4) 2 nd Law of Thermodynamics 5) Gibbs Free Energy 6) Phase Diagrams and REAL Phenomena 7) Non-Electrolyte Solutions & Simple Mixtures 8) Chemical Equilibrium 9) Kinetics

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Section 5.1. The Use Of Partial Differentials Goals 1) To understand the use of Partial Differentials in developing thermodynamic formulae.
Use Of Partial Differentials 8 Variables Of State: U, H, S, G, A, P, V and T Express V as a function of P and T: V = V(P,T) = P nRT If an ideal gas How does V change with T (at constant P) for an ideal gas : P T V = P nR

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How does V change with P (at constant T) for an ideal gas : T P V = 2 P nRT It is generally true that if: V = V(P,T) then the total differential of V is: dV = T P V dP + P T V dT = 2 P nRT dP + P nR dT
dV is an exact differential. For exact differentials, the order of differentiation doesn’t matter !! P T P V T = T P T V P For an ideal gas: P T V = P nR Therefore: T P T V P = 2 P nR

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Likewise: T P V = 2 P nRT Therefore: P T P V T = 2 P nR Same Result !!! Therefore: P T P V T = T P T V P For exact differentials, the order of differentiation doesn’t matter !!
Example: Show that: (a) T P G = V (b) P T V = T P S Solution: (a) Express G as a function of T and P: G = H T S = U + P V T S dG = dU + d (P V) d (T S) = dU + P dV + V dP T dS S dT G is a State Function. Thus, if we derive: G = G(T,P) for one path, it must be true for ANY path. Therefore, choose a reversible path with P–V work only.

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dU = dq rev + dw rev = dq rev P dV But: dq rev = T dS
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5b - Outline of the Course 1 Review and Definitions 2...

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