Lecture 11: 10.15.05 Models of the chemical potential Today: LAST TIME MORE ON THE RELATIONSHIP BETWEEN CHEMICAL POTENTIAL AND GIBBS FREL ENERGY. Chemical potentials in multicomponent systems are finked: the Gthhs-Duhem exquation. THE CHEMICAL POTENTIAL OF THE IDEAL GAS.. Models of the chemical potential in materials.... The ideal gas model Chemical potential of ideal gas mixtures.. THE GENERAL SOLUTION MODEL. 10 IDEAL SOLUTIONS 11 REFERENCES. 2 3 5 5 8 Reading: Engel and Reid 6.3, 6.4. 6.5. 9.1, 9.2, 9.5 Supplementary Reading: Last time CHEMICAL POTENTIAL MEASURES CHEMICAL DRIVING FORCES : 2-COMPONENT, 2-PHASE SYSTEM, CLOSED, AT CONST. T, P: dG = (µ_A^α - µ_A^β) dN_A^α + (µ_B^α - µ_B^β) dN_B^α = 0 EQUILIBRIUM CHEMICAL: µ_A^α = µ_A^β µ_B^α = µ_B^β EQUALITY OF CHEMICAL POTENTIALS EQUILIBRIUM IS ACHIEVED WHEN DRIVING FORCES ARE EQUAL EVERYWHERE: THERMAL: T^α = T^β MECHANICAL: P^α = P^β More on the relationship between chemical potential and Gibbs free energy * Last time, we introduced partial molar quantities, the analog of molar quantities for multicomponent systems. Remember that partial molar quantities are directly related to the total thermodynamic function for the system. Thus we have two ways to write out the 'integrated form of the Gibbs free energy, for example. [INTEGRATED] GIBBS FREE ENERGY: G = U - PV - TS = H - TS OR, USING DEFIN OF PARTIAL MOLAR QUANTITIES, G = ∑ᵢ nᵢµᵢ = ∑ᵢ nᵢ(∂G/∂nᵢ) IF I HAVE A PURE COMPONENT (C=1): µ = G/n = U/n - TS/n = H - TS CHEMICAL POTENTIAL IS THE MOLAR FREE ENERGY IN A PURE SYSTEM * Chemical potentials in multicomponent systems are linked: the Gibbs-Duhem equation: DIFFERENTIAL FORM OF G: AT CONST. T, P: dG = ∑ᵢ µᵢdnᵢ + vdp + SdT LET C=2: dG = µ_Adn_A + µ_Bdn_B FROM: I and II: dG = µ_Adn_A + µ_Bdn_B = SdT + Vdp + µ_Adn_A + µ_Bdn_B EQUATE I AND II: µ_Adn_A + µ_Bdn_B = SdT + Vdp + µ_Adn_A + µ_Bdn_B n_Adµ_A + n_B dµ_B = 0 GIBBS-DUHEM EQUATION