1 Sep. 29, 2010! readings: Ch. 5.7-5.10 assignments: Gibbs free energy, T or P dependence of ΔG 2 Changes in Gibbs free energy G = H - TS 3 Gibbs free energy and spontaneity ΔG < 0: spontaneous ΔG = 0: equilibrium ΔG > 0: spontaneous in the opposite direction 4 Gibbs free energy in chemical reactions a A + b B → c C + d D ΔG = cGC + dGD – (aGA + bGB)5 Standard state Gibbs free energy changes Gibbs free energy of formation at standard state • Tabulated for compounds • Zero for elements 6 Example: spontaneity of a reaction Is the hydrolysis of glycylglycine spontaneous at STP? Gly-Gly(aq) + H2O(ℓ) → 2 Gly(aq) ΔG°f,Gly-Gly = -493.5 kJ/mol ΔG°f,Gly = -379.9 kJ/mol ΔG°f,water = -237.1 kJ/mol 7 Standard state entropy energy changes Entropy is an absolute quantity • Tabulated for compounds • Not zero for elements 8 T dependence of Gibbs free energy changes dG = dwother + VdP - SdT9 Example: glucose fermentation at 80 °C What is ΔG for the following reaction at 80 °C? glucose(s) → 2 EtOH(ℓ) + 2 CO2(g) 10 ΔG°f,glucose = -910.5 kJ/mol ΔG°f,EtOH = -174.1 kJ/mol ΔG°f,CO2 = -394.4 kJ/mol S°glucose = 212.1 J/K⋅mol S°EtOH = 160.6 J/K⋅mol S°CO2 = 213.7 kJ/K⋅mol = (2)(-174.1 kJ/mol) + (2 )(-394.4 kJ/mol) - (1 )(-910.5 kJ/mol) = -226.5 kJ/mol!glucose(s) → 2 EtOH(ℓ) + 2 CO2(g) 11 12 Calculus gets to the same place faster dG = VdP - SdT13 glucose(s) → 2 EtOH(ℓ) + 2 CO2(g) glucose(s) → 2 EtOH(ℓ) + 2 CO2(g) 80 °C 25 °C ΔG°f,glucose = -910.5 kJ/mol ΔG°f,EtOH = -174.1 kJ/mol ΔG°f,CO2 = -394.4 kJ/mol S°glucose = 212.1 J/K⋅mol S°EtOH = 160.6 J/K⋅mol S°CO2 = 213.7 kJ/K⋅mol Glucose fermentation example 14 T dependence of Gibbs free energy changes The Gibbs-Helmholtz equation Show that 15 Gibbs-Helmholtz proof 16 Example: glucose fermentation at 80 °C What is ΔG for the following reaction at 80 °C? glucose(s) → 2 EtOH(ℓ) + 2 CO2(g) ΔG°f,glucose = -910.5 kJ/mol ΔG°f,EtOH = -174.1 kJ/mol ΔG°f,CO2 = -394.4 kJ/mol ΔH°f,glucose = -1274.4 kJ/mol ΔH°f,EtOH = -277.0 kJ/mol ΔH°f,CO2 = -393.5 kJ/mol17 HALF-EXAM 1!18 HALF-EXAM