1. Chem. 412 – Phys. Chem. I

2. Free Energy Comparisons Helmholtz F.E. (A)Gibbs F.E. (G) A = U - TSG = H - TS @Cont.T=>  A sys =  U sys - T  S sys @Cont.T=>  G sys =  H sys - T  S sys If  A sys < 0, rxn spontaneous. (Constant V & T) If  G sys < 0, rxn spontaneous. (Constant P & T) If  A sys = 0, rxn @ equilibrium.If  G sys = 0, rxn @ equilibrium. dA = -PdV – SdTdG = VdP - SdT

3. Free Energy Comparisons - I

4. Free Energy Comparisons - II

5. Free Energy Comparisons - III

6. Free Energy Comparisons - IV Helmholtz F.E. (A)Gibbs F.E. (G) A = U - TSG = H - TS @Cont.T=>  A sys =  U sys - T  S sys @Cont.T=>  G sys =  H sys - T  S sys If  A sys < 0, rxn spontaneous. (Constant V & T) If  G sys < 0, rxn spontaneous. (Constant P & T) If  A sys = 0, rxn @ equilibrium.If  G sys = 0, rxn @ equilibrium. dA = -PdV – SdTdG = VdP - SdT

7. Free Energy Comparisons – I – F12

8. Free Energy Comparisons – II – F12

9. Free Energy Comparisons – III – F12

10. Free Energy Comparisons – III – F11 10

11. Phase Diagrams

12. The Phase Diagrams of H 2 O and CO 2 Phase Diagrams

13. Phase Transitions: Clapeyron Equation Over moderate temperature ranges:

14. Phase Transitions: Clapeyron Equation – I – F14

15. Phase Transitions: Clapeyron Equation – II – F14

16. Phase Transitions: Clapeyron Equation – III – F14

17. Phase Transitions: Clapeyron Equation – I – F13

18. Phase Transitions: Clapeyron Equation – II – F13

19. Phase Transitions: Clapeyron Equation – III – F13

20. Application of Clapeyron Equation Consider:Ice  Water  (ice, 101 kPa, 273 K) = 0.917x10 3 kg m -3  (liq, 101 kPa, 273 K) = 0.988x10 3 kg m -3  H f = 6.01 kJ mol -1 ( s  liq ) Triple point at 0.6 kPa and 273.16 K What is the melting point at 1.5x10 5 kPa ( 1500 atm ) ? Application: Blade in Ice-Skating. Mathcad Key

21. Clausius-Clapeyron Equation Applicable only to:s  g & liq  g equilibria Integrated form: Indefinite Integrated form: T-dep form:

22. Clausius-Clapeyron Equation - I

23. Clausius-Clapeyron Equation - II

26. Clausius-Clapeyron Equation – I – F11 26

27. Clausius-Clapeyron Equation – II – F11

28. Standard States &  G o rxn P o for gas:ideal gas; P o = 101.325 kPa non-ideal gas; (leave for now) for liquid:pure liquid at P o for solid:most stable crystalline structure at P o T o for all substances:298.15 K exactly S o o = 0 at 0 K for pure crystals  H o f (T o ) = 0 for elements at reference state  G convention must follow that of  H &  S  G  rxn from formation values

29. Substance  H  f (kJ/mol)  G  f (kJ/mol) S  (J mol -1 K -1 ) C(s, diamond)1.882.842.43 C(s, graphite)005.69

31. P/T-Dependent Equations Variation of  G with P for an ideal gas: Variation of  G with T: Variation of K P with T:

32. P/T-Dependent Equations

33. A = U - TSG = H - TS If  A sys < 0, rxn spontaneous. (Constant V & T) If  G sys < 0, rxn spontaneous. (Constant P & T) dA = -PdV – SdTdG = VdP - SdT