Chem. 412 – Phys. Chem. I

Free Energy Comparisons Helmholtz F.E. (A)Gibbs F.E. (G) A = U - TSG = H -  A sys =  U sys - T  S  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, equilibrium.If  G sys = 0, equilibrium. dA = -PdV – SdTdG = VdP - SdT

Free Energy Comparisons - I

Free Energy Comparisons - II

Free Energy Comparisons - III

Free Energy Comparisons - IV Helmholtz F.E. (A)Gibbs F.E. (G) A = U - TSG = H -  A sys =  U sys - T  S  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, equilibrium.If  G sys = 0, equilibrium. dA = -PdV – SdTdG = VdP - SdT

Free Energy Comparisons – I – F12

Free Energy Comparisons – II – F12

Free Energy Comparisons – III – F12

Free Energy Comparisons – III – F11 10

Phase Diagrams

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

Phase Transitions: Clapeyron Equation Over moderate temperature ranges:

Phase Transitions: Clapeyron Equation – I – F14

Phase Transitions: Clapeyron Equation – II – F14

Phase Transitions: Clapeyron Equation – III – F14

Phase Transitions: Clapeyron Equation – I – F13

Phase Transitions: Clapeyron Equation – II – F13

Phase Transitions: Clapeyron Equation – III – F13

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 K What is the melting point at 1.5x10 5 kPa ( 1500 atm ) ? Application: Blade in Ice-Skating. Mathcad Key

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

Clausius-Clapeyron Equation - I

Clausius-Clapeyron Equation - II

Clausius-Clapeyron Equation – I – F11 26

Clausius-Clapeyron Equation – II – F11

Standard States &  G o rxn P o for gas:ideal gas; P o = 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: 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

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

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

P/T-Dependent Equations

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