Chem. 412 – Phys. Chem. I

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Chem. 412 – Phys. Chem. I. Free Energy Comparisons. Free Energy Comparisons - I. Free Energy Comparisons - II. Free Energy Comparisons - III. Free Energy Comparisons - IV. Free Energy Comparisons – I – F12. Free Energy Comparisons – II – F12. Free Energy Comparisons – III – F12. - PowerPoint PPT Presentation

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Chem. 412 – Phys. Chem. IChem. 412 – Phys. Chem. I

Helm holtz Free Energy (A)

Clapeyron

Standard StatesG ibbs-Helm holtzTem perature Dependence

Phase Equilibrium Clausius-Clapeyron

M aster Equations

Spontaneity Indicator G ibbs Free Energy (G)

Free Energy Functions

Free Energy ComparisonsFree Energy Comparisons

Helmholtz F.E. (A) Gibbs F.E. (G)

A = U - TS G = H - TS

@Cont.T=> Asys= Usys - T Ssys @Cont.T=> Gsys = Hsys - T Ssys

If Asys< 0, rxn spontaneous.

(Constant V & T)

If Gsys< 0, rxn spontaneous.

(Constant P & T)

If Asys = 0, rxn @ equilibrium. If Gsys= 0, rxn @ equilibrium.

dA = -PdV – SdT dG = VdP - SdT

Free Energy Comparisons - IFree Energy Comparisons - I

Free Energy Comparisons - IIFree Energy Comparisons - II

Free Energy Comparisons - IIIFree Energy Comparisons - III

Free Energy Comparisons - IVFree Energy Comparisons - IV

Helmholtz F.E. (A) Gibbs F.E. (G)

A = U - TS G = H - TS

@Cont.T=> Asys= Usys - T Ssys @Cont.T=> Gsys = Hsys - T Ssys

If Asys< 0, rxn spontaneous.

(Constant V & T)

If Gsys< 0, rxn spontaneous.

(Constant P & T)

If Asys = 0, rxn @ equilibrium. If Gsys= 0, rxn @ equilibrium.

dA = -PdV – SdT dG = VdP - SdT

Free Energy Comparisons – I – F12Free Energy Comparisons – I – F12

Free Energy Comparisons – II – F12Free Energy Comparisons – II – F12

Free Energy Comparisons – III – F12Free Energy Comparisons – III – F12

Free Energy Comparisons – III – F11Free Energy Comparisons – III – F11

10

Phase DiagramsPhase Diagrams

The Phase Diagrams of H2O and CO2

Phase DiagramsPhase Diagrams

Phase Transitions: Clapeyron EquationPhase Transitions: Clapeyron Equation

• Over moderate temperature ranges:

pt

pt

VT

H

dT

dP

1

212 ln

T

T

V

HPP

pt

pt

Phase Transitions: Clapeyron Equation – I – F14Phase Transitions: Clapeyron Equation – I – F14

Phase Transitions: Clapeyron Equation – II – F14Phase Transitions: Clapeyron Equation – II – F14

Phase Transitions: Clapeyron Equation – III – F14Phase Transitions: Clapeyron Equation – III – F14

Phase Transitions: Clapeyron Equation – I – F13Phase Transitions: Clapeyron Equation – I – F13

Phase Transitions: Clapeyron Equation – II – F13Phase Transitions: Clapeyron Equation – II – F13

Phase Transitions: Clapeyron Equation – III – F13Phase Transitions: Clapeyron Equation – III – F13

Application of Clapeyron EquationApplication of Clapeyron Equation

• Consider: Ice Water (ice, 101 kPa, 273 K) = 0.917x103 kg m-3

(liq, 101 kPa, 273 K) = 0.988x103 kg m-3

Hf = 6.01 kJ mol-1 ( s liq )

• Triple point at 0.6 kPa and 273.16 K

• What is the melting point at 1.5x105 kPa ( 1500 atm ) ? Application: Blade in Ice-Skating.

Mathcad Key

Clausius-Clapeyron EquationClausius-Clapeyron Equation

• Applicable only to: s g & liq g equilibria

• Integrated form:

• Indefinite Integrated form:

• T-dep form:

121

2 11ln

TTR

H

P

P V

)(tanln VV

HdepTNontconsRT

HP

TCT

BAP lnln

Clausius-Clapeyron Equation - IClausius-Clapeyron Equation - I

Clausius-Clapeyron Equation - IIClausius-Clapeyron Equation - II

Clausius-Clapeyron Equation – I – F11Clausius-Clapeyron Equation – I – F11

26

Clausius-Clapeyron Equation – II – F11Clausius-Clapeyron Equation – II – F11

Standard States & GorxnStandard States & Gorxn

• Po for gas: ideal gas; Po = 101.325 kPa non-ideal gas; (leave for now) for liquid: pure liquid at Po

for solid: most stable crystalline structure at Po

• To for all substances: 298.15 K exactly• So

o = 0 at 0 K for pure crystals

Hof(To) = 0 for elements at reference state

G convention must follow that of H & S

Grxn from formation values

Substance Hf (kJ/mol) Gf (kJ/mol) S (J mol-1 K-1)

C(s, diamond) 1.88 2.84 2.43

C(s, graphite) 0 0 5.69

P/T-Dependent EquationsP/T-Dependent Equations

• Variation of G with P for an ideal gas:

• Variation of G with T:

• Variation of KP with T:

Prxno

o

o KRTGP

PnRTGG lnln

2

1

22,

11, 2

/

/

T

T

rxnrxnTG

TGdT

T

H

T

Gd

To

To

tconsTR

HK rxnP tan

1ln

P/T-Dependent EquationsP/T-Dependent Equations

Helm holtz Free Energy (A)

Clapeyron

Standard StatesGibbs-Helm holtzTem perature Dependence

Phase Equilibrium Clausius-Clapeyron

M aster Equations

Spontaneity Indicator G ibbs Free Energy (G)

Free Energy Functions

A = U - TS G = H - TS

If Asys< 0, rxn spontaneous.

(Constant V & T)

If Gsys< 0, rxn spontaneous.

(Constant P & T)

dA = -PdV – SdT dG = VdP - SdT

pt

pt

VT

H

dT

dP

)ln( Prxn

o KRTG

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