Chem. 412 – Phys. Chem. I H e lm h o ltz F re e E n e rg y (A ) C la p e yron S ta n d a rd S tates G ibbs-H elm holtz T e m p e ra tu re D ependence P h a s e E q u ilib rium C lau siu s-C lap eyron M a s te r E q uatio n s S p o n ta n e ity In d ic ator G ib b s F re e E n e rg y (G ) F re e E n e rg y F unctions
Chem. 412 – Phys. Chem. I
Jan 15, 2016
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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