Thermodynamics

Chapter 20Chapter 20

Thermodynamics

Prediction of whether change will occurPrediction of whether change will occur

No indication of timeframeNo indication of timeframe

Spontaneous:Spontaneous:

occurs without external interventionoccurs without external intervention

Nonspontaneous:Nonspontaneous:

requires outside “push”requires outside “push”

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En

erg

y

Reaction progress

Reactants

Products

Domain of kinetics(the reaction pathway)

Domain ofthermodynamics

(the initial andfinal states)

Entropy and Spontaneity

Driving force for a spontaneous change is anDriving force for a spontaneous change is an

increase in entropy of the universeincrease in entropy of the universe

Entropy, SEntropy, S:: measure of disordermeasure of disorder

Spontaneous change implies:Spontaneous change implies:

more order more order less order less order

fewer ways of arranging particles fewer ways of arranging particles more more

Second Law of Thermodynamics

In any spontaneous change, there is always an In any spontaneous change, there is always an increase in entropy of the universe.increase in entropy of the universe.

Units:Units: J J

KK

0ΔS ΔS ΔS surrsysuniv

Entropy

1877 Ludwig Boltzmann:1877 Ludwig Boltzmann:

k = Boltzmann constant, R/Nk = Boltzmann constant, R/NAA

W = W = no. of possible arrangementsno. of possible arrangements

Third Law of Thermodynamics:Third Law of Thermodynamics:

The entropy of a perfect crystal at 0 K is zero.The entropy of a perfect crystal at 0 K is zero.

W lnk S

Positional EntropyWhy does a gas expand into a vacuum?Why does a gas expand into a vacuum?

Expanded state has highest positional probability Expanded state has highest positional probability of states available.of states available.

solutiongasor liquid, solid, pure

gasliquidsolid

S S

S S S

Other factors in entropy

Size:Size:

increase in S with increasing size (mass)increase in S with increasing size (mass)

Molecular complexity:Molecular complexity:

increase in S with increasing complexityincrease in S with increasing complexity

Generally effect of physical state >> complexityGenerally effect of physical state >> complexity

Reactions

For a spontaneous reaction:For a spontaneous reaction:

NaOHNaOH(s)(s) + CO + CO2(g)2(g) Na Na22COCO3(s)3(s) + H + H22OO(l)(l)

SS00 64.45 213.7 139 69.94 64.45 213.7 139 69.94 J/KJ/K

Is the reaction spontaneous as written?Is the reaction spontaneous as written?

0Sn Sn ΔS 0rr

0pp

0rxn

Spontaneity and S

Spontaneous:Spontaneous: SSunivuniv > 0 > 0

Nonspontaneous:Nonspontaneous: SSunivuniv < 0 < 0

At equilibrium:At equilibrium: SSunivuniv = 0 = 0

SSsyssys can be positive if can be positive if SSsurrsurr increases enough increases enough

surrsysuniv ΔS ΔS ΔS

16_03T

Table 16.3 Interplay of Ssys and Ssurr in Determining the Sign of Suniv

Signs of Entropy Changes

Process Spontaneous?

Yes

No (reaction will occur in opposite direction)

Yes, if Ssys has a larger magnitude than Ssurr

Yes, if Ssurr has a larger magnitude than Ssys

Ssys Ssurr Suniv

Surroundings and Suniv

Surroundings add or remove heatSurroundings add or remove heat

Exothermic:Exothermic:

qqsyssys < 0 < 0

qqsurrsurr > 0 > 0 so so SSsurrsurr > 0 > 0

Endothermic:Endothermic:

qqsyssys > 0 > 0

qqsurrsurr < 0 < 0 so so SSsurrsurr < 0 < 0

Ssurr and Ssys

SSsurrsurr:: SSsurrsurr - - qqsyssys

SSsurrsurr 1/T 1/T

At constant pressure:At constant pressure:

T

qΔS sys

surr

T

HΔS sys

surr

The Math

Given:Given:

@constant P:@constant P:

Multiply by Multiply by T:T:

Result:Result: syssyssys

syssysuniv

syssysuniv

surrsysuniv

TΔΔH ΔG

TΔΔH TΔT

ΔH ΔS ΔS

ΔS ΔS ΔS

S

SS

0ΔS implies 0 ΔG univ

Reactions and G

GG00:: Standard Free EnergyStandard Free Energy

Reactants in standard states areReactants in standard states are

converted to products in standard converted to products in standard statesstates

0rr

0pp

0rxn ΔGn ΔGn ΔG

Gibb’s Free Energy

Overall criterion for spontaneityOverall criterion for spontaneity

from the standpoint of the systemfrom the standpoint of the system

A process at constant temp. and pressure is A process at constant temp. and pressure is spontaneous in the direction spontaneous in the direction G decreasesG decreases

ST -H ΔG

G = H - TS

HH SS GG Spontaneous?Spontaneous?

““Good”: Good”: H < 0H < 0 ““Good”: Good”: S > 0S > 0 ““Good”: Good”: G < 0G < 0 ““Good”: Good”: G < 0G < 0

-- ++ -- At all At all temperaturestemperatures

-- -- ?? At low At low temperaturestemperatures

++ ++ ?? At high At high temperaturestemperatures

++ -- ++ Not at any Not at any temperaturetemperature

Summary

G < 0G < 0 Spontaneous as writtenSpontaneous as written

G > 0G > 0 Not spontaneous as writtenNot spontaneous as written

Reverse process spontaneousReverse process spontaneous

G = 0G = 0 At equilibriumAt equilibrium

A Closer Look…

TTS:S:

energy not avail. for doing workenergy not avail. for doing work

G:G:

E avail. as heat E avail. as heat –– E not avail. for work E not avail. for work

max. work available (constant T and P)max. work available (constant T and P)

Amount of work actually obtained depends on pathAmount of work actually obtained depends on path

ST -H ΔG

G and Work

GG

SpontaneousSpontaneous max. work obtainablemax. work obtainable

NonspontaneousNonspontaneousmin. work requiredmin. work required

Work and path-dependenceWork and path-dependence

wwmaxmax ( (wwminmin)) process performed reversiblyprocess performed reversibly

theoreticaltheoretical

wwactual actual < < wwmaxmax performed irreversiblyperformed irreversibly

real worldreal world

Reversible vs. Irreversible Processes

Reversible:Reversible:

The universe is exactly the same as it was before The universe is exactly the same as it was before the cyclic process.the cyclic process.

Irreversible:Irreversible:

The universe is different after the cyclic process.The universe is different after the cyclic process.

All real processes are irreversible.All real processes are irreversible.

Some work is changed to heat.Some work is changed to heat.

Free Energy and Pressure

Q:Q: reaction quotient from mass action lawreaction quotient from mass action law

RTlnQ GΔG 0

Free Energy and Equilibrium

K:K: equilibrium constantequilibrium constant

At At

equilibrium:equilibrium: G = 0G = 0

K = QK = Q

RTlnKΔG0

RTGΔ

e0

K

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0Fraction of A reacted

0.5 1.0

G

Equilibriumoccurs here

0Fraction of A reacted

0.5 1.0

G

Equilibriumoccurs here

0Fraction of A reacted

0.5 1.0

Equilibriumoccurs here

(a) (b) (c)

G

A B

G and Extent of Reaction

A B

G0B < G0

A

Spontaneous

C D

G0D> G0

C

Nonspontaneous

Temperature Dependence of K

Plot lnK vs. 1/TPlot lnK vs. 1/Tslope = -slope = -HH00/R/R intercept = intercept = SS00/R /R

*assumes *assumes HH00, , SS00 relatively T independent relatively T independent

000 ST - H RTlnK ΔG

bmxy

R

S

T

1

R

H lnK

RT

ΔG

000