1

Gibbs Free Energy Gibbs Free Energy and Spontaneityand Spontaneity

and the meaning of the universe…and the meaning of the universe…

2

Relationship Between Relationship Between S S surrsurr & H & H

WaterS Surr

q(system)(system)

S surr affected by heat transfer into or out of closed system

Entropy of the surroundings will be affected only by the heat transferred into or out of any closed system.Heat added to surroundings:Heat added to surroundings:

• • K.E. K.E. surrsurr increases; Molecules are moving faster. increases; Molecules are moving faster.• • Disorder increases since there is more Disorder increases since there is more randomnessrandomness• • Entropy increases.Entropy increases.

Note:Note: qqpp = - = - H H syssys S S surrsurr

3

Heat flow; Temperature Heat flow; Temperature DependentDependent

Remember that heat transfer is temperature dependent. Heat will transfer more efficiently with changes at low Remember that heat transfer is temperature dependent. Heat will transfer more efficiently with changes at low temperature than at high temperature.temperature than at high temperature.

i.e., 100€ to an International College student is worth more than to Raul.i.e., 100€ to an International College student is worth more than to Raul.

@ High temperature, molecules are already moving fast, an extra 10°C will not increase their velocities as much as @ High temperature, molecules are already moving fast, an extra 10°C will not increase their velocities as much as molecules at very low temperature.molecules at very low temperature.

-- H H syssys = = S Ssurrsurr units: units: J . J .TT mol Kmol K

Therefore since: Therefore since: S S univ univ = = S S syssys + + SS surr surr

S S univuniv = = S S syssys - - HH syssys

TT

4

S S univuniv and Spontaneity and Spontaneity

Criteria for Spontaneity in terms of the system:

S univ = S sys + S surr

S S univuniv = = S S syssys - - HH syssys

TT

S S univuniv H H sys sys (-)(-)

(+) (+) SpontaneousSpontaneous S S syssys (+)(+)SpontaneSpontaneousous

5

Spontaneity in terms of TSpontaneity in terms of TS S

univunivCriteria for Spontaneity in terms of the system:

S sys + S surr = S univ (1)

S S syssys - - HH sys sys == S S univuniv (2)(2)

TTNote rearranging eqn. 2

-T-TS S syssys + + H H sys sys = = -T -T S S univuniv

J. Willard Gibbs J. Willard Gibbs realized that -Trealized that -T S Sunivuniv can be defined as a can be defined as a new function provided new function provided that that T = 0T = 0

6

J. Willard GibbsJ. Willard Gibbs

The Free The Free Energy Energy change (change (G) G) is a measure is a measure of of spontaneity spontaneity of a process of a process and of the and of the useful useful energy energy available available from such a from such a process.process.

J. Willard Gibbs (1839-1903) was not particularly well known in his day, nor is his name widely recognized today, yet he is considered by some to be among the greatest scientists ever born in America. He was awarded th first doctorate in engineering granted in the United States, by Yale University. Gibbs became a professor of mathematical physics at Yale when he was 32 years old and began to publish a series of papers related to thermodynamics and equilibrium. Perhaps because his work was so theoretical, it was largely unappreciated at the time, though its great value was recognized by James Clerk Maxwell. Gibb’s work, if not his name, remains current and vital to this day.

7

G and SpontaneityG and SpontaneityDefining a new State function G:

-T -T S S univuniv= G @ T, P= 0

Consider

G = - T G = - T S S univ univ

G < 0G < 0 SpontaneousSpontaneous S S univuniv > 0 > 0

G = 0G = 0 @ equilibrium@ equilibrium S S univuniv = 0 = 0

G > 0G > 0 nonspontaneousnonspontaneous S S univuniv < < 00

(rev is spontaneous)

8

G: Pictorial ViewG: Pictorial View

Gibbs’ Free Energy can be defined in terms of the enthalpy of the system (H H syssys) and

the entropy of the system (SSsyssys)

-T -T S S univ univ == H H sys sys - T- TS S syssys = = G G

G = G = H - T H - T SS

G < 0

G > 0

G = 0@ equilb

Forward reaction occur Spontaneous in forward direction

Reverse reaction

occur nonspontaneous in forward

direction

G < 0 G > 0

See later that : G Keq or Q

9

G: Equations of Free G: Equations of Free EnergyEnergy

Gibbs’ Free Energy can be used to determine the Standard free energy (°) of formation

G = G = H - T H - T SSG°f = H°f - T S°f ° Standard State

f -formation from elements

If data is not for formation process,

then equation is slightly adjusted according to:

G° = H° - T S°

Or from tabulated thermodynamic data:

G° rxn = n G°f (prod) - n G°f (react)

10

G: Evaluation of Free G: Evaluation of Free EnergyEnergy

Consider the calculation for the following reaction:

CH3OH (g) + O2 (g) CO2 (g) + H2O (g)

Determine G°rxn

2 CH3OH (g) + 3 O2 (g) 2 CO2 (g) + 4 H2O (g)

H°H°rxnrxn - 201.2- 201.2 00 -393.5-393.5 -241.82 -241.82

S°S°rxnrxn ++ 237.6 237.6 205.0205.0 -213.6-213.6 -188.83 -188.83

G°G°rxnrxn - 161.9- 161.9 00 -394.4-394.4 -228.57 -228.57

Evaluate by:G°rxn = H° rxn - T S° rxn

X° rxn = n X°f (prod) - n X°f (react)

Or G°rxn = n G°f (prod) - n G°f (react)

11

Effect of temperature on Free Effect of temperature on Free EnergyEnergy

Temperature influence on Free Energy and Spontaneity

G = H - T S both both H, H, S (+)S (+)

(1000) (1)

lg. # sm. #

What is the sign of G ?

Temperature will dictate outcome of G.

TTlowlow: Temperature small: Temperature small

H - TS G (+)dominates negligible nonspontaneous

Thigh: Temperature large

H - TS G (-)negligible dominates spontaneous

12

Temperature Relationship Temperature Relationship and and GG

Consider Temperature affect on thermodynamic parameters

H -TS T G Spontaneity

a - ++ all - spon: T not impt

b + -- all + nonspon: T not impt

c - -- low - spon: H impt

d - -- high + nonspon : S impt

e + ++ low + nonspon : H impt

f + ++ high - spon: S impt

From this table, a spontaneous process can be made nonspontaneousFrom this table, a spontaneous process can be made nonspontaneous i.e., c & d by increasing Temperature.i.e., c & d by increasing Temperature.

13

Spontaneity: ExampleSpontaneity: ExampleExample :Example :

(c)(c) N N22FF4(g)4(g) 2NF 2NF22 (g)(g) H° - T H° - T S°S° G°G°

85 kJ 198 J/K85 kJ 198 J/K@ T Low @ T Low H° dominates H° dominates G° (+)G° (+) NonspontaneousNonspontaneous@ T High@ T High S° dominates S° dominates G° (-)G° (-) SpontaneousSpontaneous

Example :Example :

(c)(c) What temp will spontaneity switch for the reaction:What temp will spontaneity switch for the reaction:

NN22 (g) (g) + 3H+ 3H2(g)2(g) 2NH 2NH33 (g)(g) H° - T H° - T S°S° G°G°

- 92 kJ -198.5 J/K- 92 kJ -198.5 J/K@ T Low @ T Low H° dominatesH° dominates G° (-)G° (-) SpontaneousSpontaneous@ T High@ T High S° dominatesS° dominates G° (+)G° (+) NonspontaneousNonspontaneous

To go from spontaneous to nonspontaneous, To go from spontaneous to nonspontaneous, G° = 0G° = 0… … T = T = - 92kJ- 92kJ = 463.5 K = 463.5 K below spontaneousbelow spontaneous

-0.198 kJ / K-0.198 kJ / K above, nonspontaneousabove, nonspontaneous

14

Phase Change ProcessPhase Change ProcessWhat determines the spontaneity of a phase change?What determines the spontaneity of a phase change?

H:H: ss ll gg

S:S: ss ll gg

Two factors competing: Two factors competing: Which dominates will determine phase change.Which dominates will determine phase change.

Note: In a phase change: Note: In a phase change: s s ll is at equilib. is at equilib. oror G° = 0G° = 00 = 0 = H° - TH° - TS°S° H° = TH° = TS°S°

With signs for With signs for H & H & S are the same S are the same T = T = H°H° S°S°

Endo H(+) Endo H(+)

Exo H(-) Exo H(-)

S(+)

S(-) S(-)

S(+)

15

Free Energy and workFree Energy and workScience and Technology use physical and or chemical Science and Technology use physical and or chemical processes because these can do work.processes because these can do work.

Economics:Economics: To make money €, the work to be preformed must To make money €, the work to be preformed must be a possibility and efficient.be a possibility and efficient.

G provides information on spontaneity:G provides information on spontaneity: G (+) or (-) provides G (+) or (-) provides information on the spontaneity of the process @ information on the spontaneity of the process @ P, P, T = 0T = 0

Wasting time:Wasting time: G is useful because it prevents the wasted G is useful because it prevents the wasted effort on process with no inherent tendency to occur.effort on process with no inherent tendency to occur.

G isn’t whole story, Kinetics also important:G isn’t whole story, Kinetics also important: Note that Note that thermodynamically favorable process may still not occur to thermodynamically favorable process may still not occur to any appreciable extent because of the Kinetics. any appreciable extent because of the Kinetics.

- It makes sense to find a catalyst to speed up the reaction. - It makes sense to find a catalyst to speed up the reaction.

- Prevents wasting time and resource of seeking a catalyst on - Prevents wasting time and resource of seeking a catalyst on a reaction that won’t even work.a reaction that won’t even work.

16

G EquationsG Equations

G°

n G°prod - n G°

reaction

n G°prod - n G°

reaction

H° - S°H° - S°

- RT ln Keq

G - RT ln QG - RT ln Q