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Entropy and Free Energy

John C. Kotz Paul M. Treichel Gabriela C. Weaver

How to predict if a reaction can occur, given enough time?

THERMODYNAMICS

CHAPTER 19 Principles of Reactivity: Entropy and Free Energy Lectures written by John Kotz

How to predict if a reaction can occur at a reasonable rate?

KINETICS © 2006 Brooks/Cole © 2006 Brooks/Cole - ThomsonThomson

© 2006 Brooks/Cole - Thomson

Thermodynamics

Entropy, S

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• Both productproduct- and reactantreactant-favored reactions can proceed to equilibrium in a

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One property common to spontaneous processes is that the final state is more DISORDERED or RANDOM than the original.

spontaneous process. AgCl(s) (aq) + Cl–(aq) aq) AgCl(s) ' Ag+(aq) K = 1.8 x 10-10

Spontaneity is related to an increase in randomness.

Reaction is not productproduct-favored, but it moves spontaneously toward equilibrium.

The thermodynamic property related to randomness is ENTROPY, S.

• Spontaneous does not imply anything about time for reaction to occur. © 2006 Brooks/Cole - Thomson

Reaction of K with water

© 2006 Brooks/Cole - Thomson

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Directionality of Reactions

The entropy of liquid water is greater than the entropy of solid water (ice) at 0˚ C.

Probability suggests that a spontaneous reaction will result in the dispersal of energy or of matter or both.

Matter Dispersal

© 2006 Brooks/Cole - Thomson

© 2006 Brooks/Cole - Thomson

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Entropy, S

Directionality of Reactions Probability suggests that a spontaneous reaction will result in the dispersal of energy or of matter or both.

SSoo (J/K• •mol) (J/K (J/K•mol) H H22O(liq) O(liq)

Energy Dispersal

69.95 69.95

H O(gas) 188.8 188.8 H22O(gas)

S (gases) > S (liquids) > S (solids)

© 2006 Brooks/Cole - Thomson

© 2006 Brooks/Cole - Thomson

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Entropy, S

Entropy and States of Matter

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Increase in molecular complexity generally leads to increase in S.

S˚(Br2 liq) liq) < S˚ S˚(Br2 gas)

S˚(H2O sol) < S˚ S˚(H2O liq) liq)

© 2006 Brooks/Cole - Thomson

Standard Molar Entropies

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Entropy Changes for Phase Changes For a phase change,

∆S = q/T

where q = heat transferred in phase change For H2O (liq (liq)) Æ H2O(g) ∆H = q = +40,700 J/mol

ΔS = © 2006 Brooks/Cole - Thomson

© 2006 Brooks/Cole - Thomson

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q 40, 700 J/mol = = + 109 J/K • mol T 373.15 K

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Entropy Entropy and and Temperature Temperature

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Calculating ∆S for a Reaction ∆∆S Soo == Σ Σ SSoo (products) (products) -- Σ Σ SSoo (reactants) (reactants) Consider 2 H2(g) + O2(g) ---> ---> 2 H2O(liq) ∆So = 2 So (H2O) - [2 So (H2) + So (O2)]

S increases slightly with T

∆So = 2 mol (69.9 J/K• J/K•mol) [2 mol (130.7 J/K• J/K•mol) + 1 mol (205.3 J/K• J/K•mol)]

S increases a large amount with phase changes

∆So = -326.9 J/K Note that there is a decrease in S because 3 mol of gas give 2 mol of liquid.

© 2006 Brooks/Cole - Thomson

© 2006 Brooks/Cole - Thomson

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