1 principles of reactivity: entropy and free energy

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PRINCIPLES OF REACTIVITY: PRINCIPLES OF REACTIVITY: ENTROPY AND FREE ENERGYENTROPY AND FREE ENERGY

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CHAPTER OVERVIEWCHAPTER OVERVIEW

• This chapter examines factors that This chapter examines factors that determine whether a reaction is determine whether a reaction is

spontaneousspontaneous, , product-favoredproduct-favored, ,

non-spontaneousnon-spontaneous, , reactants-reactants-favored. favored.

• Review thermodynamic basics Review thermodynamic basics (next)(next)

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ThermodynamicsThermodynamics Thermodynamics is the scienceThermodynamics is the science

of heat (energy) transfer.of heat (energy) transfer.

Heat energy is associated Heat energy is associated with molecular motions.with molecular motions.

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CHEMICALCHEMICAL REACTIVITYREACTIVITY

What drives chemical reactions? What drives chemical reactions? How do they occur?How do they occur?

The first is answered by The first is answered by THERMODYNAMICSTHERMODYNAMICS and and the second by the second by KINETICSKINETICS..

Have already seen a number of “driving forces” Have already seen a number of “driving forces” for reactions that are for reactions that are PRODUCT-FAVOREDPRODUCT-FAVORED..•• formation of a precipitateformation of a precipitate•• gas formationgas formation

•• HH22O formation (acid-base reaction)O formation (acid-base reaction)

•• electron transfer in a batteryelectron transfer in a battery

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CHEMICALCHEMICAL REACTIVITYREACTIVITYBut ENERGY TRANSFER also allows us to predict But ENERGY TRANSFER also allows us to predict

reactivity.reactivity.

In general, reactions that transfer energy to their In general, reactions that transfer energy to their surroundings are product-favored.surroundings are product-favored.

So, let us consider heat transfer in chemical So, let us consider heat transfer in chemical processes.processes.

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19.1 SPONTANEOUS REACTIONS AND 19.1 SPONTANEOUS REACTIONS AND SPEED:SPEED:

THERMODYNAMICS VERSUS KINETICSTHERMODYNAMICS VERSUS KINETICS

• A spontaneous or product-favored reaction A spontaneous or product-favored reaction is one in which most of the reactants can is one in which most of the reactants can eventually be converted into products, eventually be converted into products, given sufficient time. given sufficient time.

• A non-spontaneous or reactant-favored A non-spontaneous or reactant-favored reaction is one in which little of the reaction is one in which little of the reactants will be converted into products, reactants will be converted into products, regardless of the time allowed. regardless of the time allowed.

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THERMODYNAMICS VERSUS KINETICSTHERMODYNAMICS VERSUS KINETICS

• This can also be expressed in another way. This can also be expressed in another way.

• Reactant-favored reactions are those in Reactant-favored reactions are those in which the products will be converted to which the products will be converted to reactants, given sufficient time. reactants, given sufficient time.

• Notice that the speed of the reaction is not Notice that the speed of the reaction is not an issue. an issue.

• Reaction speed is kinetics, Chapter 15. Reaction speed is kinetics, Chapter 15.

• We are studying thermodynamics.We are studying thermodynamics.

Entropy and Free EnergyEntropy and Free EnergyEntropy and Free EnergyEntropy and Free Energy

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

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

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ThermodynamicsThermodynamicsThermodynamicsThermodynamics• Is the state of a chemical system such Is the state of a chemical system such

that a rearrangement of its atoms and that a rearrangement of its atoms and molecules would decrease the energy of molecules would decrease the energy of the system? the system?

• If yes, system is favored to react — a If yes, system is favored to react — a product-favoredproduct-favored system.system.

• Most product-favored reactions are Most product-favored reactions are exothermic.exothermic.

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ThermodynamicsThermodynamicsThermodynamicsThermodynamics

• Most product-favored reactions Most product-favored reactions are exothermic.are exothermic.

• Often referred to as Often referred to as spontaneous spontaneous reactions.reactions.

• Spontaneous does not imply Spontaneous does not imply anything about time for reaction to anything about time for reaction to occur.occur.

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Thermodynamics and KineticsThermodynamics and Kinetics

Diamond is Diamond is thermodynamically thermodynamically favored to convert to favored to convert to graphite, but not graphite, but not kinetically favored.kinetically favored.

Paper burns — a product-Paper burns — a product-favored reaction. Also favored reaction. Also kinetically favored once kinetically favored once reaction begins.reaction begins.

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Product-Favored Product-Favored ReactionsReactions

In general, product-In general, product-favored reactions are favored reactions are exothermicexothermic..

FeFe22OO33(s) + 2 Al(s) ---> (s) + 2 Al(s) --->

2 Fe(s) + Al 2 Fe(s) + Al22OO33(s)(s)

ΔΔH = - 848 kJH = - 848 kJ

Thermite ReactionThermite Reaction

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Product-Favored Product-Favored ReactionsReactions

But many spontaneous reactions or processes But many spontaneous reactions or processes are endothermic or even have are endothermic or even have ΔΔH = 0.H = 0.

NHNH44NONO33(s) + heat (s) + heat NH NH44NONO33(aq)(aq)

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19.2 DIRECTIONALITY OF 19.2 DIRECTIONALITY OF REACTIONS: ENTROPYREACTIONS: ENTROPY

• Spontaneous reactions occur because they Spontaneous reactions occur because they generate a final state that is lower in energy, generate a final state that is lower in energy, that is energy dispersed, and/or a final state that is energy dispersed, and/or a final state that is more random or more disordered. that is more random or more disordered.

• The first condition is met by reactions that are The first condition is met by reactions that are exothermic. exothermic. –These reactions release heat to the universe These reactions release heat to the universe

resulting in more particles, molecules and/or resulting in more particles, molecules and/or atoms, having the energy that was originally atoms, having the energy that was originally concentrated on the reactants.concentrated on the reactants.

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Entropy, SEntropy, SEntropy, SEntropy, S One property common to One property common to

product-favored processes is product-favored processes is that the final state is more that the final state is more DISORDERED or RANDOM DISORDERED or RANDOM than the original.than the original.

SPONTANEITY IS SPONTANEITY IS RELATED TO AN RELATED TO AN INCREASE IN INCREASE IN RANDOMNESS.RANDOMNESS.

Reaction of K with water

The thermodynamic property related to randomness is ENTROPY, SENTROPY, S.

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Entropy: A Measure of Matter Entropy: A Measure of Matter Dispersal or DisorderDispersal or Disorder

• A perfect crystal at 0 Kelvin has no A perfect crystal at 0 Kelvin has no randomness or disorder. This statement is randomness or disorder. This statement is called the third law of thermodynamics. called the third law of thermodynamics.

• The thermodynamic function that represents The thermodynamic function that represents the randomness of matter is called entropy the randomness of matter is called entropy and is given the symbol S. and is given the symbol S.

• If energy is added to matter in such a way If energy is added to matter in such a way that there is essentially no temperature that there is essentially no temperature change we can calculate the change in change we can calculate the change in entropy:entropy: ΔΔS = q/TS = q/T

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EntropyEntropy

• By adding up all these small changes from By adding up all these small changes from absolute zero to any temperature, T, the absolute zero to any temperature, T, the absolute entropy, Sabsolute entropy, Soo of the substance at that of the substance at that temperature can be calculated. temperature can be calculated.

• Appendix L has a list of these values for Appendix L has a list of these values for several pure substances at 298.15 K. several pure substances at 298.15 K.

• The units on SThe units on Soo are e.u. or J/mole K. are e.u. or J/mole K.

• Table 20.1, page 917, is useful in identifying Table 20.1, page 917, is useful in identifying some general trends in entropy.some general trends in entropy.

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Entropy Entropy For similar substances:For similar substances:

• S S gasgas > S > S liquid liquid > S > S solidsolid

• S S complex moleculescomplex molecules > S > S simple moleculessimple molecules

• S S weakweak ionic bonds ionic bonds > S > S strongstrong ionic bonds ionic bonds • S S solution of solid or liquidsolution of solid or liquid > S > S solute + solventsolute + solvent

• *S *S solution of gassolution of gas << S S solute + solvent solute + solvent

**volume of area is constricted for a gas when it is in a liquidvolume of area is constricted for a gas when it is in a liquid

note the less than symbolnote the less than symbol

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

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How probable is it that reactant How probable is it that reactant molecules will react? molecules will react?

PROBABILITYPROBABILITY suggests that a suggests that a product-favored reaction will product-favored reaction will result in the result in the dispersal of dispersal of energy or of matter energy or of matter or both.or both.

Directionality of Directionality of ReactionsReactions

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Directionality of Directionality of ReactionsReactions

Probability suggests that a product-favored Probability suggests that a product-favored reaction will result in the dispersal of reaction will result in the dispersal of

energy or of matter or both.energy or of matter or both.

Matter DispersalMatter Dispersal

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

Directionality of ReactionsDirectionality of Reactions

Energy DispersalEnergy Dispersal

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Directionality of Reactions Directionality of Reactions ——

Energy DispersalEnergy Dispersal

Exothermic reactions involve a release of Exothermic reactions involve a release of stored chemical potential energy to the stored chemical potential energy to the surroundings. surroundings.

The stored potential energy starts out in a few The stored potential energy starts out in a few molecules but is finally dispersed over a great molecules but is finally dispersed over a great many molecules. many molecules.

The final state—with energy dispersed—is more The final state—with energy dispersed—is more probable and makes a reaction product-probable and makes a reaction product-favored.favored.

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

SSoo (J/K•mol) (J/K•mol)

HH22O(liq)O(liq) 69.9169.91

HH22O(gas)O(gas) 188.8 188.8

Entropy, SEntropy, SEntropy, SEntropy, S

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Entropy of a substance Entropy of a substance increases with temperature.increases with temperature.

Molecular motions of heptane, C7H16

Molecular motions of heptane at different temperatures.

Entropy, SEntropy, S

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Increase in molecular complexity Increase in molecular complexity generally leads to increase in S.generally leads to increase in S.


CHCH44 248.2248.2

CC22HH66 336.1 336.1

CC33HH88 419.4419.4


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Entropies of ionic solids depend Entropies of ionic solids depend on coulombic attractions.on coulombic attractions.


MgOMgO 26.926.9

NaFNaF 51.551.5


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Entropy usually increases Entropy usually increases when a pure liquid or solid when a pure liquid or solid dissolves in a solvent.dissolves in a solvent.


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Entropy Changes for Phase ChangesEntropy Changes for Phase Changes

For a phase change,For a phase change, ΔΔS = q/TS = q/T

where q = heat where q = heat transferred in phase transferred in phase changechange

For HFor H22O (liq) ---> HO (liq) ---> H22O(g)O(g)

ΔΔH = q = +40,700 J/molH = q = +40,700 J/mol

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Entropy Changes for Phase ChangesEntropy Changes for Phase Changes

S = qT

= 40, 700 J/mol

373.15 K = + 109 J/K • mol

For a phase change, For a phase change, ΔΔS = q/TS = q/T

where q = heat transferred in where q = heat transferred in phase changephase change

For HFor H22O (liq) ---> HO (liq) ---> H22O(g)O(g)

ΔΔH = q = +40,700 J/molH = q = +40,700 J/mol

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EntropyEntropy

• The entropy change for a change of state is The entropy change for a change of state is calculated using the equation q/T, which calculated using the equation q/T, which becomes becomes ΔΔHHfusfus / T / Too for the fusion process. for the fusion process.

• See O.H. # 89 for graphical and equation See O.H. # 89 for graphical and equation information.information.

• The The ΔΔHHoovapvap for Al is 326 kJ/mole. The normal for Al is 326 kJ/mole. The normal

boiling point is 2467boiling point is 2467ooC. Calculate the entropy C. Calculate the entropy

of vaporization, of vaporization, ΔΔSSoovapvap , for Al. 119 e.u. , for Al. 119 e.u.

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EntropyEntropy

Predict the sign of Predict the sign of ΔΔS for each reaction below:S for each reaction below:

XX(g)(g) ===> X ===> X(liq)(liq)

XX(s)(s) ===> X ===> X(liq)(liq)

XX(g)(g) ===> X ===> X(aq)(aq)

XX(liq)(liq) ===> X ===> X(aq)(aq)

XX(g) (g) ===> X ===> X(s)(s)

--

++

--

++

--

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Consider 2 HConsider 2 H22(g) + O(g) + O22(g) ---> 2 H(g) ---> 2 H22O(liq)O(liq)

ΔΔSSoo = 2 S = 2 Soo (H (H22O) - [2 SO) - [2 Soo (H (H22) + S) + Soo (O (O22)])]

ΔΔSSoo = 2 mol (69.9 J/K•mol) - = 2 mol (69.9 J/K•mol) - [2 mol (130.7 J/K•mol) + [2 mol (130.7 J/K•mol) +

1 mol (205.3 J/K•mol)] 1 mol (205.3 J/K•mol)]ΔΔSSoo = -326.9 J/K = -326.9 J/K

Note that there is a Note that there is a decrease in S decrease in S because 3 mol because 3 mol of gas give 2 mol of liquid.of gas give 2 mol of liquid.

Calculating Calculating S for a ReactionS for a Reaction

SSoo = = S Soo (products) - (products) - S Soo (reactants) (reactants)

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Figure 20.7Figure 20.7

2 NO + O2 NO + O22 2 NO 2 NO22

3 moles gas form 3 moles gas form 2 moles gas.2 moles gas.

S isS is negative.negative.

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Entropy: Second Law of Entropy: Second Law of ThermodynamicsThermodynamics

• The second law states that the The second law states that the entropy of the universe is increasing. entropy of the universe is increasing.

• For spontaneous, product-favored, For spontaneous, product-favored, reactions, reactions, ΔΔSSoo

universeuniverse > 0 . > 0 .

• This entropy change is calculated by This entropy change is calculated by considering the two terms that make considering the two terms that make up this entropy.up this entropy.

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Second Law of ThermodynamicsSecond Law of Thermodynamics

ΔΔSSoouniverseuniverse = = ΔΔSSo o

surroundingssurroundings + + ΔΔSSoosystemsystem , where , where

ΔΔSSoosurroundingssurroundings = q = qsurroundingssurroundings / T = - / T = - ΔΔHHoo

systemsystem / T and / T and

ΔΔ S Soosystemsystem= = ΔΔSSoo(products) - (products) - ΔΔSSoo(reactants), (reactants),

Equation 20.1.Equation 20.1.

Be sure to include the stoichiometric coefficient Be sure to include the stoichiometric coefficient with each term.with each term.

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2nd Law of Thermodynamics2nd Law of Thermodynamics

A reaction is spontaneous (product-favored) if A reaction is spontaneous (product-favored) if ΔΔS S for the universe is positive.for the universe is positive.

ΔΔSSuniverseuniverse = = ΔΔSSsystemsystem + + ΔΔSSsurroundingssurroundings

ΔΔSSuniverseuniverse > 0 for product-favored process > 0 for product-favored process

First calculate entropy created by matter dispersal First calculate entropy created by matter dispersal ((ΔΔSSsystemsystem))

Next, calculate entropy created by energy dispersal Next, calculate entropy created by energy dispersal ((ΔΔSSsurroundsurround))

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Dissolving NHDissolving NH44NONO33 in in water—an entropy water—an entropy driven process.driven process.


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2 H2 H22(g) + O(g) + O22(g) ---> 2 H(g) ---> 2 H22O(liq)O(liq)

ΔΔSSoosystemsystem = -326.9 J/K = -326.9 J/K


Sosurroundings =

qsurroundings

T =

-Hsystem

T

ΔΔHHoorxnrxn = = ΔΔ H Hoo

systemsystem = -571.7 kJ = -571.7 kJ

Sosurroundings =

- (-571.7 kJ)(1000 J/kJ)298.15 K

ΔΔSSoosurroundingssurroundings = +1917 J/K = +1917 J/K

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2 H2 H22(g) + O(g) + O22(g) ---> 2 (g) ---> 2

HH22O(liq)O(liq)

ΔΔSSoosystemsystem = -326.9 J/K = -326.9 J/K

ΔΔSSoosurroundingssurroundings = +1917 J/K = +1917 J/K

ΔΔSSoouniverse universe = +1590. J/K= +1590. J/K

The entropy of the The entropy of the universe is increasing, universe is increasing, so the reaction is so the reaction is product-favored. product-favored.


Enthalpy driven.Enthalpy driven.

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Second Law of ThermodynamicsSecond Law of Thermodynamics

• Table 19.2, page 804, shows how Table 19.2, page 804, shows how ΔΔHHsystemsystem and and ΔΔSSsystemsystem can be used to can be used to

predict the spontaneity of a reaction predict the spontaneity of a reaction (product-favored).(product-favored).

• There are four possible cases which we There are four possible cases which we will consider in another format using a will consider in another format using a new thermodynamic function G.new thermodynamic function G.

1 principles of reactivity: entropy and free energy

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