Chemical EquilibriumChemical Equilibrium

Foundation of equilibriumFoundation of equilibriumExpressing equilibrium: Expressing equilibrium: Equilibrium constantsEquilibrium constants

Upsetting equilibrium – Le Upsetting equilibrium – Le ChatelierChatelier

Learning objectivesLearning objectives

• Write equilibrium constant expressions Write equilibrium constant expressions for both solutions and gas phase for both solutions and gas phase reactionsreactions

• Deduce relationship between KDeduce relationship between Kcc and K and Kpp

• Use reaction quotients to predict Use reaction quotients to predict direction of reactiondirection of reaction

• Apply LeChatelier’s principle to predict Apply LeChatelier’s principle to predict consequences of changing equilibrium consequences of changing equilibrium conditionsconditions

EquilibriumEquilibrium

• Chemical equilibrium is:Chemical equilibrium is:The state reached when the The state reached when the

concentrations of reactants and concentrations of reactants and products remain constant over timeproducts remain constant over time

• Equilibrium is evident in physical Equilibrium is evident in physical processes: vapour pressure over a processes: vapour pressure over a liquid, solid and liquid coexisting at liquid, solid and liquid coexisting at the freezing pointthe freezing point

Equilibrium in a chemical Equilibrium in a chemical changechange

• Not all reactions proceed to completion – Not all reactions proceed to completion – reactants completely converted into reactants completely converted into productsproducts

• As reactants convert into products, the As reactants convert into products, the products themselves convert back into products themselves convert back into reactantsreactantsAs reactant concentration declines, the forward As reactant concentration declines, the forward

rate decreasesrate decreasesAs product concentration increases, the As product concentration increases, the

backward rate increasesbackward rate increases

Dynamic equilibriumDynamic equilibrium

• In the reactionIn the reaction

The same final concentrations of NOThe same final concentrations of NO22 and and NN22OO44 are obtained regardless of the initial are obtained regardless of the initial conditions – pure NOconditions – pure NO22 or pure N or pure N22OO44

• The reactions don’t stop, the processes The reactions don’t stop, the processes become equal in both directionsbecome equal in both directions

)()( 242 gNOgON

Reactants and products no Reactants and products no moremore

• In an equilibrium mixture, there is a In an equilibrium mixture, there is a constant, dynamic cycling of constant, dynamic cycling of materials and the identities of materials and the identities of reactant and product are lostreactant and product are lost

• By convention, the substance(s) used By convention, the substance(s) used initially are called the reactantsinitially are called the reactants

Rate perspectiveRate perspective

• As the concentration of reactant (product) As the concentration of reactant (product) decreases, the rate of disappearance also decreases, the rate of disappearance also decreasesdecreases

• The equilibrium point is reached when the The equilibrium point is reached when the rates are equalrates are equal

Equilibrium constantEquilibrium constant

• Reactions usually take place in Reactions usually take place in solution or in the gas phase. For solution or in the gas phase. For solution reactions, the equilibrium solution reactions, the equilibrium constant Kconstant Kcc is used, where is used, where concentrations are in mol/L concentrations are in mol/L

• For the equilibriumFor the equilibriumaA +bB = cC + dDaA +bB = cC + dD

ba

dc

c BA

DCK

][][

][][

Products

Reactants

Concentration M

Coefficients from equation

Notes about KNotes about Kcc

• KKcc is a constant at a given is a constant at a given temperature, regardless of the temperature, regardless of the concentrations of the reactants usedconcentrations of the reactants used

• Substances may be gases or solutionsSubstances may be gases or solutions

• KKcc has no units: each concentration is has no units: each concentration is considered as a ratio to the standard considered as a ratio to the standard state (1 M)state (1 M)

Equilibrium constant KEquilibrium constant Kpp

• For reactions in the gas phase, the partial For reactions in the gas phase, the partial pressure can be used instead of molaritypressure can be used instead of molarity

• KKpp is unitless because the ratio with is unitless because the ratio with respect to the standard state (1 atm) is respect to the standard state (1 atm) is usedused

bB

aA

dD

cC

pPP

PPK

Relationship between KRelationship between Kcc and and KKpp

PPAAV = nV = nAART so PRT so PAA = n = nAA/V/V●RT = [A]RT●RT = [A]RT

ΔΔn = (c+d)-(a+b)n = (c+d)-(a+b)

ncp

badcba

dc

p

RTKK

RTBA

DCK

)(

)(][][

][][ )()(

Heterogeneous equilibriaHeterogeneous equilibria

• Reactions often involve solid or liquid Reactions often involve solid or liquid phases in addition to gas and phases in addition to gas and solutionsolution

• Concentrations of liquids and solids Concentrations of liquids and solids are constants – independent of the are constants – independent of the amountamount

• Since they are constant they become Since they are constant they become folded into Kfolded into Kcc

Solids and liquids are Solids and liquids are ignoredignored

CaCOCaCO33(s) = CaO(s) + CO(s) = CaO(s) + CO22(g)(g)

• Include only gas or solution entities in KInclude only gas or solution entities in Kcc

][][

][

][

]][[

23

3

2

COCaO

CaCOxK

CaCO

COCaOK

c

c

Solid concentrations

are constant

Using equilibrium constantsUsing equilibrium constants

• The value of KThe value of Kcc or K or Kpp indicates the indicates the extent of a reactionextent of a reaction

• Generally:Generally:KKc c > 10> 1033, reaction goes to completion, reaction goes to completion

KKcc < 10 < 10-3-3, reaction does not proceed, reaction does not proceed

101033 > K > Kcc > 10 > 10-3-3 reactants and products reactants and products all presentall present

Reaction QuotientReaction Quotient

• Reaction QuotientReaction Quotient is the is the instanteous value obtained for Kinstanteous value obtained for Kcc for for a combination of reactants and a combination of reactants and products not yet at equilibriumproducts not yet at equilibrium

• It can be used to predict the direction It can be used to predict the direction the reaction will take from that set of the reaction will take from that set of conditionsconditions

KKcc and Q and Qcc

• In the reactionIn the reaction

• A mixture made up with [HA mixture made up with [H22] = 0.1 M, [I] = 0.1 M, [I22] = ] = 0.2 M and [HI] = 0.4 M0.2 M and [HI] = 0.4 M

• KKcc > Q > Qcc so reaction will go towards HI so reaction will go towards HI

57),(2)()( 22 cKgHIgIgH

0.82.01.0

4.0

]][[

][ 2

22

2

IH

HIQc

Predicting reactions with QPredicting reactions with Qcc

QQcc < K < Kcc, reaction goes towards products, reaction goes towards products

QQcc > K > Kcc, reaction goes towards reactants, reaction goes towards reactants

QQcc = K = Kcc, reaction is at equilibrium, reaction is at equilibrium

Calculations with KCalculations with Kcc

• Simple calculations: Simple calculations:

KKcc and all equilibrium concentrations and all equilibrium concentrations but one are given. Use Kbut one are given. Use Kc c to to calculate concentration of unknowncalculate concentration of unknown

• Complex calculations:Complex calculations:

KKcc and initial concentrations are given, and initial concentrations are given, calculate equilibrium concentrationscalculate equilibrium concentrations

I.C.E. – It’s pretty coolI.C.E. – It’s pretty cool• The ICE man cometh: it is widely The ICE man cometh: it is widely

used in equilibrium problemsused in equilibrium problems

• Given KGiven Kcc = 57 and initial = 57 and initial concentrations of [Hconcentrations of [H22] = [I] = [I22] = 0.1 M, ] = 0.1 M, find equilibrium concentrations of Hfind equilibrium concentrations of H22, , II22 and HI and HI

HH22 II22 HIHI

IInitial nitial concconc

0.10.1 0.10.1 0.00.0

CChangehange -x-x -x-x 2x2x

EEquilibriuquilibrium concm conc

0.1 - x0.1 - x 0.1 - x0.1 - x 2x2x

Solve for xSolve for x

)1.0()1.0(

)2(

]][[

][57

2

22

2

xx

x

IH

HIKc

• X = 0.136 > 0.1 so is physically unreasonableX = 0.136 > 0.1 so is physically unreasonable• X =0.0791: [HX =0.0791: [H22] = [I] = [I22] = 0.0209 M; [HI] = 0.158 ] = 0.0209 M; [HI] = 0.158

MM

MorMx

x

x

136.0,0791.0

57)1.0(

42

2

Upsetting the applecartUpsetting the applecart

• Conditions of reactions must often be Conditions of reactions must often be manipulated to optimize yield of productsmanipulated to optimize yield of productsConcentrations of reactants or productsConcentrations of reactants or productsTemperatureTemperaturePressure and volumePressure and volume

• Le Chatelier’s Principle:Le Chatelier’s Principle:If a stress is applied to a reaction mixture at If a stress is applied to a reaction mixture at

equilibrium, the system adjusts to relieve equilibrium, the system adjusts to relieve the stressthe stress

The Haber processThe Haber process

• One of the most important industrial One of the most important industrial processes is the synthesis of NHprocesses is the synthesis of NH33 from from the elements: Nthe elements: N22(g) + 3H(g) + 3H22(g) = 2NH(g) = 2NH33(g)(g)

• At 700 K, KAt 700 K, Kcc = 0.29 = 0.29

• Altering reactant concentrations:Altering reactant concentrations:Increasing [reactant]:Increasing [reactant]: reactants → products reactants → productsIncreasing [product]: products → reactantsIncreasing [product]: products → reactants

Effects of pressureEffects of pressure

• Pressure is only important if there is an Pressure is only important if there is an overall change in the number of gas molesoverall change in the number of gas moles

NN22(g) + 3H(g) + 3H22(g) = 2NH(g) = 2NH33(g)(g)

• In the Haber process there are 4 moles of In the Haber process there are 4 moles of reactants vs 2 moles of productsreactants vs 2 moles of productsIncreasing pressure: converts reactants to Increasing pressure: converts reactants to

products (fewer moles)products (fewer moles)Decreasing pressure: converts products to Decreasing pressure: converts products to

reactants (more moles)reactants (more moles)

Effects of temperatureEffects of temperature

• KKcc depends on temperature. Increasing depends on temperature. Increasing or decreasing temperature will cause or decreasing temperature will cause mixture to adjust to new value of Kmixture to adjust to new value of Kcc..

• Treat the Treat the ΔΔH of a reaction as a H of a reaction as a reactant/productreactant/product

• Raising T causes heat input into reactionRaising T causes heat input into reaction

• Lowering T causes withdrawal of heatLowering T causes withdrawal of heat

The Haber process as Function The Haber process as Function of Tof T

• The process is exothermic: heat is a productThe process is exothermic: heat is a product

• Raising T puts heat into reaction:Raising T puts heat into reaction:Equilibrium adjusts to reduce heat output – Equilibrium adjusts to reduce heat output –

moves towards reactantsmoves towards reactants• Lowering T removes heat:Lowering T removes heat:

Equilibrium adjusts to increase heat output – Equilibrium adjusts to increase heat output – moves towards productsmoves towards products

• Endothermic reactions will show the Endothermic reactions will show the opposite T- dependenceopposite T- dependence

NN22(g) + 3H(g) + 3H22(g) = 2NH(g) = 2NH33(g) + 92.2 kJ(g) + 92.2 kJ

Increasing T in Haber process Increasing T in Haber process reduces yieldreduces yield

Catalysts and equilibriumCatalysts and equilibrium

• Equilibrium depends on the initial Equilibrium depends on the initial and final statesand final states

• Catalyst lowers the transition stateCatalyst lowers the transition state

• Equilibrium is unaffected by addition Equilibrium is unaffected by addition of a catalystof a catalyst

From the rate perspectiveFrom the rate perspective

• The catalyst increases the forward The catalyst increases the forward reaction rate by lowering the energy reaction rate by lowering the energy barrierbarrier

• The rate of the backward reaction is The rate of the backward reaction is lowered by the same amountlowered by the same amount

Linking rate equations with Linking rate equations with KKcc

• For the general reaction:For the general reaction:A + B = C + DA + B = C + D

• Assume single bimolecular stepsAssume single bimolecular steps Rate of forward reaction = kRate of forward reaction = kff[A][B][A][B]

Rate of backward reaction = kRate of backward reaction = krr[C][D][C][D]

• At equilibriumAt equilibrium

cr

f KBA

DC

k

k

]][[

]][[

]][[]][[ DCkBAk rf