Chemical Kinetics

Chemical KineticsChemical Kinetics

Chapter 16Chapter 16

Thermodynamics Vs. KineticsThermodynamics Vs. Kinetics

ThermodynamicsThermodynamics - Will the reaction - Will the reaction happen under specified Conditions?happen under specified Conditions?

Thermodynamics and EquilibriumThermodynamics and Equilibrium - What - What will be the extent of the reaction?will be the extent of the reaction?

KineticsKinetics - How quickly will the reaction - How quickly will the reaction occur?occur?

KineticsKinetics - What factors will affect the rate - What factors will affect the rate of reaction:?of reaction:?

The Rate of ReactionThe Rate of Reaction

Rate of ReactionRate of Reaction – describes how fast – describes how fast reactants are used up and how products reactants are used up and how products are formedare formed

Chemical KineticsChemical Kinetics – The study of the rates – The study of the rates of reactions, what affects them, and the of reactions, what affects them, and the mechanisms (steps) in which they occur.mechanisms (steps) in which they occur.

The Rate of ReactionsThe Rate of Reactions

Rates are expressed as (Rates are expressed as (molarity / molarity / time)time)Problem – you need a way to track the Problem – you need a way to track the

change in molarity over time!change in molarity over time!Titration – following the acid concentrationTitration – following the acid concentrationLight absorption over time may changeLight absorption over time may changeChange in pressure over timeChange in pressure over time


One Step Mechanism – simplest CaseOne Step Mechanism – simplest CaseA(g) A(g) B(g) + C (g) B(g) + C (g)The rate is proportional to the The rate is proportional to the

concentration of the reactantconcentration of the reactantR R [A] or R = k[A] [A] or R = k[A]K= specific rate constantK= specific rate constant22ndnd equation only valid at given equation only valid at given

temperaturetemperature


2A(g) 2A(g) B(g) + C(g) (coefficients not one) B(g) + C(g) (coefficients not one)R R [A] [A]2 2 oror R = k[A]R = k[A]2 2

The reaction is second order with respect The reaction is second order with respect to Ato A

This relationship is found experimentallyThis relationship is found experimentallyThese relationships are only true for These relationships are only true for

simple one step mechanisms – most are simple one step mechanisms – most are NOTNOT


Rate Law ExpressionsRate Law Expressions – found – found only only through experimentationthrough experimentation, not through , not through inspection of balanced equations.inspection of balanced equations.

Variation on rate law expression:Variation on rate law expression:aA + bB aA + bB cC + dD cC + dD (-1/a) (-1/a) [A] / [A] / tt (-1/b) (-1/b) [B] / [B] / tt ( 1/c) ( 1/c) [C] / [C] / tt ( 1/d) ( 1/d) [D] / [D] / tt

Factors Affecting the Rate of Factors Affecting the Rate of ReactionReaction

1.1. The nature of the reactantsThe nature of the reactants

1.1. The state of matter (temperature The state of matter (temperature related)related)

2.2. Allotropic Form of matterAllotropic Form of matter

1.1. Diamond vs. graphite, similar Diamond vs. graphite, similar G G values, but oxidation of graphite is values, but oxidation of graphite is very rapidvery rapid

Factors Affecting the Rate of Factors Affecting the Rate of ReactionReaction

3.3. Chemical IdentityChemical Identity

1.1. Mg vs. Na in water (sodium has lower Mg vs. Na in water (sodium has lower ionization energy)ionization energy)

4.4. Particle size of the solidParticle size of the solid

1.1. Greater surface area in smaller particles Greater surface area in smaller particles can speed up the reactioncan speed up the reaction

1.1. Pulverize the solidPulverize the solid

2.2. Make an aqueous solutionMake an aqueous solution

3.3. Evaporate a liquidEvaporate a liquid

Factors Affecting Reaction RateFactors Affecting Reaction Rate

2.2. ConcentrationConcentration – effect is summarized in – effect is summarized in the rate law expression.the rate law expression.

1.1. Increasing the concentration of reactants Increasing the concentration of reactants increases the frequency of the collisions and increases the frequency of the collisions and therefore affects the rate of reactionstherefore affects the rate of reactions


2A(g) + B (g) 2A(g) + B (g) 3C(g) 3C(g)R = k [A]R = k [A]xx [B] [B]yy

X is the order of reaction with respect to AX is the order of reaction with respect to AY is the order of reaction with respect to BY is the order of reaction with respect to BThe overall rate of reaction is x + yThe overall rate of reaction is x + y

Factors Affecting Reaction RateFactors Affecting Reaction Rate

As slope changes, so As slope changes, so does the rate of reaction.does the rate of reaction.

Concentration affects the Concentration affects the rate.rate.

Rate is considered an Rate is considered an instantaneous instantaneous measurement.measurement.

Generally, we measure Generally, we measure the initial rate of reaction.the initial rate of reaction.

Example: aA + bB Example: aA + bB cC cC

ExperimentExperiment Initial [A]Initial [A] Initial [B]Initial [B] Rate of Rate of Formation Formation of C M/sof C M/s

11 0.10M0.10M 0.10M0.10M 2.0 x102.0 x10-4-4

22 0.20M0.20M 0.30M0.30M 4.0 x 104.0 x 10-4-4

33 0.10M0.10M 0.20M0.20M 2.0 x 102.0 x 10-4-4

ExampleExample

What is the order of reaction with respect What is the order of reaction with respect to [A]?to [A]?

What is the order of reaction with respect What is the order of reaction with respect to [B]?to [B]?

If the rate is reported as the rate of If the rate is reported as the rate of formation of C, what would be the rate of formation of C, what would be the rate of disappearance of A?disappearance of A?

Example 2: aA + bB Example 2: aA + bB cC cC

ExperimentExperiment Initial [A]Initial [A] Initial [B]Initial [B] Rate of Rate of reaction reaction

M/sM/s

11 0.200.20 0.0500.050 4.0 x104.0 x10-3-3

22 0.800.80 0.0500.050 1.6 x101.6 x10-2-2

33 0.400.40 0.2000.200 3.2 x103.2 x10-2-2

Example 2Example 2

What is the order of reaction with respect What is the order of reaction with respect to [A]?to [A]?

What is the order of reaction with respect What is the order of reaction with respect to [B]?to [B]?

If the rate is reported as the rate of If the rate is reported as the rate of formation of C, what would be the rate of formation of C, what would be the rate of disappearance of A?disappearance of A?

Integrated Rate Law EquationIntegrated Rate Law Equation

First Order Reaction – aA First Order Reaction – aA products productsR = k[A]R = k[A]First order in [A], 1First order in [A], 1stst order overall order overallThe Integrated Rate Equation is:The Integrated Rate Equation is:

ln([A]ln([A]oo/[A]) = akt/[A]) = akt

Rearranged: ln[A]Rearranged: ln[A]oo – ln[A] = akt – ln[A] = akt

ln[A] = -akt + ln[A]ln[A] = -akt + ln[A]oo

Y = mx + bY = mx + b

Plot of ln[A] vs TimePlot of ln[A] vs Time

First Order ReactionFirst Order Reaction

Integrated Rate EquationsIntegrated Rate Equations

First Order Reactions:First Order Reactions:Useful to approximate the time when half Useful to approximate the time when half

of the reactants are used up because the of the reactants are used up because the rate slows down considerably!rate slows down considerably!

Rearrange the equation to solve for TRearrange the equation to solve for TT=(1/ak) (ln[A]T=(1/ak) (ln[A]oo/[A])/[A])

Integrated Rate EquationsIntegrated Rate Equations

When [A] = ½ [A]When [A] = ½ [A]oo

TT1/2 1/2 = (1/ak) (ln[A]= (1/ak) (ln[A]oo/1/2[A]/1/2[A]oo))

TT1/2 1/2 = (1/ak) ln 2 = 0.693/ak= (1/ak) ln 2 = 0.693/ak

for 1for 1stst order reactions only, t order reactions only, t1/21/2 depends depends

only on the constant and does not change only on the constant and does not change as the reaction progresses.as the reaction progresses.

Practical Example: Half-life!Practical Example: Half-life!

Example 3Example 3

Cyclopentane decomposes to propene in Cyclopentane decomposes to propene in a 1a 1stst order reaction. K= 9.2 s-1 at 1000oC. order reaction. K= 9.2 s-1 at 1000oC.

A) calculate the half life at this temperature.A) calculate the half life at this temperature.

B) How much of a 3.0g sample is left after B) How much of a 3.0g sample is left after 0.50 seconds? (assume grams are in the 0.50 seconds? (assume grams are in the same proportionality as molarity)same proportionality as molarity)

Second Order ReactionsSecond Order Reactions R = k[A]R = k[A]22

If a reaction is second order to a particular If a reaction is second order to a particular reactant and second order overall, the reactant and second order overall, the Integrated Rate Equation is:Integrated Rate Equation is:

1/[A] – 1/[A]1/[A] – 1/[A]oo = akt = aktAt tAt t1/21/2 [A] = 1/2[A] [A] = 1/2[A]oo

1/(1/2)[A]1/(1/2)[A]oo – 1/[A] – 1/[A]oo = akt = akt(1/2)(1/2)

2/[A]2/[A]oo – 1/[A] – 1/[A]oo = akt = akt(1/2)(1/2)

1/[A]1/[A]o o = akt= akt(1/2) (1/2) and tand t1/21/2 = 1/ak[A] = 1/ak[A]oo Concentration varies with each passing time Concentration varies with each passing time

period…concentration dependant!period…concentration dependant!

Second Order ReactionSecond Order Reaction

The Half life of a second order reaction The Half life of a second order reaction depends on the initial concentration at the depends on the initial concentration at the beginning of THAT time period.beginning of THAT time period.

Example 4Example 4

CHCH33CHO (g) CHO (g) CH CH44 (g)+ CO (g) (g)+ CO (g)

R = [CHR = [CH33CHO]CHO]2 2 and k = 2.0 x 10and k = 2.0 x 10-2 -2 L/mole hr L/mole hr

at 527at 527ooCC

a) What is the half life if 0.10 mol is injected a) What is the half life if 0.10 mol is injected into a 1.0L vessel?into a 1.0L vessel?

b) How many moles of CHb) How many moles of CH33CHO remain CHO remain

after 200 hours?after 200 hours?

Second Order ReactionSecond Order Reaction

Zero Order ReactionsZero Order Reactions

Zero Order Reaction = aA Zero Order Reaction = aA products productsR = kR = k Integtrated Rate Law = Integtrated Rate Law = [A] = [A[A] = [Aoo] – akt] – akt

At tAt t1/21/2…1/2[A…1/2[Aoo] = [A] = [Aoo] – akt] – akt

TT1/21/2 = [A = [Aoo] / 2ak] / 2ak

Zero Order ReactionZero Order Reaction

Zero Order ReactionsZero Order Reactions

Graphical ReviewGraphical Review

Can you pick out which is Zero, Can you pick out which is Zero, First, and Second Order?First, and Second Order?

Rate LawRate Law R = kR = k R = k[A]R = k[A] R = k[A]R = k[A]22

Units of kUnits of k M/tM/t 1/time1/time 1/Mt1/Mt

Reg. IREReg. IRE [A] = [A[A] = [Aoo] – akt] – akt ln([A]ln([A]oo/[A]) = /[A]) =

aktakt1/[A] – 1/[A]1/[A] – 1/[A]oo

= akt= akt

IRE IRE y=mx+by=mx+b

S.L.GraphS.L.Graph [A] vs. t[A] vs. t ln[A] vs.tln[A] vs.t 1/[A] vs. t1/[A] vs. t

SlopeSlope -ak-ak -ak-ak akak

TT1/21/2 [A[Aoo]/2ak]/2ak .693/ak.693/ak 1/ak[A1/ak[Aoo] ]

y int.y int. [A[Aoo]] ln[Aln[Aoo]] 1/[A1/[Aoo]]

Investigating Factors Affecting Investigating Factors Affecting Reaction RateReaction Rate

Collision Theory, Transition State Collision Theory, Transition State Theory, Temperature, Catalysts Theory, Temperature, Catalysts

and Activation Energyand Activation Energy

Collision TheoryCollision Theory

Generally, any factor which increases the Generally, any factor which increases the number of molecular or ionic collisions in number of molecular or ionic collisions in solution will increase the rate of reactionsolution will increase the rate of reactionStirringStirringTemperatureTemperatureConcentrationConcentration

Not Every Collision will guarantee a Not Every Collision will guarantee a reaction! Orientation of the collision often reaction! Orientation of the collision often affects the outcome!affects the outcome!

Transition State TheoryTransition State Theory

Transition StateTransition State – short lived high energy – short lived high energy complex between reactant and product.complex between reactant and product.

Exothermic ReactionExothermic Reaction

Endothermic ReactionEndothermic Reaction

Transition StateTransition State

Ea forward – Ea reverse = Ea forward – Ea reverse = E rxnE rxnActivation energy is generally kinetic Activation energy is generally kinetic

energy, when equal or greater to the Ea, energy, when equal or greater to the Ea, the reaction will proceed, if not, the the reaction will proceed, if not, the reaction will not proceed.reaction will not proceed.

Effect of TemperatureEffect of Temperature

k increases with kelvink increases with kelvin

Theoretical ExplanationTheoretical Explanation Best model to explain Best model to explain

is is collision theorycollision theory Kinetic molecular Kinetic molecular

theorytheory says the faster says the faster the particles move, the the particles move, the more they will collidemore they will collide


ObservedObserved – reaction – reaction doesn’t increase with doesn’t increase with temperature as fast temperature as fast as the expected as the expected number of collisionsnumber of collisions

Solution – Solution – Arrhenius – 1880Arrhenius – 1880 Not all collisions are Not all collisions are

effective, there must effective, there must be a minimum be a minimum amount of energy amount of energy which must be which must be present (Ea)present (Ea)


# effective collisions = total collisions (e# effective collisions = total collisions (e(-Ea/RT)(-Ea/RT)))

Total collisions = ZTotal collisions = Z -Ea/RT = fraction of collisions with Ea or -Ea/RT = fraction of collisions with Ea or

greater at a given temperaturegreater at a given temperature

PROBLEM!PROBLEM!

Number of observed collisions were less Number of observed collisions were less than calculatedthan calculated

many of the collisions were ineffective many of the collisions were ineffective due to orientation.due to orientation.

Fudge Factor PFudge Factor PP = steric factor (<1) = fraction of collisions P = steric factor (<1) = fraction of collisions

with correct orientationwith correct orientation

Arrhenius’ EquationArrhenius’ Equation

k = Z p (ek = Z p (e(-Ea/RT)(-Ea/RT)))

Z and p combined into ultimate fudge factor A Z and p combined into ultimate fudge factor A (frequency factor)(frequency factor)

k = A (ek = A (e(-Ea/RT)(-Ea/RT))) Alternate form:Alternate form: lnk = -Ea/RT + lnA lnk = -Ea/RT + lnA Y = m x + bY = m x + b

Alternate Form 2Alternate Form 2

Ln(kLn(k11/k/k22) = -Ea/R (1/T) = -Ea/R (1/T11 – 1/T – 1/T22))

Use to directly calculate the effect of Use to directly calculate the effect of temperature on the rate constant!temperature on the rate constant!

CatalystsCatalysts

CatalystsCatalysts – substances added to a – substances added to a reaction which provide an alternative reaction which provide an alternative pathway to the reaction, thus lowering the pathway to the reaction, thus lowering the activation energy for the reaction.activation energy for the reaction.

Heterogeneous catalystsHeterogeneous catalysts – exist in the – exist in the different state as the reactants.different state as the reactants.

Homogeneous catalystsHomogeneous catalysts – exists in the – exists in the same state as the reactants.same state as the reactants.

Lowers Ea by facilitating the breaking of Lowers Ea by facilitating the breaking of bondsbonds

Increases the rate of reactionIncreases the rate of reaction

CatalystsCatalysts

Heterogeneous Heterogeneous – works by contact – works by contact (contact catalyst)(contact catalyst)AdsorbtionAdsorbtion – reactant comes in contact with – reactant comes in contact with

the catalystthe catalystDesorbtionDesorbtion – newly formed product – newly formed product

separates from the catalyst.separates from the catalyst.Page 692 graphic!Page 692 graphic!

CatalystsCatalysts

Enzymes – natural protein based catalystsEnzymes – natural protein based catalystsWork on same principlesWork on same principlesEnzyme-substrate complex provides the Enzyme-substrate complex provides the

alternative pathway to high energy alternative pathway to high energy biological processes.biological processes.

Reaction MechanismsReaction Mechanisms

Writing Rate Laws for Multi-Step Writing Rate Laws for Multi-Step ReactionsReactions

Reaction Mechanisms VocabularyReaction Mechanisms Vocabulary

Reaction MechanismsReaction Mechanisms – series of elementary – series of elementary steps by which a reaction occurs.steps by which a reaction occurs.

Elementary StepElementary Step – a reaction whose rate law – a reaction whose rate law can be written from its molecularity (the number can be written from its molecularity (the number of species that must collide to produce the of species that must collide to produce the reaction of the elementary step)reaction of the elementary step)

Reaction IntermediateReaction Intermediate – a product that is – a product that is immediately consumed in a subsequent immediately consumed in a subsequent reaction.reaction.

PROBLEM!!!PROBLEM!!!

Sometimes problems are given where the Sometimes problems are given where the overall reaction does not seem to match overall reaction does not seem to match the rate law…the rate law…

NONO22 (g) + CO (g) (g) + CO (g) NO (g) + CO NO (g) + CO2 2 (g)(g)

Rate law given as: R = k[NORate law given as: R = k[NO22]]22

There must be an explanation!There must be an explanation!

Multi Step ReactionsMulti Step Reactions

NONO22 (g) + CO (g) (g) + CO (g) NO (g) + CO NO (g) + CO2 2 (g)(g)

Rate law given as: R = k[NORate law given as: R = k[NO22]]22

Step 1Step 1 - NO - NO2(g)2(g) + NO + NO2(g)2(g) NO NO3(g)3(g) + NO + NO(g)(g) Step 2Step 2 - NO - NO3(g)3(g) + CO + CO (g)(g) NO NO2(g)2(g) + CO + CO2 (g)2 (g)

Step 1 and 2 are elementary steps and each Step 1 and 2 are elementary steps and each has their own rate constanthas their own rate constant

The elementary steps (when summed) must The elementary steps (when summed) must give the overall balanced reaction equationgive the overall balanced reaction equation

The rate law for the slow step must agree with The rate law for the slow step must agree with the experimentally determined rate lawthe experimentally determined rate law

SummarySummary

Elementary Elementary StepStep

MolecularityMolecularity Rate LawRate Law

A A prod prod UnimolecularUnimolecular R = k[A]R = k[A]

A+A A+A prod prod BimolecularBimolecular R = k[A]R = k[A]22

A + B A + B prod prod BimolecularBimolecular R = k[A][B]R = k[A][B]

2A + B 2A + B prod prod TrimolecularTrimolecular R = k[A]R = k[A]22[B][B]

A + B + C A + B + C prodprod

TrimolecularTrimolecular R = k[A][B][C]R = k[A][B][C]

Rate Determining StepRate Determining Step

Slow step = rate determining stepSlow step = rate determining step

Most reactions are multiple step reactionsMost reactions are multiple step reactions Reactions can never occur faster than its Reactions can never occur faster than its

slowest stepslowest step If Step 1 is the slow step, then COIf Step 1 is the slow step, then CO22 can can

only be produced as fast as NOonly be produced as fast as NO33 is is producedproduced

The overall rate = kThe overall rate = k11[NO[NO22]]22

Reaction MechanismsReaction Mechanisms

Deduction of Rate Mechanism:Deduction of Rate Mechanism:1.1. Experimentally determine the rate lawExperimentally determine the rate law

2.2. Propose mechanisms using two rulesPropose mechanisms using two rules

3.3. Devise experiment to eliminate less likely Devise experiment to eliminate less likely possibilities.possibilities.

ExampleExample

2NO2NO22(g) + F(g) + F22(g) (g) 2NO 2NO22F(g)F(g) Rate = k[NORate = k[NO22][F][F22]] Possible Mechanisms:Possible Mechanisms:

Step 1 – NOStep 1 – NO22 + F + F22 NO NO22F + FF + F Slow?Slow? Step 2 – F + NOStep 2 – F + NO22 NO NO22FF Fast?Fast?

Is this an acceptable mechanism?Is this an acceptable mechanism?1.1. Steps add up.Steps add up.2.2. Does the rate law agree with the rate law of Does the rate law agree with the rate law of

the slow step? (R = kthe slow step? (R = k11[NO[NO22][F][F22])])

ExceptionsExceptions

See Page 683 yellow box.See Page 683 yellow box.Particularly true of reactions Particularly true of reactions third order third order

because the tri molecular collisions aren’t because the tri molecular collisions aren’t likely to occur frequently!likely to occur frequently!

These reactions are generally explained These reactions are generally explained with mechanisms where tri molecular with mechanisms where tri molecular collisions do not occur.collisions do not occur.

ExampleExample

2NO 2NO (g)(g) + Br + Br2 (g)2 (g) 2NOBr 2NOBr (g)(g) R = k[NO]2[Br] R = k[NO]2[Br]

1)1) NO + BrNO + Br22 NOBr NOBr22 (Fast Equ. Step) (Fast Equ. Step)

2)2) NOBrNOBr2 2 + NO + NO 2NOBr (Slow) 2NOBr (Slow)

Slow Step RSlow Step R22 = k = k22[NOBr[NOBr22][NO]][NO]

RR1f1f = R = R2f2f as it is at equilibrium as it is at equilibrium

Example ContinuedExample Continued

kk1f1f [NO][Br [NO][Br22] = k] = k1R1R[NOBr[NOBr22]… rearrange]… rearrange

[NOBr[NOBr22] = (k] = (k1f1f /k /k1R1R) [NO][Br) [NO][Br22] ]

RR22 = k = k22[NOBr[NOBr22][NO]… substitute NOBr][NO]… substitute NOBr22

Overall R = kOverall R = k2 2 (k(k1f1f /k /k1R1R) [NO] [Br) [NO] [Br22] [NO]] [NO]

Example ContinuedExample Continued

kk2 2 (k(k1f1f /k /k1R1R) = overall rate constant k) = overall rate constant k

R = kR = k2 2 (k(k1f1f /k /k1R1R) [NO] [Br) [NO] [Br22] [NO]] [NO]

R = k [NO]R = k [NO]22 [Br [Br22] ]

Consistent with the overall rate lawConsistent with the overall rate law

Chemical Kinetics

Documents

Transcript of Chemical Kinetics