Kinetics and MechanismKinetics and Mechanism

16.2.1 Explain that reactions can occur by more 16.2.1 Explain that reactions can occur by more than one step and that the slowest step than one step and that the slowest step determines the rate of the reaction (rate-determines the rate of the reaction (rate-

determining step)determining step)

16.2.2 Describe the relationship between 16.2.2 Describe the relationship between reaction mechanism, order of reaction and rate-reaction mechanism, order of reaction and rate-

determining step.determining step.

16.2 Reaction mechanism16.2 Reaction mechanism

Chemical ReactionsChemical Reactions

The chance of more than two particles The chance of more than two particles colliding simultaneously with correct colliding simultaneously with correct geometry and minimum energy required is geometry and minimum energy required is very small.very small.

If there are more than 2 reactants, the If there are more than 2 reactants, the reaction must occur by a reaction must occur by a number of number of simpler steps.simpler steps.

Sometimes the Sometimes the molecularitymolecularity of a reaction can be used to of a reaction can be used to guess if an elementary reaction is a rate–determining guess if an elementary reaction is a rate–determining step. step.

Molecularity is the count of reacting particles in an Molecularity is the count of reacting particles in an elementary reaction.elementary reaction.

Termolecular reaction are almost Termolecular reaction are almost always rate limiting always rate limiting because it is a low probability event to get three particles because it is a low probability event to get three particles to hit in the same location at the same timeto hit in the same location at the same time

Reaction MechanismsReaction Mechanisms

A A reaction mechanismreaction mechanism is a series of simple is a series of simple steps that ultimately lead from the initial steps that ultimately lead from the initial reactants to the final products of a reaction.reactants to the final products of a reaction.

The mechanism must account for the The mechanism must account for the experimentally determined rate law.experimentally determined rate law.

The mechanism must be consistent with the The mechanism must be consistent with the stoichiometry of the overall or net reaction.stoichiometry of the overall or net reaction.

Step 1Step 1

Rate = Rate = kk11[I[I22]]

Step 2Step 2

Rate = Rate = kk–1–1[I][I]22

Step 3Step 3

Rate = Rate = kk22[H[H22][I]][I]22

Reaction MechanismsReaction Mechanisms

The The rate-determining steprate-determining step is the crucial step in is the crucial step in establishing the rate of the overall reaction.( it is establishing the rate of the overall reaction.( it is the slowest step and also the one with the the slowest step and also the one with the highest AE)highest AE)

Some two-step mechanisms have a slow first Some two-step mechanisms have a slow first step followed by a fast second step, while others step followed by a fast second step, while others have a fast reversible first step followed by a have a fast reversible first step followed by a slow second step.slow second step.

A Mechanism With A Slow Step A Mechanism With A Slow Step Followed By A Fast StepFollowed By A Fast Step- A Plausible Mechanism- A Plausible Mechanism

Slow step:Slow step: HH22OO22 + I + I-- H H22O + OIO + OI--

Fast step:Fast step: HH22OO22 + OI + OI-- H H22O + OO + O22 + I + I--

______________________________________________________________________________________________________________________

Net equation:Net equation: 2 H2 H22OO22 2 H 2 H22O + OO + O22

II-- - catalyst; - catalyst; OIOI-- - intermediate - intermediateThe slow step is the The slow step is the rate-determining steprate-determining step..

Rate = rate of slow step = k[HRate = rate of slow step = k[H22OO22][I][I--]]

MechanismsMechanisms

IntermediateIntermediate A species that is created in one step and A species that is created in one step and

consumed in the otherconsumed in the other

CatalystCatalyst A species that is present originally then A species that is present originally then

reforms later on during the reactionreforms later on during the reaction It is not written in the overall equation, but you It is not written in the overall equation, but you

maymay see it noted above the reaction arrow. see it noted above the reaction arrow.

Since the energy of activation for the first Since the energy of activation for the first step is so much higher than that for the step is so much higher than that for the second step, the first step of the an Ssecond step, the first step of the an SNN1 1

mechanism is the mechanism is the rate-limiting or rate-rate-limiting or rate-determining stepdetermining step. .

A Mechanism With A Slow Step A Mechanism With A Slow Step Followed By A Fast StepFollowed By A Fast Step

Slow step:Slow step: HH22OO22 + I + I-- H H22O + OIO + OI--

Fast step:Fast step: HH22OO22 + OI + OI-- H H22O + OO + O22 + I + I--

Overall:Overall: 2 H2 H22OO22 (aq) (aq) 2 H 2 H22O (l) + OO (l) + O22 (g) (g)

Facts: (1) The rate of decomposition of HFacts: (1) The rate of decomposition of H22OO22 is first is first order order in in both Hboth H22OO22 and I and I--, or second order overall., or second order overall.

(2) The reactant I(2) The reactant I-- is unchanged in the reaction is unchanged in the reaction and hence does not appear in the equation for and hence does not appear in the equation for the net the net reaction.reaction.

A Mechanism With A Fast Reversible A Mechanism With A Fast Reversible

Step Followed By A Slow StepStep Followed By A Slow Step

2 NO (g) + O2 NO (g) + O22 (g) (g) 2 NO 2 NO22 (g) (g)

Experimentally found:Experimentally found:

Rate = k[NO]Rate = k[NO]22[O[O22]]

A Mechanism With A Fast Reversible A Mechanism With A Fast Reversible Step Followed By A Slow Step – Step Followed By A Slow Step –

A Plausible MechanismA Plausible Mechanism

kk11

Fast step:Fast step: 2 NO < -- > N2 NO < -- > N22OO22

kk-1-1

kk22

Slow step:Slow step: NN22OO22 + O + O22 2 NO 2 NO22

Net equation:Net equation: 2 NO + O2 NO + O22 2 NO 2 NO22

MolecularityMolecularityThe number of molecules that participate The number of molecules that participate as reactants in anas reactants in an elementary stepelementary step

UnimolecularUnimolecular: a single molecule is : a single molecule is involved.involved. Ex: CHEx: CH33NC (can be rearranged)NC (can be rearranged) Radioactive decayRadioactive decay Its rate law is 1Its rate law is 1stst order with respect to that order with respect to that

reactantreactant

BimolecularBimolecular: Involves the collision of two : Involves the collision of two molecules (that form a transition state that molecules (that form a transition state that can not be isolated)can not be isolated) Ex: NO + OEx: NO + O33 NO NO22 + O + O22

It’s rate law is 1It’s rate law is 1stst order with respect to each order with respect to each reactant and therefore is 2reactant and therefore is 2ndnd order overall. order overall.

Rate Rate =k=k[NO][O[NO][O33]]

Termolecular: Termolecular: simultaneous collision of simultaneous collision of three molecules. Far less probable.three molecules. Far less probable.

Some possible mechanisms for the Some possible mechanisms for the reaction; 2A + B reaction; 2A + B C + D C + D

Rate Laws for Elementary stepsRate Laws for Elementary steps

Can use the equation coefficients as the Can use the equation coefficients as the reaction orders in the rate law for an reaction orders in the rate law for an elementary stepelementary step

Elementary stepElementary step MolecularityMolecularity Rate lawRate law

A A product product UniUni Rate = k[A]Rate = k[A]

2A 2A product product BiBi Rate = k[A]Rate = k[A]22

A + B A + B product product BiBi Rate = k[A][B]Rate = k[A][B]

2A + B 2A + B product product TerTer Rate = k[A]Rate = k[A]22[B][B]

Differences between intermediates and Differences between intermediates and transition statestransition states

NOTE: transition state and activated complex are the same thing!

16.3 Activation energy16.3 Activation energy

16.3.1 Describe qualitatively the relationship between 16.3.1 Describe qualitatively the relationship between the rate constant (k) and temperature (T).the rate constant (k) and temperature (T).

16.3.2 Determine activation energy (Ea) values from 16.3.2 Determine activation energy (Ea) values from the Arrhenius equation by a graphical method. the Arrhenius equation by a graphical method.

ExothermicExothermicactivation energy activation energy (the energy needed (the energy needed so that the reactants so that the reactants bonds will break and bonds will break and reform to make reform to make product)product)

Review of EndothermicReview of Endothermic

Reactants Ep is lower Reactants Ep is lower than Products Ep.than Products Ep.

Need to add more Need to add more energy to the system energy to the system for the forward reaction for the forward reaction to take place.to take place.

Still need to consider Still need to consider activation energyactivation energy

Activated ComplexActivated ComplexIs the short-lived, unstable structure Is the short-lived, unstable structure formed during a successful collision formed during a successful collision between reactant particles.between reactant particles.

Old bonds of the reactants are in the Old bonds of the reactants are in the process of breaking, and new products are process of breaking, and new products are formingforming

Ea is the minimum energy required for the Ea is the minimum energy required for the activation complex to form and for a activation complex to form and for a successful reaction to occur.successful reaction to occur.

Fast and slow reactionsFast and slow reactions

The The smallesmaller the activation r the activation energy, the energy, the fasterfaster the reaction the reaction will occur regardless if will occur regardless if exothermic or endothermic.exothermic or endothermic.

Practice:Practice:

1.1. The following hypothetical reaction has The following hypothetical reaction has an Ea of 120kJ and a an Ea of 120kJ and a ΔΔH of 80kJH of 80kJ

2a + B 2a + B 2C + D 2C + D Draw and label a potential energy diagram Draw and label a potential energy diagram

for this reaction.for this reaction. What type of reaction is this?What type of reaction is this? Calculate the activation energy for the Calculate the activation energy for the

reverse reaction.reverse reaction. Calculate the Calculate the ΔΔH for the reverse reaction.H for the reverse reaction.

2.2. Analyze the Analyze the activation energy activation energy diagram below.diagram below.What is the Ea for the What is the Ea for the forward reaction? For forward reaction? For the reverse reaction?the reverse reaction?

What is the What is the ΔΔH for the H for the forward reaction? For forward reaction? For the reverse reaction?the reverse reaction?

What is the energy of the What is the energy of the activated complex?activated complex?

At higher temperatures there is a greater At higher temperatures there is a greater proportion of molecules that would have proportion of molecules that would have enough Ea for the reaction to proceed.enough Ea for the reaction to proceed.

This is the major reason why high temps This is the major reason why high temps increase rate.increase rate.

Effect of Temperature on the Reaction RateEffect of Temperature on the Reaction Rate

The Arrhenius equation show the effect of The Arrhenius equation show the effect of temperature on the rate constant, ktemperature on the rate constant, kIt indicates that k depends exponentially on It indicates that k depends exponentially on temperaturetemperature

Arrhenius equationArrhenius equation::

kk = A e = A e--EEaa/RT/RT

EEaa – activation energy – activation energyRR – gas constant, 8.3145 J mol – gas constant, 8.3145 J mol-1-1KK-1-1

TT - Kelvin temperature - Kelvin temperatureA A – Arrhenius constant (depends on collision rate and – Arrhenius constant (depends on collision rate and

shape of molecule)shape of molecule)

kk = A e = A e--EEaa/RT/RT

As T increases, the negative exponent As T increases, the negative exponent becomes smaller, so that value of k becomes smaller, so that value of k becomes larger, which means that the rate becomes larger, which means that the rate increases.increases.

Higher T Higher T Larger k Larger k Increased Increased raterate

ln k and 1/T is linearln k and 1/T is linear

With R known, we can find With R known, we can find EaEa graphically graphically from a series of k values at different from a series of k values at different temperatures.temperatures.

ln ln kk22 = = - Ea- Ea ( 1/T ( 1/T22 – 1/T – 1/T11))

kk11 R R

Ea = -R (ln kEa = -R (ln k2 2 / k/ k11) ( 1/T) ( 1/T22 – 1/T – 1/T11) ) -1-1

ProblemProblem

The decomposition of hydrogen iodide has The decomposition of hydrogen iodide has rate constants of 9.51 x10rate constants of 9.51 x10-9-9 L/mol.s at L/mol.s at 500.0 K and 1.10 x 10500.0 K and 1.10 x 10-5-5 L/mol.s at 600.0 K. L/mol.s at 600.0 K. Find Ea. Find Ea.

SolutionSolution

Ea = -R (ln kEa = -R (ln k2 2 / k/ k11) ( 1/T) ( 1/T22 – 1/T – 1/T11) ) -1-1

Ea = - (8.314)( ln 1.10 x10-5/ 9.51 x109)(1/600.00 – 1/500.0)

= 1.76 x 105 J/mol

If rearrange the equation and convert it to:If rearrange the equation and convert it to:lnlnkk = = - - EEa a .. 1 1 ++ lnlnAA

R R TT

A graph of ln k againstA graph of ln k against 1/T 1/T will be linear with a will be linear with a slope/gradient ofslope/gradient of –Ea/R–Ea/R and an intercept on the y-and an intercept on the y-axis of lnAaxis of lnA

lnlnkk = = - - EEa a .. 1 1 ++ lnlnAA R R T T y = y = mm .. xx + + bb

Plot lnPlot lnkk vs. 1/T = straight line vs. 1/T = straight line

ReadingsReadings

Section 16.5, 16.6, 16.7, 16.8 Section 16.5, 16.6, 16.7, 16.8 Effect of temperature, concentration and Effect of temperature, concentration and

catalysts on ratecatalysts on rate Reaction mechanisms and rate lawReaction mechanisms and rate law

Pg 705-722Pg 705-722