Kinetics Part V: Reaction Mechanisms

Dr. C. Yau

Spring 2014

Jespersen Chap. 14 Sec 7

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MechanismsMechanism refers to the series of individual

steps that add up to the overall observed reaction. It tells us on the molecular level what is happening, such as what collides with what, and which the slowest step is.

Elementary reaction refers to each of the individual steps in the mechanism.

The sum of the elementary reactions must give the overall reaction.

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Reaction Mechanisms

• tell what happens on the molecular level, and in what order

• tell us which steps in a reaction are fast and slow

• The rate determining step is the slowest step of the reaction that accounts for most of the reaction time.

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Example of a reaction mechanism

For the reaction of NO with H2

2NO + 2H2 N2 + 2H2O

The proposed mechanism is...

1. 2NO N2O2 (fast)

2. N2O2 + H2 N2O + H2O (slow)

3. N2O + H2 N2 + H2O (fast)

These are the elementary rxns. Verify they add to give the overall equation.

Which is the rate determining step (rds)?4

Elementary Steps: Molecularity vs. Rate LawElementary Reactions Molecularity Rate Law for the

elementary step

A→Products Unimolecular Rate=k[A]

A+A →Products

A+B →Products

Bimolecular Rate=k[A]2

Rate=k[A][B]

A+A+B →Products

3A →Products

A+B+C →Products

Termolecular Rate=k[A]2[B]

Rate=k[A]3

Rate=k[A][B][C]

Molecularity refers to how many species are involved in the step. It is reflected in the overall order of reaction in the rate law.

Unlike the overall rate law, rate law of the elementary rxn uses the coefficients as the order of reaction.5

Rate Laws And Mechanisms• The majority of the reaction time is taken by

the rate determining step.• Substances that react in this step have the

greatest effect on the reaction rate.• The observed rate law usually matches the

rate law based on the rate determining step where the order of each reactant is its stoichiometric coefficient.

• Note: Observed rate law is NOT based on the stoichiometric coefficients of the overall rxn.

Note: "Order" does not refer to which comes first, but to the molecularity: unimolecular? bimolecular? termolecular?

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The “Transition State” in a MechanismLet us consider a simple reaction...

A + BC AB + C Reactants Products

One possible mechanism is to have this happen in one step.

Bond forming and bond breaking happening at the same time.

Reactants

Products

Transition State

PE

Reaction Coordinate

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Bond forming and bond breaking happening at the same time.

The transition state is unstable and cannot be isolated.It is the highest point of the mechanism in the PE diagram.Transition state = T.S. = activated complex

Reactants

Products

Transition State

The “Transition State” in a Mechanism

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The “Intermediate” in a MechanismLet us consider the same reaction...

A + BC AB + C Reactants Products

We can have a mechanism where 2 steps are involved.Step 1: B–C bond breaks to form B + CStep 2: A forms bond with B.

Reactant B-C

C

B

Bond begins tobreak.

C

B

C leaves.B is alone, as an intermediate.

B

A

A begins to form bond to B.

A is fully bonded to B.

Reactant T.S. Intermediate T.S. Product

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A

C

B

C

B B

A

C

B

C

B

A

ReactantsA + B-C

ProductsA-B + C

T.S.T.S.

Intermediate

B-C bond beginsto break.

B is the intermediate.

A-B bond begins to form.

An intermediate is formed during a reaction and consumed before the end of the reaction. It cannot be isolated.

Intermediates versus Catalysts

• Because catalysts interact with the reactant, they will appear in the mechanism

• Catalysts are consumed in an early step and are regenerated in a subsequent step

• Intermediates are temporary products.• Intermediates are formed in an early step and

consumed in a later step• Catalysts are there at beginning & at the end

of the rxn.• Intermediates are not there at the beginning,

nor at the end of the rxn.• Neither will show up in the overall eqn. 11

Intermediates in a mechanism 2NO N2O2 (fast)

N2O2 + H2 N2O + H2O (slow)

N2O + H2 N2 + H2O (fast)

Are there any catalysts or intermediates in this mechanism?

Catalysts are ADDED, and they reappear at the end.

Intermediates are not reactants. They appear somewhere in the elementary steps, but are consumed before the end.

(No catalyst; N2O2 and N2O are intermediates.) 12

Example 1: 2H2O2 2H2O + O2

Observed rate law: Rate = k[H2O2][I-]

The reaction mechanism that has been proposed for the decomposition of H2O2 is

1. H2O2 + I- H2O + IO- (slow)

2. H2O2 + IO- H2O + O2 + I- (fast)

The 1st step is slowest and therefore the rds.

The rate law of the rds is Rate = k[H2O2][I-] Why?

This matches the observed rate law.

Do the elementary steps shown add up to the overall reaction?

The rds is said to be "bimolecular.“ Why?

Why is I- not in the chemical equation?

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Catalysts? Intermediates?

Example 2The reaction: A + 3 B → D + F was

studied and the following mechanism was finally determined

1. A + B → D (fast)

2. B + B → E (slow)

3. E → F (very fast)

What is the expected rate law of the overall reaction?

rate=k[B]2 Check to see that elementary steps add up to give the overall reaction.

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Example 3For the reaction

2NO2Cl (g) 2 NO2 (g) + Cl2 (g)the elementary steps have been proposed as…

(1) NO2Cl (g) NO2 (g) + Cl (g)

(2) NO2Cl (g) + Cl (g) NO2 (g) + Cl2 (g)Step 1 is "unimolecular." Step 2 is "bimolecular."Do they add up to give the overall reaction?Write the rate law for each of the elementary

steps.Expt Rate Law: Rate = k[NO2Cl]

Step 1 must be rds.15

The slowest step is the rate determining step (rds).

The rds limits the rate of the overall reaction so its rate law represents the rate law for the overall reaction. Example 4:

NO2 (g) + CO (g) NO (g) + CO2 (g)

The experimental rate law is

Rate = k[NO2]2

From this we know immediately the reaction shown cannot be elementary. Can you see why not?

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Example 4 (cont'd.)NO2 (g) + CO (g) NO (g) + CO2 (g)

Proposed 2-step mechanism:

(1) NO2 + NO2 NO3 + NO

(2) NO3 + CO NO2 + CO2

Write the rate laws for these 2 elementary steps.

Given: experimental rate law: Rate = k[NO2]2

Which is the rate determining step?

How do you tell?

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Example 52NO + 2H2 N2 + 2H2O

Expt rate law: Rate = k[NO]2[H2]

which suggests 2NO + H2 N2O + H2O

and then N2O + H2 N2 + H2O

The 1st step proposed is termolecular, which is highly unlikely. Why?

It would require 3 molecules to all collide at the same time.

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Example 5: 2NO + 2H2 N2 + 2H2O cont'd

Instead: 2NO N2O2 fast

N2O2 + H2 N2O + H2O slow

N2O + H2 N2 + H2O fast

If we look only at the rds (Step 2)

Rate = k[N2O2][H2] but N2O2 is not in the overall reaction, and not in the observed rate law.

This is because N2O2 is an intermediate.

When this happens, we have to find an expression to replace [N2O2] in the rate law.19

2NO N2O2 fast N2O2 + H2 N2O + H2O slow N2O + H2 N2 + H2O fastFor the equilibrium, forward reaction has…

Rate = kf [NO]2

and the reverse reaction has…

Rate = kr [N2O2]

At equilibrium, the two rates are equal, so kf [NO]2 =kr [N2O2] which rearranges to [N2O2] =?Rate law for Step 2 is Rate = k[N2O2][H2]Substitute [N2O2] from the equilibrium step and we

have a rate law that matches the observed. 20

2NO + 2H2 N2 + 2H2O

Substitute [N2O2] = kf/kr [NO]2

into Rate = k [N2O2] [H2]

to give Rate = k kf/kr [NO]2[H2]

Since k, kf, kr are all constants, we can combine them into a new constant, k' to give

Rate = k'[NO]2[H2] and this matches the observed

Rate = k[NO]2[H2]

Do Practice Exercises

29, 30, 31 p.680 21

Potential Energy Diagram

One-step mechanism:Potential E

Reaction Coordinate

1) Where is Ea?

2) Where is ΔH?

3) Is this exothermic or endothermic?

4) Where is the transition state?

5) What is the activated complex?

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Potential Energy DiagramTwo-step mechanism:

Potential E

Reaction Coordinate

1) How do you know it has 2-steps?

2) What is at the "valley"?

3) Which step is rds?

4) Where is the ΔH of the rds?

5) How many transition states are there?

6) Which is the rds of the reverse reaction?

7) Where is the Ea of the 2nd step?

8) Is this exo- or endothermic?

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Potential Energy Diagram

Two-step mechanism:Potential E

Reaction Coordinate

1) In the reverse rxn, which is the rate determining step?

2) Where is the ΔH of the reverse rxn?

3) Is the reverse rxn exo- or endothermic?

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Potential Energy Diagram

What can you say about this mechanism? Potential E

Reaction Coordinate

How many steps are in the mechanism?

Is it exothermic or endothermic?

How many transition states are there?

What is at each "valley"?

Which step is rds? 25

PE Diagram of

Reversible vs. Irreversible Rxns

Which PE diagram more closely corresponds to a reversible reaction? Why?

Diagram A Diagram B

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Potential Energy DiagramWhat would the PE graph look like if a catalyst is added?

Potential E

Reaction Coordinate

Note that the Ea is lowered.

How does that affect the Kinetic E Diagram?

Graph for uncatalyzed rxnGraph for catalyzed rxn

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Kinetic Energy Diagram: Effect of Catalyst

Be able to explain why lowering the Ea in the KE diagram would affect the rate of reaction. 28

Applications of Catalytic Rxns• Oil industries: Catalysts help "crack" larger

hydrocarbons into smaller pieces and reform them to more useful molecules.

• Catalytic converter in your car: helps remove CO (poisonous), unburned volatile hydrocarbons and nitrogen oxides (contribute to acid rain)

• Enzymes are biological catalysts: Lactase catalyzes the breakdown of lactose (Those who are lactose-intolerant lack lactase.)

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