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Chapter 12 – Chemical Kinetics

1. Second order Rate Law2. Zero Order Rate Law3. Reaction Mechanism4. Model for Chemical Kinetics5. Collision6. Catalysis7. Heterogeneous Catalysis8. Homogeneous Catalysis

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Second-Order Rate Law• For aA products in a second-order

reaction,

• Integrated rate law is

• Plot of 1/[A] vs t will produce a straight line: slope = k

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Half-Life of a 2nd-Order Reaction

•t1/2 = half-life of the reaction•k = rate constant•Ao = initial concentration of A

•The half-life is dependent upon the initial concentration.

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Second-Order Rate Law – 12.5

Butadiene reacts to form its dimer

2C4H6(g) C8H12(g)

• Data:

[C4H6] Time

0.01000 0

0.00625 1000

0.00476 1800

0.00370 2800

0.00313 3600

0.00270 4400

0.00241 5200

0.00208 6200

a) Reaction order?b) Value of k?c) Half-life?

1/[C4H6] ln[C4H6]

100 -4.605

160 -5.075

210 -5.348

270 -5.599

320 -5.767

370 -5.915

415 -6.028

481 -6.175

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Second-Order Rate Law – 12.5

Butadiene reacts to form its dimer

2C4H6(g) C8H12(g)

• Data:

[C4H6] Time

0.01000 0

0.00625 1000

0.00476 1800

0.00370 2800

0.00313 3600

0.00270 4400

0.00241 5200

0.00208 6200

a) Reaction order?

Rate = k[C4H6]2

1/[C4H6] ln[C4H6]

100 -4.605

160 -5.075

210 -5.348

270 -5.599

320 -5.767

370 -5.915

415 -6.028

481 -6.175

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Second-Order Rate Law – 12.5

Butadiene reacts to form its dimer

2C4H6(g) C8H12(g)

• Data:

[C4H6] Time

0.01000 0

0.00625 1000

0.00476 1800

0.00370 2800

0.00313 3600

0.00270 4400

0.00241 5200

0.00208 6200

b) Value of k?k = slope

1/[C4H6] ln[C4H6]

100 -4.605

160 -5.075

210 -5.348

270 -5.599

320 -5.767

370 -5.915

415 -6.028

481 -6.175

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Second-Order Rate Law – 12.5

Butadiene reacts to form its dimer

2C4H6(g) C8H12(g)

k = 6.14x10-2 L/mol*s[A]0= 1.000x10-2 mol/L

c) Half-life?

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Zero-Order Rate Law

• Zero-order reaction the rate is constant.

• Rate does not change with respect to concentration

• Rate = k[A]o = k(1) = k• [A] = -kt + [A]o

• t1/2 = [A]o/2k

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Reaction Mechanism

The series of steps by which a chemical reaction occurs.

A chemical equation does not tell us how reactants become products - it is a summary of the overall process.

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Often Used Terms•Intermediate: formed in one step and used up in a subsequent step and so is never seen as a product.•Molecularity: the number of species that must collide to produce the reaction indicated by that step.

•Elementary Step: A reaction whose rate law can be written from its molecularity.

•uni, bi and termolecular

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Reaction Mechanism

We can define a reaction mechanism.It is a series of elementary steps that must

satisfy two requirements:1. The sum of the elementary steps must give

the overall balanced equation for the reactions.

2. The mechanism must agree with the experimentally determined rate law.

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Reaction Mechanism The reaction NO2(g) + CO(g) NO(g) + CO2(g)• has many steps in the reaction mechanism.• Rate = k[NO2]2

NO2(g) + NO2(g) NO3(g) + NO(g)NO3(g) + CO(g) NO2(g) + CO2(g)NO2(g) + NO2(g) + NO3(g) + CO(g)

NO3(g) + NO(g) + NO2(g) + CO2(g)Overall reaction:NO2(g) + CO(g) NO(g) + CO2(g)

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Rate-Determining Step•In a multistep reaction, it is the slowest step. It therefore determines the rate of reaction.

– Slow (rate determing)NO2(g) + NO2(g) NO3(g) + NO(g) – FastNO3(g) + CO(g) NO2(g) + CO2(g)Rate of formation of NO3 = [NO3]/t = K1[NO2]2 Overall rate = [NO3]/t = k1[NO2]2

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A Summary (continued)

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Model for Chemical KineticsCollision Model

•Key Idea: Molecules must collide to react.

•However, only a small fraction of collisions produces a reaction. Why?

•Arrhenius: An activation energy must be overcome.

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Reaction ProgressThe arrangement of atoms found at the top of

the potential energy barrier is call the activated complex or transition state.

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Reaction ProgressE has no effect on the rate of reaction.Rate depends on the size of the activation

energy Ea.

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Reaction Progress

A certain minimum energy is required for the molecules to “get over the hill”

At a given temperature only a fraction of the collisions possess enough energy to be effective

- Lower temperature

-Effective collisions - Small

- Higher temperature

-Effective collisions – Increase exponentially

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Reaction Progress - CollisionsCollisions with Ea = (Total Collisions)e-Ea/RT

Observed rate smaller than the rate of collisions with Ea

Molecular Orientations:

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Reaction Progress - Collisions

Requirements must satisfied for reactants to collide successfully1. Collisions must involve enough energy to produce the

reaction; Collision energy must equal or exceed the activation energy

2. Relative orientation of reactants must allow for the formation of any new bonds necessary to produce products.

Rate constant: k = zpe-Ea/RT

z = collision frequency R = 8.3145 J/K molp = steric factor (fraction with effective orientation)

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Catalysis

•Catalyst: A substance that speeds up a reaction without being consumed

•Enzyme: A large molecule (usually a protein) that catalyzes biological reactions.

•Homogeneous catalyst: Present in the same phase as the reacting molecules.

•Heterogeneous catalyst: Present in a different phase than the reacting molecules.

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Catalysis

Increases the number of effective collisions by providing a reaction pathway with a lower activation energy

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Heterogeneous Catalysis

Heterogeneous catalysis most often involves gaseous reactant being absorbed on the surface of a solid surface.

Hydrogenation is an example:Changes C=C into saturated H-C-C-H

1. Adsorption to addition of a substance to the surface of another.

2. Migration of absorbed reactants on the surface

3. Reaction of absorbed substances

4. Desorption of products

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Heterogeneous catalytic ethylene hydrogenation: C2H4 + H2 → C2H6

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Homogeneous Catalysis

• Reactants and Catalysis are in the same phase. Gas-Gas or Liquid-Liquid

• N2(g) + O2(g) 2NO(g)

• Product of high-temperature combustion when N2 is present. However catalytic in production of ozone

• 2NO(g) + O2(g) 2NO2(g)

• NO2(g) NO(g) + O(g) (light)

• O2(g) + O(g) O3(g)

• 3/2O2(g) O3(g)

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Homogeneous Catalysis

• In the upper atmosphere, NO has opposite effect.

• 2NO(g) + O3(g) NO2(g) + O2(g)

• O + NO2(g) NO(g) + O2(g)

• O3(g) + O(g) 2O2(g)

• Nitric Oxide is catalytic in production of O2.

• O3 required in upper atmosphere to block uv radiation.

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Homogeneous Catalysis

• Freon - ChloroFluoroCarbons

• CCl2F2(g) CClF2(g) + Cl(g) Light

• Cl + O3(g) ClO(g) + O2(g)

• O(g) + ClO(g) Cl(g) + O2(g)

• O3(g) + O(g) 2O2(g)

• Cl(g) destroyer of ozone – catalytic in destruction of O3.