CHEMICAL KINETICS

HOMOGENEOUS REACTIONS

in which all reactants and products are in one phase

KINETICS Chemical kinetics, also known as reaction kinetics, is the study of rates of

chemical processes

KINETICS

Reaction RatesFactors affecting rate

Quantitative rate expressions

Determination

Factors

Models for Rates

Reaction Mechanisms

Effects of catalysts

RATES

Change in concentration of a reactant or product per unit rate

. per unit volume of the fluid for fluid-phase reactions, per unit area (or unit mass) of the

t

A

t- t

A - A

t time,in Change

A conc, in Change

0t

0t

B A

TemperatureFactors affecting

rate

Complexity

Bond strengths

Etc.

Nature Of The Reactants

STATE OF SUBDIVISION/SURFACE AREA

EFFECT OF CONCENTRATION

2 4 2 3 4 2O O H C O H C

CONCENTRATION

Time(s) [NO2] [NO] [O2]

0 0.0100 0.0000 0.000050 0.0079 0.0021 0.0011

100 0.0065 0.0035 0.0018150 0.0055 0.0045 0.0023200 0.0048 0.0052 0.0026250 0.0043 0.0057 0.0029300 0.0038 0.0062 0.0031350 0.0034 0.0066 0.0033400 0.0031 0.0069 0.0035

22 O 2NO 2NO

Graph: Concentration vs. time

Concentration vs Time

0

0.002

0.004

0.006

0.008

0.01

0.012

0 50 100 150 200 250 300 350 400 450

Time, sec

Co

nc.

,mo

l/L

[NO2]

[NO]

[O2]

22 O 2NO 2NO

M10725.1

0 - 400

0.0100 - 0.0031

t- t

NO - NO

t

NO 5

0400

0240022

-[NO2]/t time period(s)

–4.20E-05 0 - 50 –2.80E-05 50 - 100 –2.00E-05 100 - 150 –1.40E-05 150 - 200 –1.00E-05 200 - 250 –1.00E-05 250 - 300 –8.00E-06 300 - 350 –6.00E-06 350 - 400 –1.75E-05 0 - 400

Concentration vs Time

0

0.002

0.004

0.006

0.008

0.01

0.012

0 50 100 150 200 250 300 350 400 450

Time, sec

Co

nc.,

mo

l/L

[NO2]

[NO]

[O2]

Instantaneous rate

x

y line tangent of slope

t

NO rate 2

s 375

M0.009

t

NO s 100 @ rate 2

s

M10.42 s 100 @ rate 5-

Slope of tangent line at a point on the graph

INSTANTANEOUS RATE

Concentration vs Time

0

0.002

0.004

0.006

0.008

0.01

0.012

0 50 100 150 200 250 300 350 400 450

Time, sec

Co

nc.,

mo

l/L

[NO2]

[NO]

[O2]

12_291

0.000370s

O2

0.0025

0.005

0.0075

0.0100

0.0006

70s

0.0026

110 s

NO2

NO

50 100 150 200 250 300 350 400

Con

cent

ratio

ns (m

ol/L

)

Time (s)

[NO2 ]

t

Concentration vs Time

0

0.002

0.004

0.006

0.008

0.01

0.012

0 50 100 150 200 250 300 350 400 450

Time, sec

Con

c.,m

ol/L

[NO2]

[NO]

[O2]

t

NO rate 2

x

y line tangent of slope

s 225

M0.010

t

NO s 0 @ rate 2

s

M10.44 s 0 @ rate 5-

Slope of tangent line at time 0 (y intercept)

Initial Rate (t = 0)

RATE LAWS nm BAk rate k = rate constantm, n = order

22 O 2NO 2NO

rate = k[NO2]n

Order of Reaction In chemical kinetics, the order of reaction with respect to a certain reactant, is defined

as the power to which its concentration term.

Introduction to Rate Laws

Reversible chemical reactions

Forward:

Backward:

Equilibrium

:

22 O 2NO 2NO

2NO O 2NO 22

22 O 2NO 2NO

Introduction

Dominant Reaction:

Rate Law:

k, k’: specific rate constant

n : order of reactant

can be zero, fractional, or negative

22 O 2NO 2NO

n22 NOk

t

NO rate

-

n22 NOk

t

O erat

Method of Initial Rates

Unknown: k, m, n

Initial rate: instantaneous rate just after reaction is initiated

nm BAk rate

Initial Rates, NO2 decomposition

22 O 2NO 2NO

Experiment

Initial Conc.

[NO2]

Rate [O2]

Formation

1 0.01 7.1 x 10-5

2 0.02 2.8 x 10-4

n22 NOk

t

NO rate

-

General:

Substituting:

Solution:

n21

n22

NOk-

NOk-

1 rate

2 rate

n1

n2

5-

-4

0.010k-

0.020k-

10 7.1

10 2.8

2 ln n 4ln

2 n(2) 4 n

so

Rate constant

Rate 17.1 x 10-5 M s-1 = -k[0.01 M]2

k = 0.71 M-1 s-1

Rate 22.8 x 10-4 M s-1 = -k[0.02 M]2

k = 0.70 M-1 s-1

n22 NOk

t

NO rate

-

222 NO70.0

t

NO law rate

Experiment

Initial Conc.

[H2]

Initial Conc.

[I2] Rate

1 0.0113 0.0011 1.9 x 10-23

2 0.0220 0.0033 1.1 x 10-22

3 0.0550 0.0011 9.3 x 10-23

4 0.0220 0.0056 1.9 x 10-22

2HI I H 22

O2 + 2 NO 2NO2

Types

Differential:

Rate dependence on concentration

Integrated:

Concentration dependence on time

n22 NOk

t

NO rate

-

n22 NOk

t

O erat

First Order Reactions

For aA products

Differential:

Integrated: first order reaction (order = 1) has a rate proportional to the concentration of one of the reactants. A common example of a first-order reaction is the phenomenon of radioactive decay. The rate law is:

rate = k[A] (or B instead of A), with k having the units of sec-1

Akt

A rate

-

0Alnkt - Aln t

kt A

Aln 0

t

The rate of reaction is proportional to the concentration of A

Half-life, first order reactions

Integrated law:

Half-life:

Half of initial reacted

[A]t = ½[A]0

Independent of [A]0

kt A

Aln 0

t

k

0.693 t

k

ln2 t

21

21

First order

Plot:

ln[A] vs. time

ln[A]

time

ln[A]0

slope = -k 0Alnkt - Aln t

bmx y

SECOND-ORDER REACTION

A second-order reaction (order = 2) has a rate proportional to the concentration of the square of a single reactant or the product of the concentration of two reactants:

rate = k[A]2 (or substitute B for A or k multiplied by the concentration of A times the concentration of B), with the units of the rate constant M-1sec-1

SECOND ORDER

Plot:

1 vs. time

[A]time

1 [A]o

slope = k

bmx y

0A

1 kt

A

1

t

1 [A]

SECOND ORDER REACTIONS

For aA products

Differential:

Integrated:

2Akt

A rate

-

kt A

1

A

1

0

t

0A

1 kt

A

1

t

HALF-LIFE, SECOND ORDER REACTIONS

Integrated law:

Half-life:

Half of initial reacted

[A]t = ½[A]0

Inversely proportional to [A]0

kt A

1

A

1

0

t

0Ak

1 t

21

Zero-order reactions (order = 0) have a constant rate. This rate is independent of the concentration of the reactants. The rate law is:

rate = k, with k having the units of M/sec.

Zero Order Reactions

For aA products

Differential:

Integrated:

kAkt

A rate 0

-

kt- AA 0 t

0Akt - A t

Zero order

Plot:

[A] vs. time

[A]

time

[A]0

slope = -kbmx y

0Akt - A t

Graphical Method

First order

Second order

Zero order

Straight line

0Alnkt - Aln t

0A

1 kt

A

1

t

0Akt - A t

bmx y

SummaryConditions set so dominant forward reaction

Differential Rate Lawsrate as a function of concentrationmethod of initial rates

Integrated Rate Lawsconcentration as a function of timegraphical method

Experimental data collectionRate law types can be interconverted

Reaction Mechanism

Chemical equation: Summary

Mechanism: Series of elementary steps

Elementary Steps: Reactions with rate laws

from molecularity

Molecularity: Number of species that must

collide to produce reaction

Reaction Mechanism

Proposed elementary steps must satisfy conditions:

— reasonable reactions

— sum of steps = overall balanced reaction

— mechanism rate law = experimental rate law

Intermediates

—appear in steps

—produced in one step

—used in subsequent

—not in overall equation

Rate-determining step

In a multi-step process:

SLOWEST step

Determines overall reaction rate

“Bottleneck”

Model for Kinetics

Collision Theory

rate determined by particle collisions

collision frequency and energy

Cl + NOCl → Cl2 + NO

Transition State Theory

how reactants convert to products

p fZ rate a

Z: no. of bimolecular collisions per secondfa: fraction with Ea

P: fraction with correct orientationEa: activation energy

Collision Theory (Bimolecular Collsions)

Arrhenius Equation

k: rate constant

Ea: activation energy (minimum required)T:absolute temperatureR: universal gas constantA: orientation factor

Energy & orientation requirements for reaction

RT

Ea

Ae k

Hydrolysis of an ester

Transition State Theory

Ea and internal energy:

Bonds breaking and forming

Atoms rearranging

“Transition State”

Unstable intermediate

At point of highest energy

forward reaction reverse reaction

I- + CH3Cl Cl- + CH3I

Catalysts

• Speed reaction• Are not consumed

• Alternative pathway for reaction with lower Ea

Types

Homogeneous

Heterogeneous

Enzymes are biological catalysts

12_304

Ea (uncatalyzed )

Effectivecollisions(uncatalyzed)

Effectivecollisions(catalyzed)

Ea (catalyzed )

(a) (b)

Nu

mb

er

of

co

llis

ion

s

with

a g

ive

n e

ne

rgy

Nu

mb

er

of

co

llis

ion

s

with

a g

ive

n e

ne

rgy

Energy Energy

Adsorption, activation, reaction, desorption