Kinetics

…or Reaction Rates

Change•The ice melted.

•The Coke went flat.

•The nail rusted.

Expressing Change•The ice melted.

•The Coke went flat.

•The nail rusted.

mL/min

g/min

g/min

Expressing Change•Reaction Rate.

•Change in something divided by change in time

amount time

Reaction Rate•As a rxn occurs, what

happens to the amount of reactant?Rate = – reactant amt

time

Reaction Rate•Consider:

Mg(s) + 2HCl(aq) MgCl2(aq) + H2(g)Rate = –mol Mg = –mol HCl = t 2t

mol MgCl2 = mol H2 t t

Reaction Rate of a one-way reaction

• Will be determined by looking at the reactants only

• Decreases as time progresses. Why?

• What eventually happens to the amount of reactant?

Reaction Rate of an equilibrium rxn

• Will be determined by looking at the reactants only

• Decreases as time progresses. Why?

• What eventually happens to the rate?

• Does the reaction stop?

Reaction Rate

2NO2(g) 2NO(g) + O2(g)

Reaction Rate

Time (s)

[Con

cen

trati

on]

(mol/L) NO2

NO

O2

Necessities of Reaction•Proper orientation

2HI H2 + I2

Necessities of Reaction•Sufficient energy--Activation

energy (Ea)

Rxn progress

En

erg

y

Ea

2HI

H2 + I2

Activated Complex

ΔH

Factors that affect Reaction Rate

•Concentration•Temperature•Surface Area•Presence of a catalyst•Rate-determining step…or the

slowest step in a rxn mechanism

Rate Law•Relates the rate as a function

of the reactant(s)•Units of rate are always

mol/L-s unless otherwise stated

•Two types: –Differential– Integrated

Differential Rate Law•For the rxn: A B…

differentialRate = k[A]x

k is the rate law constant…units are dependent on the order

x is the order of reactant A

Order

•may not be determined by looking at the coefficients of the reactants•unless the rxn is the rate-determining step

•must be determined experimentally

Order

•If the rate does not change when the reactant is doubled, then the order is zero; and rate is dependent solely on the value of kRate = k[A]0 or Rate = k

Order

•If the rate doubles when the reactant is doubled, then the order is first; and rate is dependent on the concentration of the reactantRate = k[A]1

Order

•If the rate quadruples when the reactant is doubled, then the order is second; and rate is dependent on the square of the concentration of the reactantRate = k[A]2

Overall Order of Reaction

•is the sum of the individual orders

•When Rate = k[A]0, the overall order is zero

•When Rate = k[A]1, the overall order is one

Overall Order of Reaction

•If a differential rate law for the following rxn:A + B Cis Rate = k[A]1[B]2

•then the overall order is three–What must the units of k be in this reaction?

Integrated Rate LawFor the rxn:

2N2O5 4NO2 + O2

The following data were collected:

[N2O5] Time(s)1.00 0

0.88 200

0.78 400

0.69 600

0.61 800

Integrated Rate Law

If we think the reactant is zero order:

Rate = k[N2O5]0

Integrating the rate law gives us:

[N2O5] = -kt + [N2O5]o

Integrated Rate LawIf we plot Time vs. [N2O5], then we get

Time (s)

[N2O

5]

(mol/L)

Integrated Rate Law

Since the plot gave a curve rather than a line, the order of the N2O5 cannot be zero.

If we try looking at it as if it were first order, then we will need to integrate the rate law.

Integrated Rate Law

If we think the reactant will be first order:

Rate = k[N2O5]1

Integrating the rate law gives us:

ln [N2O5] = -kt + ln[N2O5]o

Integrated Rate LawIf we plot Time vs. ln[N2O5], then we get

Time (s)

ln[N

2O

5]

(mol/L)

Integrated Rate Law

Since the plot gave a line, the order of the N2O5 is first or one.

Integrated Rate Law

If we think the reactant will besecond order:

Rate = k[N2O5]2

Integrating the rate law gives us:

[N2O5]-1 = kt + [N2O5]o-1

Integrated Rate LawIf we plot Time vs. [N2O5]-1, then we get

Time (s)

[N2O

5]-

1 (

L/ m

ol)

1/2 Life• First-order— t½= 0.693

k

• Second-order— t½= __1__

k[A]o

• Zero-order— t½= [A]o

2k

First-order Half-Life

• All first-order reactions have half-lives independent of the initial concentration of the reactant.

• All radioactive decays follow first-order kinetics.

First-order Half-Life Problem

• On November 23, 1999 I had Technetium-99 injected into my bloodstream for a bone scan. The half-life of Tc-99 is 6.0 hours.– What percentage of the original

amount of Tc-99 is left in my body today?

Second-order Half-Life• All second-order reactions have

half-lives dependent on the initial concentration of the reactant.

• A second half-life will be longer than a first half-life because the initial concentration changes

• For each successive half-life, [A]o is halved; thus, for each successive half-life, the half-life is doubled

Second-order Half-Life Problem

• The decomposition of NOCl is a second- order reaction where

k = 4.00 x 10-8s-1.– For an initial concentration of

0.50M, what is the half-life?– How much is left after 1 x 108s? – What is the half-life for an initial

concentration of NOCl of 0.25M?

Zero-order Half-Life• Most often occur when a catalyst is

needed for the reaction to proceed.

• The catalyst determines how much reactant will be used.

• Since the rate is constant the half-life may be determined using either the rate law constant or the rate itself.

Reaction Mechanism

•Most reactions do not occur in a single step

•Rather, they happen in a series of steps called elementary steps

•The sum of the elementary steps gives the overall reaction.

Reaction Mechanism• Intermediates are substances that

are formed in one elementary step and consumed in a subsequent elementary step. They are rarely part of the rate law.

•Catalysts are substances added to a step that are also produced in a subsequent step. They are rarely part of the rate law.

Reaction Mechanism•Rate-determining step—the

slowest step. If it is the first or only step, then the rate law may be written from its molecularity.–The differential rate law may be written from the reactants in the rate-determining step.

Reaction Mechanism•Consider the following elementary

steps: Step 1: OCl- + H20 HOCl + OH- fast

Step 2: HOCl + I- HOI + Cl- slow

Step 3: HOI + OH- H20 + OI-

fast• What is the overall balanced equation?• What is the differential rate law?• What substance(s) is an intermediate?

A catalyst?

Reaction Mechanism• What is the overall balanced

equation?

• What is the differential rate law?

• What substance(s) is an intermediate? A catalyst?

OCl- + I- Cl- + OI-

Rate = k[I-]

HOCl, HOI, OH-; H2O

Reaction Mechanism•A catalyst is a substance that

increases the rate of reaction.– It does so by lowering the Ea required for the reaction to occur.

A Catalyst’s Effect

Rxn progress

En

erg

y

Ea

Uncatalyzed

Catalyzed

Reaction MechanismThe reaction H2 + Cl2 2HCl occurs infour steps.

Step 1:Cl Cl

energyCl

Cl

Reaction Mechanism

Step 2:

H ClCl H H H

Reaction Mechanism

Step 3:

H ClCl HCl Cl

Reaction Mechanism

Step 4:

Cl Cl Cl Cl

Cl Cl

energy

Cl Cl

Cl H H H

Cl HCl Cl

Cl Cl Cl Cl

H Cl

H Cl

Collision Theory• Molecules must move toward each

other (through random motion).• Molecules must hit with the proper

orientation.• Molecules must hit with sufficient

energy.• Molecules will separate after

reaction occurs.

Collision Theory

• k = Ae –Ea/RT

• Take the ln of each side and…

lnk = -Ea 1 + lnA R T

y m x b

Collision Theory

• Plot 1/T vs. lnk to determine Ea or A.

• If you have two sets of data…

ln k2 = Ea 1 1_ k1 R T1 T2

Activation Energy

• for a one-way reaction

Activation Energy

• for a reversible reaction

Activation Energy Problem

Given the following kinetics data for the reaction: NO(g) + O3(g) NO2(g) + 02(g)

Determine the activation energy.

T (K) k (L/mol-s)195 1.08 x 109

230 2.95 x 109

260 5.42 x 109

298 12.0 x 109

369 35.5 x 109

Reaction Mechanism

• A series of elementary steps must satisfy two requirements for the reaction:– The sum of the elementary steps

must give the overall balanced equation for the reaction.

– The mechanism must agree with the observed rate law.

Catalyst– provides a surface whereby the

reacting molecules might position themselves more favorably for collision

– lowers Ea

– Homogeneous (i.e. enzymes) are in the same phase as the reacting molecules

– Heterogeneous (i.e. Pt or Pd pieces in the catalytic converter of a car) are in a different phase and promote adsorption

Enzymes•are proteins in living

organisms that catalyze biological reactions.–Salivary amylase–Lactase

Inhibitors•are elements or compounds

used to decrease the rate of a reaction.–Tetraethyl lead

•Oops! Along came catalytic converters…

–Methyl t-butyl ether (MTBE) and ethanol

Collision Theory• Concentration• Temperature• k is a measure of the fraction of

collisions with sufficient energy to produce a reaction– k = Ae –Ea/RT (Arrhenius equation)

•A—frequency factor (motion/orientation)

•Ea—activation energy (J/mol)

Reaction Mechanism Problem #1

• The balanced equation for the reaction of nitric oxide with hydrogen is2NO + 2H2 2H20 + N2

The experimentally determined rate law is: rate = k[NO]2[H2]

The following mechanism has been proposed:

Reaction Mechanism Problem #1 (cont.)

NO + H2 N + H2O (slow)

N + NO N2O (fast)

N2O + H2 N2 + H2O (fast)

Is this mechanism consistent with theobserved rate law?

k1

k2

k3

Reaction Mechanism Problem #2

NO + H2 N + H2O (fast, with equal rates)

N + NO N2O (slow)

N2O + H2 N2 + H2O (fast)

Is this mechanism consistent with theobserved rate law?

k1

k2

k3

k-1

Reaction Mechanism Problem #3

NO + H2 N + H2O (fast)

N + NO N2O (fast)

N2O + H2 N2 + H2O (slow)

Is this mechanism consistent with theobserved rate law?

k1

k2

k3