Chapter 14Chapter 14Chemical KineticsChemical Kinetics

CHEMISTRY The Central Science

9th Edition

• Kinetics is the study of how fast chemical reactions occur.

• There are 4 important factors which affect the rates of chemical reactions:• reactant concentration,

• temperature,

• action of catalysts, and

• surface area.

KineticsKinetics

• The speed of a reaction is defined as the change that occurs per unit time.• It is determined by measuring the change in concentration of a

reactant or product with time.

• The speed the of the reaction is called the reaction rate.

• For a reaction A B

• Suppose A reacts to form B. Let us begin with 1.00 mol A.

Reaction RatesReaction Rates

t

B of moles

in time changeB of moles ofnumber in change

rate Average

Change in Concentration of Change in Concentration of ReactionsReactions

10 20

– At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present.

– At t = 10 min, there is 0.54 mol A and 0.26 mol B.

– At t = 20 min, there is 0.30 mol A and 0.70 mol B.

– Calculating,

Calculating Reaction Rates Calculating Reaction Rates Using ProductsUsing Products

mol/min 026.0min 0min 10mol 0 mol 26.0

min 0min 100at B of moles10at B of moles

B of molesrate Average

ttt

• For the reaction A B there are two ways of measuring rate:• the speed at which the products appear (i.e. change in moles of

B per unit time), or

• the speed at which the reactants disappear (i.e. the change in moles of A per unit time).

• The equation, when calculating rates of reactants, is multiplied by -1 to compensate for the negative concentration.

– By convention rates are expressed as positive numbers.

Calculating Reaction Rates Calculating Reaction Rates Using ReactantsUsing Reactants

t

A of molesA respect to with rate Average

• Most useful units for rates are to look at molarity. Since volume is constant, molarity and moles are directly proportional.

• Consider:

• C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Reaction RatesReaction Rates

Reactants Products

Reaction Rates for CReaction Rates for C44HH99ClCl

• C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

• We can calculate the average rate in terms of the disappearance of C4H9Cl.

• The units for average rate are mol/L·s or M/s.

• The average rate decreases with time.

• We plot [C4H9Cl] versus time.

• The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve.

• Instantaneous rate is different from average rate.

• We usually call the instantaneous rate the rate.

Properties of CProperties of C44HH99ClCl

ReactionReaction

Instantaneous Reaction Rates Instantaneous Reaction Rates for Cfor C44HH99ClCl

• For the reaction

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

we know

• In general for

aA + bB cC + dD

Reaction Rates and StoichiometryReaction Rates and Stoichiometry

tt

OHHCClHCRate 9494

tdtctbta

D1C1B1A1Rate

• In general rates increase as concentrations increase.

NH4+(aq) + NO2

-(aq) N2(g) + 2H2O(l)

Concentration and Rate Concentration and Rate Table Table

• For the reaction

NH4+(aq) + NO2

-(aq) N2(g) + 2H2O(l)

we note – as [NH4

+] doubles with [NO2-] constant the rate doubles,

– as [NO2-] doubles with [NH4

+] constant, the rate doubles,

– We conclude rate [NH4+][NO2

-].

• Rate law:

• The constant k is the rate constant.

Concentration and Rate Concentration and Rate EquationEquation

]NO][NH[Rate 24k

• For a general reaction with rate law

we say the reaction is mth order in reactant 1 and nth order in reactant 2.

• The overall order of reaction is m + n + ….• A reaction can be zeroth order if m, n, … are zero.• Note the values of the exponents (orders) have to be

determined experimentally. They are not simply related to stoichiometry.

Exponents in the Rate Exponents in the Rate LawLaw

nmk ]2reactant []1reactant [Rate

• A reaction is zero order in a reactant if the change in concentration of that reactant produces no effect.

• A reaction is first order if doubling the concentration causes the rate to double.

• A reaction is nth order if doubling the concentration causes an 2n increase in rate.

• Note that the rate constant does not depend on concentration.

Determining Order of ReactionsDetermining Order of Reactions

First Order Reactions• Goal: convert rate law into a convenient equation to give

concentrations as a function of time.• For a first order reaction, the rate doubles as the

concentration of a reactant doubles.

Concentration Change with TimeConcentration Change with Time

kt

kt

kt

t

t

0

0

A

Aln

AlnAln

]A[A][

Rate

• A plot of ln[A]t versus t is a straight line with slope -k and intercept ln[A]0.

• Put into simple math language : y = mx + b• Plotting of this equation for given reaction should yield a

straight line if the reaction is first order.• In the above we use the natural logarithm, ln, which is

log to the base e.

Plotting First Order ReactionsPlotting First Order Reactions

• Left graph plotted with pressure vs. t, and right graph plotted with ln(pressure) vs. t.

Example Plots of a 1Example Plots of a 1stst Order Reaction Order Reaction

0AlnAln ktt

Second Order Reactions• For a second order reaction with just one reactant

• A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0

• Put into simple math language: y = mx + b

• For a second order reaction, a plot of ln[A]t vs. t is not linear.• However, a plot of 1/[A]t versus t is a straight line

Concentration Change with TimeConcentration Change with Time

0A1

A1 kt

t

• Left is Ln[NO2] vs t, and right is 1/[NO2] vs. t.

Example plots of a 2Example plots of a 2ndnd Order Reaction Order Reaction

0A1

A1 kt

t

First Order Reactions• Half-life is the time taken for the concentration of a

reactant to drop to half its original value.

• For a first order process, half life, t½ is the time taken for [A]0 to reach ½[A]0.

• Mathematically defined by:

• The half-life for a 1st order reactions depends only on k

Half-Life ReactionsHalf-Life Reactions

kk

t693.0ln

21

21

Second Order• Mathematically defined by:

• A second order reaction’s half-life depends on the initial concentration of the reactants

Half-Life ReactionHalf-Life Reaction

0A

12

1

kt

The Collision Model• Most reactions speed up as temperature increases. (E.g.

food spoils when not refrigerated.)• When two light sticks are placed in water: one at room

temperature and one in ice, the one at room temperature is brighter than the one in ice.

• The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.

Temperature and RateTemperature and Rate

The Collision ModelThe Collision Model

• As temperature increases, the rate increases.

• Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases.

• The collision model: in order for molecules to react they must collide.

• The greater the number of collisions the faster the rate.• The more molecules present, the greater the probability

of collision and the faster the rate.• Faster moving molecule collide with greater energy and

more frequently, increasing reaction rates.

Collision Model: The Central Idea Collision Model: The Central Idea

The Collision Model• The higher the temperature, the more energy available to

the molecules and the faster the rate.• Complication: not all collisions lead to products. In fact,

only a small fraction of collisions lead to product.• Why is this?

The Orientation Factor• In order for reaction to occur the reactant molecules must

collide in the correct orientation and with enough energy to form products.

The Speed of a ReactionThe Speed of a Reaction

• Consider:

Cl + NOCl NO + Cl2

• There are two possible ways that Cl atoms and NOCl molecules can collide; one is effective and one is not.

The Orientation FactorThe Orientation Factor

• Arrhenius: molecules must posses a minimum amount of energy to react. Why?• In order to form products, bonds must be broken in the

reactants.

• Bond breakage requires energy.

• Activation energy, Ea, is the minimum energy required to initiate a chemical reaction.

Activation EnergyActivation Energy

Energy Profile for Methly IsonitrileEnergy Profile for Methly Isonitrile

• How does a methyl isonitrile molecule gain enough energy to overcome the activation energy barrier?

• From kinetic molecular theory, we know that as temperature increases, the total kinetic energy increases.

• We can show the fraction of molecules, f, with energy equal to or greater than Ea is

• where R is the gas constant (8.314 J/mol·K).

Fraction of Molecules Fraction of Molecules Possessing EPossessing Eaa

RTEa

ef

Activation Energy, EActivation Energy, Eaa, Plot, Plot

• Arrhenius discovered most reaction-rate data obeyed the Arrhenius equation:

• k is the rate constant, Ea is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K.

• A is called the frequency factor.– A is a measure of the probability of a favorable collision.

• Both A and Ea are specific to a given reaction.

The Arrhenius EquationThe Arrhenius Equation

RTEa

Aek

• If we have a lot of data, we can determine Ea and A graphically by rearranging the Arrhenius equation:

• From the above equation, a plot of ln k versus 1/T will have slope of –Ea/R and intercept of ln A.

Determing Activation EnergyDeterming Activation Energy

ARTE

k a lnln

Ln Ln kk versus 1/T versus 1/T

• Ea can be determined by finding the slope of the line.

• The balanced chemical equation provides information about the beginning and end of reaction.

• The reaction mechanism gives the path of the reaction (i.e., process by which a reaction occurs).• Mechanisms provide a very detailed picture of which

bonds are broken and formed during the course of a reaction.

Elementary Steps• Elementary step: any process that occurs in a single step.

Reaction MechanismsReaction Mechanisms

• Molecularity: the number of molecules present in an elementary step.• Unimolecular: one molecule in the elementary step,

• Bimolecular: two molecules in the elementary step, and

• Termolecular: three molecules in the elementary step.

• It is not common to see termolecular processes (statistically improbable).

Properties of the Elementary Properties of the Elementary Step ProcessStep Process

• Some reaction proceed through more than one step:• Consider the reaction of NO2 and CO

NO2(g) + NO2(g) NO3(g) + NO(g)

NO3(g) + CO(g) NO2(g) + CO2(g)

• Notice that if we add the above steps, we get the overall reaction:

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

• The elementary steps must add to give the balanced chemical equation.

• Intermediate: a species which appears in an elementary step which is not a reactant or product

Multistep MechanismsMultistep Mechanisms

Rate Laws for Elementary Steps• The rate law of an elementary step is determined by its

molecularity:– Unimolecular processes are first order,

– Bimolecular processes are second order, and

– Termolecular processes are third order.

Rate Laws for Multistep Mechanisms• Rate-determining step: is the slowest of the elementary

steps.

Reaction MechanismsReaction Mechanisms

• Rate Laws for Elementary Steps

Table 14.3, Page 551Table 14.3, Page 551

• It is possible for an intermediate to be a reactant.• Consider

2NO(g) + Br2(g) 2NOBr(g)

• The experimentally determined rate law is

Rate = k[NO]2[Br2]• Consider the following mechanism

Initial Fast Step of a MechanismsInitial Fast Step of a Mechanisms

NO(g) + Br2(g) NOBr2(g)k1

k-1

NOBr2(g) + NO(g) 2NOBr(g)k2

Step 1:

Step 2:

(fast)

(slow)

• The rate law is (based on Step 2):

Rate = k2[NOBr2][NO]

• The rate law should not depend on the concentration of an intermediate (intermediates are usually unstable).

• Assume NOBr2 is unstable, so we express the concentration of NOBr2 in terms of NOBr and Br2 assuming there is an equilibrium in step 1 we have

Intermediate as a Reactant Intermediate as a Reactant

]NO][Br[]NOBr[ 21

12

kk

• By definition of equilibrium:

• Therefore, the overall rate law becomes

• Note the final rate law is consistent with the experimentally observed rate law.

]NOBr[]NO][Br[ 2121 kk

][BrNO][NO][]NO][Br[Rate 22

1

122

1

12

kk

kkk

k

Intermediate as a Reactant Conts. Intermediate as a Reactant Conts.

• A catalyst changes the rate of a chemical reaction.• Catalyst lower the overall Ea for a chemical reaction.

• There are two types of catalyst:• Homogeneous and heterogeneous

• Example: Cl atoms are catalysts for the destruction of ozone.

Homogeneous Catalysis• The catalyst and reaction is in one phase.

Heterogeneous Catalysis• The catalyst and reaction exists in a different phase.

CatalysisCatalysis

The Effects of a CatalystThe Effects of a Catalyst

• Catalysts can operate by increasing the number of effective collisions (i.e., from the Arrhenius equation: catalysts increase k which results in increasing A or decreasing Ea.

• A catalyst may add intermediates to the reaction.• Example: In the presence of Br-, Br2(aq) is generated as an

intermediate in the decomposition of H2O2.

Functions of the CatalysisFunctions of the Catalysis

End of Chapter 14End of Chapter 14Chemical KineticsChemical Kinetics