Important Important questions in questions in chemistrychemistry

How much and how far?How much and how far?How fast?How fast?

Reaction rates and rate lawsReaction rates and rate lawsReaction mechanismReaction mechanismMechanism and temperature Mechanism and temperature dependencedependenceCatalysisCatalysis

Learning objectivesLearning objectives► Describe factors affecting rates of reactionDescribe factors affecting rates of reaction► Describe reaction rate in terms of reactants and productsDescribe reaction rate in terms of reactants and products► Determine rate of reaction from concentration over timeDetermine rate of reaction from concentration over time► Use method of initial rates to determine orders of reaction and Use method of initial rates to determine orders of reaction and

rate constantrate constant► Apply integrated rate law equations to determine order of Apply integrated rate law equations to determine order of

reaction and rate constantreaction and rate constant► Apply order of reaction to identifying possible reaction Apply order of reaction to identifying possible reaction

mechanismsmechanisms► Describe factors that affect the pre-factor in the Arrhenius Describe factors that affect the pre-factor in the Arrhenius

rate equationrate equation► Apply Arrhenius rate equation to determine activation energyApply Arrhenius rate equation to determine activation energy► Describe general principles behind the function of catalystsDescribe general principles behind the function of catalysts

Thermodynamics and Thermodynamics and kineticskinetics

►Thermodynamics addresses the firstThermodynamics addresses the first►Kinetics addresses the secondKinetics addresses the second

►They are distinct areas and have They are distinct areas and have nothing to say to each othernothing to say to each other A reaction may be favoured by A reaction may be favoured by

thermodynamics but not happen because thermodynamics but not happen because of kinetic obstaclesof kinetic obstacles

The paradox of the reaction The paradox of the reaction between Hbetween H22 and O and O22

►The reaction is very favorable, and yet The reaction is very favorable, and yet a mixture of hydrogen and oxygen can a mixture of hydrogen and oxygen can remain unreacted for centuries – for remain unreacted for centuries – for eternityeternity

Underlying principlesUnderlying principles

►All molecules are in motionAll molecules are in motion►Molecules undergo collisions as a Molecules undergo collisions as a

resultresult►SomeSome collisions result in reactions to collisions result in reactions to

give productsgive products

Reaction pathway in Reaction pathway in energyenergy

► All reactions have an energy barrierAll reactions have an energy barrier► Molecules must have enough energy to leapMolecules must have enough energy to leap► Molecules with insufficient energy don’t Molecules with insufficient energy don’t

make itmake it

Thermodynamics considers Thermodynamics considers the before and afterthe before and after

Reactants at equilibrium

Province of kinetics

Products at equilibrium

Rate a minuteRate a minute

► Rate is defined as:Rate is defined as:

Concentration change/time changeConcentration change/time change► In typical reactionIn typical reaction

► Rate is measured either by measuring Rate is measured either by measuring decrease in [reactant] or increase in decrease in [reactant] or increase in [product][product]

► Units of rate are mol/LUnits of rate are mol/L●●ss

HIIH 222

Plot of concentration vs Plot of concentration vs timetime

►Rate of appearance of product (or Rate of appearance of product (or disappearance of reactant) depends disappearance of reactant) depends on the number of moles in the on the number of moles in the equationequation

t

ON

t

NO

t

O

5222

2

1

4

1

2252 42 ONOON

General rate of reactionGeneral rate of reaction

►Divide the actual rate of Divide the actual rate of appearance/disappearance by the appearance/disappearance by the coefficient in the balanced equationcoefficient in the balanced equation

►Usually rate changes with time: the Usually rate changes with time: the longer the time, the slower the rate – longer the time, the slower the rate – reactants reactants are used upare used up

t

ON

t

NO

t

OGenRate

5222

2

1

4

1

Comparison of instantaneous Comparison of instantaneous rate with an interval raterate with an interval rate

► As As ΔΔt decreases, measured rate t decreases, measured rate ΔΔ[NO[NO22]/]/ΔΔt t approaches slope of curve d[NOapproaches slope of curve d[NO22]/dt]/dt

► Rate measured over time interval is an Rate measured over time interval is an approximationapproximation

► Rate of reaction at the very beginning (t = Rate of reaction at the very beginning (t = 0) is the 0) is the initialinitial rate – when [product] = 0 rate – when [product] = 0

Laws and OrderLaws and Order

►For the typical reactionFor the typical reactionaA + bB = productsaA + bB = products

►The rate is given by the following The rate is given by the following rate rate lawlaw

kk is the rate constant is the rate constantm and n are m and n are ordersorders of reaction with of reaction with

respect to A and B respectivelyrespect to A and B respectively

nm BAkt

ARate ][][

Inconstancy of rate Inconstancy of rate constants constants

►kk is for a specific reaction is for a specific reaction►Units of Units of kk depend on overall reaction depend on overall reaction

orderorder►kk does not change with [reactants] or does not change with [reactants] or

[products][products]►kk does not change with time does not change with time►kk does depend on temperature does depend on temperature►kk does depend on presence of a catalyst does depend on presence of a catalyst

Significance of ordersSignificance of orders► Orders of reaction are usually small integer Orders of reaction are usually small integer

numbers 0, 1, 2numbers 0, 1, 2► In complex processes ½ or other fractions, In complex processes ½ or other fractions,

or even negative numbers can be observedor even negative numbers can be observed► Significance of order on relationship of Significance of order on relationship of

concentration and rateconcentration and rate

Order of reaction Order of reaction mm

Effect on rate of Effect on rate of doubling doubling concentration (2concentration (2mm))

00

11

22

NoneNone

DoublesDoubles

QuadruplesQuadruples

Overall reaction orderOverall reaction order

►Sum over individual ordersSum over individual ordersOrder = m + n + …+Order = m + n + …+

►Reaction order is determined Reaction order is determined experimentally and experimentally and cannotcannot be be predicted from the chemical equation predicted from the chemical equation alonealone A complete description of the reaction A complete description of the reaction

mechanism is required to predict reaction mechanism is required to predict reaction ordersorders

Experimental orders are used to identify Experimental orders are used to identify reaction mechanismsreaction mechanisms

Strategies for determining Strategies for determining orders of reactionorders of reaction

►1: Method of initial rates1: Method of initial rates At At tt = 0, [product] = 0 = 0, [product] = 0 Vary concentration of one reactant, Vary concentration of one reactant,

keeping other(s) constantkeeping other(s) constant Compare ratios of rates at different Compare ratios of rates at different

[reactant] in turn[reactant] in turn Reaction is second order in NO and first Reaction is second order in NO and first

order in Oorder in O22

][][ 2

22 ONOkt

NORate

The common rate laws and The common rate laws and unitsunits

► Rate of reaction and rate constant (Rate of reaction and rate constant (kk) are ) are not the samenot the same Rate of reaction depends on concentrationsRate of reaction depends on concentrations Rate constant does notRate constant does not Rate of reaction always has units of M/sRate of reaction always has units of M/s Rate constant has units that depend on rate Rate constant has units that depend on rate

equationequation

2: Integrated rate law 2: Integrated rate law methodmethod

►General first order dependenceGeneral first order dependence

► IntegrateIntegrate

►ButBut

►A plot of ln[A]A plot of ln[A]tt vs t is linear vs t is linear

0]ln[]ln[ AktA t

kt

A

A t 0][

ln

][Ak

dt

AdRate

First order reaction and First order reaction and half-lifehalf-life

►The half-life is the time required for the The half-life is the time required for the concentration of the reactant to halveconcentration of the reactant to halve

►When [A]When [A]tt = = ½[A]½[A]00

►The half-life is constant since it The half-life is constant since it depends on depends on k k only only

kt

A

A t 0][

ln

2/12

1ln kt

Integrated rate law for Integrated rate law for second ordersecond order

►General second order dependenceGeneral second order dependence

► In this case the plot of 1/[A]In this case the plot of 1/[A]tt vs t is vs t is linearlinear

01

][

1

Akt

A t

2][Akdt

AdRate

Zero-order reactionsZero-order reactions

►Uncommon but not impossibleUncommon but not impossible

► Integrated rate lawIntegrated rate law

►Plot of [A]Plot of [A]tt vs vs tt gives a straight line gives a straight line with slope with slope -k-k

0][][ AktA

kAk

dt

AdRate 0][