• The amount of time required for a The amount of time required for a chemical rxn to come to completion can chemical rxn to come to completion can vary tremendously vary tremendously

– When you strike a match it seems flame up When you strike a match it seems flame up instantlyinstantly

– Coal is made over millions of years from Coal is made over millions of years from very slow chemical reactionsvery slow chemical reactions

• Chemists find it useful, although difficult, Chemists find it useful, although difficult, to study a reactions progress over a to study a reactions progress over a period of time, which is called period of time, which is called KineticsKinetics..

Collision TheoryCollision Theory

• The concept of The concept of raterate is familiar is familiar– A fast sprinter may cover 100 m in 11.5 sA fast sprinter may cover 100 m in 11.5 s– A slower sprinter may take 15 s to run the A slower sprinter may take 15 s to run the

same distancesame distance• On average the 1On average the 1stst sprinter runs at a sprinter runs at a

speed of speed of 8.7m/s8.7m/s• The 2The 2ndnd runs at a speed of 6.7m/s runs at a speed of 6.7m/s

– Both speeds are expressions of rates of Both speeds are expressions of rates of traveltravel

Collision TheoryCollision Theory

• The word rate can be used as a The word rate can be used as a synonym of speedsynonym of speed– RatesRates measure the speed of any change measure the speed of any change

that occurs within an interval of timethat occurs within an interval of time– The interval of time may range from The interval of time may range from

fractions of a second to centuriesfractions of a second to centuries• Rates of chemical change usually are Rates of chemical change usually are

expressed as the expressed as the amount of reactant amount of reactant forming products per unit time.forming products per unit time.

Collision TheoryCollision Theory

• Rates of chem rxns are related to the Rates of chem rxns are related to the properties of atoms, ions, and molecules properties of atoms, ions, and molecules through a model called through a model called collision theorycollision theory

• According to collision theory, atoms, According to collision theory, atoms, ions, and molecules can react to form ions, and molecules can react to form products when they collideproducts when they collide– provided that the particles have enough provided that the particles have enough

kinetic energykinetic energy

Collision TheoryCollision Theory

• The minimum amount of energy that the The minimum amount of energy that the particles or reactants must have in order particles or reactants must have in order to react is called the rxn’s to react is called the rxn’s activation activation energy.energy.

– In a sense the activation energy is a In a sense the activation energy is a barrierbarrier that reactants must get over to be that reactants must get over to be converted to productsconverted to products

– The higher the barrier the larger the The higher the barrier the larger the investment of energy in order to get the rxn investment of energy in order to get the rxn to proceedto proceed

Collision TheoryCollision Theory

• During a rxn, a particle that is neither During a rxn, a particle that is neither reactant nor product forms momentarily, reactant nor product forms momentarily, called an called an activated complex activated complex

– if there is sufficient energy if there is sufficient energy – and if the atoms are oriented properlyand if the atoms are oriented properly

• An activated complex is a kind of An activated complex is a kind of transition moleculetransition molecule which has similarities which has similarities to reactants & productsto reactants & products

– An activated complex is the arrangement of An activated complex is the arrangement of atoms at the peak of the activation-energy atoms at the peak of the activation-energy barrier.barrier.

Collision TheoryCollision Theory

• Collision theoryCollision theory explains why some explains why some naturally occurring rxns are naturally occurring rxns are immeasurably slow at room temp.immeasurably slow at room temp.

– Carbon and Oxygen react when charcoal Carbon and Oxygen react when charcoal burns, but this reaction has a high burns, but this reaction has a high activation energyactivation energy

– At room temp, the collisions of oxygen and At room temp, the collisions of oxygen and carbon molecules aren’t energetic enough carbon molecules aren’t energetic enough to reactto react

– But the rxn can be helped along a number But the rxn can be helped along a number of waysof ways

Collision TheoryCollision Theory

• It is possible to vary the conditions of the It is possible to vary the conditions of the rxn, the rate of almost any rxn can be rxn, the rate of almost any rxn can be modifiedmodified

o collision theory can help explain why the collision theory can help explain why the rates can be modifiedrates can be modified

• Several strategies can be used:Several strategies can be used:o Increase the Increase the temperaturetemperatureo Increase the Increase the concentrationconcentrationo Decrease the Decrease the particle sizeparticle sizeo Employ a Employ a catalystcatalyst

Reaction RatesReaction Rates

• Increasing the temp speeds up the rxn, Increasing the temp speeds up the rxn, while lowering the temp while lowering the temp slows downslows down the the rxnrxn

• Increasing the temp increases the Increasing the temp increases the frequencyfrequency of the collisions of the collisions

– Collisions taking place more often more Collisions taking place more often more likely they are to sticklikely they are to stick

• And the extra energy increases the And the extra energy increases the powerpower of the collisionsof the collisions

– Also increasing the likelihood of a Also increasing the likelihood of a successful collision successful collision

TemperatureTemperature

• Just sitting out, charcoal Just sitting out, charcoal does not reactdoes not react at a measurable rateat a measurable rate– However, when a starter flame touches the However, when a starter flame touches the

charcoal, atoms of reactants collide with charcoal, atoms of reactants collide with higher energy and higher energy and greater frequencygreater frequency

– Some of the collisions are high enough in Some of the collisions are high enough in energy that the product COenergy that the product CO22 is formed is formed

o The energy released by the rxn The energy released by the rxn then supp-lies enough energy to then supp-lies enough energy to get more C and Oget more C and O22 over the over the activation-energy barrieractivation-energy barrier• Evidence of this would be if you Evidence of this would be if you

remove the starter flame,remove the starter flame, the rxn the rxn will continue on its own.will continue on its own.

• The more reacting particles you have in a The more reacting particles you have in a given volume, the given volume, the higher the rate of rxnhigher the rate of rxn..

• Cramming more particles into a fixed Cramming more particles into a fixed volume increases the volume increases the concentrationconcentration of of reactants,reactants,

– Increasing the concentration, increases the Increasing the concentration, increases the frequency of the collisions, and therefore frequency of the collisions, and therefore increasingincreasing the reaction rate. the reaction rate.

ConcentrationConcentration

• The smaller the particle size, the The smaller the particle size, the larger larger the surfacethe surface area for a given mass of area for a given mass of particlesparticles

• The total surface area of a solid or liquid The total surface area of a solid or liquid reactant has an important effect on the reactant has an important effect on the rate of reactionrate of reaction..

• An increase in surface area increases the An increase in surface area increases the amount of the reactant amount of the reactant exposed for exposed for collisioncollision to take place… to take place…

– Which increases the collision frequency Which increases the collision frequency and the reaction rate.and the reaction rate.

Particle SizeParticle Size

o One way to increase the surface One way to increase the surface area of solid reactants is to area of solid reactants is to dissolve themdissolve them

• which separates the particles and which separates the particles and makes them more accessible to makes them more accessible to other reactants.other reactants.

o Grinding solids into a fine powder Grinding solids into a fine powder also increases the surface area of also increases the surface area of reactantsreactants

• Small dust-like particles can be Small dust-like particles can be very dangerous, can be highly very dangerous, can be highly explosiveexplosive

Particle SizeParticle Size

o An increase in temp is not always An increase in temp is not always the best way to increase the rate the best way to increase the rate of rxnof rxn

• A A catalystcatalyst is often better. is often better.o A catalyst is a substance that A catalyst is a substance that

increases the rate of a rxn without increases the rate of a rxn without being changed during the rxnbeing changed during the rxn

•They permit rxns to proceed at They permit rxns to proceed at lower energy than is normally lower energy than is normally requiredrequired

o With a lower activation energy With a lower activation energy more reactants can form productsmore reactants can form products in a given amount of time.in a given amount of time.

CatalystCatalyst

CatalystCatalyst

o Since catalysts are not consumed Since catalysts are not consumed during a rxn, they do not appear during a rxn, they do not appear as reactants or products in the as reactants or products in the chem eqnchem eqn

• Often writtenOften written above the rxn above the rxn arrow(s)arrow(s)

o Catalysts are crucial for many life Catalysts are crucial for many life processes.processes.

• Your body temp is only 37°C and Your body temp is only 37°C and cannot be raised significantly cannot be raised significantly without dangerwithout danger

o Without catalysts, few rxns in the Without catalysts, few rxns in the body would proceed fast enough body would proceed fast enough at that tempat that temp

CatalystCatalyst

• Enzymes, biological catalysts, Enzymes, biological catalysts, increase the rates of biological increase the rates of biological rxnsrxns

o When you eat a meal containing When you eat a meal containing protein, enzymes in your digestive protein, enzymes in your digestive tract break down the protein tract break down the protein molecules in a few hrs..molecules in a few hrs..

• Without enzymes, the digestion of Without enzymes, the digestion of proteins at 37proteins at 37C takes yrsC takes yrso An inhibitor is a substance that An inhibitor is a substance that

interferes with the action of a interferes with the action of a catalystcatalyst

• An inhibitor could work by An inhibitor could work by reacting with or “poisoning” the reacting with or “poisoning” the catalyst itselfcatalyst itself

• The rate of a rxn depends in part on the The rate of a rxn depends in part on the concentrationconcentration of the reactants of the reactants– Concentration is a measure of how much Concentration is a measure of how much

stuff is available to reactstuff is available to react• For a rxn in which reactant A reacts to For a rxn in which reactant A reacts to

form product B in 1 step, you can write a form product B in 1 step, you can write a simple rxn eqn: simple rxn eqn: A A B B

• The speed that A forms B is dependent The speed that A forms B is dependent on how the conc of A on how the conc of A changes over timechanges over time– As the conc of A decreases the rate of the As the conc of A decreases the rate of the

rxn generally decreasesrxn generally decreases

Rate LawsRate Laws

Rate =Rate =AAtt

You can express the rate as the You can express the rate as the change in A (change in A (A) with respect to the A) with respect to the change in time (change in time (t)t)

• The rate of disappearance of A is The rate of disappearance of A is proportional to the concentration or mol-proportional to the concentration or mol-arity arity (# of moles/Liter(# of moles/Liter) of reactant A) of reactant A

• This proportionality can be expressed as This proportionality can be expressed as a constant (a constant (kk) multiplied by the ) multiplied by the concentration of reactant Aconcentration of reactant A

kk••[A][A]

Rate LawsRate Laws

• This mathematical expression is an This mathematical expression is an example of a example of a rate lawrate law

– An expression which relates the rate of a An expression which relates the rate of a rxn to the conc of reactantsrxn to the conc of reactants

• The The magnitudemagnitude of the rate constant (k) of the rate constant (k) depends on the conditions at which the depends on the conditions at which the rxn is conductedrxn is conducted

– If reactant A reacts to form product B If reactant A reacts to form product B quickly, the value of k will be quickly, the value of k will be largelarge

– If reactant A reacts to form B slowly, the If reactant A reacts to form B slowly, the value of k will be value of k will be smallsmall

Rate LawsRate Laws

• Rxns are classified as either Rxns are classified as either zerozero-order, -order, firstfirst-order, -order, secondsecond-order, or mixed order -order, or mixed order (higher order) rxns.(higher order) rxns.

– The rate of chemical rxns and the size of The rate of chemical rxns and the size of the rate constant (the rate constant (kk) is dependent on the ) is dependent on the ““orderorder” of the rxn” of the rxn

• Zero-Order RxnsZero-Order Rxns– (Order = 0) have a constant rate. This rate (Order = 0) have a constant rate. This rate

is independent of the is independent of the conc of the reactantsconc of the reactants. . The rate law is: The rate law is: kk, with k having the units of , with k having the units of M/sec.M/sec.

Rate LawsRate Laws

• First-Order ReactionsFirst-Order Reactions– (order = 1) has a rate proportional to the (order = 1) has a rate proportional to the

conc of one of the reactants. A common conc of one of the reactants. A common example of a first-order rxn is the example of a first-order rxn is the phenomenon of radioactive decay. The phenomenon of radioactive decay. The rate law is: rate law is: k[A]k[A]11 (or B instead of A), with k (or B instead of A), with k having the units of sechaving the units of sec-1-1

Rate LawsRate Laws

• Second-Order ReactionsSecond-Order Reactions– (order = 2) has a rate proportional to the (order = 2) has a rate proportional to the

conc of the square of a single reactant or conc of the square of a single reactant or the product of the conc of two reactants. the product of the conc of two reactants.

– Rate law =Rate law =k[A]k[A]22 (or substitute B for A or k (or substitute B for A or k multiplied by the concentration of A, [A], multiplied by the concentration of A, [A], times the concentration of B, [B]), with the times the concentration of B, [B]), with the units of the rate constant Munits of the rate constant M-1-1secsec-1-1

Rate LawsRate Laws

• Rate laws can only be determined Rate laws can only be determined experimentally.experimentally.– It is not an easy process to determine the It is not an easy process to determine the

order of the reaction or the rate constantorder of the reaction or the rate constant– Unless you determine a class of rate laws Unless you determine a class of rate laws

called called Integrated Rate Laws.Integrated Rate Laws.

Determining Rate LawsDetermining Rate Laws

o Integrated Rate Laws are Integrated Rate Laws are determined by determined by graphinggraphing a series a series of rate data and analyzing the of rate data and analyzing the graph looking for a specific graph looking for a specific pattern.pattern.

• The Zero order integrated rate law shows The Zero order integrated rate law shows that its rate is independent of the [A]that its rate is independent of the [A]– Where [A] vs. t is a Where [A] vs. t is a

straight line with straight line with a a slope of - kslope of - k

Integrated Rate Law: Zero Integrated Rate Law: Zero OrderOrder

0[A]kt [A]

Zero OrderZero Order

Rate LawRate Law kkRate Rate

ConstantConstant Slope = - k Slope = - k Integrated Integrated Rate LawRate Law [A] = -kt + [A][A] = -kt + [A]00

GraphGraph [A] versus t[A] versus t ½ Life½ Life t t ½½=[A]=[A]00/2k /2k

• The first order integrated rate law can be The first order integrated rate law can be used to determine the concentration of [A] at used to determine the concentration of [A] at any time.any time.– It can be determined graphicallyIt can be determined graphically

• Where Where – y = ln[A]y = ln[A]– x = timex = time

Integrated Rate Law: First Integrated Rate Law: First OrderOrder

• m = -km = -k• b = ln[A]b = ln[A] 0 0

First OrderFirst Order

Rate LawRate Law k[A]k[A]Rate Rate

ConstantConstant Slope = - k Slope = - k Integrated Integrated Rate LawRate Law ln[A] = -kt + ln[A]ln[A] = -kt + ln[A]00

GraphGraph ln[A] versus tln[A] versus t ½ Life½ Life t t ½½=0.693/k =0.693/k

• The second order integrated rate law The second order integrated rate law can be used to determine the can be used to determine the concentration of [A] at any time.concentration of [A] at any time.– It can be determined graphicallyIt can be determined graphically

• Where Where – y = 1/[A]y = 1/[A]– x = timex = time

Integrated Integrated Rate Law: Rate Law: Second Second OrderOrder

• m = km = k• b = 1/[A]b = 1/[A] 0 0

Second OrderSecond Order

Rate LawRate Law k[A]k[A]22

Rate Rate ConstantConstant Slope = k Slope = k Integrated Integrated

Rate LawRate Law

GraphGraph 1/[A] versus t1/[A] versus t ½ Life½ Life t t ½½=1/k[A]=1/k[A]00

0[A]1 kt[A]

1

• In some kinds of rxns, such as double In some kinds of rxns, such as double replacement, 2 substances react to give replacement, 2 substances react to give productsproducts

• The coefficients in the eqn for such a rxn The coefficients in the eqn for such a rxn can be represented by lower-case letters: can be represented by lower-case letters: aA + bB aA + bB cC + dD cC + dD

• For a 1 step rxn of A+B, the rate of rxn is For a 1 step rxn of A+B, the rate of rxn is dependent on the concentrations of dependent on the concentrations of reactants A & Breactants A & B

• It’s rate law would follow the eqn:It’s rate law would follow the eqn:

Rate = k[A]Rate = k[A]aa[B][B]bb

Rate LawsRate Laws

o When each of the exponents a & When each of the exponents a & b in the rate law equals 1, the rxn b in the rate law equals 1, the rxn is said to be 1is said to be 1stst order in A, 1 order in A, 1stst order in B, &order in B, & 22ndnd order overall order overall

o The overall order of a rxn is theThe overall order of a rxn is the sum of the exponents for the sum of the exponents for the individual reactantsindividual reactants

o If enough info were available, you If enough info were available, you could graph all the energy could graph all the energy changes that occur as the changes that occur as the reactants are converted to reactants are converted to products in a chem rxnproducts in a chem rxn

Rate LawsRate Laws

o Such a graph would be called aSuch a graph would be called a rxn rxn progress curveprogress curve

o The simplest would be a one-step, The simplest would be a one-step, elementary rxnelementary rxn• Reactants form products in a Reactants form products in a

single stepsingle step• 1 activated complex1 activated complex• 1 energy peak1 energy peak

Rate LawsRate Laws

• For a more complex rxn, or a higher order For a more complex rxn, or a higher order rxn, the rxn progress curve resembles a rxn, the rxn progress curve resembles a series of series of hills & valleyshills & valleys

– The peaks correspond to the energies of the The peaks correspond to the energies of the activated complexesactivated complexes

– Each valley represents an Each valley represents an intermediate intermediate productproduct which becomes a react of the next which becomes a react of the next stage of the rxnstage of the rxn

• Intermediates have a significant lifetime Intermediates have a significant lifetime compared with an compared with an activated complexactivated complex

– They have real ionic or molecular structures They have real ionic or molecular structures and some stabilityand some stability

Reaction MechanismReaction Mechanism

• Intermediates do not appear in the Intermediates do not appear in the overall eqn for a rxnoverall eqn for a rxn

• For example in the following overall rxn:For example in the following overall rxn:

HH22(g) + 2ICl(g) <==> I(g) + 2ICl(g) <==> I22(g) + (g) + 2HCl(g) 2HCl(g)

Reaction MechanismReaction Mechanism

o This reaction is not exactly accurateThis reaction is not exactly accurate• There is an intermediate reaction in There is an intermediate reaction in

between the reactants and products.between the reactants and products.

1) H1) H22(g) + 2ICl(g) (g) + 2ICl(g) ICl(g) + HCl(g) + ICl(g) + HCl(g) + HI(g) HI(g) 2) ICl(g) + HCl(g) + HI(g) 2) ICl(g) + HCl(g) + HI(g) I I22(g) (g)

+2HCl(g)+2HCl(g)

Reaction Reaction MechanismMechanism

o If a chem rxn proceeds in a If a chem rxn proceeds in a sequence of steps, the rate law is sequence of steps, the rate law is determined by the slowest step determined by the slowest step because it has the lowest rate.because it has the lowest rate.

• The slowest-rate step is called The slowest-rate step is called the the rate-determining steprate-determining step

o Consider this rxn: NOConsider this rxn: NO22 + CO + CO NO NO + CO+ CO22

• the rxn is believed to be a 2 step the rxn is believed to be a 2 step process following this mechanismprocess following this mechanism

Reaction MechanismReaction Mechanism

Step 1: Step 1: NONO22 + NO + NO22 NO + NO NO + NO33Step 2: Step 2: NONO33 + CO + CO NO NO22 + CO + CO22

SLOWSLOWFASTFAST

o In the 1In the 1stst step step • 2 molecules of NO2 molecules of NO22 collide, collide,

forming the intermediate NOforming the intermediate NO33. . • The NOThe NO33 species collides with a species collides with a

molecule of CO and reacts quickly molecule of CO and reacts quickly to produce 1 molecules each of to produce 1 molecules each of NONO22 and CO and CO22

o The 1The 1stst step is the slower of the 2 step is the slower of the 2 steps and is therefore the rate-steps and is therefore the rate-determining stepdetermining step

Reaction MechanismReaction Mechanism

Its rate law: Its rate law: R=k[NOR=k[NO22]]22

The rate determining step and the The rate determining step and the rate law are both determined rate law are both determined

experimentallyexperimentally