Chapter 14: Chemical Kinetics

AP/IB ChemistryAP/IB Chemistry

Reaction Rate: Reaction Rate: speed of a chemical speed of a chemical reactionreactionChange in concentration of Change in concentration of

reactant or product in a given reactant or product in a given amount of timeamount of time

Units:Units: M/s M/s

Collision theory explains that chemical Collision theory explains that chemical reactions occur through collisions reactions occur through collisions between molecules or atomsbetween molecules or atoms

Reactant molecules must collide to Reactant molecules must collide to reactreact

Things to think about…Things to think about… Number of collisions, or collision frequencyNumber of collisions, or collision frequency Concentration of reactantsConcentration of reactants TemperatureTemperature Energy of collisionsEnergy of collisions Appropriate collision orientationAppropriate collision orientation

There are 4 factors that affect There are 4 factors that affect reaction ratesreaction ratesPhysical state of reactantsPhysical state of reactantsConcentration of reactantsConcentration of reactantsTemperatureTemperaturePresence or absence of catalystsPresence or absence of catalysts

Catalysts:Catalysts: increase RR without increase RR without being used upbeing used up

Know: biological enzymesKnow: biological enzymes

For a reaction A For a reaction A B B

Aside: [B] means “molarity of B in mol/L”Aside: [B] means “molarity of B in mol/L”

t

B

t

B ofmolarity B of appearance of rate Average

M/s 0175.0s 0s 40

M 0 M 70.0

][][

rate Average

12

12

tt

BBt

B

At At tt = 0 there is 1.00 = 0 there is 1.00 MM A and no B A and no B At At tt = 20 s, there is 0.54 = 20 s, there is 0.54 MM A and A and

0.46 0.46 MM B B At At tt = 40 s, there is 0.30 = 40 s, there is 0.30 MM A and A and

0.70 0.70 MM B B

For A For A B there are 2 ways of B there are 2 ways of measuring rate:measuring rate:

Speed at which products appearSpeed at which products appear Speed at which reactants disappearSpeed at which reactants disappear

NOTE: rates always expressed as NOTE: rates always expressed as positive #’spositive #’s

t

A

Aof ncedisappeara of rate Average

Calculate the Calculate the average rate average rate in terms of the in terms of the disappearance of reactant over some time disappearance of reactant over some time intervalinterval

Instantaneous rate: Instantaneous rate: the RR at any given instantthe RR at any given instant Determined from the slope of the tangent to Determined from the slope of the tangent to

the rate curve (derivative)the rate curve (derivative) Instantaneous rate is different from average Instantaneous rate is different from average

rate!rate! We usually call the instantaneous rate the We usually call the instantaneous rate the

“reaction rate”“reaction rate” Initial rate: Initial rate: instantaneous rate at instantaneous rate at tt=0=0

In general, for the reaction:In general, for the reaction:

aaAA + b + bBB c cCC + d + dDD

aa, , bb, , cc and and dd are the stoichiometric are the stoichiometric coefficients of the balanced coefficients of the balanced chemical equationchemical equation

tdtctbta

D1C1B1A1

Rate

The decomposition of dinitrogen pentoxide The decomposition of dinitrogen pentoxide proceeds according to the following proceeds according to the following equation:equation:

2 N2 N22OO5 5 (g)(g) 4 NO 4 NO2 2 (g)(g) + O + O2 2 (g)(g)

If the rate of decomposition of NIf the rate of decomposition of N22OO55 at a at a particular instant in a reaction vessel is particular instant in a reaction vessel is 4.2 x 104.2 x 10-7-7 MM/s, what is the rate of /s, what is the rate of appearance of NOappearance of NO22? Of O? Of O22??

Rate Law:Rate Law: an expression that relates the an expression that relates the reaction rate to the concentration of reactantsreaction rate to the concentration of reactants

Example: if the rate law for the reaction,Example: if the rate law for the reaction,

2 N2 N22OO5 5 (g)(g) 4 NO 4 NO2 2 (g)(g) + O + O2 2 (g)(g)

is:is:

Rate = Rate = k k [N[N22OO55]] It tells you that reaction rate is directly It tells you that reaction rate is directly

proportional to concentration of proportional to concentration of NN22OO55

If you double [If you double [NN22OO55], reaction rate doubles], reaction rate doubles kk is the rate constant is the rate constant

For the reaction:For the reaction:

NHNH44++

((aqaq)) + NO + NO22--((aqaq)) N N2(2(gg)) + 2H + 2H22OO((ll))

we note that:we note that: As [NHAs [NH44

++] doubles, with [NO] doubles, with [NO22--] held constant, ] held constant,

the rate doubles the rate doubles As [NOAs [NO22

--] doubles, with [NH] doubles, with [NH44++] constant, the ] constant, the

rate doublesrate doubles Rate is directly proportional to concentration of Rate is directly proportional to concentration of

both reactantsboth reactants Rate law:Rate law:

]NO][NH[Rate 24k

aaA + A + bbB B ccC + C + ddDD

Rate = Rate = kk[A][A]mm[B][B]nn

Exponents Exponents mm and and nn are small whole are small whole numbers (0, 1, 2) called the numbers (0, 1, 2) called the kinetic orderskinetic orders

The reaction is The reaction is mmthth-order in reactant 1 -order in reactant 1 and and nnthth-order in reactant 2-order in reactant 2 The The overall order overall order of reaction is of reaction is m + n + m + n +

…. (sum of all exponents)…. (sum of all exponents) Values of the exponents (orders) have to Values of the exponents (orders) have to

be be determined experimentallydetermined experimentally

If If exponent is 0exponent is 0, the order for that reactant is , the order for that reactant is zero-orderzero-order Means that Means that as the [reactant] changesas the [reactant] changes, it , it

produces produces no effectno effect in RR in RR If the If the exponent is 1exponent is 1, the rate is , the rate is first-orderfirst-order

Means that Means that as the [reactant] doublesas the [reactant] doubles, the , the RR RR doublesdoubles, as [reactant] triples, RR triples, etc., as [reactant] triples, RR triples, etc.

If the If the exponent is exponent is 2, the rate is 2, the rate is second ordersecond order Means that as the Means that as the [reactant] doubles[reactant] doubles, the , the RR RR

quadruplesquadruples, or , or as [reactant] triplesas [reactant] triples, , RR goes RR goes up by factor of 9up by factor of 9

RR depends on concentration of RR depends on concentration of reactantsreactants

Rate constant (Rate constant (kk) is experimentally ) is experimentally determined determined and depends on:and depends on:TemperatureTemperaturePresence or absence of a catalystPresence or absence of a catalyst

The following data were obtained for the The following data were obtained for the reactionreaction

A + B A + B C C

Determine the rate law for the reaction.Determine the rate law for the reaction.

Trial Number

Initial [A](M)

Initial [B](M)

Initial Rate(M/s)

1 0.20 1.00 5.0 x 10-2

2 0.20 2.00 2.0 x 10-1

3 0.40 2.00 4.0 x 10-1

There is a relationship between There is a relationship between concentration of reactants and time:concentration of reactants and time:

For a For a first order reaction:first order reaction:

ln[A]ln[A]tt = – = –ktkt + ln[A] + ln[A]00 kk = rate constant = rate constant tt = time = time [A][A]00 = = concentration at start of reactionconcentration at start of reaction

[A][A]tt = = concentration at time, concentration at time, tt

ln[A]ln[A]tt = – = –ktkt + ln[A] + ln[A]00

y = mx + by = mx + b

There is a relationship between There is a relationship between concentration of reactants and time:concentration of reactants and time:

For a For a second order reaction:second order reaction:

Rate = Rate = kk[A][A]22

0A1

A1 ktt

y = mx + by = mx + b

• Half-life: time it takes for the concentration Half-life: time it takes for the concentration of a reactant to drop to half its original valueof a reactant to drop to half its original value

• For a first order process:For a first order process:• Half life, Half life, tt½½ is the time it takes for [A] is the time it takes for [A]00 to to

reach ½[A]reach ½[A]00

• Radioactive decay is a type of half-life Radioactive decay is a type of half-life processprocess

kk

t693.0ln

21

21

The half-life of a first-order reaction is 6.00 x 10-2 s. What is the rate constant for the reaction?

RR RR increases w/ increases w/ increasing increasing temptemp

Why?Why? As temp As temp

increases, increases, rate rate constant (constant (kk) ) increasesincreases

Arrhenius: molecules must posses a Arrhenius: molecules must posses a minimum amount of energy to react. minimum amount of energy to react. Why?Why? To form products, bonds are broken in To form products, bonds are broken in

reactantsreactants Bond breakage requires energyBond breakage requires energy

Activation energyActivation energy, , EEaa, is the minimum , is the minimum energy required to initiate a chemical energy required to initiate a chemical reactionreaction EEaa changes from reaction to reaction changes from reaction to reaction

Arrhenius discovered RR data obey the Arrhenius discovered RR data obey the Arrhenius equation:Arrhenius equation:

kk = rate constant = rate constant EEaa = = activation energyactivation energy RR = gas constant (8.314 J/K-mol) = gas constant (8.314 J/K-mol) TT = temperature = temperature AA = frequency factor = frequency factor

Related to number of collisionsRelated to number of collisions Both Both AA and and EEaa are specific to a given are specific to a given

reactionreaction

RTEa

Aek

If there is a lot of data, determine If there is a lot of data, determine EEaa and and AA graphically by rearranging Arrhenius graphically by rearranging Arrhenius equation:equation:

y = mx + by = mx + b

ARTE

k a lnln

Reaction Mechanisms: Reaction Mechanisms: the process by the process by which a chemical reaction occurswhich a chemical reaction occurs Gives the path of a reactionGives the path of a reaction

Remember:Remember: reactions take place as a reactions take place as a result of collisions between the reactantsresult of collisions between the reactants

Elementary ReactionsElementary Reactions: chemical rxns that : chemical rxns that occur in a single stepoccur in a single step Molecules that collide must be correctly Molecules that collide must be correctly

oriented and have enough energy to oriented and have enough energy to reactreact

Multistep Mechanism: Multistep Mechanism: consists of a sequence consists of a sequence of elementary rxnsof elementary rxns

Net change = balanced chemical eqnNet change = balanced chemical eqn

NONO22 + NO + NO22 NO NO33 + NO + NO

NONO33 + CO + CO NO NO22 + CO + CO22

NONO22 + CO + CO NO + CO NO + CO22

Chemical eqns for elementary rxns in a Chemical eqns for elementary rxns in a multistep mechanism must add up the give multistep mechanism must add up the give correct chemical eqncorrect chemical eqn

Most rxns involve >2 elementary rxnsMost rxns involve >2 elementary rxns Each rxn has its own Each rxn has its own kk and and EEaa

Rate-Determining Step: Rate-Determining Step: in a multistep in a multistep rxn, one step is usually much slower than rxn, one step is usually much slower than the othersthe others The rate of the whole reaction can’t be The rate of the whole reaction can’t be

faster than the rate of the slowest faster than the rate of the slowest elementary stepelementary step

The slowest step in a multistep rxn limits The slowest step in a multistep rxn limits the overall ratethe overall rate

If If step 1 is slow step 1 is slow and and step 2 is faststep 2 is fast, step 1 , step 1 is rate-limitingis rate-limiting

Overall rate and rate law of rxn has to be Overall rate and rate law of rxn has to be equal to that of step 1equal to that of step 1

OO33 reacts with NO reacts with NO22 to produce N to produce N22OO55 and O and O22::

The reaction is believed to occur in 2 steps:The reaction is believed to occur in 2 steps:OO33 + NO + NO22 NO NO33 + O + O22 (slow) (slow) Rate = k[O3]

[NO2]

NONO33 + NO + NO22 N N22OO55 (fast) (fast) Rate =

k[NO3]2[NO2]

What is the predicted rate law?What is the predicted rate law?

Catalyst:Catalyst: changes the rate of a chemical changes the rate of a chemical reaction without being used upreaction without being used up

Generally, catalysts lower the Generally, catalysts lower the EEaa of a of a reactionreaction

Two types of catalysts:Two types of catalysts: HomogeneousHomogeneous HeterogeneousHeterogeneous

• Cl atoms are catalysts for the destruction Cl atoms are catalysts for the destruction of Oof O33

Homogenous Catalyst: Homogenous Catalyst: catalyst present in same catalyst present in same phase as the reactantsphase as the reactants

HH22OO22 decomposes very slowly decomposes very slowly

2H2H22OO2 (2 (aqaq)) 2H 2H22OO ( (ll)) + O + O2 (2 (gg))

In the presence of bromide ion, decomposition In the presence of bromide ion, decomposition occurs quickly:occurs quickly:

2Br2Br- - ((aqaq)) + H + H22OO2 (2 (aqaq)) + 2H + 2H+ +

((aqaq)) Br Br2 (2 (aqaq)) + 2H + 2H22O O ((ll))

BrBr2 (2 (aqaq)) + H + H22OO2 (2 (aqaq)) 2Br 2Br- - ((aqaq)) + 2H + 2H+ +

((aqaq)) + O + O2 (2 (gg))

2H2H22OO2 (2 (aqaq)) 2H 2H22OO ( (ll)) + O + O2 (2 (gg))

BrBr-- is a catalyst because it is recovered at the is a catalyst because it is recovered at the end of the reactionend of the reaction

Heterogenous CatalystHeterogenous Catalyst: catalyst present in a : catalyst present in a different phase as the reactantsdifferent phase as the reactants

Reaction occurs on the surface of solidsReaction occurs on the surface of solids Example: decomposition of HExample: decomposition of H22OO22 by silver by silver