kinetics (the study of reaction rates) part 1

Kinetics Kinetics (the study of reaction rates)(the study of reaction rates)

Part 1Part 1Ch. 14 in TextCh. 14 in Text

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I.I. What you (maybe) already What you (maybe) already know about kineticsknow about kinetics

A) DefinitionsA) Definitions What is a reaction rate?What is a reaction rate?

What is a reaction mechanism?What is a reaction mechanism?

B) Kinetics ActivityB) Kinetics Activity

How did this activity demonstrate How did this activity demonstrate reaction rate?reaction rate?

How did this activity demonstrate a How did this activity demonstrate a mechanism?mechanism?

Concentration vs. Time PlotsConcentration vs. Time Plots

C) Factors Affecting Rxn RateC) Factors Affecting Rxn Rate

FactorFactor Effect On Effect On RateRate

Why?Why?

1. Catalyst1. Catalyst

2. Inc. Temp.2. Inc. Temp.

3. Inc. Surface 3. Inc. Surface AreaArea

4. Inc. 4. Inc. ConcentrationConcentration

5. Inc. Pressure5. Inc. Pressure

D) Potential Energy DiagramsD) Potential Energy Diagrams

HW: 14.1, 14.42

II.II. Calculating RatesCalculating RatesA) Average RateA) Average Rate

The speed of a rxn for a The speed of a rxn for a given given time intervaltime interval

When plotted as When plotted as concentration over time, it concentration over time, it looks like a straight line for looks like a straight line for each time intervaleach time interval

With many intervals, looks With many intervals, looks like a smooth curvelike a smooth curve

Note: Note: molarity of species molarity of species A is represented by [A]A is represented by [A]

Ex) A Ex) A → B→ B

Avg. Rate = -Δ[A]/Δt = +Δ[B]/Δt Avg. Rate = -Δ[A]/Δt = +Δ[B]/Δt = = final M – initial Mfinal M – initial M final t – initial tfinal t – initial t

Note:Note: Both will be positive in Both will be positive in endend

Units: M/s or mol/L•s or MsUnits: M/s or mol/L•s or Ms-1-1

What happens to rate with What happens to rate with time?time?

B) Instantaneous RateB) Instantaneous Rate

The speed of a rxn at a The speed of a rxn at a specific timespecific time rather than rather than an intervalan interval

Draw a straight line at Draw a straight line at the point (called a the point (called a tangent)tangent)

Take slope of tangent Take slope of tangent to get ratio of Δ[A] to Δtto get ratio of Δ[A] to Δt

This represents the This represents the instantaneous rateinstantaneous rate

Concentration vs. Time Concentration vs. Time PlotsPlots

C) Rate StoichiometryC) Rate Stoichiometry

If not a 1:1 ratio of reactants to products, If not a 1:1 ratio of reactants to products, we must take into account the coefficientswe must take into account the coefficients

Ex) 2HI(g) Ex) 2HI(g) → H→ H22(g) + I(g) + I22(g) (g)

Rate = Rate = -1 -1 Δ[HI]Δ[HI] = = Δ[HΔ[H22]] = = Δ[IΔ[I22]]

2 Δt 2 Δt Δt Δt ΔtΔt In general:In general: aA + bB aA + bB → cC + dD→ cC + dD Rate = Rate = -1 -1 Δ[A]Δ[A] = = -1 Δ[B]-1 Δ[B] = = 1 Δ[C]1 Δ[C] = = 1 1

Δ[D]Δ[D] a Δt a Δt b Δt b Δt c Δtc Δt d Δt d Δt

Ex) 2NEx) 2N22OO55 → 4NO→ 4NO22 + O + O22 If the rate of decomposition If the rate of decomposition

of dinitrogen pentoxide is of dinitrogen pentoxide is 4.27 x 104.27 x 10-7-7 Ms Ms-1-1, what is the , what is the rate of appearance of NOrate of appearance of NO22??

HW: 14.4, 14.10, 14.12

III) Rate LawsIII) Rate LawsA) DefinitionsA) Definitions

Rate LawRate Law- mathematical - mathematical expression that shows how rate expression that shows how rate depends on concentration; takes depends on concentration; takes into account into account exponentially exponentially changing rateschanging rates

Rate ConstantRate Constant- k; relates - k; relates concentration to rateconcentration to rate

Reaction OrderReaction Order- exponents of - exponents of concentrations of reactants; concentrations of reactants; determined using experimental determined using experimental data NOT from stoichiometry of data NOT from stoichiometry of equation; usually 0, 1, 2 but can equation; usually 0, 1, 2 but can be fraction or negativebe fraction or negative

Overall OrderOverall Order- sum of all - sum of all exponentsexponents

B) OrdersB) Orders Ex 1) A + B Ex 1) A + B →→ C C Rate = k [A]Rate = k [A]mm[B][B]nn

A isA is B is B is Overall order isOverall order is Ex 2)NHEx 2)NH44

++ + NO+ NO22

-- → N→ N22 + 2H + 2H22OO Rate = k [Rate = k [NHNH44

++][NO][NO22--]]

NHNH44+ + is is

NONO22-- is is

Overall order isOverall order is Units of k areUnits of k are

Ex 3) CHClEx 3) CHCl33 + Cl + Cl22 → CCl→ CCl44 + HCl + HCl

Rate = k [CHClRate = k [CHCl33] [Cl] [Cl22]]1/21/2

CHClCHCl3 3 isis

ClCl22 is is Overall order is Overall order is Units of k areUnits of k are

HW: 14.14

C) Using Initial Concentrations C) Using Initial Concentrations to Experimentally Determine to Experimentally Determine

Rate LawsRate Laws

If the order of If the order of a particular a particular

reactant is…reactant is…

……the effect on the effect on the rate if its the rate if its

concentration concentration is is doubleddoubled is… is…

00

11

22

33

If the order of a If the order of a particular particular

reactant is…reactant is…

……the effect on the the effect on the rate if its rate if its

concentration is concentration is tripledtripled is… is…

00

11

22

33

ExampleExample

Find where only Find where only oneone reactant is reactant is changing (controlled experiment) and changing (controlled experiment) and see how it affects the ratesee how it affects the rate

Experiment Number [A](M) [B](M)Initial Rate

(M/s)1 0.100 0.100 4.0   x 10–5

2 0.100 0.200 8.0   x 10–5

3 0.200 0.100 16.0 x  10–5

Now find the rate constant valueNow find the rate constant value Pick one of the trials, and plug-n- Pick one of the trials, and plug-n-

chug! (or do all and take avg.)chug! (or do all and take avg.)

HW: 14.16, 14.18, 14.20, 14.22, 14.24

IV. The Changing of IV. The Changing of Concentration with TimeConcentration with Time

We want to have an We want to have an equation that allows us to equation that allows us to determine the concentration determine the concentration at any timeat any time

We won’t deal with calculus We won’t deal with calculus in this class, so we won’t in this class, so we won’t worry about how to derive worry about how to derive these equations. Still, you these equations. Still, you need to know need to know whichwhich equationequation goes with goes with which which orderorder reaction reaction

A) First-Order RxnsA) First-Order Rxns The rate doubles as the The rate doubles as the

reactant concentration reactant concentration doubles.doubles.

t= given or final time t= given or final time (sec)(sec)

0= initial time (sec)0= initial time (sec)

In format, (y =  mx + b):

ExampleExample The first-order rate constant for the The first-order rate constant for the

decomposition of Ndecomposition of N22OO55 is 6.82 x 10 is 6.82 x 10-3-3

ss-1-1. If we start with 0.0300 moles of . If we start with 0.0300 moles of NN22OO55 in 2.5 L, how many moles of in 2.5 L, how many moles of

NN22OO55 will remain after 2.5 minutes? will remain after 2.5 minutes?

B) Half-Life B) Half-Life A process that represents A process that represents

the time it takes for the the time it takes for the concentration of the concentration of the reactant to decrease by reactant to decrease by halfhalf

Independent of the initial Independent of the initial amount for first-order amount for first-order rxnsrxns         

ExampleExample

What is the half-life of NWhat is the half-life of N22OO55? ?

C) Second-Order RxnsC) Second-Order Rxns

Rate depends on the Rate depends on the reactant concentration reactant concentration squared or two squared or two reactants each to the reactants each to the first powerfirst power

ExampleExample

The reaction A --> products is The reaction A --> products is second order in A. Initially second order in A. Initially [A][A]00 = 1.00 M; and after 25 mins,  = 1.00 M; and after 25 mins,

[A] = 0.25 M. What is the rate [A] = 0.25 M. What is the rate constant for this reaction?constant for this reaction?

HW: 14.25, 14.26, 14.28, 14.30, 14.32

Kinetics Kinetics Part 2Part 2

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V.V. The Arrhenius EquationThe Arrhenius EquationA) BackgroundA) Background

According to the collision model According to the collision model of kinetics, the more collisions of kinetics, the more collisions there are, the faster the rxnthere are, the faster the rxn

In 1888, Swedish chemist In 1888, Swedish chemist Svante August Arrhenius Svante August Arrhenius proposed the idea that proposed the idea that molecules need to have an molecules need to have an effective collisioneffective collision in order for a in order for a rxn to proceedrxn to proceed

Svante Arrhenius

An effective collision is one in which An effective collision is one in which molecules collide with:molecules collide with: The proper orientationThe proper orientation The minimum amount of energy The minimum amount of energy

required to initiate the rxn (activation required to initiate the rxn (activation energy or Eenergy or Eaa))

The value of EThe value of Eaa depends depends on the particular rxnon the particular rxn

It is always positiveIt is always positive Can also be thought of as Can also be thought of as

the energy required to the energy required to produce the highest produce the highest energy arrangement of energy arrangement of particles in the mechanism particles in the mechanism ((activated complexactivated complex or or transition statetransition state) which is ) which is the top of the “hill”the top of the “hill”

At higher temps, there is a At higher temps, there is a greater chance that greater chance that molecules will possess the molecules will possess the EEaa, thus increasing the rxn , thus increasing the rxn raterate HW: 14.38

B) The MathsB) The Maths ff = = ee-Ea/RT-Ea/RT where where

ff is the fraction of molecules that have an energy equal is the fraction of molecules that have an energy equal to or greater than the activation energyto or greater than the activation energy

ee is some letter from math that represents something is some letter from math that represents something EEaa is the activation energy in J/mol is the activation energy in J/mol RR is the gas constant (special guest appearance in this is the gas constant (special guest appearance in this

unit!) written as 8.314 J/mol·Kunit!) written as 8.314 J/mol·K TT is the temperature in K is the temperature in K

Arrhenius incorporated the previous Arrhenius incorporated the previous equation with the number of equation with the number of collisions/sec and the fraction of collisions/sec and the fraction of collisions with the correct orientation collisions with the correct orientation to obtain his equation:to obtain his equation:

kk = = AeAe-Ea/RT-Ea/RT wherewhere k k is the rate constant (notice it is is the rate constant (notice it is

dependent on temperature)dependent on temperature) A A is the frequency factor constant which is the frequency factor constant which

takes into account collision frequency takes into account collision frequency and the probability that the collisions are and the probability that the collisions are favorably orientedfavorably oriented

As As EEaa increases, increases, kk becomes smaller becomes smaller

HW: 14.40

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VI.VI. Reaction MechanismsReaction MechanismsA) BackgroundA) Background

Series of steps taken to get Series of steps taken to get to the final productsto the final products

Relevant to kinetics Relevant to kinetics because each step because each step ultimately affects the ultimately affects the overall rateoverall rate

Represented by a series of Represented by a series of equations that should equations that should “cancel out” to the final “cancel out” to the final equationequation

The net equation is like the The net equation is like the “before” and “after” “before” and “after” snapshots, but tells us snapshots, but tells us nothing of the actual nothing of the actual mechanism which must be mechanism which must be determined experimentallydetermined experimentally

B) Elementary StepsB) Elementary Steps Any single step processAny single step process # of molecules involved in # of molecules involved in

an elementary step is an elementary step is called the called the molecularitymolecularity

Unimolecular =Unimolecular = AB AB A + B A + B

Bimolecular =Bimolecular = A + B A + B AB AB

Termolecular = Termolecular = (very rare and unlikely, but (very rare and unlikely, but possible)possible) A + B + C A + B + C ABC ABC

C) Multistep MechanismsC) Multistep Mechanisms Involve Involve intermediatesintermediates = =

temporary products that are temporary products that are consumed in subsequent consumed in subsequent stepssteps

1) NO1) NO22 + NO + NO22 NO NO33 + NO + NO

2) NO2) NO33 + CO + CO NO NO22 + CO + CO22

What is the intermediate?What is the intermediate?

What is the chemical What is the chemical equation?equation?

You Try: You Try: 1) O1) O33 O O22 + O + O

2) O2) O33 + O + O 2O 2O22

Describe the molecularity Describe the molecularity of each step.of each step.

Write the overall equation.Write the overall equation.

Identify any intermediates.Identify any intermediates.

HW: 14.54

VII.VII. How mechanisms affect How mechanisms affect rate lawsrate laws

A) Elementary StepsA) Elementary Steps The rate laws of the elementary steps The rate laws of the elementary steps

determine the overall rate lawdetermine the overall rate law The molecularity of each elementary The molecularity of each elementary

step determines its orderstep determines its order Unimolecular is 1Unimolecular is 1stst order order Bimolecular is 2Bimolecular is 2ndnd order order Termolecular is 3Termolecular is 3rdrd order order

Thus, although the stoichiometry of Thus, although the stoichiometry of the overall rxn does not determine the overall rxn does not determine the rate law, the stoichiometry of the the rate law, the stoichiometry of the elementary steps does!elementary steps does!

MolecularityMolecularity Elementary Elementary StepStep

Rate LawRate Law

UnimolecularUnimolecular A A products products

BimolecularBimolecular A + A A + A productsproducts

BimolecularBimolecular A + B A + B productsproducts

TermolecularTermolecular A + A + A A + A + A productsproducts

TermolecularTermolecular A + A + B A + A + B productsproducts

TermolecularTermolecular A + B + C A + B + C productsproducts

HW: 14.56

B) Mechanisms with a Slow B) Mechanisms with a Slow Initial StepInitial Step

The slowest step in a rxn is The slowest step in a rxn is called the called the rate-determining rate-determining stepstep because it determines because it determines the final rate lawthe final rate law

Given:Given:NONO22 + CO + CO NO + NO +

COCO22

If this occurred as a single If this occurred as a single bimolecular elementary bimolecular elementary step you would expect the step you would expect the rate law to be:rate law to be: Rate = kRate = k

But the actual observed rate law is:But the actual observed rate law is: Rate = k [NORate = k [NO22]]22

We can now propose a mechanism We can now propose a mechanism that would lead to this experimental that would lead to this experimental rate law:rate law: 1) NO1) NO22 + NO + NO22 NO NO33 + NO (slow) + NO (slow)

2) NO2) NO33 + CO + CO NO NO22 + CO + CO22 (fast) (fast)

Since Step 1 is slow, it limits how fast Since Step 1 is slow, it limits how fast Step 2 can go. Thus, Step 1 is the Step 2 can go. Thus, Step 1 is the rate-determining step and is all we rate-determining step and is all we need to get the rate law…need to get the rate law…

C) Mechanisms with a Fast C) Mechanisms with a Fast Initial StepInitial Step

Given:Given: 2NO + Br2NO + Br22 2NOBr 2NOBr

Experimental Rate Law:Experimental Rate Law: Rate = k [NO]Rate = k [NO]22[Br[Br22]]

Proposed Mechanism:Proposed Mechanism: NO + NO + BrNO + NO + Br22 2NOBr 2NOBr

Why is this an unlikely Why is this an unlikely mechanism?mechanism?

Alternative mechanism:Alternative mechanism: 1) NO + Br1) NO + Br22 NOBr⇄ NOBr⇄ 22 (fast) (fast)

2) NOBr2) NOBr22 + NO + NO 2NOBr (slow) 2NOBr (slow)

Step 2 is now rate-determining:Step 2 is now rate-determining: Rate = kRate = k22 [NOBr [NOBr22][NO]][NO]

Why is this rate law Why is this rate law unacceptable?unacceptable?

Since Step 1 is an equilibrium, the Since Step 1 is an equilibrium, the rate of the forward rxn = rate of the rate of the forward rxn = rate of the reverse rxnreverse rxn NO + BrNO + Br22 NOBr NOBr22

Rate = kRate = k11 [NO][Br [NO][Br22]]

NOBrNOBr22 NO + Br NO + Br22

Rate = kRate = k-1-1 [NOBr [NOBr22]]

kk11 [NO][Br [NO][Br22] = k] = k-1-1 [NOBr [NOBr22]]

Solve for [NOBrSolve for [NOBr22] so we can ] so we can

substitute for it in our rate lawsubstitute for it in our rate law

The moral of the story: when a The moral of the story: when a fastfast step precedes a step precedes a slowslow step, solve for step, solve for the concentration of the intermediate the concentration of the intermediate by assuming that an equilibrium is by assuming that an equilibrium is established in the fast step!established in the fast step! HW: 14.60,

14.82

VIII.VIII. CatalystsCatalysts

A substance that A substance that increases the increases the speed of a rxn speed of a rxn without being without being consumed in the consumed in the rxn; lowers Erxn; lowers Eaa by by

allowing alternate allowing alternate rxn pathwayrxn pathway

A) Homogeneous CatalysisA) Homogeneous Catalysis

The catalyst is in the same The catalyst is in the same phase as the reactantsphase as the reactants Ex) KClOEx) KClO33(s) (s) KCl(s) + O KCl(s) + O22(g)(g)

B) Heterogeneous CatalysisB) Heterogeneous Catalysis

The catalyst is in a different phase The catalyst is in a different phase than the reactantsthan the reactants

Active SiteActive Site = place where rxn will = place where rxn will occuroccur

AdsorptionAdsorption = binding of molecules to = binding of molecules to a surfacea surface

Reactants must adsorb to an active Reactants must adsorb to an active site on the catalyst for the rxn to site on the catalyst for the rxn to proceedproceed

VideoVideo

C) EnzymesC) Enzymes Biological catalystsBiological catalysts A A substratesubstrate binds to the binds to the

enzymeenzyme in the in the lock and key lock and key modelmodel

The The enzyme-substrateenzyme-substrate complex creates products complex creates products then releases themthen releases them

InhibitorsInhibitors bind to a substrate bind to a substrate site of enzyme to prevent site of enzyme to prevent binding (nerve poisons and binding (nerve poisons and toxic metal ions)toxic metal ions) HW: 14.64

Stop! Stop!

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