Different Types ofDifferent Types ofComposite Reactions

Simultaneous:A Y and A Z

Opposing:A B ZA Y and A Z A B Z

Consecutive: Consecutive with opposition:A X Y

ppA X Y

In order for the system to be at complete equilibrium, thetime derivative of all species concentrations must be zero!

Kinetics for a Simple Consecutive Reaction

1 2 and Xk kA X Z 1

0k tA A e with

2 1 (2)d X

k X k Adt

1

becomes

kt

dt

d Xk X k A e

1

2 1 0

2 1 0 a "standard form" o.d.e. with solutionkt

k X k A edt

d Xk X k A e

dt

1 2

2 1 0

20

2 1

kt k t

dtkX e e A

k k

and

2 11 2

0 02 1

1k t ktk e k eZ A A X Ak k

Quasi Steady State Approximation

1 2 and Xk kA X Z Consider the differential rate equations for [A], [X] and [Z].

(1)d A

k Let [A] = [A]

1 (1)

0 (2)

k Adt

d Xk X k A

Let [A]t=0 = [A]0and [X]t=0 = [Z]t=0 = 0

ktA A 11 1

022

2 1 0

or (

(2)

2.5)ktk kX

k X k Adt

A A ek k

1

0ktA A e

Make QSS approx22

2 (3)d Z

k Xdt

k k

11 0

0

tkt

k

Z k A e dt

For (2) and (2.5) to be compatible , we must have (k1/k2) << 1 1

01 kte A

Compare Exact and Steady State S l ti f k 20 kSolutions for k2 = 20 k1

k1t

Sample Problem (10.3)Given reaction with stoichiometry:

A + B Y + Zh f ll h hThe reaction follows the mechanism:

A Xk1

k

X + B Y + Z

k–1

k2

Obtain an expression for the rate using the steady state treatmenta. What is the rate determining step if the second reaction rate is

slow relative to the initial equilibrium rates?qb. What is the rate determining step if the second reaction rate is

rapid relative to the initial equilibrium rates?

Rate Determining Steps

Is the slow step ALWAYS rate determining?

ConcepTest  1p

Reaction: 2 O3 3 O2Reaction:       2 O3 3 O2

Mechanism: O3 O + O2 (fast)k1k–1

O + O3 2 O2        (slow)What is the rate equation for O3 loss?

–1k2

A.  Rate = k [O3]2

at s t e ate equat o o O3 oss

B. Rate = k [O3] [O2]C.  Rate = k [O3]

2 [O2]–1

3

B. Rate = k [O3 ]–1 [O2]

SolutionReaction:       2 O3 3 O2

Mechanism: O3 O + O2 (fast)

O + O 2 O (slow)

k1k–1

k2O + O3 2 O2        (slow)What is the rate equation for O3 loss?

2

1 3 1 2

1 3

1 equilibrium :Rxn k O k Ok O

O

O

1 2

2

with a slow second step, the equilibrium is maintainedk O

O

2

3 31 32 3

1 22 3

2

Rated O O

kk O

O k O kdt

Ok O O

Exam 2Exam Subject matter:

Gibbs EnergyGibbs EnergyStandard ΔG for reactions Pressure dependence of ΔG for ideal gases, liquids, solidsChemical potential

EquilibriumEquilibrium constants, ideal gas equilibriaShifts of equilibrium at constant TLe Chatelier PrincipleLe Chatelier PrincipleRelationship between standard Gibbs energy change and

the equilibrium constantKinetics

R t t l h i th d f i iti l tRates, rate laws, mechanisms, method of initial ratesArrhenius rate law – physical interpretationReaction paths, potential energy surfacesMolecular basis of reactionsMolecular bas s of react onsElementary reactions, composite reactionsFast and slow rate approximations; steady state

rate determining steps; catalyzed reactions

Exam 2Exam

~ 6 problems (weights given) – budget your timep g g g yClosed book Don’t memorize formulas/constantsYou will be given things you needYou will be given things you need

Study lecture material, examples, and homework!Exam will not be heavily numeric, but will emphasize

tsconceptsProbably more numerical than last time (bring calculators)If a problem seems lengthy, do another problem & come p g y pback later Understanding homework will be useful

Potential Energy SurfacesE gy fThe Born Oppenheimer approximation:Generally a very accurate Generally a very accurate approximation, and one of the most important concepts in all of physical science.Without it, there would be no chemistry as we know it.B-O approximation allows the construction of potential energy construction of potential energy surfaces for molecules and reactions.Still too many nuclear degrees of freedom!S l t l i t t Select only important ones

NO2 + CO NO + CO2

Expected rate = k [NO2] [CO2]Observed rate = k [NO2]2 Composite RxDeduce a possible and reasonable mechanism

NO2 + NO2 NO3 + NO                  slow

NO + CO NO + CO f t

2NO2 + CO     NO + CO2 + NO2Overall,

NO3 + CO     NO2 + CO2 fast

2 2 2

NO3 is an intermediate product that is not seen eitheras a reactant or as a product.

Let’s look at the reaction profile (ala Zeb)

as a reactant or as a product.

NO2 + CO NO + CO2

In this two-step reaction, there2 2 3NO NO NO NO

gy

pare two barriers, one for eachelementary step. The well between the two t iti t t h ld ti

3 2 2NO CO NO CO

tial

Ene

rg transition states holds a reactiveintermediate.A reactive intermediate is acompound formed transiently but

Pote

nt compound formed transiently, butabsent in the overall reaction.

Reaction Coordinate

We need to do better than just using a 1-D energy sliceWe need to do better than just using a 1 D energy slice,namely a multidimensional potential energy surfacepotential energy surface!