Chem 1310: Introduction to physical chemistry

Part 2: Chemical Kinetics

Peter H.M. Budzelaar

Kinetics vs Thermodynamics

Thermodynamics show why a reaction wants to proceed.

Kinetics can explain how it proceeds.

The two topics are complementary:you will need both to understand chemistry.

Kinetics -the rates of chemical reactions

• How fast does a reaction go?• Does the rate change over time?• Can it be influenced?• What does all this say

about how the reaction proceeds?

Convoluted reaction pathsMost reactions follow a complicated course.

You might see (on paper):

CH4 + Cl2 CH3Cl + HCl

But what actually happens is:

Cl2 + h 2 Cl· start ("initiation")

Cl· + CH4 HCl + CH3· production

CH3· + Cl2 CH3Cl + Cl· ("propagation")

2 Cl· Cl2 stop

CH3· + Cl · CH3Cl ("termination")

2 CH3· C2H6

Convoluted reaction paths

Kinetics, the study of the rates of reactions, can help us establish mechanisms and predict what will happen in "new" circumstances.

What is a rate?

Rate of a reaction:the number of moles L-1 s-1 of reactants passing into products.

Why the units:twice the volume, same concentration: twice as many molecules go.same volume, concentrations, wait twice as long: twice as many molecules go (approx...).

What is a rate?

We usually mean the rate at any given moment (the instantaneous rate, t very small) rather than over a whole second or other time spin (the average rate, a larger t).

Don't forget stoichiometry here! If not all components in a reaction have coefficient 1, we define the "rate of the reaction" as the rate of (dis)appearance of the components divided by their coefficients.

t

product

t

reactantrate

][][

What is a rate? (2)

The rate belongs to the reaction as written.

Compare with H calculations, where we also give the result for the equation as written.

ttttrate

]OH[

6

1]N[

2

1]O[

3

1]NH[

4

1 2223

Example:

4 NH3 + 3 O2 2 N2 + 6 H2O

(using smallest possible integer coefficients)

Rates, rate lawsand elementary steps

A "rate law" expresses the dependence of the rate on the concentrations of reactants.

For an elementary step

A X + ...

we would expect an expression like:

rate = k [A]

Similarly, for

A + B X + ...

one would expect

rate = k [A][B]

Rates, rate lawsand elementary steps

The k values ("rate constants") depend on the temperature, and are different for different reactions.

Most "real" reactions consist of many steps. If we would know them, we could construct an expression for the overall rate. This can depend on concentrations in a complicated fashion, as we will see.

Catalysts, compounds that accelerate reactions, work by enabling alternative paths (new elementary steps), not by affecting rate constants of existing elementary steps.

Measuring rate laws

The dependence of rate on concentrations may be simple, as in

rate = k [A]

or it can be complicated, as in

In practice, you measure the dependence of the rate on concentrations, then fit to various reasonable "laws".

]B][cat[]L[1

]B][A[2

321

k

kkkrate

Measuring rate lawsfrom initial rates

• Start reaction at a certain concentration.• Measure conversion in the first 0.1 or so seconds.

initial rate at the original concentration

• Do the same at 0.5, 0.25, 0.125 etc times the original concentration(s). initial rates at different concentrations

• If there is more than one reactant, vary the concentration of each one independently.

Measuring rate lawsfrom initial rates

• Test for first-order kinetics:if rate [A], then etc

or plot rate vs [A] straight line

We write rate (in mol L-1 s-1) = k [A], k in s-1.

If there are more components, the reaction may be first-order in each: rate = k [A][B], k in L mol-1 s-1.

25.0

0.1

)5.0(

)0.1(

rate

rate

Measuring rate lawsfrom initial rates

• If first-order doesn't work, test for second-order kinetics:if rate [A]2, then etc

or plot rate vs [A]2 (or rate vs [A]) straight line

We write rate (in mol L-1 s-1) = k [A]2, k in L mol-1 s-1.

• If the rate does not depend on a particular reactant, we say it is zero-order in that reactant.

4)5.0(

)0.1(

)5.0(

)0.1(2

2

rate

rate

Measuring rate lawsfrom reaction progress

Measuring rate lawsfrom reaction progress

Follow reaction in time, try to fit the curve with various models.Do this for several initial concentrations, to verify the model!

For a first-order reaction:

Limit for small t:

This is a differential equation.

The solution is(verify by differentiation)

To check for this model: plot ln [A] vs t:

]A[]A[

kt

rate

]A[]A[

ktd

drate

tkt e 0]A[]A[

tkt 0]A[ln]A[ln

Measuring rate lawsfrom reaction progress

For a second-order reaction:

Solution:

To check for this model: plot 1/[A] vs t:

For a zero-order reaction:

Solution:

(obviously not valid for large t!)

2]A[]A[

ktd

drate

0]A/[1

1]A[

tkt

tkt

0]A[

1

]A[

1

ktd

drate

]A[

tkt 0]A[]A[

First-order reactions and half-life

Half-life: time to go from a certain initial reactant concentration to half this initial value.

This does not mean that after two half-lifes all reactant has been consumed! Rather, every half-life reduces the concentration by a factor of 2.

kkt

tkAAA

AA

t

t

693.02ln

]ln[2ln]ln[]ln[

][½][

½

½00½

0½

First-order reactions and half-life

8/][][

8ln]ln[2ln3]ln[3]ln[]ln[

4/][][

4ln]ln[2ln2]ln[2]ln[]ln[

0½3

00½0½3

0½2

00½0½2

AA

AAtkAA

AA

AAtkAA

t

t

t

t

This is called exponential decay.

Back to the microscopic model

Why are some reactions faster than others?At any given moment, only asmall fraction of the moleculeshave enough energy to hopover the barrier. The fractionbecomes larger if the barrieris reduced (easier, faster reaction)or if the temperature is raised(more of the molecules haveenough energy).

reactant

product

transition state

reaction coordinate

0 1en

ergy

activation energy (e.g. H‡)

reaction energy (e.g. H)

averagethermalenergy

Intermezzo: explosive reactions

Once a few molecules hop over, the reaction produces so much energy that many more can follow. Heat is produced faster than it can dissipate even via diffusion of the gaseous products.

A detonator is used to provide the initial bit of energy.

Ammonium nitrate can decompose explosively.– To what?

– Why would adding kerosene improve the explosive power?

The Arrhenius expression

Nearly all reactions have a similar temperature dependence:

RT

Ea

eAk

Frequency factor:what fraction of collisionscould in principlelead to a reaction.

Energy term:what fraction of moleculeswill have enough energyto pass the barrier.

The Arrhenius plot

Plot ln k vs 1/T:

ln k = ln A -Ea/RT

intercept= ln A

slope= -Ea/R

The rate-limiting step

The slowest step in a sequence of elementary steps

(the "bottleneck").

The overall rate is determined by this step.

Typically corresponds to the highest barrier (activation energy) on the path, since frequency factors are usually not too different.

The rate-limiting step

Overall rate = rate of RLS

reaction coordinate

0 1

ener

gy

2 3

Ea1

Ea2

Ea3

rate-limiting step(in solution)

Rates and mechanismsSingle-step mechanism:

rate = rate of single step

e.g. rate = k[A][B], no problem

Multi-step mechanism:

• if first step is RLS,treat as single-step (remaining steps don't matter)

• if later step is RLS, things get complicated

rate = k2[B], but we don't know [B]. What now?

A B C ...k1

k-1

k2

(RLS)

Steady-state approximation

When the reaction starts, we have [B] = 0. It builds up from A, then starts to deplete as also [A] decreases. For a long time it will be nearly constant.

]A[]B[

]A[]B[

0]B)[(]A[]B[]B[]A[]B[

21

212

21

1

211211

kk

kkkrate

kk

k

kkkkkkt

this is what we obtain as kin a first-order rate law

Question: what wouldan Arrhenius plotof "k" produce now?

CatalysisNot faster reactions but new reactions made possible by reaction with the catalyst.

The catalyst does react!It might be regeneratedat the end of the reaction,but it is not chemically inert.

Catalysis is not "homeopathic"!

ener

gy

uncatalyzed reaction

catalyzed reaction

The best catalyst?

What is the most common, most versatile catalystin chemistry?

The best catalyst?

What is the most common, most versatile catalystin chemistry?

H+

Enzymes - the catalysts of natureEnzymes are proteins containing one or more regions or groups specifically adapted to promote a chemical reaction. This may be a single H+/OH- catalyzed reaction of something more complicated, including transition-metal catalysis.

The protein provides a semi-rigid environment where the reaction can take place. It is usually (shape-)selective, able to distinguish between subtly different substrates and to produce products with high selectivity.

Enzymes - the catalysts of natureEnzymes require water to be stable.

They will irreversibly denature at high temperatures.This is an example of catalyst deactivation.

Enzymes can get poisoned by molecules that bind to them but do not undergo the desired reaction.

Enzyme kineticsTypical behaviour:

Steady-state (assume [ES] is constant, [E]+[ES]=E0):

For small [S]: (like a regular two-step reaction)

For large [S]: (all enzyme present as E-S complex, rate limited by E0)

"Saturation kinetics"

E + S ES EP E + Pk1

k-1

k2

211

021

1

21

022 ]S[

]S[E

]S[1

E]ES[

kkk

kk

kkk

kkrate

21

021 ]S[E

kk

kkrate

002 E][,E ESkrate

Man-made catalysts

• Homogeneous: in same phase as reactants(usually solution)

• Heterogeneous: different phases(usually solid catalyst, gaseous reactants)

Homogeneous catalysts

• Typically small, well-defined transition-metal complexes. Designed to do a specific type of reaction on a specific type of functional group, for a class of substrates.

• Not as specific/selective as enzymes.• Work under mild conditions (0-120°C).• Used for synthesis of fine

chemicals/pharmaceuticals.

An example ofa homogeneous catalyst

MeOH

MeI

HI

H2O

MeCOOH

MeCOI

CO

Rh(CO)2I2

Rh(CO)2I3Me Rh(CO)2I3(COMe)

CH3OH + CO CH3COOH

Heterogeneous catalysts

• Typically metals, metal oxides or silicate-like materials with a range of "active sites".

• Tend to produces mixtures of products, with distributions determined by product stabilities.

• Used in petrochemical industry and oil refining.

An example ofa heterogeneous catalyst

• Via dissociation to atoms.

• Works equally well for all NxOy compounds.

• Products are N2 and O2 because N-O bond is weak.

• Requires high temperature to work.

• Can be poisoned: lead in gasoline precipitates on surfaces, blocks active sites.

M M MM MMMMMM

NO

O N N O

N2 O2