chemistry 130 chemical kinetics dr. john f. c. turner 409 buehler hall [email protected]

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Chemistry 130 Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall [email protected]

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Page 1: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemistry 130

Chemical Kinetics

Dr. John F. C. Turner

409 Buehler Hall

[email protected]

Page 2: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical change

There are two parts to the science of chemistry

The description of matter on an atomic basis as it is observed to exist

The description and control of the change of the form of matter

We have started to study one of the fundamental parts of the first, which is thermodynamics

Chemical kinetics is the major part of the second

Page 3: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical change

A chemical reaction converts one ensemble of atoms or molecules into another, different, ensemble of atoms.

Reactions take place at very different rates. Some are very slow:

Growth rate ~ 1mm per million years

Chemical composition: Fe, Mn hydroxides and oxides

Page 4: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical change

A chemical reaction converts one ensemble of atoms or molecules into another, different, ensemble of atoms.

Reactions take place at very different rates. Some are very fast:

2H2l O2l 2H2Ol

Initial impact and explosion

A few milliseconds later

Page 5: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical change

Even a simple reaction such as the reaction between hydrogen and oxygen

can be very complicated:

2H2g O2g 2H2Og

explosion

steady reaction

explosionexplosion

steady reaction

Page 6: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical change

There is an obvious and intuitive difference in rate between the reaction or explosion of oxygen and hydrogen and the accretion reactions of manganese nodules.

The hydrogen-oxygen reaction is very very fast (and can take you to the moon) the second is very very slow (and can't).

Chemical kinetics is the quantification of

(i) how fast a reaction proceeds

(ii) how it happens on an atomic or molecular level.

The first is an empirical measurement with respect to concentration of products and reactants

The second is the mechanism of the reaction, which includes a description of the energetics of the reacting system.

Page 7: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Basic properties of chemical change

In every chemical reaction, the quantity of the reactants decreases and the quantity of the products increases.

Heat is either produced or absorbed by the system; equally heat passes into the universe from the system or leaves the universe and moves into the system.

For the reactions of hydrogen with iodine and chlorine:

and so the formation of hydrogen iodide is endothermic, whereas the formation of hydrogen chloride is exothermic

H2g I2g 2HIg H fHI = 26.5 kJmol−1

H2g Cl2g 2HClg H fHCl = −96.3 kJmol−1

Page 8: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Basic properties of chemical change

For a spontaneous reaction, the chemical composition of the reaction changes smoothly and continuously to a new, constant chemical composition.

In this respect, the initial chemical composition is unstable with respect to the final composition.

This final composition is the thermodynamically most stable under the specific conditions of the reaction. We call this the thermodynamic minimum.

The speed at which a reacting chemical system achieves this new, most stable composition is not determined by the size of the stabilization that the system undergoes when the reaction takes place. Very exothermic reactions are not necessarily fast reactions.

The heat change is not automatically related to the rate of reaction.

Page 9: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Basic properties of chemical change

The heat change is not automatically related to the rate of reaction.

Both of these reactions are the same but the rates are completely different

2Fes 32

O2g Fe2O3s H f = −824.2kJ mol−1

Page 10: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate of reaction

In both, the hydrogen and the halogen are consumed – they are reactants – and the hydrohalic acid is generated – it is a product.

Writing the concentration of X as [X], we can define the velocity or rate of the reaction by measuring the change in the concentrations of the reactants with time i.e.

Because hydrogen and iodine are both destroyed in the reaction, the rate is negative.

H2g I2g 2HIg

H2g Cl2g 2HClg

Rate = −[H2] t

= −[ I2] t

=12

[HI ] t

note that [H2] = [H2] t − [H2]0

Page 11: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate of reaction

In general, for a reaction

the rate of reaction is given by

where a,b,c and d are the stoichiometric coefficients for the balanced reaction.

aA bB cC dD

rate = −1a

[A] t

= −1b

[B] t

= 1c

[C] t

= 1d

[D] t

Page 12: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

On what does the rate of reaction depend?

The rate of reaction depends on several variables. The most basic are the temperature of the system, which is a measure of the energy content as

and the number of particles, n.

Pressure and volume are also important 'masked' variables of the particle number.

For an ideal or perfect gas,

and, in general,

q = C p T

PV = nRT

c = nV

Page 13: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Empirical dependencies

For a reaction

Empirically, the rate of reaction depends on the concentration of the reactants according to

where k is the rate constant and n and m are experimentally determined indices of the concentration.

n and m are not necessarily related to the stoichiometric coefficients (a,b,c and d) and can be integers, fractions or zero

aA bB cC dD

rate = k[A ]n[B]m

Page 14: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Empirical dependencies

The relationship

is the rate law and contains the concentration or 'particle number' dependency.

There is no relationship between the stoichiometric constants of a reaction and the concentration indices.

rate = k[A ]n[B]m

Page 15: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Empirical dependencies

For a general reaction

the rate law can be written in terms of the change in the concentration of the reactants by combining

and

to give

rate = k[A ]n[B]m

aA bB cC dD

rate = −1a

[A] t

= −1b

[B] t

= 1c

[C] t

= 1d

[D] t

−1a

[A] t

= −1b

[B] t

= 1c

[C] t

= 1d

[D] t

= k[A]n[B]m

Page 16: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Classification of reaction rates

The complete rate law for the general reaction

is

The order of the reaction with respect to A is n

The order of the reaction with respect to B is m

The overall order of the reaction is n+m

aA bB cC dD

−1a

[A] t

= −1b

[B] t

= 1c

[C] t

= 1d

[D] t

= k[A]n[B]m

Page 17: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Classification of reaction rates

For the reaction

the rate law is given by

The order of the reaction with respect to H2 is 1

The order of the reaction with respect to I2 is 1

The overall order of the reaction is 1+1 = 2

rate = − [H2] t

= − [ICl ]

t= k[H2][ ICl ]

H2g IClg I2g 2HClg

Page 18: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Classification of reaction rates

For the reaction

the rate law is given by

The order of the reaction with respect to NO is 2

The order of the reaction with respect to Cl2 is 1

The overall order of the reaction is 2+1 = 3

rate = − [Cl2]

t= −

12

[NO] t

= k[Cl2][NO]2

Cl2g 2NOg 2NOClg

Page 19: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Classification of reaction rates

For the reaction

the rate law is given by

The order of the reaction with respect to is 1 and the overall reaction order is 1

rate = − [ Np93

239 ]

t= k[ Np93

239 ]

Np s93239 Pus94

239

Np93239

Page 20: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Classification of reaction rates

For the reaction

we have already seen that the rate law is given by

It would be convenient to think that the reaction

would follow the same experimental rate law........

H2g I2g 2HIg

rate = − [H2] t

= − [I2] t

=12

[HI ] t

= k[H2][ I2]

H2g Br2g 2HIg

Page 21: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Classification of reaction rates

However,

follows the experimental rate law

The details of the rate law are therefore absolutely empirical, although they can be explained by the mechanism of the reaction – the intimate changes in the arrangement of atoms during the course of the reaction

rate =[HBr ]

t=

k[H2][Br2]12

1k'[HBr ][Br2]

H2g Br2g 2HBrg

Page 22: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Page 23: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemistry 130

Chemical Kinetics

Dr. John F. C. Turner

409 Buehler Hall

[email protected]

Page 24: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

1. Chemical kinetics describes the speed at which one chemical composition transforms into another chemical composition.

2. The velocity of the chemical reaction is not related to the magnitude of the difference in enthalpy between products and reactants.

3. The experimental rate law for the general reaction

is written as

where k is a constant and {a,b,c,d} are not related to {n,m}

aA bB cC dD

−1a

[A] t

= −1b

[B] t

= 1c

[C] t

= 1d

[D] t

= k[A]n[B]m

Page 25: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

The rate of reaction depends on the path between the reactants and the products

Thermodynamics details the difference between the state function of the product and the state function of the reactant.

(State functions include

Enthalpy

Entropy

Free Energy)

Page 26: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

Because a state function is independent of the path by which the system adopts its particular state, there is no information about the path from the thermodynamics of the system.

Stoichiometry is not related to the orders of reactants in the experimental rate law.

Page 27: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Initial rates

The initial rate of a reaction is the rate at t = 0. It is determined from the tangent or slope of the plot of concentration vs. time:

The tangent is found in the normal manner:

slope = y2− y1 x2−x1

Note that the initial rate is related to the average rate by

lim t0 { [H2O2]

t }

Page 28: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Initial rates and the order of reaction

The method of initial rates is an important method for determining the order of the reaction.

The general reaction obeys the experimental rate law

so if we vary the concentration of A with all other conditions fixed, the ratio of the initial rates will give us the order of the reaction with respect to A

Similarly, using the same approach with B will give us the order of the reaction with respect to B, and therefore the overall order of the reaction.

aA bB cC dD

−1a

[A] t

= k[A]n[B]m

Page 29: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Initial rates and the order of reaction

Cl2g 2NOg 2NOCl g

Expt

123

[NO]0 / M

0.01250.01250.0250

[Cl2]0 / M

0.02250.05100.0225

0 / x 10−5Ms−1

2.274.559.08

From the ratio of different concentrations of the same reactant, we can calculate the order of the reaction with respect to that reactant from the ratio of the rates.

ForCl2g from experiments 1 and 2

[Cl2]0,2

[Cl2]0,1

= 0.05100.0225

= 2

0,2

0,1

=4.552.27

= 2

= k[Cl2]n[NO ]m

When we double the concentration of chlorine, we double the rate, so as

then n = 1 as the rate changes linearly with the chlorine concentration

Page 30: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Initial rates and the order of reaction

Cl2g 2NOg 2NOClg

Expt

123

[NO]0 / M

0.01250.01250.0250

[Cl2]0 / M

0.02250.05100.0225

0 / x 10−5Ms−1

2.274.559.08

From the ratio of different concentrations of the same reactant, we can calculate the order of the reaction with respect to that reactant from the ratio of the rates.

ForNOg from experiments 1 and 3

[NO]0,3

[NO]0,1

= 0.02500.0125

= 2

0,3

0,1

= 9.082.27

= 4

= k[Cl2]n[NO ]m

When we double the concentration of nitric oxide, we quadruple the rate, so as

then m = 2 as the rate changes with the square of the nitric oxide concentration

Page 31: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Initial rates and the order of reaction

In general, this method can be applied to any reaction, though it may be complicated in the case of a reaction such as

H2g Br2g 2HBrg

= [HBr ]

t=

k[H2][Br2]12

1k'[HBr][Br2]

Page 32: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Time dependence of the rate law

So far we have defined the rate for the general reaction

as

but we also know that the initial rate is the tangent to the concentration – time curve, implying that

This last relationship is the key to the time dependence. When , we can replace the D with a 'd', the symbol for the microscopic or infinitesimal change

aA bB cC dD

−1a

[A] t

= k[A]n[B]m

lim t0 { [A]

t } t0

Page 33: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Time dependence of the rate law

In this case,

which is the differential change of concentration with time.

The rules of differential changes are termed the calculus and we have already used the calculus implicitly when we took the tangent to the concentration curve.

The instantaneous rate law is therefore

for the general reaction

lim t0 {[A]

t } = d[A]dt

−1a

d[A]dt

= k[A]n[B]m

aA bB cC dD

Page 34: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Time dependence of the rate law

Using the calculus, we can directly calculate the time dependence of the rate law, by integrating the differential rate law.

The results are:

Order Experimental rate law Integrated rate law

0 −1a

[A] t

= k [A] t = −kt[A]0

1 −1a

[A] t

= k[A ] ln[A ] t = −kt ln[A]0

2 −1a

[A] t

= k[A ]21

[A] t

= kt1

[A]0

Page 35: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Time dependence of the rate law

The integrated rate laws for reactions of different orders allow us to calculate the concentration of any reactant at any time during the reaction.

They also allow us to determine the rate constant for the reaction from experimental results.

Order Experimental rate law Integrated rate law

0 −1a

[A ] t

= k [A ] t = −kt[A ]0

1 −1a

[A ] t

= k[A ] ln[A] t = −kt ln [A ]0

2 −1a

[A ] t

= k[A ]2 1[A] t

= kt 1[A ]0

Page 36: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Half-lives: first order reactions

The half-life of a reaction is the time at which half the reactant has been consumed.

At this time,

and when this concentration is substituted for in the integrated rate law, an expression for the half-life results.

For a first order reaction, the integrated rate equation is

and so the half-life of a first order reaction is given by

[A ] t =12

[A ] 0

[A ] t

ln{ [A] t

[A]0} = −kt

ln{1/2[A]0

[A]0} = ln{12} = −ln2 = −kt1/2

t1/2 = ln2k

Page 37: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Half-lives: first order reactions

The half-life of a first order reaction is

and is therefore independent of the quantity of reactant present.

Also, if we know the half-life, we automatically know the rate constant for the reaction.

The half-life is a common parameter in nuclear chemistry as radioactive decay is a first order process.

t1/2 = ln2k

0 100%1 50%2 25%3 12.5%4 6.25%5 3.125%6 1.5625%7 0.78125%⋯ ⋯

N100%

2Nt1/2 U92238 ≃ 4.47×109 years

t1/2 Pu94239 ≃ 24,100 years

t1/2 Ds110271 ≃ ≃210 ms

Page 38: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Half-lives: second order reactions

The integrated rate equation for a second order reaction is given by

when then

and so the half-life of a second order reaction is dependent on the initial concentration

1[A ] t

= kt 1[A ]0

[A ] t =12

[A ] 0

2[A]0

= kt 1[A] 0

1[A]0

= kt1/2

t1/2 = 1k[A]0

Page 39: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate constant

So far, we have seen that an empirical rate law can be established for a chemical reaction that defines the rates in terms of the concentration – this is the experimental or differential rate law and is of the form

We have also seen that this expression can be manipulated using the calculus to yield the integrated rate law, which details the time dependence of the reaction:

−1a

d[A]dt

= k[A]n[B]m

Order Experimental rate law Integrated rate law

0 −1a

[A] t

= k [A] t = −kt[A]0

1 −1a

[A] t

= k[A ] ln[A ] t = −kt ln[A]0

2 −1a

[A] t

= k[A ]2 1[A] t

= kt 1[A]0

Page 40: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate constant

We have not discussed the temperature dependence of a reaction.

The rate constant, k, is a constant only for a given temperature and in general is a function of temperature.

The temperature dependence of the rate law requires a theory of chemical kinetics on an intimate, microscopic level – this theory is termed transition state theory.

−1a

d[A]dt

= k T [A]n[B]m

Page 41: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

First Quiz

The first quiz will be on Wednesday in discussion and will cover

Chapter 12

Chapter 13 to date

Page 42: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Page 43: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemistry 130

Chemical Kinetics

Dr. John F. C. Turner

409 Buehler Hall

[email protected]

Page 44: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

1. Chemical kinetics describes the speed at which one chemical composition transforms into another chemical composition.

2. The velocity of the chemical reaction is not related to the magnitude of the difference in enthalpy between products and reactants.

3. The experimental rate law for the general reaction

is written as

where k is a constant and {a,b,c,d} are not related to {n,m}

aA bB cC dD

= −1a

[A ] t

= −1b

[B] t

= 1c

[C] t

= 1d

[D] t

= k[A]n[B]m

Page 45: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

4. The integrated rate laws for reactions of different orders allow us to calculate the concentration of any reactant at any time during the reaction.

From the experimental rate law, we have

● the concentration dependence of the reaction from the order of the reaction

● the time dependence from the integrated rate equation

Order Experimental rate law Integrated rate law0 = k [A ] t = −kt[A ]0

1 = k[A] ln[A] t = −kt ln [A ]0

2 = k[A]2 1[A] t

= kt 1[A ]0

Page 46: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

5. The order of the reaction is determined by the molecularity of the slowest elementary step in the reaction mechanism. This step is termed the Rate-Determining Step (rds).

6. An elementary step of a reaction is microscopically reversible.

7. The energy barrier for the reaction is termed the activation energy, EA and the rate constant is related to the activation

energy by the Arrhenius equation

8. The temperature dependence of the rate constant is given by

k = Ae−EA

RT

ln k2

k1 =

EA

R [ 1T1

− 1T2 ]

Page 47: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate constant

To understand the temperature dependence and the physical origin of the order of the reaction, we require a theory of chemical reactions on microscopic scale –and a reaction mechanism.

The first requirement for a reaction is that a collision between two reactants must take place.

Many reactions involve the transfer of an atom or a group of atoms between reactant molecules, which necessarily means that the molecules must be close.

A second requirement is that the orientation of the molecules must be correct

Page 48: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate constant

Molecules in the gas phase are moving very rapidly and are colliding continuously. The distribution of velocities is given by the Maxwell-Boltzmann distribution:

f vdv = 4 v2 m2 kT

3/2

exp−mv2

2kT dv

Page 49: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate constant

The momentum distribution is given by

f pdp = 4 p2 12 mkT

3/2

exp −p2

2mkT dp

The individual energies are broadly distributed and only some of the collisions are result in reaction.

There is an intrinsic barrier to reaction, over and above the frequency of collision.

Page 50: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The rate constant

Only a proportion of the molecules have sufficient energy to react. There must be an energetic barrier to reaction.

Page 51: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Transition state theory

Consider the reaction between carbon monoxide and nitrogen dioxide:

COg NO2g CO2g NOgWe know what the result of this reaction is:

Page 52: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Transition state theory

Consider the reaction between carbon monoxide and nitrogen dioxide:We know what the result of this reaction is and we can measure the enthalpy of reaction between the two compositions – the reactants and the products

Page 53: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Transition state theory

We also know that not all collisions result in reaction – there is an energy barrier; this barrier is called the activation energy, EA

Page 54: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Transition state theory

The point at the highest energy on the path between reactants and products is termed the transition state.

Page 55: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Transition state theory

In the transition state, the bonds between atoms in the reactants are beginning to break and rearrange to form the bonds that are present in the products. The transition state is occupied by the activated complex

An activated complex is not a stable species and lies part way between the reactants and the products.

It exists for approximately the time taken for a molecule to vibrate - and then falls apart to yield the products of the reaction.

~ 10−15 s

Page 56: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Transition state theory

We can also think of the reverse reaction as passing through the same transition state – this is termed microscopic reversibility and there is an associated activation energy for the reverse reaction.

In this way, we can think of any chemical reaction as consisting of a forward reaction and a reverse reaction, differentiated by the activation energy for each process.

We write the reaction as

where ‡ represents the activated complex at the transition state.

COg NO2g [O=C⋯O⋯N=O ]‡ CO2g NOg

Page 57: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Transition state theory

For the reaction between carbon monoxide and nitric oxide, the full reaction path is

Page 58: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Energetics of transition state theory

Transition state theory provides a reasonable qualitative description of the reaction path.

Quantification of the reaction path was first successfully achieved by Svante Arrhenius (Nobel Prize, 1903).

The rate constant was already known to vary with temperature and the general rate law should account for this observation:

= k [A ]n [B]m

Page 59: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Energetics of transition state theory

Arrhenius formulated the temperature dependence of the rate constant as

k = Ae−EA

RT

A is termed the pre-exponential factor and is the product of the collision frequency and an alignment factor

EA is the activation energy

R is the universal gas constant

T is the thermodynamic or absolute temperature in K

R = 8.314 J mol−1 K−1

Page 60: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Energetics of transition state theory

As

then

and so

which is the temperature dependence of the rate constant.

k = Ae−EA

RT

ln k = ln A −EA

RT

ln k2

k1 =

EA

R [ 1T1

− 1T2 ]

Page 61: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Order, mechanism and rates

For an elementary reaction, i.e. a reaction that is a single intermolecular or interatomic reaction on the overall path from reactants to products, the number of molecules or atoms present in the transition state determine the order of the reaction.

When there is more than one elementary reaction, it is the slowest elementary reaction that determines the experimental rate law.

For simple reactions, there are two major types of elementary reaction:

Unimolecular – one molecule dissociates or changes before the reaction moves to products

Bimolecular – two molecules react together to form the activated complex.

(Termolecular reactions involving a simultaneous collision between three molecules are exceedingly unlikely)

Page 62: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Order, mechanism and rates

Elementary reactions are also microscopically reversible and the forward and back reactions are present at the same time, governed by the activation energies for both processes.

It is the slowest elementary reaction along the path that determines the rate.

This is termed the rate-determining step in the mechanism.

So, the molecularity of the activated complex at the transition state of the rate-determining step is shown in the order of the reaction.

Page 63: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Reaction Mechanisms

A reaction mechanism is the series of elementary steps that make up the observed, macroscopic reaction.

An acceptable mechanism must

● reproduce the rate law

● account for all of the products that are formed and the stoichiometry of the net reaction

● account for any geometrical or stereochemical features of the reaction

A mechanism is a model of the reaction and can only be supported or refuted by experimental evidence. It cannot be proved.

The two dominant elementary reactions are unimolecular and bimolecular

unimolecular 1 molecule in the rds bimolecular 2 molecules the rds

Page 64: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Mechanism types: unimolecular

The reaction profile for a bimolecular reaction is the one that we are already familiar with.

There is a single transition state and activated complex.

Page 65: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Mechanism types

The rate law for the hydrolysis of methyl bromide (MeBr) by hydroxide ion is

MeBr OH- MeOH Br-

= k[MeBr ][OH-]

Page 66: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Mechanism types: bimolecular

A bimolecular reaction has a slow first step followed by a fast second step.

The species in the well between the first activation barrier and the second activation barrier is termed an intermediate.

There are two transition states and two activated complexes and each step is an elementary reaction.

EA1EA2

Page 67: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Mechanism types: bimolecular

An example of a bimolecular reaction is the hydrolysis of tertiary butyl bromide with hydroxide:

The intermediate in this case is

EA1EA2

Me3CBr OH- Me3COH Br-

= k[Me3CBr ]

Me3C+

Me3C+

Me3CBr OH -

Me3COH Br-

Page 68: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130 Osias Beert, Flemish painter (b. ca. 1580, Antwerpen, d. 1624, Antwerpen)

Page 69: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemistry 130

Chemical Kinetics

Dr. John F. C. Turner

409 Buehler Hall

[email protected]

Page 70: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

1. Chemical kinetics describes the speed at which one chemical composition transforms into another chemical composition.

2. The velocity of the chemical reaction is not related to the magnitude of the difference in enthalpy between products and reactants.

3. The experimental rate law for the general reaction

is written as

where k is a constant and {a,b,c,d} are not related to {n,m}

aA bB cC dD

= −1a

[A ] t

= −1b

[B] t

= 1c

[C] t

= 1d

[D] t

= k[A]n[B]m

Page 71: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

4. The integrated rate laws for reactions of different orders allow us to calculate the concentration of any reactant at any time during the reaction.

From the experimental rate law, we have

● the concentration dependence of the reaction from the order of the reaction

● the time dependence from the integrated rate equation

Order Experimental rate law Integrated rate law0 = k [A ] t = −kt[A ]0

1 = k[A] ln[A] t = −kt ln [A ]0

2 = k[A]2 1[A] t

= kt 1[A ]0

Page 72: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Chemical kinetics so far

5. The order of the reaction is determined by the molecularity of the slowest elementary step in the reaction mechanism. This step is termed the Rate-Determining Step (rds).

6. An elementary step of a reaction is microscopically reversible.

7. The energy barrier for the reaction is termed the activation energy, EA and the rate constant is related to the activation

energy by the Arrhenius equation

8. The temperature dependence of the rate constant is given by

k = Ae−EA

RT

ln k2

k1 =

EA

R [ 1T1

− 1T2 ]

Page 73: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Activation energy and mechanism

The rate of a reaction depends on the slowest elementary step on the path – the rate determining step. For a path with a single elementary step, we know what the path looks like:

MeBr OH- MeOH Br-

= k[MeBr ][OH-]

The rate constant is determined by the activation energy EA and

the order of the reaction by the molecularity of the step.

k = Ae−EA

RT

= k[MeBr ][OH-]

Page 74: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

The steady state approximation is a simple case of a kinetic path that contains more than one elementary step and shows the general approach for more complicated reaction profiles.

The reaction contains a fast step which is reversible, followed by a fast, irreversible reaction that gives the products

A B C Dk1

k−1

Page 75: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

The reaction between nitric oxide and oxygen can be described by the steady state approximation.

The reaction proceeds via

If this were a single elementary reaction, the activated complex would be the result of a termolecular reaction, which is vanishingly likely.

2NOg O2g 2NO2g

= k[O2][NO]2

Page 76: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

The first step of the reaction is association of two NO molecules

NOg NOg O=N−N=Og

k1

k−1

2NOg O2g 2NO2g

= k[O2][NO]2

The activation energies of the forward reaction and reverse reaction are similar and so the rate constants are similar. We write this reaction as an equilibrium

Page 77: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

The second step of the reaction is the reaction of the (NO)2 molecule with

oxygenO=N−N=O O2g 2NO2g

2NOg O2g 2NO2g

= k[O2][NO]2

This reaction is fast and the activation energy is much larger for the reverse reaction than the forward reaction and is therefore essentially irreversible

Page 78: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

2NOg O2g 2NO2g

= k[O2][NO]2

We can evaluate these reactions to reproduce the observed stoichiometric reaction

2NOg O=N−N=O

O=N−N=O O2g 2NO2g

2NOg O2g 2NO2g

Page 79: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

2NOg O2g 2NO2g

= k[O2][NO]2

We can also to reproduce the observed rate law

Page 80: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

Associative equilibrium:

We assume that the rates are equal

k1

k−1

forward = k1[NO]2

backward = k−1[ONNO]

forward = backward

k1[NO]2 = k−1[ONNO][ONNO] =

k1[NO]2

k−1

Page 81: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

The slow, irreversible step:

We know the concentration of (NO)2

and so

= k2[ONNO] [O2]

[ONNO] =k1[NO]2

k−1

= k2[ONNO][O2] = k2k1[NO]2

k−1k2[O2] = k2k1

k−1[NO]2[O2]

Page 82: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

The steady state approximation

The final rate law is

as

= k2[ONNO][O2] = k2k1[NO]2

k−1k2[O2] = k2k1

k−1[NO]2[O2]

= k2k1

k−1[NO]2[O2] = k'[NO]2[O2]

k' = k2k1

k−1

Page 83: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

A catalyst is a material that accelerates the rate of reaction but is not consumed by it and is therefore unchanged at the end of the reaction.

Catalysts work by providing a different path for the reaction, which has a lower activation energy.~30 % of the GDP of the US depends on catalysis

Gasoline Polypropylene and polyethylene

Sulfuric acid PharmaceuticalsFuel Cells

Fertilizers

http://www.uyseg.org/catalysis/cat_contents.htm

Page 84: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

There are two simple divisions of catalysis

Homogeneous Heterogeneous

A homogeneous catalyst is one that is in the same phase as the reactants – a solute in a liquid, a liquid in a liquid, a gas in a gas etc

A heterogeneous catalyst is one that is not in the same phase – a solid-liquid system or a solid-gas system

http://www.uyseg.org/catalysis/cat_contents.htm

Page 85: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

The rate is accelerated by lowering of the activation energy.

The catalyst also arranges or organizes the reactants so that they achieve the reacting configuration more efficiently. The catalyst will often change the entropy of the elementary steps along the reacting paths.

http://www.uyseg.org/catalysis/cat_contents.htm

Page 86: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

.

http://www.uyseg.org/catalysis/cat_contents.htm

Page 87: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

.

http://www.uyseg.org/catalysis/cat_contents.htm

Page 88: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

.

http://www.uyseg.org/catalysis/cat_contents.htm

Page 89: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

.

http://www.uyseg.org/catalysis/cat_contents.htm

Page 90: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130

Catalysis

.

http://www.uyseg.org/catalysis/cat_contents.htm

Page 91: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130 Osias Beert, Flemish painter (b. ca. 1580, Antwerpen, d. 1624, Antwerpen)

Page 92: Chemistry 130 Chemical Kinetics Dr. John F. C. Turner 409 Buehler Hall jturner@ion.chem.utk.edu

Chemistry 130 Osias Beert, Flemish painter (b. ca. 1580, Antwerpen, d. 1624, Antwerpen)