Syllabus for the kinetics part of the course

A brief six week introduction to chemical kinetics

Instructor - Professor James Schlegel

Text Chemical Kinetics by Kenneth A. Connors, VCH Publishers,
Inc.
**
I am told that the book store will have this book by March 22, 1999**
**
Now I am told that this book will not be available until late April - TOO
LATE**

I will copy the problems for you and my notes should be sufficient.
You can use most any Physical Chemistry text to get the material.
A good one is Physical Chemistry by Atkins (the publisher is Freeman).
There is another book I used two years ago by James Espenson but it is
very expensive for its size. McGraw-Hill is the publisher and the
title is Chemical Kinetics and Reaction Mechanisms.

**DATE
STUDY
PROBLEMS**

March 24
Introduction to kinetics

and review of simple rate equations
Chap.1: 1-7 Chap. 2: 1-8, 10

March 31 Complicated rate equations Chap. 3: 1, 2, 4 handouts

April 7 Complicated rate equations More handouts

**
MATERIAL COVERED**

A. __Basic definitions and concepts, including:__

order
flooding technique or isolation method

mechanism
rate law or rate expression

activation energy
pseudo, apparent or observed rate constants

pre-exponential term
mean reaction time or relaxation time

half-life
reaction intermediate

B. __Methods of establishing a rate law and
evaluation of rate constants__

Integrated rate equations

Infinite-time method: use a physical property when this property is directly
proportional to concentration

Guggenheim method

Time-lag method (Kezdy-Swinbourne)

Differential rate equations

Intial rate method - order with respect to concentration

Continous slope method - order with respect to time

Isolation method - pseudo (or observed) rate constants

Competition methods (Parallel reactions)

The steady-state approximation and the pre-equilibrium approximation

Consecutive reactions and concurrent reactions

Reversible first order reactions (compare treatment with that for relaxation kinetics)

April 14 Fast reactions and theory Chap. 4: 2, 3, 5

April 21 More theory

April 28 Review.

**
MATERIAL COVERED**

A. Perturbation methods and relaxation kinetics

B. Transition state theory

Thermodynamic activation parameters, DH^{#},
DS^{#},
DG^{#
}and
K^{#} .

May 5
Examination

**
CHEMICAL KINETICS**

Classical thermodynamics is the study of chemical reactions after they come to equilibrium - time is not a variable.

Chemical kinetics is the study of the progress of chemical reactions - time is a variable.

Interested in what happens when a reaction progresses from initial state to final state - MECHANISM

The simplest case AB + C ----> A + BC one step reaction - one transition state

If the reaction proceeds through an intermediate - two
transition states

Methods used to obtain a mechanism for a given reaction

1. Rates of reaction under various conditions

2. Establish reactant and product structures - identify transition state (reaction may be under thermodynamic control)

3. Isotopic substitution - R-COOR'
+ OH^{-} ---->
RCOO^{-} + R'OH
run in enriched H_{2}O and O^{18} is found in the acid
product

4. Identification of intermediates

a. Isolate

b. Detect by physical means, spectroscopy

c. Trapping - react with a trapping agent

5. Stereochemical course of reaction - e.g.
establish SN_{1} vs SN_{2} for nucleophilic attack at a
saturated carbon

Rates of Reaction --- Observations and definitions

Rate a concentration
R = -d(reactant)/dt = d(product)/dt
= k[concentration]^{n}

A. Order of reactions

1. Simple orders
e.g. unimolecular decomposition, nuclear decay, bimolecular collision

2. Non integral orders

a. CH_{3}CHO ---> CH_{4} + CO
R = k[CH_{3}CHO]^{3/2}

b. CO + Cl_{2} ----> COCl_{2}
R = d[COCl_{2}]/dt = k [Cl_{2}]^{3/2} [CO]

3. In most cases the
rate law or rate expression is complex and often refer to:

a. Order with respect to a given reactant or product

b. Order under certain limiting conditions

e.g.
H_{2} + Br_{2} ---> 2HBr

The rate law for the thermochemical reaction

R = d[HBr]/dt = {k[H_{2}][Br_{2}]^{1/2}}/{1
+ k'{[HBr]/[ Br_{2}]}}

Look up and compare this rate law with the one for this reaction occurring photochemically

4. Order is not obtained form stoichiometric equation -- obtained experimentally

Consider
the above reaction -----

limiting conditions: Br_{2}
>> HBr R = k'[H_{2}][Br_{2}]^{1/2}

HBr >> Br_{2}
R = k'{[H_{2}][Br_{2}]^{3/2}/[HBr]}

A mechanism ------

Br_{2} -----> 2Br
===> [Br_{2}]^{1/2}

Br + H_{2 } ------> HBr + H
===> [H_{2}]

H + Br_{2} ------>HBr + Br
===> [Br_{2}]

H + HBr ------> H_{2 } + Br
===> [HBr]^{-1}

2Br ---> Br_{2}

The H_{2} + I_{2} = 2HI reaction
was considered to be a simple bimolecular reaction and many theoretical
and experimental papers were written supporting this.

BUT the mechanism was updated
(work of Sullivan, C&E News Jan 16, 1967, pg 40)

I_{2 } == 2I

2I + H_{2} ---> 2HI

No such thing as **the** mechanism

Basic approaches used to analyze kinetic data.

Treat first order kinetic data

1. Method of
integration

Different ways to treat data

2. Differential methods

3. Isolation method

**Integration**

A --> P
-d[A]/dt = d[P]/dt = k[A]^{n}

where n = order

First order processes are most often encountered n = 1

Can use [A] = conc. of A at any time or use A_{o} - x

where x is the extent of the reaction

-dA/dt = - d(A_{o}
- x )/dt = dx/dt = k[A] = k(A_{o} - x )

-d[A]/dt = k[A] or -d(A_{o}
- x)/dt = k(A_{o} - x) get the same result

ln{[A]/[A_{o}]}
= - kt
ln{(A_{o}-x)/A_{o}} = -kt

A = A_{o}e^{-kt }
(A - x ) = A_{o}e^{-kt}

Different ways to treat first order kinetic data

1.Infinite time method

2. Guggenheim

3. Kezdy-Swinbourne

4. Half-life

Different ways topresent the data

1. Graph

2. Tabulate

3. Linear regression on computer or calculator

Can do a general regression analysis (non-linear)

Infinite time method

For first order, can plot
ln(Poo-P) to get a straight line with slope equal
to -k as long as the property, P, is directly

proportional to concentration

Spectroscopy |A_{oo}-A|

Dilatometry |V_{oo}-V|

Conductance |L_{oo}-L|
= |1/R_{oo} - 1/R|

Polarimetry |a_{oo}-a|

and in general. |P_{oo}- P| a
concentration of reactant in limiting concentration

Full integrated equation yields ln[(P_{oo}-
P)/(P_{oo}- P_{o})]
= -kt

k = -(1/t) ln[(P_{oo}- P)/(P_{oo}-
P_{o})] and to obtain k:

a. take average from a table

b. linear regression

c. graph

Guggenheim and time lag methods are used if you cannot
obtain P_{oo}.

Consider P_{t} and
P_{t+t} where
t is a constant time interval. Then,

(P_{oo}-
P_{t}) = (P_{oo}- P_{o})e^{-kt}
and (P_{oo}-
P_{t+t}) = (P_{oo}-
P_{o})e^{-k(t+t)}

Pt
= physical property measured at time t

Pt+t = physical property measured at time t
+ t

Two approaches: Plot ln(P_{t}- P_{t+t})
vs t ==> slope = -k
Guggenheim

Plot P_{t }vs P_{t+t}
==> slope = e^{kt }
Time lag

Guggenheim:

(P_{oo}- P_{t+t})
- (P_{oo}- P_{t}) = (P_{oo}-
P_{o})[e^{-kt}e^{-kt}-
e^{-kt}]

(P_{t}- P_{t+t})
= (P_{oo}- P_{o})[e^{-kt}
- 1] e^{-kt}

ln(P_{t}- P_{t+t})
= ln(P_{oo}- P_{o})[e^{-kt}
- 1] - kt in the
form y = b + mx

Time lag:

(P_{oo}- P_{t+t})
= (P_{oo}- P_{o})e^{-kt}e^{-kt}

(P_{oo}-
P_{t}) = (P_{oo}- P_{o})e^{-kt}
by division one obtains [(P_{oo}-
P_{t+t})]/[(P_{oo}-
P_{t})] = e^{-kt}

Rearranging: P_{t} = P_{oo}(e^{kt
}-1)
+ P_{t+t}e^{-kt}_{ }
This plot will also yield P_{oo}.

**Differential methods used to determine order
R = k[A] ^{n} log(R) =
log(k) + nlog[A]**

Initial rate method: Obtain initial rate at
several different concentrations and from a

plot of log(R) vs log[A] obtain the order - refer
to this as the order with respect to concentration

Continuous slope method: From a plot of [A]
vs time obtain the slope at various times (which identifies

a concentration, [A], on this curve and a plot of
log(R) (which equals log(d[A]/dt)) vs log[A] yields the

oder, n - refer tothis as the order with respect
to concentration. If the order from the initial rate method is

not the same as the order from the continuous slope
method, then the reaction is autocatalytic or autoinhibitory.

If n_{time}>n_{conc} then it is autocatalytic

**Reversible reactions (also the treatment of data from perturbation
or relaxation techniques)**

Consider:
can show that the first order rate constant, k_{obs} = k_{f }
+ k_{b}

Also for
can show that k_{obs} = k_{f} ([A_{o}] +
[B_{o}]) + k_{b}

For A == B
A = A_{o} - x B = B_{o }- x

A + B = A_{o} + B_{o} = A_{oo}
+ B_{oo}
k = k_{1}/k_{-1} = B_{oo}/A_{oo}
oo represents equilibrium concentrations

-d[A]/dt =