THERMODYNAMICS and  KINETICS 534                 SPRING 1999
                                 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 H2O and O18 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 SN1 vs SN2 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. CH3CHO ---> CH4  +  CO        R = k[CH3CHO]3/2
            b. CO  +  Cl2  ----> COCl2            R = d[COCl2]/dt  = k [Cl2]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.        H2  +  Br2  --->   2HBr
The rate law for the thermochemical reaction
                      R  =  d[HBr]/dt =    {k[H2][Br2]1/2}/{1  +  k'{[HBr]/[ Br2]}}

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:        Br2 >> HBr          R = k'[H2][Br2]1/2

                                                     HBr >> Br2           R = k'{[H2][Br2]3/2/[HBr]}

                A mechanism ------

                                                          Br2    ----->  2Br                ===> [Br2]1/2
                                                          Br  +  H ------>  HBr  +  H     ===> [H2]
                                                          H  +   Br2  ------>HBr  +  Br    ===> [Br2]
                                                          H  +  HBr ------>  H +  Br     ===> [HBr]-1
                                                          2Br ---> Br2

The H2  +  I2  =  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 == 2I
                                2I  +  H2  --->  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 Ao - x
                                                    where x is the extent of the reaction
        -dA/dt = - d(Ao - x )/dt = dx/dt = k[A] = k(Ao - x )
    -d[A]/dt = k[A]   or  -d(Ao - x)/dt = k(Ao - x)    get the same result

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

                A = Aoe-kt                             (A - x ) = Aoe-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 |Aoo-A|
            Dilatometry  |Voo-V|
            Conductance |Loo-L| = |1/Roo - 1/R|
            Polarimetry |aoo-a|
                                  and in general. |Poo- P| a concentration of reactant in limiting concentration

Full integrated equation yields   ln[(Poo- P)/(Poo- Po)] = -kt

                k = -(1/t) ln[(Poo- P)/(Poo- Po)] 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 Poo.

        Consider Pt and Pt+t where t is a constant time interval.  Then,

        (Poo-  Pt)  = (Poo-  Po)e-kt      and      (Poo-  Pt+t) = (Poo-  Po)e-k(t+t)

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

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

                              Plot Pt vs Pt+t  ==>  slope = ekt                Time lag

Guggenheim:
                                (Poo-  Pt+t) - (Poo-  Pt) =  (Poo-  Po)[e-kte-kt- e-kt]
                                (Pt-  Pt+t)  =  (Poo-  Po)[e-kt - 1] e-kt
                                ln(Pt-  Pt+t)  =  ln(Poo-  Po)[e-kt - 1] - kt          in the form y = b + mx

Time lag:
    (Poo-  Pt+t)  =  (Poo-  Po)e-kte-kt
        (Poo-  Pt) = (Poo-  Po)e-kt   by division one obtains  [(Poo-  Pt+t)]/[(Poo- Pt)] = e-kt

Rearranging:  Pt = Poo(ekt -1) + Pt+te-kt                        This plot will also yield Poo.

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  ntime>nconc 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,  kobs = k + kb
 

Also for    can show that  kobs = kf ([Ao] + [Bo]) + kb

        For A == B          A = Ao - x    B = Bo - x
                                A + B = Ao + Bo =  Aoo +  Boo            k = k1/k-1 =  Boo/Aoo     oo represents equilibrium concentrations
    -d[A]/dt =