Chapter 12 Chemical Kinetics by hcj



Chapter 13 Chemical Kinetics

I) Introductory Remarks

       1. To use chemistry, chemists must understand the characteristics of chemical
       reactions. These characteristics include the following.

              - stoichiometry of reaction
              - energetics (thermodynamics)
              - rate of reaction
              - spontaneity of reaction

       2. Spontaneity refers to the inherent tendency for a reaction to occur; however, it
       implies nothing about the speed of the reaction. Spontaneous does NOT mean fast
       as in everyday speech.

       3. To be useful ($$$), chemical reactions must occur at a reasonable rate.
       Chemists must be aware of the stoichiometry, thermodynamics, and the factors
       that govern the rate of a reaction.

       4. Chemical Kinetics - area of chemistry that studies the factors that control the
       rates of chemical reactions.

       5. Reaction Mechanism - the series of steps by which a reaction takes place.

II) Reaction Rates

       1. Consider the reaction H2 (g) + I2 (g)  2 HI (g) and the experimental
       data presented in Figure 13.2.

       2. Results in Fig. 13.2 show that concentration of H2 decreases with time while
       the concentrations of HI increases with time.

       3. Rate = change in quantity over the change in time.

       4. Reaction rate = change in concentration / change in time

              Example:               Rate = - [H2] / t             H2 is a reactant
                                     Rate = [HI] / t               HI is a product
               = final condition - initial condition (for a given quantity)
              [ ] denotes molar concentrations (moles solute / L solution)

       5. Instantaneous Rate = value of a rate at a particular time. The value of a rate at
       time (t=0), the beginning of a reaction, is called the initial rate.

       6. Stoichiometry of a reaction determines the relative rates of consumption of
       reactants & generation of products.

III) Introduction to Rate Laws

       1. Chemical reactions are reversible; there is a forward reaction and a reverse
       reaction. For the rate of reaction, we can speak of a forward & reverse reaction

       2. Want to study reaction rates under conditions where only one direction
       predominates. This is usually the forward direction ( i.e., reactants to products).

       3. If the rates for the forward and reverse reaction are equal, then we are speaking
       of a system @ chemical equilibrium. More on this in chapter 14.

       4. Rate law - expression that shows how the rate depends on the concentration of
       reactants. Rate laws must be determined experimentally; do not just use the
       coefficients of a balanced reaction to write out a rate law.

                                 Rate = k [A] n

               k = rate constant
               n = order of the reactant          (n can be any integer number or a fraction)

               Overall reaction order - sum of the individual reaction orders for a given
               rate law.

       5. How does one go about finding the rate law for a given chemical reaction?

               Graphical Methods

               Method of Initial Rates

                      - Initial rate of a reaction is the instantaneous rate determined just
                      after the reaction begins (just after t=0).

                      - Several experiments are carried out using different initial
                      concentrations, and the initial rate is determined for each run.

                      - Results are then compared to see how the initial rate depends on
                      the initial concentrations.

                      - Overall reaction order (molecularity) - sum of the individual
                      reaction orders for a given rate law.
                      - Review Example Problems

IV) Types of Rate Laws: Integrated Rate Laws

       1. First Order Rate Laws

                     - General Reaction:           aA  products

                     -      Rate Law:                      -  [A ] / t = k [ A ]

                     -      Integrated Rate Law:           ln [A] = -kt + ln [Ao]

                     -      Significance of the above two equations is that a plot of ln
                            [A] versus time always gives a straight line and is an
                            indicator of first order kinetics.

                     -      Integrated Rate Law:           ln { [A] / [Ao] } = -kt

                     -      Half-Life Equation:            t1/2 = 0.693 / k

                                   i)      Half-life (t1/2) is defined as the time required
                                           for a reactant to reach half its original
                                   ii)     Half-life is independent of concentration
                                           for a first order reaction.

                     -      Review Example Problems.

       2. Second Order Rate Laws

                     - General Reaction:           aA  products

                     -      Rate Law:                      -  [A ] / t = k [ A ] 2

                     -      Integrated Rate Law:           1 / [A] = kt + 1 / [Ao]

                     -      Significance of the above two equations is that a plot of
                     -      1/ [A] versus time always gives a straight line with a slope
                            equal to k.

                     -      Half-Life Equation:            t1/2 = 1 / k [Ao]

                                   iii)    Half-life (t1/2) is defined as the time required
                                           for a reactant to reach half its original

                                  iv)      Half-life is dependent on both k and [Ao]
                                           for a second order reaction.
                                  v)       For a second order reaction, each successive
                                           half-life is double the preceding one
                                           (provided the effects of the reverse reaction
                                           can be ignored, which is usually the case).

                    -      Review Example Problems.

      3. Zero Order Rate Laws

                    - General Reaction:           aA  products

                    -      Rate Law:                      k [A] o = k (1) = k

                    -      Integrated Rate Law:           [A] = -kt + [Ao]

                    -      Plot of [A] verus time gives a straight line with slope = -k.
                           The significance of the above two equations is the rate is
                           always constant for zero order kinetics.

                    -      Half-Life Equation:            t1/2 = [Ao] / 2 k

                                  vi)      Zero order reactions are typically found
                                           associated with reactions involving metal
                                           catalysts or enzymes.

      4. More Complicated Kinetic Systems

                    - Example:    BrO3 - + 5 Br - + 6 H +  3 Br2 + 3 H2O

                    - Want to study kinetics of complicated systems by observing the
                    behavior of one reactant at a time.

      5. Review Summary Section & Table 13.2

V) Reaction Mechanisms

      1. Most chemical reactions can be explained in terms of a reaction mechanism,
         a series of steps that show how the reactants become products. The balanced
         chemical equation for a reaction tells us the reactants, products, and the
         stoichiometry, but gives no information about the reaction mechanism.

      2. Consider the following example.

               NO2 + CO  NO + CO2                 Rate = k [ NO2]2

3. The mechanism for this process is thought to involve the following steps:

               NO2 + NO2  NO3 + NO
               NO3 + CO  NO2 + CO2

It is important to know the following basic terms for these come up all the time.

               -      Reaction intermediate = a species that is neither a reactant
                      or a product but is formed and consumed during the
                      reaction sequence.
               -      Elementary step = an individual step in a reaction
               -      Molecularity = number of species that must collide to
                      produce the reaction indicated by that step. A reaction
                      involving one molecule is unimolecular, two would be
                      bimolecular, etc.

4.   The sum of the elementary steps must give the overall balanced chemical
     equation for the reaction and the proposed mechanism must agree with
     the experimentally determined rate law.

               NO2 + NO2  NO3 + NO

            NO3 + CO  NO2 + CO2

NO2 + NO2 + NO3 + CO  NO3 + NO + NO2 + CO2

Note: The reaction is same as balanced reaction NO2 + CO  NO + CO2

5.   The rate determining step is the slowest step in a reaction mechanism; the
     overall rate of a reaction is governed by this step.

6.   Reaction mechanisms represent possible paths in going from reactants to
     products and are always under scrutiny.

VI) Chemical Kinetic Model

       1. What are some of the variables that affect rates of reactions?

                      -      concentrations of reactants
                      -      temperature (As T increases, rate increases

       2. Collision Model

                      -      Molecules must collide in order to react.
                      -      Molecules must possess sufficient kinetic energy to
                             overcome Ea (activation energy) and must also have the
                             correct orientation for the reaction to occur.

       3.   Arrhenius Equation

                      -      k = A e -Ea / RT         R = 8.314 J/ mole K

                      -      ln k = - Ea / R (1/T) + ln (A)

                      -      ln ( k2 / k1) = - Ea / R [ (1 / T1 - 1 / T2) ]

                      -      Review Examples
VII) Catalysis

       1. A catalyst is a substance that speeds up a chemical reaction without being
          consumed in that process. Biological catalysts are called enzymes and are
          responsible for many of the processes that occur in living systems.
       2. Catalysts work by lowering the energy of activation (Ea) for a system.
       3. Catalysts are classified into two major groups

                      a) Homogeneous catalysts are present in the same phase as the
                         reacting molecules.
                      b) Heterogeneous catalysts are present in a different phase as the
                         reacting molecules.

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