Why do we study Kinetics

1
Introduction

• Why do we study Kinetics?
• To obtain important information about how fast
  reactants are converted to products.
• How fast a reaction reaches equilibrium
• To obtain a detailed picture of what molecules do
  to each other when they react.
• Reaction mechanism - the sequence of physical
  and chemical processes by which the conversion
  from reactants to products occurs.
• To learn ways to control or optimize reaction
  rates and/or yields by manipulating reaction
  conditions (economic implications are important
  in reactor design).
• Concentration
• Temperature
• Pressure
• Presence of a catalyst

A
B
2
Kinetics vs. Equilibrium Thermodynamics

• The final equilibrium state does not depend on
  the path used in going from the initial state to
  the final state.
• The rate at which the system reaches equilibrium
  does depend on the path taken.
• In general, the time required to reach
  equilibrium in chemical reactions can vary over
  many orders of magnitude.
• Often, the product of a reaction is not the one
  which is the most stable energetically (i.e., the
  thermodynamic product), but is the one produced
  the fastest (i.e., the kinetic product).
• Equilibrium
• Reactions spontaneously go to equilibrium
• A?B is spontaneous when ?Agt ?B
• A?B is spontaneous when ?Alt ?B
• When ?A ?B , neither A?B or A?B is spontaneous
  and the system has reached a state of chemical
  equilibrium.
• Limits the extent of a spontaneous reaction.
• Given an infinite amount of time, a closed system
  will reach its equilibrium state
• Significant quantities of reactants and products
• Negligible quantities of reactants complete

3
Le Chateliers Principle

• If an external stress is applied to a system at
  chemical equilibrium, the equilibrium point will
  change to relieve that stress.
• Energy is required to move a reaction away from
  equilibrium
• Heating an exothermic reaction shifts the
  equilibrium to the left.
• The minimum free energy state for the system at a
  particular temperature.
• Independent of reaction path.
• (a) rxn goes to completion
• (b) A B at equilibrium
• (c) rxn does not go
• Dynamic equilibrium is maintained because the
  forward rxn is proceeding at exactly the same
  rate as the reverse rxn.
• Law of Mass Action
• kA k-1B
• The free energy of the system, G, changes
• with the extent of reaction, ?, until the
• equilibrium state is achieved.

4
The Equilibrium Constant

• For the general reaction
• The equilibrium constant, Keq, is defined as
• From the Law of Mass Action
• For a reaction that goes to equilibrium, Keq is
  related to the Gibbs Free Energy as
• Where,

5
Dependence of Keq on Temperature

• From Le Chateliers Principle, heat can shift the
  equilibrium.
• The temperature dependence of the equilibrium
  constant is governed by the heat of reaction,
  ?Ho.
• The vant Hoff equation (two forms below) is
  obtained from the Gibbs-Helmholtz equation
• Integration yields

An increase in T causes a decrease in Keq for an
exothermic reaction.
6
Properties of the Equilibrium Constant

• For the reaction
• Or
• And thus, K1 (K2)2
• For a series of reactions

7
The Reaction Rate

• The rate of a reaction dictates how fast products
  are formed or how fast reactants are consumed.
• The reaction rate may be defined in the
  differential form
• Rates are most commonly written in terms of
  "moles per liter per time" (e.g., Msec-1).
• For the general reaction
• The rate may be defined in any one of the
  following ways
• When the reaction is balanced in terms of moles,
  the derivatives are normalized by the
  stoichiometric coefficients.
• Note Always define the specific rate that you
  are using!

8
Factors Affecting Reaction Rates

• Fundamental Effects
• Temperature - usually, ?T ?rate (always, if
  elementary process)
• Concentration (Pressure) - ?C usually ?rate
  however, it may ?rate.
• Catalysts - not consumed in the overall reaction
  - ?rate
• Process Effects
• Heat Transfer - temperature gradients, thermal
  conductivity
• Mass Transfer - mixing efficiency, viscosity
• In general, many reactions may be possible, but
  the observed reactions are the ones which proceed
  the fastest Consider the dehydration of ethanol
  for the desired production of diethyl ether
• CH3CH2OH ? CH2CH2 H2O (conc.
  H2SO4, 170oC)
• or
• 2CH3CH2OH ? CH3CH2OCH2CH3 H2O (dil. H2SO4,
  140oC)
• The different products are not due to differences
  in equilibria.
• Rather, ethylene is formed faster than diethyl
  ether at the high temperature.
• At the low temperature, diethyl ether is formed
  faster.

9
The Differential Rate Law

• The net rate for an equilibrium reaction which
  proceeds from left to right is
• net reaction rate forward rate - reverse
  rate
• At equilibrium, the net reaction rate is zero,
  and the forward rate equals the reverse rate.
• When a reaction mixture is far from its
  equilibrium composition, either the forward or
  reverse rate is dominant, depending on the
  reactant or product concentrations.
• For the forward reaction
• A ? B
• the first order differential rate law is
• where k is the first order rate constant with
  units (time) -1. In general, rate constants have
  units (time)-1(concentration)1-n, where n is the
  overall order of the reaction.
• Since the rate kA, a plot of rate vs. A
  yields a straight line with a slope equal to the
  rate constant, k.

10
The Differential Rate Law(continued)

• A second order differential rate law may be given
  by
• such that a plot of rate vs. A2 yields a
  straight line with a slope equal to k.
• In general,
• rate kA?B?C? ...
• Where, ? ? ? ... "overall order of the
  reaction"
• (The reaction is order ? with respect to A,
  etc.)

11
Order of the Reaction

• The order of the reaction with respect to each
  reagent must be found experimentally and cannot
  be deduced or predicted from the net equation for
  the reaction.
• For example,
• H2 Br2 ? 2HBr
• has the following rate law
• This reaction is first order with respect to
  hydrogen, one-half order with respect to bromine,
  and three-halves order overall.
• This kinetic behavior is in contrast to that of
• H2 I2 ? 2HI
• which has the following rate law

12
The Integrated Rate Law

• The differential rate laws show how the rate of
  reactions depend on concentration.
• Now, the integrated rate laws will show how the
  concentrations depend on time.
• For a first order reaction, we know that
• This ordinary differential equation can be
  solved,
• and rearranged to yield the integrated rate law
• From the integrated rate law for this first order
  reaction, it is clear that the change in A with
  time is an exponential decay function.

Thus, a plot of lnA vs. time will yield a
straight line with a slope equal to -k and an
intercept of lnAo.
13
The Integrated Rate Law(continued)

• For a single reactant, second order reaction
• the ordinary differential equation may be solved,
• to yield the integrated rate law for the second
  order reaction
• Thus, a plot of 1/A vs. time will yield a
  straight line with a slope of k and an intercept
  of 1/Ao.

14
The Half-Life (t1/2) of Simple Kinetic Processes

• Any kinetic process has a characteristic time
  called the half-life, t1/2.
• The half-life is the time it takes for the
  process to be half-completed.
• For chemical reactions, the half-life is the time
  it takes to reduce the concentration of a
  particular reactant to one-half of its original
  concentration.
• Thus, at t t1/2
• For a first order reaction
• For a second order reaction

15
Reactions and Mechanisms

• All complex chemical transformations can be
  broken down into a series of elementary reactions
  which are either unimolecular, bimolecular, or
  rarely, trimolecular.
• The detailed description of these events is
  termed the mechanism of the reaction.
• Elementary reactions Simple reactions that yield
  rate equations which correspond to the reaction
  stoichiometry.
• Elemenatry reactions describe molecular events
  order and molecularity are the same, such that
• Unimolecular - follows 1st order kinetics.
• Bimolecular - follows 2nd order kinetics.
• A mechanism (or kinetic scheme) is a collection
  of the elementary reactions for a net process.
• Note that, depending on the manner in which the
  stoichiometry of the overall reaction is
  described, algebraic manipulations of the
  elementary reactions may be required for the
  individual steps to add up to the overall
  reaction.
• Consider the net reaction
• The mechanism for this reaction could follow the
  elementary trimolecular reaction, or more likely,
  the sequence of elementary reactions given below.

16
Elementary Steps

• Since the rate law for an elementary step
  corresponds to the stoichiometry,

17
The Rate Limiting Step

• The overall products E and F cannot be formed
  faster than the rate of the slowest step in the
  three step sequence above.
• Thus, the slowest step in the sequence is the
  rate limiting step.
• While we may define the overall rate in any of
  four ways,
• If step 1 is the rate limiting step, then the
  observed rate law will be
• In this case, the complex overall mechanism
  follows simple bimolecular kinetics.

18
The Mass Balance

• A complete Mass Balance analysis considers the
  rates of consumption and formation of all species
  in the total reaction mechanism such that

19
The Steady-State Approximation

• We may now impose the Steady-State (Bodenstein)
  Approximation by assuming that, after a very
  short period of time, the concentration of
  intermediates (i.e., C and D) reaches a low,
  steady-state, "equilibrium" value.
• Since the concentrations of these intermediates,
  which are being formed and consumed, are low,
  then the change in the concentrations of these
  intermediates is assumed to be zero.
• Thus
• After substituting for C and D into the mass
  balances, we recover the rate

20
The Reaction Mechanism

• Consider the overall reaction
• 2NO2 F2 ? 2NO2F
• which follows the experimentally observed rate
  law
• Obviously, this overall reaction is not an
  elementary process because the rate determining
  step is only first-order with respect to NO2.
• Thus, the most logical mechanism follows a series
  of steps
• such that kexp k1

21
The Reaction Mechanism(continued)

• For the reaction
• 2Br- 2H H2O2 ? Br2 2H2O
• which follows the rate law
• the rate determining step is a trimolecular
  reaction among a hydrogen peroxide molecule, a
  bromide ion, and a proton.
• This may be shown as
• and the faster second step must be
• HOBr Br- H ? Br2 H2O

22
The Reaction Mechanism(continued)

• As suggested earlier, the mechanism of a reaction
  may change if the conditions under which it is
  run are altered. For example, consider the
  reaction
• NO2 CO ? CO2 NO
• At high temperatures (gt 500 K) the rate is found
  to be
• however, at low temperatures, the rate law is
  found to be
• Of the two possible reactions,
• a) NO2 CO ? CO2 NO (favored at high
  T)
• b) NO2 NO2 ? NO3 NO (favored at low
  T)
• the latter is favored at low temperatures.

23
The Reaction Mechanism(continued)

• Recall the reaction shown earlier
• H2 Br2 ? 2HBr
• which has the following experimental rate law
• Considerable experimentation has shown the
  mechanism to be
• where M may be any molecule of any gas.

24
The Reaction Mechanism(continued)

• The previous reaction scheme is a chain mechanism
  because
• steps 2) and 3) convert H2 and Br to HBr without
  a net consumption of the active free radicals.
• Since step 2) is the rate determining step, the
  rate law for the overall reaction is given by
• Since it would be more convenient to have the
  rate law expressed in terms of the bromine
  molecule concentration, the equilibrium condition
  may be used, such that
• Note it must be assumed that the equilibrium step
  is fast relative to the slow step.
• Thus, by substituting this equilibrium
  relationship into the rate law from step 2), we
  find
• which has the same form as the experimental rate
  law. Furthermore,
• This example shows the importance of
  understanding the origin of the experimental rate
  law in determining the reaction mechanism.
• Note that the factor of 2 arises from the manner
  in which we defined the experimental rate law.

25
The Reaction Mechanism(continued)

• The rate law sometimes cannot positively be used
  to determine the mechanism.
• For example, consider the reaction
• 2NO O2 ? 2NO2
• which follows the rate law
• Both mechanisms below are consistent with the
  rate law.
• or

26
The Reaction Mechanism(continued)

• As a further example of the link between the
  reaction mechanism and the rate law, consider the
  following reaction
• 2NO H2 ? N2O H2O
• One proposed mechanism is
• With the rapid equilibrium,
• and the rate of the slow step
• Combining, we obtain the experimental rate law

27
The Reaction Mechanism(continued)

• Another possible mechanism for the above reaction
  involving a fast equilibrium is
• which also leads to
• If the equilibrium step is not very fast relative
  to the rate determining step (RDS), then another
  possible mechanistic treatment may be as follows
• A mass balance on N2O2 yields,

28
Example Problem

• The following overall gas phase reaction
• H2(g) I2(g) ? 2HI
• Has been found to proceed by the following
  mechanism
• Show that this mechanism is consistent with the
  experimental rate law
• What is the origin of the experimental rate
  constant?
• What does the experimental rate law suggest about
  the relative rates of the above elementary steps?
• Under what conditions would the rate shift to
  follow the rate law?

I2(g)
2I(g)
k2
H2(g) 2I(g)
2HI(g)
29
Searching for a Mechanism

• Uncovering a reaction mechanism requires
  extensive chemical investigation.
• Define the stoichiometry.
• Monitor reactant or product concentrations with
  time for deriving empirical rate expressions.
• Propose the mechanism of the reaction.
• Test the mechanism
• Since there are numerous interrelationships
  between these three areas of investigation, this
  is usually not a trivial process.
• the proposed stoichiometry may change based on
  the kinetic data, which in turn may have been
  formulated based on the mechanistic studies.
• Rules and Clues and Suggestions for Developing a
  Mechanism
• The mechanism must add up to the overall
  reaction.
• The mechanism must result in the proper kinetics.
• The mechanism must match all other experimental
  information.
• The stoichiometry can distinguish between a
  single or multiple reactions.
• A complicated stoichiometry or one which changes
  with the conditions or extent of the reaction is
  clear evidence of multiple reactions.
• The stoichiometry can suggest whether the
  reaction is elementary or not.
• No elementary reactions with molecularity greater
  than 3 have been observed to date.
• For example, the following reaction is not
  elementary.

30
Developing a Mechanism (continued)

• The principle of microscopic reversibility must
  be preserved.
• The forward and reverse reactions must proceed
  via the same pathway and through the same
  activated complex.
• Thus, the reversible reaction
• 2NH3 ? N2 3H2
• cannot be elementary since the reverse reaction
  (tetramolecular) is highly improbable.
• NOTE All steps may be considered as reversible
  the "irreversible" reactions are those which have
  extremely large equilibrium constants (reactant
  concentration is negligibly low at equilibrium).
• Microscopic reversibility also indicates that
  structural changes such as bond rupture or
  formation, transfer of atoms or molecular
  fragments, or molecular syntheses are likely to
  occur one step at a time.
• Trimolecular (3rd order) elementary steps are
  usually slow.
• Inverse orders often arise from rapid equilibria
  prior to the RDS.
• If a stoichiometric coefficient for a reactant
  exceeds the species order in the rate law, then
  there are often one or more intermediates after
  the RDS.
• When a rate law contains noninteger orders, there
  are usually intermediates present in the reaction
  sequence.

31
Developing a Mechanism (continued)

• A change in Ea with temperature indicates a
  shift in the controlling mechanism of the
  reaction.
• A rise in Ea with temperature indicates that the
  controlling mechanism has shifted to an alternate
  or parallel path.
• A drop in Ea indicates a shift of the RDS to
  another reaction in the succession of elementary
  steps.
• These concepts may be visualized graphically as
• Parallel Reactions A high Ea pathway governs at
  high T. The reaction proceeds along path of
  least resistance.
• Series Reactions The slow step in the mechanism
  changes. The reaction is always limited by the
  slowest step.
• Finally, the most likely mechanism is usually
  the simplest.

Mech. 1
A ? R
High Ea
Mech. 2
Low Ea
ln k
ln k
High Ea
Low Ea
1/T
1/T
32
Testing Kinetic Models

• Propose a feasible mechanism for the reaction
• which follows the rate law
• Note that the reaction is evidently not
  elementary, or it would follow
• Kinetic Model I
• With this mechanism,

2A B
A2B
33
Testing Kinetic Models(continued)

• If we impose the steady-state approximation for
  A2
• such that
• the rate expression in terms of measurable
  quantities becomes
• It is common practice to restrict the more
  general model, such as above, by arbitrarily
  selecting the magnitudes of the various rate
  constants.
• In this way, one of the restricted (simpler)
  forms may match the observed kinetics. Thus, for
  k-1 very small
• Or for k-2 very small

34
Testing Kinetic Models(continued)

• Since neither of the above rate expressions
  matches the experimentally observed rate law, the
  hypothesized Model I must be incorrect.
• However, the similarity between the above
  expression (for k-2 very small) and the
  experimental rate law does hint that the correct
  mechanism will involve a similar form with the
  intermediate reacting with A instead of B in the
  rate determining step.
• Thus, the mechanism for the Kinetic Model II is
• Now, the rate expression is
• If we impose the steady-state approximation for
  AB

35
Testing Kinetic Models(continued)

• the rate expression in terms of measurable
  quantities becomes (again)
• Thus, restriction of this model with the
  condition that k-2 is negligible yields
• This is the same form as the experimental rate
  law, and thus, the kinetic Model II is consistent
  with the experimental observations.
• Note that the condition requiring k-2 to be
  negligibly small indicates that the second step
  may be considered as an irreversible reaction.

36
Temperature Dependence of the Reaction Rate

• The rate expression may be thought of as
  consisting of a temperature dependent term (i.e.,
  the rate constant, k) and a composition dependent
  term or terms.
• In practically all cases, the temperature
  dependence of the reaction rate constant has been
  found to be well represented by Arrhenius' Law
• where A is the pre-exponential term known as the
  frequency factor, Ea is the activation energy for
  the reaction, R is the gas constant, and T is the
  absolute temperature.
• The Arrhenius Law is often encountered in the
  logarithmic form
• which when plotted, yields an approximately
  straight line

37
Temperature Dependence of the Reaction Rate
(continued)

• The following equation is useful for calculating
  rate constants at various temperatures given
  knowledge of the activation energy, Ea, and the
  magnitude of the rate constant at one
  temperature.
• A plot of lnk vs. 1/T gives a straight line with
  a large slope for a high Ea and a low slope for a
  small Ea.
• Ea is almost always positive.
• Reactions with a high Ea are very temperature
  sensitive reactions with a low Ea are not so
  sensitive.
• Reactions are much more temperature-sensitive at
  low temperatures than at high temperatures.
• It is important to note that the Arrhenius Law is
  an empirical relationship that fits experimental
  data very well over wide temperature ranges, and
  is suggested to be a very good approximation to
  the "true" temperature dependency by the
  following theoretical approaches.
• Collision Theory
• Transition State Theory

38
Collision Theory

• In order for two molecules to react, they must
  "collide."
• From this collision theory, the minimum condition
  for the following reaction to occur,
• A B ? R
• is that the centers of mass of molecules A and B
  must come to within a certain critical distance
  of one another.
• The exact value of this critical distance, ?,
  depends on the nature of the reacting molecules,
  but is expected to be within ca. 2 or 3 Å (i.e.,
  about the length of a chemical bond).
• For bimolecular collisions of unlike molecules A
  and B, kinetic theory gives
• where
• nA and nB (NCA or B)/103, number of molecules
  of A or B per cm3
• k Boltzmann's constant 1.3 x 10-16 erg/oK
• T absolute temperature
• M mass of molecule A or B in gms (MW/NA)
• While the above expression yields the collision
  rate for bimolecular reactions, experimental
  evidence has shown that only a small fraction of
  collisions result in the conversion of reactants
  to product.
• Thus, the true reaction rate is much lower than
  the collision rate.
• This suggests that only the more energetic
  collisions (i.e., those having an energy in
  excess of a minimum energy, E) will lead to
  reaction.

39
Collision Theory (continued)

• Experimental evidence has shown that reaction
  rates are generally very sensitive to
  temperature.
• However, this temperature dependency is more
  complex than that indicated in the above
  equation, which shows that
• Thus, to combine the requirement of energetic
  collisions and a complex temperature dependency
  with the collision theory, we must consider the
  energy distribution function of molecules from
  the Maxwell-Boltzmann Distribution Law of gases.
• This energy distribution takes the form of
• and is visualized graphically as

40
Collision Theory (continued)

• If the molecular kinetic energy required for
  reaction is defined as the activation energy, Ea,
  the above figure shows that as the temperature
  increases, the fraction of molecules having an
  energy greater than the critical Ea increases
  dramatically.
• Thus, the rate expression may be modified as
• Thus, collision theory predicts that the
  temperature dependency of the rate of reaction
  follows
• Note that for a 10 degree increase in
  temperature, the T1/2 term increases the rate by
  a factor of
• while the exponential term increases the rate by
  a factor of
• Therefore, since the overwhelming factor is the
  exponential term, the rate effectively follows

41
Collision Theory (continued)

• In addition to the minimum energy requirement,
  molecules with three dimensional structure must
  collide with the proper orientation for reaction.
  When both energy and orientation factors are
  considered, the theoretical expression for the
  rate of a bimolecular reaction becomes
• where the quantity P is the steric factor related
  to the orientation requirement (i.e., a
  probability of proper orientation during the
  collision).
• In general, P is on the order of 10-1 for simple
  atoms and molecules, but may decrease to 10-5 for
  complex molecules.
• Therefore, the temperature dependency of the rate
  constant becomes
• which is of course the Arrhenius equation.
• The frequency factor, A, expresses the rate at
  which molecules approach close enough in the
  proper orientation to react.
• From these theoretical treatments, it would seem
  possible to predict reaction rates. In practice,
  however, this is rarely done satisfactorily
  because the exact structure of the transition
  state is poorly understood, which makes it very
  difficult to predict Ea and A.

42
Transition State Theory

• Transition-state theory suggests that reactants
  combine to form unstable intermediates called
  activated complexes (i.e., the transition states)
  which then decompose spontaneously into products.
  
• Thus, for an elementary, reversible reaction,
• we have the following conceptual scheme
• Transition-state theory views the reaction rate
  to be governed by the rate of intermediate
  decomposition.
• The rate of intermediate formation is assumed to
  be so rapid that it is present in equilibrium
  concentrations at all times.
• From these considerations, the mechanism may be
  treated as
• where an equilibrium exists between the
  concentration of reactants and activated complex,
  such that

43
Transition State Theory(continued)

• Transition-state theory also submits that the
  rate constant for the decomposition of an
  activated complex is the same for all reactions,
  and is given by
• where h is Planck's constant (h 6.63 x 10-27
  erg?sec)
• kT is the thermal energy.
• Thus, the observed reaction rate (from the
  rate-limiting elementary step) is given by
• Notice that while the rate constant for the
  intermediate decomposition is relatively large
  and the same for all reactions, the rate of the
  overall reaction is directly proportional to the
  thermodynamic equilibrium constant.
• From thermodynamic principles, the equilibrium
  constant, Keq may be expressed in terms of the
  free energy, ?G
• Thus, the rate of the forward mechanism (i.e.,
  the pathway which produces AB) becomes

44
Transition State Theory(continued)

• Since both ?S and ?H vary very slowly with
  temperature, the middle term, e?S/R, is
  considered to be a constant.
• Thus, for the forward reaction of the elementary,
  reversible reaction,
• the forward rate constant is of the form
• where,
• If the activation energy, Ea, is defined as the
  change in enthalpy for the forward equilibrium
  reaction, ?Hfor (which is always positive), then
  the transition-state theory for an overall
  exothermic reaction (i.e., ?Hnet lt 0) may be
  visualized graphically as

45
Transition State Theory(continued)

• Transformation of reactants to products
• Where, E1 ?Hfor E2 ?Hrev and ?Hr ?Hnet
• Once the activated complex, AB, is formed from A
  and B, it can either revert back into A B or
  form the new product AB. Similarly, we can start
  with AB to form AB, which then either reverts
  back to AB or forms A B.
• This transition-state theory suggests that the
  rate at which A and B react to form AB is
  governed by Ea, and not by ?Hnet.

AB
46
Transition State Theory(continued)

• By defining Ea ?H, transition-state theory
  predicts that the rate constant will be of the
  form
• Again, it can be shown that the overwhelming
  dependence on temperature resides in the
  exponential term.
• Thus, Arrhenius' Law is a good approximation to
  temperature dependency of both collision and
  transition-state theories.
• It should be noted that the Arrhenius equation is
  usually not followed over a very wide temperature
  range (e.g., a plot of lnk vs. 1/T may deviate
  from linearity).
• Thus, more sophisticated treatments may be
  required.
• The thermodynamic arguments (above) for the
  transition-state theory are valid only for
  elementary reactions.
• Very large deviations from the exponential
  Arrhenius expression often mean that the
  experimental rate constant being measured is a
  combination of rate constants (and/or equilibrium
  constants) for several elementary reaction with
  different activation energies and frequency
  factors.

47
Reaction Rates in Solution

• The theoretical treatments of reaction rates
  described earlier, (i.e., Collision Theory), were
  considered for simple gas phase systems in which
  no more than three molecules collide at the same
  time.
• The situation is quite different for reactions
  which take place in the more condensed
  environments of solutions.
• Reactants in solution are not "free" to move
  towards each other and collide due to the
  significant forces from neighboring solvent
  molecules.
• Reactions in solution are often complicated
  events in which the behavior of the surrounding
  solvent molecules must be considered.
• Three general factors influence reaction rates in
  solution.
• 1. The rate at which initially separated reactant
  molecules come together and become neighbors.
  This is called the rate of encounters.
• 2. The time that two reactants spend as neighbors
  before moving away from each other. This is
  called the duration of an encounter. During this
  time, the reactants may collide with each other
  hundreds of times.
• 3. The requirement of energy and orientation
  which two neighboring reactant molecules must
  satisfy in order to react.
• Any one of these three factors may dominate in
  governing the reaction rate.
• Factors 1 and 3 are similar to the factors
  considered for gas phase reactions, while factor
  2 is unique to dense phases (e.g., liquids).

48
Diffusion Controlled Reactions

• Some reactions occur as soon as the reactant
  molecules come together.
• For these fast reactions, the activation energy
  and orientation requirements are negligible.
• The reaction rate is limited only by the first
  factor (i.e., the rate at which encounters
  occur).
• In solution, reactant molecules move through the
  liquid medium by diffusion, and thus the rate is
  diffusion limited or is said to be diffusion
  controlled.
• A simple mechanism for these reactions may be
  given by
• where kD is the rate constant for diffusion of A
  and B towards each other, k-D is the rate
  constant for diffusion of A and B away from each
  other, and kc is the rate constant for the
  conversion of the complex (AB) to product R
  (i.e., the rate constant with out diffusive
  effects).
• Using the Steady-State Approximation on (AB) see
  later

49
Diffusion Controlled Reactions(continued)

• If the equilibrium is not fast compared to the
  second step, then the rate expression may be
  given by
• When kc is very large (i.e., a fast reaction once
  the reactants encounter each other) relative to
  k-D, the rate constant kc cancels out and thus
  the rate is controlled by kD.
• The rate of diffusion controlled reactions often
  depend on the nature of the solvent.
• As the viscosity of the medium decreases, the
  rate of reaction increases.
• In addition, the characteristics of the diffusing
  species are also important, as shown in the Table
  below.

50
The Solvent Cage Effect

• The second factor which affects the rate of
  reactions in solution involves the effects of
  solvent molecules on the motions of reactant
  molecules.
• Once two reactant molecules diffuse together,
  their first collision may not satisfy the energy
  and orientation requirements for reaction.
• The surrounding solvent molecules create a
  "solvent cage" which inhibits the separation of
  the reactant molecules.
• This solvent "cage effect" provides the
  opportunity for the molecules to undergo many
  more collisions before finally either reacting or
  diffusing away from each other.
• The duration of such an encounter may be 10-10
  sec, during which the reactant molecules may
  collide 100's of times.
• The cage effect tends to increase the reaction
  rate by increasing the opportunity for reactant
  molecules to find the required energy and/or
  orientation to react during the caged encounter.
• In contrast to gas phase reactions, in which
  molecules collide only once during an encounter,
  solution phase reactions involve encounters which
  may consist of many collisions.

51
The Melt Cage in Reactive Extrusion(Functionaliza
tion of Polypropylene)
Conventional approach using symmetric peroxides,
ROOR
Maleic anhydride must diffuse through melt to
find the polymeric radical.
Alternative using functionalized peroxides
Functionalized peroxides create polymeric
radical and graft in the same melt cage.
Greater grafting efficiency compared to the
conventional approach!
Bohn, C.C. Manning, S.C. Moore, R.B. A
Comparison of Carboxylated and Maleated
Polypropylene as Reactive Compatibilizers in
Polypropylene/Polyamide-6,6 Blends, J. Appl.
Polym. Sci. 2001, 79, 2398-2407.
52
Energy and Orientation Requirement for Reactions
in Solution

• The third factor which affects the rate of
  reactions in solution involves the energy and
  orientation requirement.
• primarily governed by the nature of the reacting
  species.
• the solvent may play a role as shown in the
  following example
• (CH3)3CCl OH- ? (CH3)3COH Cl-
• proceeds by the mechanism
• (CH3)3CCl ? (CH3)3C Cl- (slow)
• (CH3)3C OH- ? (CH3)3COH
  (fast)
• This reaction is first order with respect to
  (CH3)3CCl and does not depend on the
  concentration of OH-.
• The rate does depend on the nature of the
  solvent.
• If the polarity of the solvent is systematically
  varied in mixed solvents of water with acetone,
  then the reaction rate is 104 times faster in a
  9010 (water-acetone) solvent relative to a 1090
  (water-acetone) solvent.
• The RDS involves the production of a pair of ions
  which is more easily accomplished in a highly
  polar solvent in which the ions are more stable.
  
• In general, reactions in solution will occur
  fastest in solvents in which the activated
  complex is most stable (i.e., thus yielding a low
  Ea).
• In the above example, the activated complex is
  highly polar, and is fastest in the more polar
  solvents.

53
Catalysis

• By formal definition, a catalyst is a substance
  which increases the rate of a reaction without
  itself undergoing change.
• Consider the base catalyzed hydrolysis of an
  ester
• the overall reaction is
• CH3COOC2H5 H2O ? C2H5OH CH3COOH
• The hydroxide ion is not required by the
  stoichiometry of the overall reaction, but its
  addition does increase the reaction rate.
• Notice, however, that one of the products is an
  acid.
• As the reaction proceeds, the OH- is, in fact,
  consumed.
• Thus, a practical definition for a catalyst may
  be any substance which can increase a rate of
  reaction while not being required in the
  stoichiometry of the overall reaction.
• Catalysts increase reaction rates by providing
  new, faster paths by which a reaction can
  proceed.
• Consider the reaction
• A B ? AB (very slow, high Ea)
• The rate of this reaction may be increased by the
  use of substance C, which is a homogeneous
  catalyst (i.e., the catalytic process occurs in
  one phase) that provides an alternate reaction
  pathway

54
Catalysis (continued)

• The above catalytic scheme may be represented
  graphically by
• Note that careful consideration of the reaction
  conditions must be realized because the catalyst
  also increases the rate of the reverse reaction.
• Heterogeneous catalysts pertain to two phases, in
  which the rate of reaction is increased by
  reaction pathways involving the phase or surface
  boundaries.
• These systems often involve adsorption of
  reactants onto the catalyst surface.
• For example, the hydrogenation of ethylene
• H2 C2H4 ? C2H6
• is catalyzed in the presence of small Ni, Pt or
  Pd particles (with a high surface area).
• These metals can adsorb large quantities of H2
  which greatly increases the local concentration
  of reactant.
• Furthermore, the metal lattice allows the H2
  molecules to dissociate into much more reactive
  hydrogen atoms.