Reaction Mechanisms Chemical Mechanisms By describing how

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 Reaction Mechanisms
Chemical Mechanisms 
By describing how atoms  and  molecules interact to  generate products, mechanisms help us to understand
how  the  world  around us  functions  at a  fundamental level.  A mechanism  is a series  of elementary steps
whose  sum  is  the  overall  reaction.  An  elementary  step  is  a  reaction  that  is meant  to  represent a  single
collision or vibration that leads to a chemical change. For a mechanism to be considered valid, its sum must
equal  the  overall  balanced  equation,  its  predicted  rate  law  must  agree  with  experimental  data,  and  its
predictions of intermediates must not be contrary to experimental observations. A mechanism may never be
proven because  we cannot ever see a  chemical reaction--both the time scale of an elementary step and the
size of atoms are too small. Furthermore, we must guess at the identity of many intermediates because they
are usually so reactive that they can not  be isolated. Instead, a chemist proposes reaction mechanisms  and
tests  their  validity  against  experimental  data,  ruling  out  mechanisms  that  are  inconsistent  with  results.
These experiments may be strategically designed to trap an intermediate product to prove its existence as a
stepping-point in the total reaction. 
To aid in our understanding of mechanisms,  we will draw reaction coordinate  diagrams that trace the free
energy  path  of  a  reaction  from reactants  to  products.  The  activation energy  of  a  reaction represents  the
difference in energy between the reactants and the highest point on a reaction coordinate diagram. We will
derive the Arrhenius Equation, which relates the rate constant for a reaction to its activation energy. Local
minima  on  the  reaction  coordinate  diagram  are  positions  occupied  by  intermediates.  By  comparing  the
reaction coordinate diagram for a catalyzed and a uncatalyzed process, we can see that catalysts function by
altering the route the reaction takes from reactants to products without the catalyst being altered. 
Terms 
Activation  Energy   -   The difference in energy  between  the  reactants and the  transition  state  that is  the
energy barrier the reactants must overcome to achieve a chemical reaction. 
Catalyst  -  A substance that lowers the activation energy for a chemical reaction without being chemically
altered by the reaction. 
Elementary  Step   -   A  reaction  that  represents  a  single  collision  or  intramolecular  step  in  a  reaction
mechanism. 
Homogeneous Catalyst  -  A catalyst that is in the same phase as the reactants. 
Intermediate  -  A species that is both produced and consumed in a chemical reaction. As such, it does not
appear  in  the  overall  reaction  but  is  proposed  to  be  produced  in  one  elementary  step  and  consumed  in
another. 
Kinetics  -  The study of the rate and mechanism of chemical reactions. 
Mechanism   -   The  series  of  elementary  steps  that  combine  to  produce  the  path  molecules  take  from
reactant(s) to product(s) in a chemical reaction. 
Order  -  In  the rate law of a reaction, the power to which the concentration of a reagent is raised. Or, the
sum of the powers on the concentration terms in the rate law. 
Rate   -   The  speed  of  a  reaction measured  in amount  or  reagent  consumed  or  product produced  per unit
time. 
Rate Constant   -  The proportionality constant  in  the rate law expression.  This  factor is a measure of  the
intrinsic reactivity of the reaction but is not constant with respect to temperature. 
Rate Law  -  An expression of the dependence of the rate of a reaction on the concentrations of reactants. 
Rate Limiting Step  -  The slowest elementary  step in a mechanism.  The rate  of the  reaction  must equal
the rate of the slowest step because the reaction can go no faster than its slowest step. 
Reaction Coordinate Diagram  -  A plot of free energy versus the reaction coordinate for a  reaction that
provides a pictorial representation of the lowest energy path from reactants to products. 
Steady-State  Approximation  -  The assumption that  the rate of  formation  and  consumption  of a highly
reactive  intermediate  are  equal  so  that  the  change  in  intermediate  concentration  with  respect  to  time  is
approximated to be zero. 
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Transition  State   -   The  species  with  the  highest  energy  between  reactants  and  products  on  a  reaction
coordinate  diagram,  it  is  a  short-lived  species  that represents a combination  of product-like and reactant-
like properties. 
 
Mechanisms of Chemical Reactions 
Properties of Mechanisms 
Mechanisms  describe  in  a  stepwise  manner  the  exact  collisions  and  events  that  are  required  for  the
conversion of  reactants into  products. Mechanisms achieve that  goal by  breaking up  the overall balanced
chemical equation into a series of elementary steps. An elementary step is written to mean a single collision
or  molecular  vibration  that  results  in  a  chemical  reaction.  The  following  picture  of  an  elementary  s tep
shows a single collision between water and boron trifluoride: 
 
Figure %: Schematic representation of an elementary step 
The molecularity  of  an elementary  step describes  the  number  of  reactive  partners  in  the  elementary step.
For example, the above elementary step is called  bimolecular  because two molecules collide. Commonly,
elementary steps are mono-, bi-, or termolecular. The probability of four molecules colliding at exactly the
same place  and time  is so  small that  we  can  safely assume  that no reaction will  ever  be  tetramolecular.
Because take  up a large amount of space, we  will represent elementary steps in this (www.moalims.com)
Note  as  normal  reactions  with  molecular  formula  line  equations.  You  will  know  from  the  context  (i.e.
talking about the steps of a mechanism) whether the reaction is an elementary step or an overall reaction. 
To better understand mechanisms, let's consider the following mechanism for the decomposition of  ozone,
O3 : 
 
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The above mechanism exhibits a property of all mechanisms: it is a series of elementary steps whose sum is
the overall balanced reaction. Note the presence of the oxygen atom, O, intermediate in the above equation.
It is an intermediate because it is both  created and destroyed in the mechanism and does not appear in the
net equation. 
Another  property  of  mechanisms  is  that  they  must  predict  the  experimentally  determined  rate  law.  To
calculate the rate law from a mechanism you need to first know the rate limiting step. The rate limiting step
determines  the rate  of  the reaction  because it  is  the  slowest  step.  You  can rationalize  that a reaction can
only go  so  fast as its  slowest step by thinking about what happens  when you encounter an accident on the
highway that closes all but one lane. You may have been able to race along at 65 m.p.h. (depending on your
state's laws) before  you reached the lane closure but the  slow passage  of cars past the  accident limits your
rate. You can only go as fast through that one lane as the slowest car in front of you. 
In the above , the first reaction is labeled as "slow". This reaction is the rate determining step because it is
the slowest step. As we have stated, that means that the rate of the overall reaction is equal to the rate of the
rate  determining  step.  The rate of  an  elementary  step  is  the  rate  constant  for that  step  multiplied  by the
concentrations of  the reactants  raised to  their  stoichiometric  powers.  Note  that  this rule  only  applies for
elementary steps. The rate of an overall reaction is NOT the product of the concentrations of the reactants
raised  to  their  stoichiometric  powers.  The  rate  law  for  the  first  elementary  step  in  the  is  rate  =  k  [O3].
Because this step is the rate determining step, the rate law is also the rate law for the overall reaction. Using
similar techniques we can calculate the rate law predicted by any mechanism. We then check the predicted
rate law against the experimentally determined rate law to test the validity of the propos ed mechanism. 
Reaction Coordinate Diagrams 
We can follow the progress of a reaction  on its way from  reactants to products by graphing the energy  of
the species versus the reaction coordinate. We will be vague in describing the reaction coordinate because
its definition is a mess of other variables composed to best make sense of the progress of the reaction. The
value  of  the  reaction  coordinate  is  between  zero  and  one.  Understanding  the  meaning  of  the  reaction
coordinate is not important, just know that small values of reaction coordinate (0-0.2)  mean little reaction
has taken place and large values (0.8-1.0) mean that the reaction is almost over. It is a kind of scale of the
progress of a reaction. A typical reaction coordinate diagram for a mechanism with a single step is shown
below: 
 
Figure %: A reaction coordinate diagram for a single-step reaction 
Note that the reactants are placed on the left and the products on the right. The choice of the energy levels
of  the  reactants  and products is  dictated  by  their  energies,  those  with higher  energies  are higher  on  the
diagram  and  those  with  lower  energies  are lower  on  the  diagram. The  difference  is energy  between  the
reactants and  the transition state  is  called  the activation energy.  The activation energy is  the height of  the
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energy barrier  of the  reaction. The  transition  state is the point  of maximum energy on  the diagram  which
represents  a  species  possessing  both  reactant-like  and  product-like  properties.  Because  it  is  so  high  in
energy, the transition state is very reactive and can never be isolated due to its extremely short lifetime. The
relative energy  of  the  reactants  and  products, the  E  on the  diagram,  determines whether the  reaction  is
exothermic  or  endothermic.  A reaction  will  be  exothermic  if  the  energy  of  the  products  is  less  than  the
energy  of  the  reactants.  A reaction  is  endothermic  when  the  energy  of  the  products  is  greater  than  the
energy of the  reactants. The is for an exothermic reaction.  Below  is  a  reaction  coordinate diagram for an
endothermic reaction. 
 
Figure %: Reaction coordinate diagram for an endothermic reaction 
If  a reaction has n elementary  steps  in its mechanism, there will be n–1 minima  between  the products  and
reactants representing  intermediates. There  will  also be n maxima representing the n transition states. For
example, a reaction with three elementary steps could have the following reaction coordinate diagram. 
 
Figure %: Reaction coordinate diagram for a three-step reaction 
One confusing point about reaction coordinate diagrams is how to determine what the rate determining step
is. Even experienced chemists consistently get this type of problem wrong. The rate determining step is not
the  one  with  the  highest  activation  energy  for  the  step.  The  rate  determining  step  is  the  step  whose
transition state has the highest energy. 
Activation Energy and the Arrhenius Equation 
Intuitively,  it  makes  sense  that a  reaction  with a  higher  activation barrier  will be slower.  Think of how
much harder you must roll a ball up a large hill than a smaller one. Let's consider chemical reactions more
deeply to derive an equation which describes the relationship between the rate constant of a reaction and its
activation barrier. To simplify our derivation, we will assume that the reaction has a one-step mechanism.
This elementary step represents  a collision as shown in . Therefore, the frequency of the collisions, f, will
be important in our equation. Notice that only a certain orientation of the molecules will lead to a reaction.
For example, the following collision will not lead to a reaction. The reagent molecules simply bounce off of
one another: 
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Figure %: Only specific orientations during a collision will lead to a reaction. 
Therefore, we will need to include an orientation factor (or steric factor), p, that takes into account the fact
that  only  a  certain  fraction  of  collisions  will  lead  to  reaction  due  to  the  orientation  of  the  molecules.
Another factor we must consider is that only a certain fraction of the molecules colliding will have enough
energy  to  overcome the activation  barrier. The Boltzmann distribution  is a thermodynamic  equation  that
tells  us  what  fraction  of  the  molecules  have  a  certain  amount  of  energy.  As  you  know,  at  higher
temperatures the average kinetic energy of the molecules increases. Therefore, at higher temperatures more
molecules have an energy greater than the activation energy--as shown in . 
 
Figure %: Boltzmann distributions for T1 greater than T2 
Combining the above considerations, we state the following relationship between the rate constant and the
activation energy, called the Arrhenius equation: 
 
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The  variable  k  is  the rate  constant,  which  is  dependent  on  the  frequency  of  the  collisions  f,  orientation
factor  p,  activation  energy  Ea ,  and  temperature  T.  From  the  expression  for  the  Arrhenius  equation  you
should  note  that  a  small  increase  in  activation  energy  leads  to  a  large  decrease  in  rate  constant.
Furthermore, temperature has  a  similarly exponential  effect  on the  rate constant. An experimental rule of
thumb is that a 10oC increase in temperature leads to a doubling of the rate constant. 
One application of the Arrhenius equation that is useful is the determination of the activation  energy  for a
reaction. Taking the natural log of the Arrhenius equation gives a linear equation: 
 
A  graph  of ln k  versus  1  / T should  give  a  straight  line whose  slope  is  -  Ea   /  R.  By measuring  the  rate
constant at a range of different temperatures, you can  construct a  graph to determine the activation energy
of a reaction. 
Catalysis 
A  catalyst  speeds  up  a  reaction  without  being  explicit  in  the  overall  balanced  equation.  It  does  this  by
providing  an  alternate  mechanism  for  the  reaction  that  has  a  lower  activation  barrier  than  does  the
uncatalyzed pathway. Compare the catalytic  and regular mechanisms  for the hydrogenation of ethylene to
ethane and their associated reaction coordinate diagrams in : 
 
Figure %: Mechanisms of ethylene hydrogenation 
As you can see, the catalyst changes the  mechanism of  the reaction and lowers the activation energy. The
catalyst,  because  it  does  not  appear  in  the  overall  balanced  equation  has  absolutely  no  effect  on  the
thermodynamics of the reaction. 
There  are  two  types  of  catalysts--heterogeneous  catalysts  and  homogeneous  catalysts.  There  is  no
fundamental  difference  in how  these catalysts  work. The difference  lies in  whether  the  catalyst  is  in  the
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same  phase  (solid,  liquid,  or  gas)  as  the  reagents.  A  homogeneous  catalyst  is  in  the  same  phase  as  the
reactants while a heterogeneous catalyst is not. An enzyme is a biological homogeneous catalyst. 
Problems and Solutions 
Problem : 
Identify the intermediates and the catalysts (if any) in the following mechanism. 
 
Solution for Problem 1 >>
H2O  is  a  catalyst  because  it  does  not  appear  in  the  overall  balanced  equation  but  is  involved  in  the
mechanism.  HOCl, OH-,  and  HOBr are intermediates because they  are both  created and  consumed  in  the
reaction and do not appear in the overall balanced equation. 
Problem : 
What is the activation energy of a reaction that doubles in rate with a 10o C rise in temperature? Assume the
starting temperature is 298 K. 
Solution for Problem 2 >>
To solve this problem we  will  use the Arrhenius equation. By taking the ratio of the two  equations for the
rate constants at T1 and T2, we can cancel out the frequency and orientation factors. The rest of the solution
is algebraic manipulation. 
 
 
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