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									         Chapter 15: Kinetics
• The speed with which the reactants
  disappear and the products form is called
  the rate of the reaction
• A study of the rate of reaction can give
  detailed information about how reactants
  change into products
• The series of individual steps that add up to
  the overall observed reaction is called the
  reaction mechanism
•    There are five principle factors that
     influence reaction rates:
    1) Chemical nature of the reactants
    2) Ability of the reactants to come in contact
       with each other
    3) Concentration of the reactants
    4) Temperature
    5) Availability of of rate-accelerating agents
       called catalysts
The progress of the reaction A  B. The number of A molecules (in
red) decreases with time while the number of B molecules (in blue)
increases. The steeper the concentration versus time curve, the
faster the reaction rate. The film strip represents the relative number
of A and B molecules at each time.
• Chemical nature of the reactants
  – Bonds break and form during reactions
     • The most fundamental difference in reaction rates
       lie in the reactants themselves
     • Some reactions are fast by nature and others slow
• Ability of the reactants to meet
  – Most reactions require that particles (atoms,
    molecules, or ions) collide before the reaction
    can occur
  – This depends on the phase of the reactants
– In a homogeneous reaction the reactants are in
  the same phase
   • For example both reactants in the gas (vapor) phase
– In a heterogeneous reaction the reactants are
  in different phases
   • For example one reactant in the liquid and the
     second in the solid phase
– In heterogeneous reactions the reactants meet
  only at the intersection between the phases
– Thus the area of contact between the phases
  determines the rate of the reaction
Effect of crushing
a solid. When a
single solid is
subdivided into
much smaller
pieces, the total
surface area on all
of the pieces
becomes very
large.
• Concentration of the reactants
  – Both homogeneous and heterogeneous reaction
    rates are affected by reactant concentration
     • For example, red hot steel wool bursts into flames in
       the presence of pure oxygen
• Temperature of the system
  – The rates for almost all chemical reactions
    increase as the temperature is increased
     • Cold-blooded creatures, such as insects and reptiles,
       become sluggish at lower temperatures as their
       metabolism slows down
• Presence of a catalyst
  – A catalysts is a substance that increases the rate
    of a chemical reaction without being consumed
  – Enzymes are biological catalysts that direct our
    body chemistry
• A rate is always expressed as a ratio
• One way to describe a reaction rate is to
  select one component of the reaction and
  describe the change in concentration per
  unit of time
                           (conc. of X at time t 2  conc. of X at time t1 )
rate with respect to X 
                                              (t 2  t1 )
                            (conc. of X )
                       
                                 t


• Molarity (mol/L) is normally the
  concentration unit and the second (s) is the
  most often used unit of time
• Typically, the reaction rate has the units
               mol/L         -1 -1
                     or mol L s
                s
• By convention, reaction rates are reported
  as a positive number even when the
  monitored species concentration decreases
  with time
• If the rate is known with respect to one
  species, the coefficients of the balanced
  chemical equation can be used to find the
  rates with respect to the other species
• Consider the combustion of propane:
  C3 H 8 ( g )  5O2 ( g )  3CO2 ( g )  4 H 2O( g )
• Compared to the rate with respect to
  propane:
  – Rate with respect to oxygen is five times faster
  – Rate with respect to carbon dioxide is three
    times faster
  – Rate with respect to water is four times faster
• Since the rates are all related any may be
  monitored to determine the reaction rate
• A reaction rate is generally not constant
  throughout the reaction
• Since most reactions depend on the
  concentration of reactants, the rate changes
  as they are used up
• The rate at any particular moment is called
  the instantaneous rate
• It can be calculated from a concentration
  versus time plot
A plot of the concentration of HI versus time for the reaction:
2HI(g)  H2(g) + I2(g). The slope is negative because we are
measuring the disappearance of HI. When used to express the
rate it is used as a positive number.
• The rate of a homogeneous reaction at any
  instant is proportional to the product of the
  molar concentrations of the reactants raised
  to a power determined from experiment
  For thegeneral reaction
  A  B  products
  The rate of reaction can be expressedas
  rate  k[ A] [ B]
             m    n


  k  the rate constant for the reaction
• Consider the following reaction:
   H 2 SeO3  6 I   4 H   Se  2 I 3  3H 2O
• From experiment, the rate law (determined
  from initial rates) is
                                  3     2
   rate  k[ H 2 SeO3 ] [ I ] [ H ]
                         1


• At 0oC, k equals 5.0 x 105 L5 mol-5 s-1
• Thus, at 0oC
                                                   1
      rate  (5.0 10 L mol s )
                             5     -5         -5

                                         3         2
                 [ H 2 SeO3 ][I ] [ H ]
• The exponents in the rate law are generally
  unrelated to the chemical equation’s
  coefficients
  – Never simply assume the exponents and
    coefficients are the same
  – The exponents must be determined from the
    results of experiments
• The exponent in a rate law is called the
  order of reaction with respect to the
  corresponding reactant
• For the rate law:
                              3     2
    rate  k[ H 2 SeO3 ] [ I ] [ H ]
                         1


• We can say
  – The reaction is first order with respect to
    H2SeO3
  – The reaction is third order with respect to I-
  – The reaction is second order with respect to H+
  – The reaction order is sixth order overall
• Exponents in a rate law can be fractional,
  negative, and even zero
• Looking for patterns in experimental data
  provide way to determine the exponents in a
  rate law
• One of the easiest ways to reveal patterns in
  data is to form ratios of results using
  different sets of conditions
• This technique is generally applicable
• Again consider the hypothetical reaction
        A  B  products
       rate  k[ A] [ M ]
                    m     n
• Suppose the experimental concentration-
  rate data for five experiments is:
               Inital Conc.
               [ A]      [ B]     Initial Rate
     Expt (mol L-1 ) (mol L-1 ) (mol L-1 s -1 )
       1   0.10       0.10        0.20
       2    0.20      0.10        0.40
       3      0.30      0.10         0.60
       4      0.30      0.20         2.40
       5      0.30      0.30         5.40
• For experiments 1, 2, and 3 [B] is held
  constant, so any change in rate must be due
  to changes in [A]
• The rate law says that at constant [B] the
  rate is proportional to [A]m
                        m
         rate2  [ A]2 
                [ A] 
              
         rate1  1    
         rate2  0.40 mol L-1 s -1 
                0.20 mol L-1 s -1   2
                                        Thus m=1
         rate1                    
                m                     m
         [ A]2    0.20 mol L -1
        
         [ A]                  2m
                    0.10 mol L-1 
         1                     
• This means that the reactions is first order
  with respect to reactant A
• For experiments 3, 4, and 5 [A] is held
  constant, so any change must be due to
  changes in [B]
• The rate law says that at constant [A] the
  rate is proportional to [B]n
• Using the results from experiment 3 and 4:
                  n
   rate4  [ B ]4 
                
   rate3  [ B ]3 
                 
   rate4  2.40 mol L-1 s -1 
          0.60 mol L-1 s -1   4
                           
   rate3                            Thus n=2
                             
          n                     n
   [ B ]4   0.20 mol L -1
                         2n
   [ B ]   0.10 mol L-1 
        3               

• The reaction is second order in B and
  rate=k[A][B]2
• The rate constant (k) can be determined
  using data from any experiment
• Using experiment 1:
                                   -1 -1
         rate           0.20 mol L s
  k          2
                            -1          -1 2
      [ A][B]     (0.10 mol L )(0.10mol L )
     2.0  10 L mol s
             2   2    -2   -1


• Using data from a different experiment
  might give a slightly different value
• The relationship between concentration and
  time can be derived from the rate law and
  calculus
• Integration of the rate laws gives the
  integrated rate laws
• Integrate laws give concentration as a
  function of time
• Integrated laws can get very complicated, so
  only a few simple forms will be considered
• First order reactions
  – Rate law is: rate = k [A]
  – The integrate rate law can be expressed as:
          [ A]0                          kt
       ln        kt or [ A]t  [ A]0 e
          [ A]t
     • [A]0 is [A] at t (time) = 0
     • [A]t is [A] at t = t
     • e = base of natural logarithms = 2.71828…
• Graphical methods can be used to determine
  the first-order rate constant, note
            [ A]0
         ln        kt
            [ A]t
         ln[ A]0  ln[ A]t  kt
         ln[ A]t  ln[ A]0   kt
         ln[ A]t   kt  ln[ A]0
                         
            y     mx  b
• A plot of ln[A]t versus t gives a straight line
  with a slope of -k




The decomposition of N2O5. (a) A graph of concentration versus
time for the decomposition at 45oC. (b) A straight line is obtained
from a logarithm versus time plot. The slope is negative the rate
constant.
• The simplest second-order rate law has the
  form
            rate  k [ B ]   2

• The integrated form of this equation is
      1     1
                kt
    [ B]t [ B]0
   [ B]0  the initial concentrat of B
                                ion
   [ B]t  the concentrat of B at time t
                        ion
• Graphical methods can also be applied to
  second-order reactions
• A plot of 1/[B]t versus t gives a straight line
  with a slope of k
                                    Second-order
                                    kinetics. A plot of
                                    1/[HI] versus
                                    time (using the
                                    data in Table
                                    15.1).
• The amount of time required for half of a
  reactant to disappear is called the half-life,
  t1/2
   – The half-life of a first-order reaction is not
     affected by the initial concentration
                                    [ A]0
       First - order rate law : ln         kt
                                    [ A]t
                              1
       at t  t1/ 2 , [ A]t  [ A]0 , substituting
                              2
           [ A]0                         ln 2
       ln 1           kt1/ 2 or t1/ 2 
           2
             [ A]0                        k
First-order radioactive decay of iodine-131. The
initial concentration is represented by [I]0.
– The half-life of a second-order reactions does
  depend on the initial concentration
                               1     1
    Second- order rate law :             kt
                             [ B]t [ B]0
                           1
    at t  t1/ 2 , [ B]t  [ B]0 , substituting
                           2
       1            1
    1
                        kt1/ 2
    2
      [ B]0 [ B]0
      1                            ln 2
           kt1/ 2   or t1/ 2   
    [ B]0                         k[ B]0
• One of the simplest models to explain reactions
  rates is collision theory
• According to collision theory, the rate of reaction
  is proportional to the effective number of
  collisions per second among the reacting
  molecules
• An effective collision is one that actually gives
  product molecules
• The number of all types of collisions increase with
  concentration, including effective collisions
• There are a number of reasons why only a
  small fraction of all the collisions leads to
  the formation of product:
  – Only a small fraction of the collisions are
    energetic enough to lead to products
  – Molecular orientation is important because a
    collision on the “wrong side” of a reacting
    species cannot produce any product
     • This becomes more important as the complexity of
       the reactants increases
The key step in the decomposition of NO2Cl to NO2 and Cl2 is
the collision of a Cl atom with a NO2Cl molecules. (a) A poorly
orientated collision. (b) An effectively orientated collision.
– The minimum energy kinetic energy the
  colliding particles must have is called the
  activation energy, Ea
– In a successful collision, the activation energy
  changes to potential energy as the bonds
  rearrange to for products
– Activation energies can be large, so only a
  small fraction of the well-orientated, colliding
  molecules have it
– Temperature increases increase the average
  kinetic energy of the reacting particles
Kinetic energy distribution for a reaction at two different
temperatures. At the higher temperature, a larger fraction of the
collisions have sufficient energy for reaction to occur. The shaded
area under the curves represent the reacting fraction of the
collisions.
• Transition state theory explains what
  happens when reactant particles come
  together
• Potential-energy diagrams are used to help
  visualize the relationship between the
  activation energy and the development of
  total potential energy
• The potential energy is plotted against
  reaction coordinate or reaction progress
The potential-energy diagram for an exothermic
reaction. The extent of reaction is represented as the
reaction coordinate.
A successful (a) and unsuccessful (b) collision for
an exothermic reaction.
• Activation energies and heats of reactions
  can be determined from potential-energy
  diagrams
                                   Potential-energy
                                   diagram for an
                                   endothermic
                                   reaction. The
                                   heat of reaction
                                   and activation
                                   energy are
                                   labeled.
 • Reactions generally have different
   activation energies in the forward and
   reverse direction




Activation energy barrier for the forward and reverse reactions.
• The brief moment during a successful
  collision that the reactant bonds are partially
  broken and the product bonds are partially
  formed is called the transition state
• The potential energy of the transition state
  is a maximum of the potential-energy
  diagram
• The unstable chemical species that “exists”
  momentarily is called the activated
  complex
Formation of the activated complex in the reaction between
NO2Cl and Cl.
                 NO2Cl+ClNO2+Cl2
• The activation energy is related to the rate
  constant by the Arrhenius equation
                    Ea / RT
          k  Ae
  k = rate constant
  Ea = activation energy
  e = base of the natural logarithm
  R = gas constant = 8.314 J mol-1 K-1
  T = Kelvin temperature
  A = frequency factor or pre-exponential factor
• The Arrhenius equation can be put in
  standard slope-intercept form by taking the
  natural logarithm
       ln k  ln A  Ea / RT or
        ln k  ln A  ( Ea / R)  (1 / T )
                                  
         y  b         m         x
• A plot of ln k versus (1/T) gives a straight
  line with slope = -Ea/RT
• The activation energy can be related to the
  rate constant at two temperatures
            k2   Ea  1 1 
        ln   
           k           
                       T T 
            1     R  2     1
• The reaction’s mechanism is the series of
  simple reactions called elementary
  processes
• The rate law of an elementary process can
  be written from its chemical equation
• The overall rate law determined for the
  mechanism must agree with the observed
  rate law
• The exponents in the rate law for an
  elementary process are equal to the
  coefficients of the reactants in chemical
  equation
       Elementary process:
       2NO2  NO3  NO
       rate  k[NO2 ]
                    2
• Multistep reactions are common
• The sum of the element processes must give
  the overall reaction
• The slow set in a multistep reaction limits
  how fast the final products can form and is
  called the rate-determining or rate-
  limiting step
• Simultaneous collisions between three or
  more particles is extremely rate
• A reaction that depended a three-body
  collision would be extremely slow
• Thus, reaction mechanism seldom include
  elementary process that involve more than
  two-body or bimolecular collisions
• Consider the reaction
     2NO  2H2  N 2  2H2O
     rate  k[NO] [H2 ] (experimental)
                 2


• The mechanism is thought to be
                 
         2NO        N 2O 2             (fast)
 N 2 O 2  H 2  N 2 O  H 2 O (slow)
 N 2O  H 2  N 2  H 2O                 (fast)
• The second step is the rate-limiting step,
  which gives
      rate  k[ N 2O2 ][H 2 ]
• N2O2 is a reactive intermediate, and can be
  eliminated from the expression
• The first step is a fast equilibrium
• At equilibrium, the rate of the forward and
  reverse reaction are equal
     rate(forwa  k f [ NO]2
                rd)
    rate(reverse)  k r [ N 2 O 2 ]   thus
    k f [ NO]2  k r [ N 2 O 2 ] or
                   kf
    [ N 2O 2 ]             2
                        [ NO]
                   kr
• Substituting, the rate law becomes
  rate  k[ N 2 O 2 ][H 2 ]
            kf 
  rate  k  [ NO] [H 2 ] or
           k 
                       2

            r
  rate  k '[ NO] [H 2 ]
                  2


• Which is consistent with the experimental
  rate law
• A catalyst is a substance that changes the
  rate of a chemical reaction without itself
  being used up
  – Positive catalysts speed up reactions
  – Negative catalysts or inhibitors slow reactions
• (Positive) catalysts speed reactions by
  allowing the rate-limiting step to proceed
  with a lower activation energy
• Thus a larger fraction of the collisions are
  effective
(a) The catalyst provides an alternate, low-energy path from
the reactants to the products. (b) A larger fraction of
molecules have sufficient energy to react when the catalyzed
path is available.
• Catalysts can be divided into two groups
  – Homogeneous catalysts exist in the same phase
    as the reactants
  – Heterogeneous catalysts exist in a separate
    phase
• NO2 is a homogeneous catalyst for the
  production of sulfuric acid in the lead
  chamber process
• The mechanism is:
         S  O 2  SO 2
   SO 2  O 2  SO 3
           1
           2

   SO 3  H 2 O  H 2SO 4
• The second step is slow, but is catalyzed by
  NO2:
        NO2  SO2  NO  SO3
           NO 1 O2 NO2
               2
• Heterogeneous catalysts are typically solids
• Consider the synthesis of ammonia from
  hydrogen and nitrogen by the Haber process
         3H 2  N 2  2NH 3
• The reaction takes place on the surface of
  an iron catalyst that contains traces of
  aluminum and potassium oxides
• The hydrogen and nitrogen binds to the
  catalyst lowering the activation energy
The Haber process. Catalytic formation of ammonia molecules
from hydrogen and nitrogen on the surface of a catalyst.

								
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