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CHEMICAL KINETICS
Four factors affect reaction rates
 Concentration of reactants
 Temperature of reaction
 Presence or absence of a catalyst
 Surface area of liquid or solid reactants
Reaction Rates
 Reaction speed defined as the change that occurs per unit
time
o It is determined by measuring the disappearance of a
reactant or the appearance of a product
o The speed of a reaction is the reaction rate
 For reaction AB : Avg rate = change in the number of
moles of B / change in time
o  B= moles of B at final time- moles of B initial
o At t= 0, there is 1 mole of A and no B
o At t= 10 min, there is .74 mol A and .26 mol B
o At t=20 min, there is.54 mol A and .46 mol B
o Avg rate=  B/  T= Mol B at 10min- Mol B at 0 min/
10min –0 min= .026mol/min
o Or Avg rate= -  Mol A / t ; note the negative sign. It
means reactants are disappearing
Rates in Terms of Concentration
 The most useful measure is molarity
 Since volume is constant, molarity and moles are directly
proportional
 Units for average rate are mol/L sec or M/sec
 The average rate of a reaction decreases over time. Why?
 The rate at any specific point in time is the instantaneous
rate
 If we plot the concentration of a reactant vs time, the rate at
any instant is the slope of the straight tangent to the curve
at that point
Stoichiometry
 For the reaction :
C4H9Cl + H2OC4H9OH + HCl
Rate= - [C4H9]/t = [C4H9OH] /t
What if stoichiometry is not one to one?
 2HI H2 + I2
Rate = - [HI]/ 2 t = [H2]/ t = [I2]/ t
Generalized : For the reaction
aA + bB  cC + d D
Rate = - [A]/at = - [B]/ b t= [C]/ct = [D]/dt
Dependence of rate on concentration
 In general, rate increases with increased concentration of
Reactants and decreases with decreasing concentration
 We often examine the effect of concentration by measuring
the reaction rate at the beginning of a reaction
 Consider A + B C + D
We find that if we hold [B] constant and double [A], the
rate doubles. Therefore , the rate is directly proportional
to [A].
If we hold [A] constant and double [B], then the rate
doubles. Therefore, the rate is directly proportional to [B]
 The overall concentration dependence is given by the rate
law. For this example the rate law is:
Rate = k [A] [B] where k is the rate constant
Reaction Order
 For any reaction with rate law:
o Rate= k[A]m [B]n, the exponents are called reaction
orders. The overall reaction order is the sum of the
exponents.
o This reaction is first order in[A] and first order in [B]
And second order overall
 Reaction orders must be determined experimentally
o They do not necessarily correspond to stoichiometric
coefficients
o They are typically 0,1 or 2
o However , they can be fractional or negative
Units of rate constants
 Units of the rate constant depend on the overall reaction
order
 For a second order reaction:
Units of rate = (Units of rate constant) (units of
concentration) (units of concentration)
 Therefore : Units of rate constant= Units of rate/ (Units of
concentration)2= M/sec/M2= M-1 S-1
Using Initial Rates to determine rate laws
 To determine the rate law, we observe the effect of changing
the initial concentrations
o If the reaction is zero order, changing the
concentration has no effect on rate
o If the reaction is first order, doubling the
concentration will double the rate( change is directly
proportional) What if concentration is halved?
o If the reaction is second order, doubling the
concentration will result in a 4X increase (22).
Tripling the concentration will cause a 9X increase
o A reaction is nth order if doubling the concentration
causes a 2n increase in rate
o The reaction rate, NOT THE RATE CONSTANT,
depends on concentration.
First order Reaction
 ln[A]t = -kt + ln[A]0 is the equation for a first order
reaction. Note the similarity to y = mx + b. In this case , a
plot of ln[A]t vs t yields a straight line with a slope –k and
an intercept of ln[A]0
 Half-life is the time required for the initial concentration of
a reactant to decrease to one half its original value
 T1/2 = .693/k Note that the half life of a first order reaction is
independent of the initial concentration of the reactant
Second order reactions
 1/ [A]t = kt + 1/[A]0 A plot of 1/[A]t versus t is a straight
line with a slope k and an intercept of 1/[A]0
 For a second order reaction a plot of ln[A]t is not a straight
line
 T1/2 = 1/k[A]0 Half life is dependent on initial concentration
 Note that a second order process can have the form : Rate=
k[A] [B] . The reaction is second order overall but first
order in reactant concentration
Temperature and Rate
 As temperature increases, the rate increases
 Since the rate law does not have temperature in it, the rate
constant must be temperature dependent
The Collision Model
 Rates of reaction are effected by concentration and
temperature
 The collision model, which is based on kinetic molecular
theory, explains this
o In order for molecules to react they must collide
o The greater the number of collisions the faster the
rate
o If you have more molecules the probability of collision
increases and the frequency of collision
o Higher temperature ( higher KE ) gives the molecules
higher energy and increases the number of
collisions(moving faster)
o However , not all collisions lead to reaction. Only a
small fraction of collisions lead to reaction
Activation Energy
 Arrhenius: molecules must possess a minimum amount of
energy to react. Why?
o To form products , bonds in the reactants must be
broken
o Breaking bonds requires energy
o Molecules moving too slowly, KE too low, do not react
 Activation energy, Ea is the minimum energy required to
start a reaction
o Ea varies with the reaction
 Consider the rearrangement of methyl nitrile to acetonitrile
o Energy is required to stretch the bond between the
methyl group and the nitrile group and to allow the
nitrile group to rotate
o The carbon carbon bond forms
o The energy associated with the molecule drops
o The energy level between the starting molecule and
the highest energy state found along the reaction
pathway is the activation energy.
 The chemical species at the top of the barrier is
the activated complex or the transition state
 The energy change for the reaction is the difference in
energy between the products and the reactants
o  Erxn has no effect on reaction rate
 The activation energy is the difference in energy between
the reactant and the activated complex.
o Rate depends on activation energy. The lower Ea , the
faster the reaction
 How does this relate to temperature
o At any particular temperature, molecules present
have an average kinetic energy associated with the
population
o In the same population , some molecules have more
energy than average , some have less.
 The fraction of molecules with energy equal to
or greater than Ea is given by f = e-Ea/RT
 As we increase temperature, f becomes larger
Orientation Factor
 Orientation has a major effect on whether or not a reaction
will occur
 Consider the reaction between NOCl and Cl
Cl + NOCl  NO + Cl2
 If the Cl collides with the Cl the reaction proceeds
 If the Cl collides with the O, no reaction occurs
Arrhenius Equation
 Arrhenius discovered that most reaction rate data obeys an
equation based on 3 factors
o Number of collisions per unit time
o Fraction of collisions with the correct orientation
o Fraction of molecules that have energy greater than
or equal to Ea
 lnk = -Ea/RT + ln A where k is the rate constant, Ea is the
activation energy, R is the gas constant(8.314J/Kmol) T is
the temperature in K
 A is the frequency factor. It is related to the frequency of
collision and the probability that the orientation will be
correct
 Both A and Ea are specific to a reaction
 Rearranging the equation we get lnk = -Ea/RT + lnA. Once
again , if you graph the lnk vs 1/T you get a straight line
with a slope –Ea/R
Reaction Mechanisms
 Balanced chemical equations provide information about
substances present at the beginning and end of a reaction
 The reaction mechanism is the process by which the
reaction occurs
Elementary Steps
 Any process that occurs in a single step
 The number of molecules present in an elementary step
gives the molecularity
o Unimolecular-one molecule
o Bimolecular- two molecules
o Termolecular- three molecules
 A multistep mechanism consists of a series of elementary
steps
o Elementary step must give a balanced reaction
o Some multistep reactions include intermediates
 Species that appear in an elementary step but
not as a product or reactant
 Intermediates are formed in one elementary
step and consumed in another
 They are not found in the balanced equation for
the reaction
Rate Laws for Multistep Reactions
 Rate laws of the elementary steps determine the overall rate
law
 Rate law of the elementary step is determined by
molecularity
o Uni- processes are first order
o Bi- processes are second order
o Ter- processes are third order
 Most reactions have more than one elementary step
o Often one step is much slower
o This step limits the reaction rate and governs the rate
law
Consider: NO2 + CO  NO + CO2
 The experimentally derived rate law is : rate = k[NO2]2
 A proposed mechanism is
o Step 1 : NO2 + NO2  NO3 + NO slow
o Step 2 : NO3 + CO  NO2 + CO2 fast
 Note NO3 is an intermediate
 The rate law for the slow step is rate = k[NO2]2
 This theoretical rate law is in agreement with the
experimental
 This supports(does not prove) a proposed mechanism
Mechanisms with an initial fast step
 Consider the reaction 2NO + Br2  2NOBr
 The experimentally determined rate is : Rate = k[NO]2 [Br2]
 Proposed Mechanism
o Step 1 : NO + Br2  NOBr2 fast
o Step 2 : NOBr2 + NO  2NOBr slow
o The theoretical rate law for the slow step is : rate = k2
[NOBr2] [NO]
 Problem: this rate law depends on the concentration of an
intermediate
o Intermediates are usually unstable and have
low/unknown concentrations
o We can express [NOBr2] in terms of NOBr and Br2
by assuming an equilibrium in Step 1
o In a dynamic equilibrium the e forward rate equals
the reverse rate
 Therefore we get k1 [NO] [Br2] = k-1[NOBr2]
 Rearranging : [NOBr2] = k1/k-1[NO] [Br2]
 Substituting in the rate law : rate = k2 k1/k2
1[NO] [Br2] [NO] = k[NO] [Br2]
 This is consistent with the experimental rate
law
Catalysis
 A catalyst is a substance that changes the rate of a reaction
without undergoing a permanent change
 There are 2 types of catalysts : homogeneous and
heterogeneous
Homogeneous Catalysts
 A catalyst that is present in the same phase as the reactants
 How do catalysts increase rates?
o By lowering the activation energy
o Increasing the number of collisions
o Catalysts provide a completely different mechanism
for reaction
Heterogeneous Catalysts
 A catalyst that exists in a different phase from the reactants.
Ie. Solid catalyst and gas reactants: the catalytic convertor on
a car