CHM 120
CHAPTER 16
KINETICS: Rates and
Mechanisms of Chemical
Reactions
Dr. Floyd Beckford
Lyon College
CHEMICAL KINETICS
• Two factors control the outcome of chemical
reactions:
1. Chemical Thermodynamics
2. Chemical Kinetics
• Chemical Kinetics: study of rates of chemical
reactions and mechanisms by which they occur
• A reaction may be spontaneous but does not
occur at measurable rates
REACTION RATES
•
Rate of reaction describes how fast
reactants are used up and products are formed
•
There are 4 basic factors that affect
reaction rates
(i) Concentration
(ii) Physical state
(iii) Temperature
(iv) Catalysts
• For every reaction the particles must come into
intimate contact with each other
• High concentrations by definition implies that
particles are closer together (than dilute
solutions)
• So rate increases with concentration
• The degree of intimacy of particles obviously
depends on the physical nature of the particles
• Particles in the liquid state are closer than in
the solid state
• Likewise, particles in a finely divided solid will
be closer than in a chunk of the solid
• In both situations, there is a larger surface
area available for the reaction to take place
• This leads to an increase in rate
• Temperature affects rate by affecting the
number and energy of collisions
• So an increase in temperature will have the
effect of increasing reaction rate
• Rate of reaction is typically measured as the
change in concentration with time
• This change may be a decrease or an increase
• Likewise the concentration change may be of
reactants or products
concentration change
Rate =
time change
in [products]
in [reactants]
Rate = ______________
= ______________
change in time
change in time
• Rate has units of moles per liter per unit time
- M s-1, M h-1
• Consider the hypothetical reaction
aA + bB  cC + dD
• We can write
Rate of = - 1 [A] = - 1 [B] =
a t
reaction
b t
1 [C] = 1 [D]
c t
d t
• Note the use of the negative sign
- rate is defined as a positive quantity
- rate of disappearance of a reactant is
negative
2N2O5(g)  4NO2(g) + O2(g)
Rate of = - 1 [N2O5] = 1 [NO2] =
reaction
2
4
t
t
[O2]
t
C2H4(g) + O3(g)
C2H4O(g) + O2(g)
• Rate may be expressed in three main ways:
1. Average reaction rate: a measure of the
change in concentration with time
2. Instantaneous rate: rate of change of
concentration at any particular instant during the
reaction
3. Initial rate: instantaneous rate at t = 0
- that is, when the reactants are first
mixed
RATE LAW
• Consider the following reaction
aA + bB  products
• Rate of reaction changes as concentration of
reactants change at constant temperature
• RATE LAW: equation describing the relationship
between concentration of a reactant and the rate
Rate = k[A]m[B]n
where k is called the rate constant
• m, n are called reaction orders
- they indicate the sensitivity of the rate to
concentration changes of each reactant
• NOTE: the orders have nothing to do with the
stoichiometric coefficients in the balanced
overall equation
• An exponent of 0 means the reaction is zero
order in that reactant - rate does not depend
on the concentration of that reactant
• An exponent of 1  rate is directly proportional
to the concentration of that reactant
- if concentration is doubled, rate doubles
- reaction is first order in that reactant
• An exponent of 2  rate is quadrupled if the
concentration of that reactant is doubled
- reaction is second order in that reactant
• The overall reaction order is the sum of all the
orders
Rate = k[A][B]0 m = 1 and n = 0
- reaction is first order in A and zero order
in B
- overall order = 1 + 0 = 1
- usually written: Rate = k[A]
• Remember: the values of the reaction orders
must be determined from experiment; they
cannot be found by looking at the equation
DETERMINATION OF THE RATE LAW
• The method of initial rates may be used
- involves measuring the initial rates as a
function of the initial concentrations
- avoids problems of reversible reactions
- initially there are no products so they
cannot affect the measured rate
• In this method the experiments are chosen so
as to check the effect of a single reactant on
the rate
THE RATE CONSTANT
1. The units of k depends on the overall order of
reaction
2. The value of k is independent of concentration
and time
3. The value refers to a specific temperature
and changes if we change temperature
4. Its value is for a specific reaction
THE INTEGRATED RATE EQUATION
• This is the equation that relates concentration
and time
• Consider a first-order reaction
aA  products
Rate = k[A]
conc. after
time = t
initial
conc.
ln
[A]t
[A]0
= -kt
time
[A]t
= -kt
log
2.303
[A]0
• The equation may be written in the form for a
linear plot
log [A]t
-kt
=
+ log [A]0
2.303
• A plot of log [A]t vs. t is linear plot with slope
= -k/2.303
• Note that this plot gives a straight line ONLY
if the reaction is first-order
Half-life
• The half-life, t1/2, is defined as the time it
takes for the reactant concentration to drop
to half its initial value
t1/2
= ln 2 = 0.693
k
k
• Note: the half-life for a first order reaction
does not depend on the initial concentration
• The value of the half-life is constant
Second order reactions
• Consider a reaction that is 2nd order in reactant
A and 2nd overall
aA  products and Rate = k[A]2
1 = kt + 1
[A]0
[A]t
• A plot of 1/[A]t vs. t gives a straight line with
slope = k
t1/2
1
=
k[A]0
RATES AND TEMPERATURE
• Recall that temperature is the only factor that
affects the rate constant
• In general rates increase with temperature
activation
energy
-(Ea/RT)
k = Ae
rate
constant
absolute
temperature
constant
(related to
collision frequemcy)
• This is ARRHENIUS’ EQUATION
• Can be arranged in the form of a straight line
ln k = (-Ea/R)(1/T) + ln A
• Plot ln k vs. 1/T  slope = -Ea/R
If T
increases
REACTION
SPEEDS UP
Ea/RT
decreases
k
increases
-Ea/RT
increases
e-Ea/RT
increases
• Another form of Arrhenius’ equation:
ln
k2
k1
=-
Ea
R
1 - 1
T2
T1
COLLISION THEORY: a reaction results when
reactant molecules, which are properly oriented
and have the appropriate energy, collide
• The necessary energy is the activation energy,
Ea
• Not all collisions leads to a reaction
• For effective collisions proper orientation of
the molecules must be possible
TRANSITION STATE THEORY
• During a chemical reaction, reactants do not
suddenly convert to products
• The formation of products is a continuous
process of bonding breaking and forming
• At some point, a transitional species is formed
containing “partial” bonds
• This species is called the transition state or
activated complex
• The transition state is the configuration of
atoms at the maximum of the reaction energy
diagram
• The activation energy is therefore the energy
needed to reach the transition state
• Note also that the transition state can go on
to form products or break apart to reform the
reactants
REACTION MECHANISMS
• MECHANISM: the step-by-step pathway by
which a reaction occurs
• Each step is called an elementary step
NO2(g) + CO(g)  NO(g) + CO2(g)
Mechanism:
NO2(g) + NO2(g)  NO(g) + NO3(g)
NO3(g) + CO(g)  NO2(g) + CO2(g)
• NO3 is a reaction intermediate
• Elementary reactions are classified by the
molecularity
A  B + C
unimolecular
A + B  C + D
bimolecular
A + 2B  E
termolecular
• Termolecular reactions are very unlikely
• For ANY SINGLE ELEMENTARY
REACTION – reaction orders are equal to the
coefficients for that step
A + B
kelem
C + D
Rate = kelem[A][B]
• The slow step is called the rate-determining
step (RDS)
• A reaction can never occur faster than its
slowest step
1. Overall reaction = sum of all elementary steps
2. The mechanism proposed must be consistent
with the rate law
NO2(g) + NO2(g)
NO3(g) + CO(g)
NO2(g) + CO(g)
k1
k2
NO(g) + NO3(g)
NO2(g) + CO2(g)
NO(g) + CO2(g)
• There may be more than one plausible
mechanism
• The experimentally determined reaction orders
indicate the number of molecules of the reactants
- in the RDS (if it occurs first)
- the RDS and any fast steps before it
CATALYSIS
• Reaction rates are also affected by catalysts
• Catalyst: a substance that increases the rate of
a reaction without being consumed in the reaction
• Catalysts work by providing alternative pathways
that have lower activation energies
•A catalyst may be homogeneous or heterogeneous
• Homogeneous: catalyst and reactants are in the
same phase
2Ce4+(aq) + Tl+(aq)
Mn2+
2Ce3+(aq) + Tl3+(aq)
• Heterogeneous: catalyst in a different phase
• Typically: a solid in a liquid
• An important example: catalytic converters in
automobile
- convert pollutants to CO2 H2O, O2, N2
- usually Pt, Pd, V2O5, Cr2O3, CuO
• Cars must use unleaded fuels – lead poisons the
catalytic bed