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Chemical Kinetics
The study of rates of chemical reactions,
the factors that affect the rates, and the
sequence of steps by which a reaction
occurs.
In some situations, it is important that reaction rates are very fast.
An airbag will deploy in 1/25 of a second.
Some reactions occur very slowly over time such as the
reaction of pigments and varnish with light and
pollutants in the air paintings are exposed to.
Some reactions are so slow
that for all intents and
purposes, the reactants are
completely stable and no
reaction takes place. For
example, the combustion of
diamond is a spontaneous
process at room temperature,
but a diamond will remain
stable in air at room
temperature for what seems
like forever. The combustion
of diamond is said to be
kinetically stable but
thermodynamically
unstable.
Rate – How much something changes in a unit of time.
Rate of Rxn – Change in concentration per unit of time.
A + B  C + D
Rate = Rate of Disappearance = _ [A]2 - [A]1 = _ ∆[A]
t2 – t1
∆t
Rate = Rate of Appearance =
[ ] = concentration = M
t = time ( s = seconds)
M s-1 = M/s
[C]2 - [C]1 =
t2 – t1
∆[C]
∆t
Calculate the rate of reaction in M/s for the
reaction below where the concentration of
B is initially 0.35M and 10 minutes later the
concentration of B is 0.10M.
A + B  C + D
The stoichiometry dictates the relationship between the rates of
appearance and disappearance for each reactant or product.
aA
+
bB

cC
+
dD
General Rate of Rxn : An overall rate for the entire reaction. The
general rate has the same value regardless of which reactant or
product we investigate because it considers the stoichiometric
relationship between reactants and products.
rate of disappearance of reactant or
of formation of product
General rate of reaction =
stoichiometric coefficient of that reactant
or product in the balanced equation
General Rate = _ 1 ∆[A] = _ 1 ∆[B] = 1 ∆[C] = 1 ∆[D]
a ∆t
b ∆t
c ∆t
d ∆t
General Rate = _ 1 ∆[A] = _ 1 ∆[B] = 1 ∆[C] = 1 ∆[D]
a ∆t
b ∆t
c ∆t
d ∆t
The decomposition of N2O5 proceeds as follows:
2N2O5  4 NO2 +
O2
If the rate of decomposition of N2O5 at a particular
instant in a reaction vessel is 4.2 x 10-7 M/s, what is
the rate of appearance of NO2? O2? What is the
general rate for this reaction?
NO2 = 8.4 x 10-7M/s O2 = 2.1 x 10-7 M/s
If the rate of consumption of H2O2 is 4.6 M/h, then …
… the rate of formation of H2O must also be 4.6 M/h, and …
… the rate of formation of O2 is 2.3 M/h
Measuring Reaction Rates
 In general, the greater the concentration of a reactant,
the faster the reaction goes.
 When we calculate change in concentration over change
in time, we calculate the average rate of reaction. At the
beginning of a time interval for a reaction, rate is faster
and the end rate is slower.
 The rate of reaction at a given point in time is an
instantaneous rate of reaction.
 The instantaneous rate of reaction at the beginning of a
reaction is called the initial rate of reaction.
Average vs. Instantaneous Rate
Instantaneous rate is
the slope of the
tangent to the curve
at a particular time.
We often are interested
in the initial instantaneous rate; for the initial
concentrations of
reactants and products
are known at this time.
Collision Theory
• Collisions are vital for chemical change, either to
provide the energy required for a particle to
change (a bond to break) and/or to bring the
reactants into contact. (As particles approach
each other there is a repulsion of the electron
clouds of the particles.)
• Activation Energy (Ea) – the minimum amount
of energy required in a collision to allow a
reaction to take place.
Collision Theory
In order to react, the two colliding particles
must:
• Collide with each other
• Must collide with enough energy to
overcome the activation energy of the
reaction
• Must collide with the correct geometrical
alignment - the reactive parts of the
molecule must come in contact in the correct
way. (This is often called the steric factor and
is very important in large organic molecules)
Importance of Orientation
One hydrogen atom
can approach another
from any direction …
Effective collision; the
I atom can bond to the
C atom to form CH3I
… and reaction will still occur; the
spherical symmetry of the atoms means
that orientation does not matter.
Ineffective collision;
orientation is important
in this reaction.
Any factor that either increases the frequency of the
collisions or increases the energy with which they
collide will make the reaction go faster.
Factors mainly affecting
the number of collisions
Factors mainly affecting
the proportion of
collisions with the
required Ea
Concentration/Pressure
(for gases)
Temperature
Surface Area
Catalyst
Grain Silo Explosion
1977 Mineapolis
Grain Elevator
Explosion
The rate of reaction between
two reactants, A & B, can be
followed experimentally. The
rate will be found to be
proportional to the
concentration of A raised to
some power and also to the
concentration of B raised to
a power.
Rate Law (Rate Expression)- Shows how the concentration
of reactants affect the rate of the reaction.
Rate of Reaction = k [Reactant 1]m [Reactant 2]n
k = rate constant: the constant of proportionality
The value of K changes with changing temperature.
Reaction Order – The power to which the concentration of a
reactant is raised in a rate law.
m & n = reaction orders for reactants – these are
determined by examining experimental
data. If no number is shown, m & n = 1.
The sum of m + n = the overall reaction order.
The order of reaction and the rate law can only be
determined using experimental data.
To determine reaction order, examine experimental data:
IF:
Rate does not change with changing concentration:
Rxn Order = 0
IF:
Rate doubles with double in concentration, triples with triple
concentration, etc. In other words, the changes in concentration
produce proportional changes in rate:
Rxn Order = 1
IF:
Doubling concentration increases rate by factor of 22 = 4 or
tripling increases rate by 32 = 9 and so on, in other words, the
changes in concentration produce exponential changes in rate:
Rxn Order = 2
Method of Initial Rates
• The method of initial rates is a method of establishing
the rate law for a reaction—finding the values of the
exponents in the rate law, and the value of k.
• A series of experiments is performed in which the initial
concentration of one reactant is varied. Concentrations
of the other reactants are held constant.
• When we double the concentration of a reactant A, if:
– there is no effect on the rate, the reaction is zero-order
in A.
– the rate doubles, the reaction is first-order in A.
– the rate quadruples, the reaction is second-order in A.
– the rate increases eight times, the reaction is thirdorder in A.
The concentration of
NO was held the
same in Experiments
1 and 2 …
… while the
concentration of
Cl2 in Experiment
2 is twice that of
Experiment 1.
The rate in Experiment 2 is
twice that in Experiment 1,
so the reaction must be first
order in Cl2.
Which two experiments are
used to find the order of the
reaction in NO?
How do we find the value of k
after obtaining the order of the
reaction in NO and in Cl2?
O Order Rxn:
The rate of reaction does not depend on
concentration of reactant but rather some
other factor such as the absorption of light or
the amount of surface area a reactant has.
Rate Law: Rate = K
1st Order Rxn:
Rate depends on the concentration of a
single reactant raised to the 1st power.
Rate Law: Rate = k[A]
K = Rate = mol dm-3 s-1 = s-1
[A]
mol dm-3
2nd Order Reaction:
Rate depends on the reactant concentration
raised to the second power or on the
concentrations of two different reactants,
each raised to the first power.
Rate Law: Rate = k[A]2 or k[A][B]
K = rate = mol dm-3 s-1 = dm3 mol-1 s-1
[A]2 (mol dm-3)2
3rd Order Reaction
Rate depends on the concentration of one
reactant raised to the second power and
the concentration of another reactant
raised to the first power.
Rate = k[A]2[B] or rate = k[A][B]2
K = rate = mol dm-3 s-1 = dm6 mol-2 s-1
[A]2[B]
(mol dm-3)3
The following data were measured for the
reaction of nitric oxide with hydrogen:
[NO](M) [H2] (M) Initial Rate
Exp. #
(M/s)
1
0.10
0.10
1.23 x 10-3
2
0.10
0.20
2.46 x 10-3
3
0.20
0.10
4.92 x 10-3
a. Determine the rate law for this reaction.
b. Calculate the rate constant.
c. Calculate the rate when [NO] = 0.050M and[H2] = 0.150M.
Example 13.3
For the reaction 2 NO(g) + Cl2(g)  2 NOCl(g)
described in the text and in Table 13.2,
(a) what is the initial rate for a hypothetical Experiment
4, which has [NO] = 0.0500 M and [Cl2] = 0.0255 M?
(b) What is the value of k for the reaction?
Half Life t(1/2)
Half life is the time it takes for the
concentration of a reactant to fall to half its
initial value.
By viewing a graph of time vs.
concentration the half life for a reaction
can be determined and this allows us to
determine the order of the reaction.
Half Life
Each t(1/2)
t(1/2)
Zero Order
is half the preceding t(1/2)
First Order
Constant half-life = t(1/2)
Second Order
Each t(1/2) is double the preceding t(1/2)
Shown here are graphs of [A] versus time for two
different experiments dealing with the reaction
A  products. What is the order of this reaction?
The first order rate constant for the decomposition
of a certain insecticide in water at 12°C is 1.45/yr.
A quantity of this insecticide is washed into a lake
on June 1, leading to a concentration of
5.0 x 10 –7g/ml of water. Assume that the average
temperature of the lake is 12°C.
What is the concentration of the insecticide on
June 1st of the following year?
How long will it take for the concentration of the
insecticide to drop to 3.0 x 10 –7g/cm3?