Rates of Reactions

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Chapter 14

• Rates of Reactions
• Kinetics

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I. Introduction
A) Demonstrations
B) Chemical Kinetics is the study of the rates
(speeds) of chemical reactions and the mechanisms
of chemical reactions.
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C) The rate of a chemical reaction is a measure
of how fast reactants are consumed and/or how
fast products are made.
D) The mechanism of a reaction is a detailed
description of the way a reaction occurs. It is a
sequence of elementary steps which lead from
reactants to products.
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Mechanisms can be proven wrong through
_____________, but they can never be called
_________________________ since they
are, in general, educated guesses.
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Practical reasons for studying kinetics Some
reactions we would like to speed up drug
delivery, paint drying, destruction of air
pollutants in auto exhaust breakdown of materials
in landfills.
Some reactions we would like to slow down
food decay, rubber decay, human aging,
destruction of the ozone layer, rusting, corrosion
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E) Some reactions take place in a fraction of a
second and other take many years. What variables
affect the reaction rate?
1) The characteristics of the reactants and the
products.
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2) The concentration of the reactants in some
reactions the rate is unaffected by the
concentration of one of the reactants as long as
it is there in some amount.
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3) The presence of a catalyst, a substance that
4)The temperature at which the reaction occurs.
Increasing the temperature usually increases the
rate. A general rule is
5) The surface area of a solid reactant or
catalyst affects the rate.
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G) Reaction rate is the increase in molar
concentration of product of a reaction per unit
time or the decrease in molar concentration of a
reactant per unit time.
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For example, for the reaction 2 N2O5 ? 4 NO2
O2 The following table shows the concentration of
N2O5 as a function of time at 45 oC.
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Time in min N2O5 mol/L
0 0.01756
20 0.0093
40 0.00531
60 0.00295
80 0.00167
100 0.00095
160 0.00014
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1) The rate of reaction can be written in the
form
2) Usually the rate is a rapidly changing
quantity, as the reaction proceeds the reactants
are used up and there remains less and less
material to undergo reaction.
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3)Generally we obtain for a reactant a curve
which resembles the one below.
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If we take the first 2 points from the table
above, we can find as avg. rate of decomposition
of N2O5.
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You should be able to see that the avg. rate is
decreasing, hence the curve.
Even though we obtain a negative value for the
rate, since N2O5 is decreasing, rates are
reported as positive values.
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Look at the graph again,
And make the time interval smaller and smaller,
we can obtain an instantaneous rate.
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The instantaneous rate is equal to the slope of
the line at that point. Calculus??? To what is
the slope of the line at that point equal?
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4) How is data obtained for a concentration curve?
a) Monitor a color change.
b) Measure pressure if a gas is produced.
c) Monitor a change in pH if an acid or base
reaction.
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5) A look at the change in rate over time for
another reaction 2 NO2(g) ? 2 NO(g) O2(g) at
300oC
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H) What does the balanced equation tell us about
rates? The equation we will look at is H2 (g)
I2 (g) ----gt 2 HI(g) H2 and I2 must disappear
at the same rate since 1 molecule of H2 reacts
with 1 molecule of I2.
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In the same amount of time, 2 molecules of HI
must appear. The rate of appearance of HI must
equal twice the rate of disappearance of H2 (g)
and I2 (g).
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The rate of disappearance of H2(g) the rate of
disappearance of I2(g) ½ the rate of appearance
of HI.
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In general, for the equation aA bB -----gt cC
dD To obtain a rate equation of the rates of
the substances in relation to each other we
divide through by the coefficients.
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But we usually want the first reagent in terms of
all the others, so we multiply by the coefficient
of the first reagent.
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II. The Rate Law (Rate expression), Rate Constant
Order of Reaction
A) The following equation has been studied in the
gaseous state and the data at 250 K may be
summarized as follows
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F2(g) 2 ClO2(g) ---gt 2 ClO2F(g)
B) From this data the answers to the following
questions can be obtained
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1) What is the rate law of the reaction?
2) What is the order of the reaction?
3) What is the value of the rate constant k?
4) What is the rate of formation of ClO2F when
F2is 0.010 mol/L andClO2 is 0.020 mol/L?
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C) What is a rate law? 1) In 1864 it was
discovered that the rate of a reaction is
proportional to some power of the concentration
of reactants at constant temperature.
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2) In general, for the equation aA
bB ? cC dD
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rate law rate equation rate expression
k is the specific rate constant which is
independent of concentration.
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k depends on the nature of the reactants fast
reactions have large k's and slow reactions have
small k's ordinarily k ________________
with temperature.
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THE EXPONENTS x AND y MUST BE EXPERIMENTALLY
DETERMINED.
They are not automatically obtained from the
balanced equation.
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Some experimentally determined rate laws for
equations are as follows a) 2 N2O5 (soln) ? 2
N2O4 (soln) O2 (g)
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Notice that the exponent is NOT 2, the
coefficient in the balanced equation, but has
been experimentally determined to be 1.
The reaction order with respect to a given
species equals the exponent of the concentration
of that species in the rate law as determined
experimentally.
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The order of the above reaction with respect to
N2O5 is 1.
The order of a reaction is the sum of the
exponents of the reactants in a rate law.
The order of the above reaction, since 1 is the
only exponent, is 1 as well. It is a first order
reaction.
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This means that when we double the concentration
of N2O5, we double the rate of reaction OR if we
halve the concentration, we halve the rate.
b) For the reaction 2 NO O2 ? 2 NO2
What is the situation here?
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D) The answers to the questions then are obtained
in the following manner.
The rate law for
F2(g) 2 ClO2(g) ---gt 2 ClO2F(g)
will look like the following.
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Your job is to find the values of x and y from
the experimental data.
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You need to do two division problems to find x
and y.
What is the order of the reaction with respect to
F2? _______
What is the order of the reaction with respect to
ClO2? ______
What is the overall order of the reaction?
__________
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To find k, the rate constant, we take the
experimentally determined rate law, put the data
in from one of the experiments and solve for k.
The units of k are important.
k _________________
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To find the rate of formation of ClO2F when F2
is 0.010 M and the ClO2 is 0.020 M, we need to
look at the relationship between the rate of
formation of ClO2, and the rate of
disappearance of F2.
Rate __________________________
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Transparency in class problem collect it
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IV. A graphical method is often used to show the
order of a reaction, or from a graph we can
obtain the order of a reaction.

1. For the general reaction of A ---gt products
2. If the reaction is first order, we can write

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When we divide both sides by A and multiply
both sides by dt we obtain the following
Those of you who have had calculus should
recognize this as
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Which can be changed to the following in log to
the base 10.
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The above equations can be rewritten in a more
familiar form.
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THIS MEANS THAT IF WE PLOT ln A vs. t AND
OBTAIN A STRAIGHT LINE THE RATE IS FIRST ORDER.
Or plot log A vs. t.
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Slope of the line is -k/2.303. The rate constant
k then is to -slope of the line times 2.303.
If we plot lnA vs.time then the slope of the
line is equal to -k.
C) Half-life - t½ is the time required for half
of the original concentration of the limiting
reactant to be consumed.
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Half-life is _________________ to the rate
constant k.
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A fast reaction with a large k has a
_________________ half-life, a slow reaction with
a small k has a ___________________ half-life.
D) For the reaction A ----gt B C We obtain
the following data.
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Prove that the reaction is first order in A.
Calculate the half-life of the reaction, t½.
What is our criterion for a first order reaction?
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We make the following table.
When we plot log A vs. t we obtain a
_________________, therefore the reaction is
first order.
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The equation for the line is
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V. Second order reaction for a single reactant A)
A ----gt products B) The rate law is rate
kA2 C) The integrated form of the rate law
gives us the following
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D) A straight line is obtained with slope ____.
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E) This means that we can tell the difference
between a first order and second order reaction
by ________________________________.
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G) The half-life of a second order reaction
depends on the initial concentration of the
reactant as can be seen from the following
derivation
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H) When we compare this to the formula for the
half-life of a first order reaction, we notice
that the t½ for the first order reaction is
__________________of the initial concentration of
the reactant.
The t½ for the second order reaction is
________________________to the initial
concentration of the reactant.
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I) The following equations will be given to you
on an exam or quiz for you to apply to questions
in an appropriate manner.
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VI. Collision Theory A)Consider the elementary
process A2(g) B2(g) ---gt 2AB
B) Collision theory assumes that for gas
molecules to react they must collide.
C) Binary collisions per unit time at room
temperature and 1 atm pressure are extremely
large, approx. 1 x 1031 collisions per Liter-sec.
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D) With this many collisions, why isn't there an
immediate explosion when we put H2(g) and O2(g)
together in a balloon?
E) Why isn't every collision an effective
collision i.e. one that gives product?
F) For a reaction to occur reactant molecules
must collide with an energy greater than some
minimum value and with the proper orientation.
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G) The minimum energy of collision required for
two molecules to react is called the activation
energy, Ea. The value of Ea depends on a
particular reaction.

H) Effect of temperature
1) The rates of almost all chemical
reactions_________ when T is raised. Generally
speaking for a _________ increase, the reaction
rate ________.
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2) What is the relationship between temperature
and collision theory?
a) Approx. ___ of the reaction rate increase due
to an increase in temperature is accounted for by
the increase in the number of___________.
b) Approx. ____of the reaction rate increase is
accounted for by the increase in the number of
high energy _______________.
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3) Recall our graph of the number of molecules
vs. speed in a gas sample.
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J) Arrhenius in 1889 proposed the following
equation which relates the rate constant k to the
temperature
where k is the rate constant from the rate
equation ( rate kA)
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A is the frequency factor (the collision factor
and the orientation factor) .
e is the base of the natural logarithms 2.718
Ea is the activation energy in Joules per mole.
R is the molar gas constant, 8.3143 J/K mol.
T is the temperature in Kelvins.
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J) The most valuable use for this equation is in
determining the activation energy of a reaction
from rate experiments at different temperatures.
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L) Ea is best obtained graphically.
This is of the form y mx b
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If we plot the log of k vs 1/T we obtain the
slope of the line which is equal to - Ea/ 2.303
R. then Ea - 2.303 R slope.
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L) The equation can be used to compare rates at
various temperatures when Ea is known, OR the Ea
can be obtained from a comparison of two sets of
rate data. r1 k1 Ax at T1 r2 k2 Ax at T2
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We divide equation 1 by equation 2, take the log
of both sides, and substitute for log k
Ea/2.303RT. This should give
We remove the negative sign and we get the
equation which we will use and which will be
given to you on the exam or quiz.
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1) An example The activation energy for the
reaction involved in the souring of raw milk is
75 kJ. Milk will sour in about 8 hours at 21oC
(room temp-70oF). How long will raw milk last in
a refrigerator at 5oC?
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2) The gas phase reaction between methane and
diatomic sulfur is given by the equation CH 4(g)
2 S2(g) ---gt CS2(g) 2 H2S(g) At 550 oC the
rate constant, k1, for the reaction is 1.1 L/mol
sec. At 625 oC the rate constant, k2, is 6.4
L/mol sec. What is the activation energy of this
reaction?
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N) Transition State Theory 1) The hypothetical
elementary process of A2 B2 --gt 2 AB can be
represented as the following
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is an activated complex. It is a transition state
species that __________________________.
In the past, these could not be detected only
postulated. Now with laser technology we can
detect species which exist for only a femto
second(1x10-15), and evidence for the existence
of some intermediates is available.
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2) We can graph the potential energy changes
which occur during the course of a reaction.
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3) We have shown reactions in which DH is -
(negative). The reactions are exothermic. DHrxn
Eaf - Ear
4) Potential energy diagrams are helpful in
visualizing why it is that highly exothermic
reactions can be very slow. If Ea is large then
__________________ .
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VII. The mechanism of a reaction A) The
mechanism of a reaction is the detailed pathway
followed when reactants are converted to products.

• B) It must agree with
• ____________________ .
• ____________________ .
• ____________________ .

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C) What do we mean by the rate determining step?
Let's look at a factory where toasted corn puffs
are made.
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What is the rate determining step? ___
How fast can the factory produce packages of corn
puffs with a prize? _________________
What does the factory need to do to improve the
rate of production? __________________
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D) For the reaction 2 NO F2 ---gt 2
NOF nitric oxide plus fluorine gives nitrosyl
fluoride
1) The experimentally determined rate law is
rate k NOF2
2) A mechanism is proposed on the basis of the
rate equation and other information gained from a
study of similar reactions over a period of
years.
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3) Remember that the mechanism is ___ .
4) A suggested mechanism for this reaction is
NO F2 --gt NOF F (slow step) NO F --gt NOF
(fast step)

• The sum of these two reactions gives
• NO F2 F --gt 2 NOF F
• Subtracting F from both sides gives the

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5) The rate determining step is the _____ .
6) Each step is an elementary reaction and the
rate equation can be written directly from a
_________________ elementary reaction.
7) The rate law of our reaction is rate k
NOF2. The proposed mechanism satisfies the
requirements ___________ ________________________
__________ .
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E) Let's look at another equation its
experimentally determined rate law and the
proposed mechanism to see if they are in
agreement. 2 O3 --gt3 O2
1) The experimentally determined rate law is
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2) The proposed mechanism is
The rate of the overall reaction is simply the
rate of step ______ .
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Rate k2O3O
There is a problem. We do NOT report rate laws
with the concentrations of species which are not
in the _________ .
How can we convert Rate k2O3O to
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3) We need to use a combination of knowledge from
chemistry and algebra to change one rate law to
another.
The chemical knowledge we bring to the situation
is that at equilibrium, since both step 1 and
step 2 are fast and 2 is the reverse of 1 we will
make their rates equal.
k1O3 k-1O2O
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Then we can use algebra to solve for O, since
that is what we want to __________
We can then substitute this relationship of O
into the rate law we obtained from ____________
to obtain
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F) Catalysts 1) The rates of many reactions are
increased by the presence of a catalyst, a
substance which increases the rate of reaction
without being consumed by it.
2) How is this possible?
3) NO (nitric oxide) catalyzes the decomposition
of O3. The following mechanism is proposed for
this reaction
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What should you notice about NO?
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4) A catalyst acts by making available a new
reaction mechanism with a lower activation
energy, Ea.
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Sometimes is orients the molecules for a
successful collision, for example the
lock and key model mechanism of enzymes.
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Other times it provides an alternate pathway for
the reaction.The depletion of ozone in the
stratosphere by Cl atoms provides an example of
the lowering of activation energy by a catalyst.
The uncatalyzed reaction has such a large
activation energy as can be seen from the
following diagram that its rate is extremely slow.
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VIII. Review - Factors which affect the rate of
reaction A) Nature of the reactants -
B) Concentration -
C) Temperature -
D) Catalysts -
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THE END