2. Objectives & Concepts
See the following Learning
Objectives on pages 712.
Understand these Concepts:
16.1-3, 16.5-15
Master these Skills:
16.2-6, 16.8
6. Expressing the Reaction Rate
reaction rate - changes in the concentrations of reactants or
products per unit time
reactant concentrations decrease while product concentrations
increase
A
for
rate of reaction = -
B
change in concentration of A
change in time
-
(conc A)
t
=-
conc A2-conc A1
t2-t1
8. Table 16.1
Concentration of O3 at Various Times in
its Reaction with C2H4 at 303 K
Concentration of O3
Time (s)
(mol/L)
0.0
3.20x10-
10.
0
20.0
5
2.42x105
1.95x10-
30.0
5
1.63x10-
40.0
5
1.40x10-
50.0
5
1.23x10-
60.0
5
1.10x105
[C2H4]
rate = t
=-
[O3]
t
9. Figure 16.5 - Three types of reaction rates for the
reaction of O3 and C2H4.
10. Figure 16.6A Plots of [reactant] and [product]
vs. time.
C2H4 + O3 → C2H4O + O2
[O2] increases just as fast as
[C2H4] decreases.
Rate = =
[C2H4]
t
[C2H4O]
t
==
[O3]
t
[O2]
t
11. Figure 16.6B
Plots of [reactant] and
[product] vs. time.
H2 + I2 → 2HI
[HI] increases twice as
fast as [H2] decreases.
Rate = -
Rate =
[H2]
t
[IH]
t
=-
= -2
[I2]
t
[H2]
t
=1
2
= -2
[HI]
t
[I2]
t
The expression for the rate of a
reaction and its numerical value
depend on which substance serves as
the reference.
12. Factors That Influence Reaction
Rate
Particles must collide in order to react.
The higher the concentration of reactants, the greater
the reaction rate.
The physical state of the reactants influences reaction
rate.
A higher concentration of reactant particles allows a greater
number of collisions.
Substances must mix in order for particles to collide.
The higher the temperature, the greater the reaction
rate.
At higher temperatures particles have more energy and therefore
collide more often and more effectively.
13. Figure
16.3
The effect of surface area on
reaction rate.
A hot steel nail glows
feebly when placed in O2.
The same mass of steel
wool bursts into flame.
14. Collision Theory and
Concentration
The basic principle of collision theory is that particles must
collide in order to react.
An increase in the concentration of a reactant leads to a larger
number of collisions, hence increasing reaction rate.
The number of collisions depends on the product of the
numbers of reactant particles, not their sum.
Concentrations are multiplied in the rate law, not added.
15. Figure 16.13 - The number of possible collisions is
the product, not the sum, of reactant
concentrations.
add another
6 collisions
4 collisions
add another
9 collisions
16. Temperature and the Rate
Constant
Temperature has a dramatic effect on reaction rate.
For many reactions, an increase of 10 C will double or triple
the rate.
Experimental data shows that k increases exponentially as T
increases. This is expressed in the Arrhenius equation:
k = Ae -Ea/RT
Higher T
larger k
k = rate constant
A = frequency
factor
Ea = activation
energy
increased rate
17. Activation Energy
In order to be effective, collisions between particles must
exceed a certain energy threshold.
When particles collide effectively, they reach an activated state.
The energy difference between the reactants and the activated
state is the activation energy (Ea) for the reaction.
The lower the activation energy, the faster the reaction.
Smaller Ea
larger f
larger k
increased rate
18. Figure 16.15Energy-level diagram for a reaction.
Collisions must occur with
sufficient energy to reach
an activated state.
This particular reaction is
reversible and is exothermic in
the forward direction.
19. Temperature and Collision Energy
An increase in temperature causes an increase in the kinetic
energy of the particles. This leads to more frequent collisions
and reaction rate increases.
At a higher temperature, the fraction of collisions with sufficient
energy equal to or greater than Ea increases. Reaction rate
therefore increases.
20. Figure 16.16 The effect of temperature on the
distribution of collision energies.
21. Molecular Structure and Reaction
Rate
For a collision between particles to be effective, it must have both
sufficient energy and the appropriate relative orientation
between the reacting particles.
The term A in the Arrhenius equation is the frequency factor for
the reaction.
k = Ae -Ea/RT
A = pZ
p = orientation probability factor
Z = collision frequency
The term p is specific for each reaction and is related to the
structural complexity of the reactants.
22. Figure 16.18The importance of molecular orientation to
an effective collision.
NO(g) + NO3(g) → 2NO2(g
There is only one relative
orientation of these two
molecules that leads to
an effective collision.
23. Transition State
Theory
An effective collision between particles leads to the formation of a
transition state or activated complex.
The transition state is an unstable species that contains partial
bonds. It is a transitional species partway between reactants and
products.
Transition states cannot be isolated.
The transition state exists at the point of maximum potential
energy.
The energy required to form the transition state is the
activation energy.
24. Figure 16.19 - The transition state of the reaction
between BrCH3 and OH-.
BrCH3 + OH- → Br- + CH3OH
The transition state contains partial bonds (dashed)
between C and Br and between C and O. It has a trigonal
bypyramidal shape.
25. Figure 16.20 - Depicting the reaction between BrCH3 and
OH-.
26. Figure 16.21 - Reaction energy diagrams and possible
transition states for two reactions.
27. Catalysis: Speeding up a
Reaction
A catalyst is a substance that increases the reaction rate without
itself being consumed in the reaction.
In general, a catalyst provides an alternative reaction pathway that
has a lower total activation energy than the uncatalyzed
reaction.
A catalyst will speed up both the forward and the reverse reactions.
A catalyst does not affect either H or the overall yield for a
reaction.
28. Figure 16.23 - Reaction energy diagram for a catalyzed
(green) and uncatalyzed (red) process.
29. Figure 16.24 - The catalyzed decomposition of H2O2.
A homogeneous catalyst is in the same phase as the reaction.
A small amount of NaBr is
added to a solution of
H2O2.
Oxygen gas forms quickly as Br-(aq)
catalyzes the H2O2 decomposition; the
intermediate Br2 turns the solution
orange.
31. Rate Law Expression
The rate law expression must be
determined experimentally. They
cannot be written down by merely
looking at the balanced chemical
equation.
32. Rate Law Expression
For the reaction
aA + bB ----->
Rate = k[A]m[B]n
cC
+
dD
where:
k = specific rate constant
m = order of the reaction with respect
to A
n = order of the reaction with respect
to B
n+m = overall order of the reaction
33. Reaction Orders
A reaction has an individual order “with respect to” or “in” each
reactant.
For the simple reaction A → products:
If the rate doubles when [A] doubles, the rate depends on [A]1 and
the reaction is first order with respect to A.
If the rate quadruples when [A] doubles, the rate depends on [A]2
and the reaction is second order with respect to [A].
If the rate does not change when [A] doubles, the rate does not
depend on [A], and the reaction is zero order with respect to A.
34. Figure 16.7 Plots of reactant concentration, [A], vs.
time for first-, second-, and zero-order
reactions.
35. Figure 16.8 Plots of rate vs. reactant concentration,
[A], for first-, second-, and zero-order
reactions.
36. Table 16.5
An Overview of Zero-Order, First-Order,
and Simple Second-Order Reactions
Zero Order
First Order
Second Order
Rate law
rate = k
rate = k[A]
rate = k[A]2
Units for k
mol/L·s
1/s
L/mol·s
Half-life
[A]0
2k
Integrated rate law
in straight-line form
[A]t = -kt + [A]0
ln[A]t = -kt + ln[A]0
Plot for straight line
[A]t vs. t
ln[A]t vs. t
Slope, y intercept
-k, [A]0
-k, ln[A]0
ln 2
k
1
k[A]0
1
1
= kt +
[A]t
[A]0
1
vs. t
[A]t
k, 1
[A]0
37. Rate Law Expression
For the reaction
2N2O5(g) -----> 4NO2(g) +
O2(g)
Experimentally it was determined
Rate = k[N2O5]
The reaction is ____order in N2O5
and _____order overall.
38. Rate Law Expression
For the reaction
(CH3)3CBr(aq) + OH-(aq) ----->
(CH3)3COH(aq) + Br-(aq)
Experimentally it was determined
that the
Rate = k[CH3)3CBr]
The reaction is ___order in
(CH3)3CBr , ____order in OH- and
___order overall.
39. Rate Law Expression
For the reaction
2NO(g) + O2(g) -----> 2NO2(g)
It was experimentally determined
that
Rate = k[NO]2[O2]
The reaction is ____order in NO ,
___order in O2 and _____order
overall.
40. Sample Problem 16.2 Determining Reaction Order from Rate Laws
PROBLEM:
For each of the following reactions, determine the reaction order
with respect to each reactant and the overall order from the
given rate law.
(a) 2NO(g) + O2(g)
(b) CH3CHO(g)
2NO2(g); rate = k[NO]2[O2]
CH4(g) + CO(g); rate = k[CH3CHO]3/2
(c) H2O2(aq) + 3I-(aq) + 2H+(aq)
I3-(aq) + 2H2O(l); rate = k[H2O2][I-]
PLAN: Look at the rate law and not the coefficients of the chemical reaction.
SOLUTION:
(a) The reaction is 2nd order in NO, 1st order in O2, and 3rd order overall.
(b) The reaction is 3/2 order in CH3CHO and 3/2 order overall.
(c) The reaction is 1st order in H2O2, 1st order in I- and zero order in H+,
while being 2nd order overall.
41. Experimental Determination of the
Rate Law
The order of the reaction for each
reactant can be determined by
changing individually the
concentration of each reactant and
observing the new rate of the
reaction.
42. Experimental Determination of the
Rate Law
Order
Rate
0
1
2
3
4
Change [A]
x2
x2
x2
x2
x2
Change in
0
x2
x4(22)
x8(23)
x16(24)
43. Example
The following rate data were obtained
at 25oC for the following reaction.
Determine the rate law expression and
the specific rate constant for the
reaction.
2A(g) + B(g) -----> 3C(g)
Experiment [A]o
[B]o
RateM/s
1
0.10M
0.10M 2.0x10-4
2
0.20M
0.10M 4.0x10-4
3
0.10M
0.20M 2.0x10-4
44.
45.
46. Example
The following data were obtained
for the following reaction at 25oC.
Determine the rate law and the
specific rate constant for the
reaction.
50. Example
For a reaction having the rate law
expression
Rate = k[A][B]
fill in the blanks of the following
data sheet.
Exp.
[A]
[B]
Rate(Ms-1)
1
0.20M
0.050M
4.0x10-3
2
3
_____
0.40M
0.050M
_____
1.6x10-2
3.2x10-2
51.
52. Example
For the reaction
2A(g) + 3B(g) ---> C(g) + 2D(g)
fill in the blank for the following
table
Exp.
[A]o
[B]o
Rate(M/s)
1
2
3
4
0.10M
0.20M
0.10M
_____
0.10M
0.10M
0.20M
0.30M
2.0x10-3
8.0x10-3
4.0x10-3
24x10-3
53.
54. The Integrated Rate Equation
The integrated rate equations will
vary depending on the overall order
of the reaction.
For a first order, first order overall
reaction the equation will be
ln[A]/[A]o = -kt where time is time,
[A]o is the [A] at t=0 and [A] is [A]
at time t
55. The Integrated Rate Equation
Use the integrated rate equation to
determine the time required for
one-half of the concentration on A
to be consumed.
This time is called the half-life.
t1/2 = 0.693/k
56. Reaction Halflife
The half-life (t1/2) for a reaction is the time taken for the
concentration of a reactant to drop to half its initial value.
For a first-order reaction, t1/2 does not depend on the starting
concentration.
t1/2 =
ln 2
k
=
0.693
k
The half-life for a first-order reaction is a constant.
Radioactive decay is a first-order process. The half-life for a
radioactive nucleus is a useful indicator of its stability.
57. Examples
The first order decomposition of
cyclopropane to propene is a first
order, first order overall process with
k=9.2s-1 at 1000oC. Determine the
half-life of cyclpropane at 1000oC.
Determine the amount of a 3.0 g
sample of cyclopropane remaining
after 0.50 seconds.
Determine the time required for a 3.0
g sample to be reduced to 0.80g.
58.
59.
60. Examples
The half-life for the following first
order reaction is 688 hours at
1000oC. Determine the specific rate
constant, k, at 1000oC and the
amount of a 3.0 g sample of CS2
that remains after 48 hours.
CS2(g) -----> CS(g) + S(g)
