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CHAPTER 14
Chemical Kinetics
2
Chapter Goals
1. The Rate of a Reaction
Factors That Affect Reaction Rates
2. Nature of the Reactants
3. Concentrations of the Reactants: The Rate-Law Expression
4. Concentration Versus Time: The Integrated Rate Equation
5. Collision Theory of Reaction Rates
3
Chapter Goals
6. Transition State Theory
7. Reaction Mechanisms and the Rate-Law Expression
8. Temperature: The Arrhenius Equation
9. Catalysts
4
The Rate of a Reaction
Kinetics is the study of rates of chemical reactions and the mechanisms by which they occur.
The reaction rate is the increase in concentration of a product per unit time or decrease in concentration of a reactant per unit time.
A reaction mechanism is the series of molecular steps by which a reaction occurs.
5
The Rate of a Reaction Thermodynamics (Chapter 15) determines if a reaction can occur. Kinetics (Chapter 16) determines how quickly a reaction occurs.
Some reactions that are thermodynamically feasible are kinetically so slow as to be imperceptible.
OUSINSTANTANE
kJ -79=G OHOH+H
SLOW VERY
kJ 396G COO C
o2982
-aq
+aq
o298g2g2diamond
l
6
The Rate of Reaction
Consider the hypothetical reaction,
A(g) + B(g) C(g) + D(g)
equimolar amounts of reactants, A and B, will be consumed while products, C and D, will be formed as indicated in this graph:
7
0
0.2
0.4
0.6
0.8
1
1.2
0 50 100
150
200
250
300
350
Time
Con
cent
rati
ons
of
Rea
ctan
ts &
Pro
duct
s
[A] & [B]
[C] & [D]
[A] is the symbol for the concentration of A in M ( mol/L). Note that the reaction does not go entirely to completion.
The [A] and [B] > 0 plus the [C] and [D] < 1.
8
The Rate of Reaction
Reaction rates are the rates at which reactants disappear or products appear.
This movie is an illustration of a reaction rate.
9
The Rate of Reaction
Mathematically, the rate of a reaction can be written as:
t d
D+
t c
C+or
t b
B-
t a
A-= Rate
10
The Rate of Reaction
The rate of a simple one-step reaction is directly proportional to the concentration of the reacting substance.
[A] is the concentration of A in molarity or moles/L. k is the specific rate constant.
k is an important quantity in this chapter.
Ak = Rateor ARate
C + BA (g)(g)(g)
11
The Rate of Reaction
For a simple expression like Rate = k[A] If the initial concentration of A is doubled, the
initial rate of reaction is doubled. If the reaction is proceeding twice as fast, the amount
of time required for the reaction to reach equilibrium would be:
A. The same as the initial time.B. Twice the initial time.C. Half the initial time.
If the initial concentration of A is halved the initial rate of reaction is cut in half.
12
The Rate of Reaction
If more than one reactant molecule appears in the equation for a one-step reaction, we can experimentally determine that the reaction rate is proportional to the molar concentration of the reactant raised to the power of the number of molecules involved in the reaction.
22
ggg
Xk = Rateor XRate
Z+ YX 2
13
The Rate of Reaction
Rate Law Expressions must be determined experimentally.
The rate law cannot be determined from the balanced chemical equation.
This is a trap for new students of kinetics. The balanced reactions will not work because most chemical
reactions are not one-step reactions.
Other names for rate law expressions are:1. rate laws
2. rate equations
3. rate expressions
14
The Rate of Reaction Important terminology for kinetics. The order of a reaction can be expressed in terms of
either:1 each reactant in the reaction or2 the overall reaction.
Order for the overall reaction is the sum of the orders for each reactant in the reaction.
For example:
overall.order first and
ONin order first isreaction This
ONk= Rate
O + NO4ON 2
52
52
g2g2g52
15
The Rate of Reaction
A second example is:
overall.order first and ,OHin order zero
CBr,CHin order first isreaction This
]CBrCHk[= Rate
BrCOHCHOHCBrCH
-
33
33
-aqaq33
-aqaq33
16
The Rate of Reaction
A final example of the order of a reaction is:
ALLYEXPERIMENT DETERMINED
ARE SEXPRESSION RATE ALL REMEMBER,
overallorder third and ,Oin order first
NO,in order second isreaction This
isreaction This Ok[NO]=Rate
NO 2O+NO 2
2
22
g2g2g
17
The Rate of Reaction Given the following one step reaction and its rate-law expression.
Remember, the rate expression would have to be experimentally determined.
Because it is a second order rate-law expression: If the [A] is doubled the rate of the reaction will increase
by a factor of 4. 22 = 4 If the [A] is halved the rate of the reaction will decrease by
a factor of 4. (1/2)2 = 1/4
2ggg
Ak = Rate
CBA 2
18
Factors That Affect Reaction Rates
There are several factors that can influence the rate of a reaction:
1. The nature of the reactants.
2. The concentration of the reactants.
3. The temperature of the reaction.
4. The presence of a catalyst. We will look at each factor individually.
19
Nature of Reactants
This is a very broad category that encompasses the different reacting properties of substances.
For example sodium reacts with water explosively at room temperature to liberate hydrogen and form sodium hydroxide.
burns. and ignites H The
reaction. rapid and violent a is This
HNaOH 2OH 2Na 2
2
g2aq2s
20
Nature of Reactants
• Calcium reacts with water only slowly at room temperature to liberate hydrogen and form calcium hydroxide.
reaction. slowrather a is This
HOHCaOH 2Ca g2aq22s
21
Nature of Reactants
• The reaction of magnesium with water at room temperature is so slow that that the evolution of hydrogen is not perceptible to the human eye.
reaction No OH Mg 2s
22
Nature of Reactants
However, Mg reacts with steam rapidly to liberate H2 and form magnesium oxide.
The differences in the rate of these three reactions can be attributed to the changing “nature of the reactants”.
g2sC100
2s HMgOOHMg o
23
Concentrations of Reactants: The Rate-Law Expression
This movie illustrates how changing the concentration of reactants affects the rate.
24
Concentrations of Reactants: The Rate-Law Expression This is a simplified representation of the
effect of different numbers of molecules in the same volume. The increase in the molecule numbers is
indicative of an increase in concentration.
A(g) + B (g) Products
A B
A B
A B BA B
A BA BA B
4 different possible A-B collisions
6 different possible A-B collisions
9 different possible A-B collisions
25
Concentrations of Reactants: The Rate-Law Expression
Example 16-1: The following rate data were obtained at 25oC for the following reaction. What are the rate-law expression and the specific rate-constant for this reaction?
2 A(g) + B(g) 3 C(g)
Experiment
Number
Initial [A]
(M)
Initial [B]
(M)
Initial rate of formation of
C (M/s)
1 0.10 0.10 2.0 x 10-4
2 0.20 0.30 4.0 x 10-4
3 0.10 0.20 2.0 x 10-4
26
Concentrations of Reactants: The Rate-Law Expression
.Bignorecan can weThus,
k[A]=Rateor BAk=Rate
012
constant. remains rate initial that theNotice
2.by increases [B] that theandconstant is [A] the
thatsee we3 and 1 sexperiment compare weIf
BAk=Rate
:form theof bemust law rate The
0 xx
y
yx
y
27
Concentrations of Reactants: The Rate-Law Expression
You do it!
xx
reaction? for this
k of units and value theisWhat
overall.order 1 andA to
respect order with 1 isreaction This
k[A]=Rateor k[A]= Rate
122
2.by increases rate theand
2by increases [A] that theNotice
2. and 1 sexperiment compare Next,
st
st
1
28
Concentrations of Reactants: The Rate-Law Expression
[A] 10 x 2.0=Rate
as written becan law rate theThus
10 x 2.0 10.0
10 x 2.0=k
1 experiment from [A] and Rate of values theUsing
A
Rate=k
law.rate thefromk of value thefindcan We
s13-
s13-s
4-
M
M
29
Concentrations of Reactants: The Rate-Law Expression
Example 16-2: The following data were obtained for the following reaction at 25oC. What are the rate-law expression and the specific rate constant for the reaction?
2 A(g) + B(g) + 2 C(g) 3 D(g) + 2 E(g) Experiment
Initial [A]
(M)
Initial [B]
(M)
Initial [C]
(M)
Initial rate of
formation of D (M/s)
1 0.20 0.10 0.10 2.0 x 10-4
2 0.20 0.30 0.20 6.0 x 10-4
3 0.20 0.10 0.30 2.0 x 10-4
4 0.60 0.30 0.40 1.8 x 10-3
30
Concentrations of Reactants: The Rate-Law Expression
yxzyx
z z
BAk=Rateor CBAk=Rate
013
constant. remains rate but the 3by increases C The
constant.remain B and A that Notice
3. and 1 sexperiment Compare
31
Concentrations of Reactants: The Rate-Law Expression
BAk=Rateor BAk=Rate
133
3.by increases rate theand 3by increases B The
constant. remains A The
2. and 1 sexperiment compare Next,
1 xx
y y
32
Concentrations of Reactants: The Rate-Law Expression
overall.order 2 and B, respect to order with1
A, respect to order with 1 isreaction This
BAk=Rateor BAk= Rate
133
3.by increases rate theand 3by increases A The
constant. remains B The
4. and 2 sexperiment compare Next,
ndst
st
11
xx
33
Concentrations of Reactants: The Rate-Law Expression
BA100.1 = Rate
as written becan law-rate theThus,
100.1
0.10 0.20
100.2
BA
Rate=k
4.or 3, 2, 1, experiment from data theuseCan
k. of units and value thedetermine Finally,
s12
s12
s4
M
M
M
MM
34
Concentrations of Reactants: The Rate-Law Expression
Example 16-3: consider a chemical reaction between compounds A and B that is first order with respect to A, first order with respect to B, and second order overall. From the information given below, fill in the blanks.
You do it!Experiment
Initial Rate
(M/s)
Initial [A]
(M)
Initial [B]
(M)
1 4.0 x 10-3 0.20 0.050
2 1.6 x 10-2 ? 0.050
3 3.2 x 10-2 0.40 ?
35
Concentrations of Reactants: The Rate-Law Expression
BA40.0 Rate theThus
40.0
0.050 0.20
100.4
BA
Rate=k
k. of value thedeterminecan we1 experiment From
BAk=Rate
s 1
s 1
s3
M
M
M
MM
36
Concentrations of Reactants: The Rate-Law Expression
M
MM
M
80.0]A[
050.0s0.40
s106.1]A[
k[B]
Rate[A]
2 experiment from data andk of value theUse
1-1
1-2
37
Concentrations of Reactants: The Rate-Law Expression
M
MM
M
20.0[B]
40.0s0.40
s102.3[B]
k[A]
R[B]
determinecan we3 experiment from Similarly,
1-1
1-2
38
Concentration vs. Time: The Integrated Rate Equation The integrated rate equation relates time and
concentration for chemical and nuclear reactions. From the integrated rate equation we can predict
the amount of product that is produced in a given amount of time.
Initially we will look at the integrated rate equation for first order reactions.These reactions are 1st order in the reactant and 1st
order overall.
39
Concentration vs. Time: The Integrated Rate Equation An example of a reaction that is 1st order in the
reactant and 1st order overall is:
a A products
This is a common reaction type for many chemical reactions and all simple radioactive decays.
Two examples of this type are:
2 N2O5(g) 2 N2O4(g) + O2(g)
238U 234Th + 4He
40
Concentration vs. Time: The Integrated Rate Equation
where:
[A]0= mol/L of A at time t=0. [A] = mol/L of A at time t.
k = specific rate constant. t = time elapsed since beginning of reaction.
a = stoichiometric coefficient of A in balanced overall equation.
The integrated rate equation for first order reactions is:
k t aA
Aln 0
41
Concentration vs. Time: The Integrated Rate Equation
Solve the first order integrated rate equation for t.
Define the half-life, t1/2, of a reactant as the time required for half of the reactant to be consumed, or the time at which [A]=1/2[A]0.
A
Aln
k a
1t 0
42
Concentration vs. Time: The Integrated Rate Equation
At time t = t1/2, the expression becomes:
k a
693.0t
2lnk a
1t
A1/2
Aln
k a
1t
1/2
1/2
0
01/2
43
Concentration vs. Time: The Integrated Rate Equation
Example 16-4: Cyclopropane, an anesthetic, decomposes to propene according to the following equation.
The reaction is first order in cyclopropane with k = 9.2 s-1 at 10000C. Calculate the half life of cyclopropane at 10000C.
CH2 CH2
CH2CH2CH3
CH
(g) (g)
s 075.0s 2.9
693.0
k
693.0t
1-1/2
44
Concentration vs. Time: The Integrated Rate Equation
Example 16-5: Refer to Example 16-4. How much of a 3.0 g sample of cyclopropane remains after 0.50 seconds? The integrated rate laws can be used for any unit
that represents moles or concentration. In this example we will use grams rather than
mol/L.
45
Concentration vs. Time: The Integrated Rate Equation
remains 1%or g 03.0eA
5.31.16.4Aln
6.4Aln 1.1
s 50.0s 2.9Aln -3.0ln
k t AlnAln
.logarithms of laws theusemust We
reaction for thisk t k t aA
Aln
3.5-
1-
0
0
46
Concentration vs. Time: The Integrated Rate Equation
Example 16-6: The half-life for the following first order reaction is 688 hours at 10000C. Calculate the specific rate constant, k, at 10000C and the amount of a 3.0 g sample of CS2 that remains after 48 hours.
CS2(g) CS(g) + S(g)
You do it!
47
Concentration vs. Time: The Integrated Rate Equation
1-
1/2
1/2
hr 00101.0hr 688
0.693k
t
0.693k
k
693.0t
1. areaction For this
48
Concentration vs. Time: The Integrated Rate Equation
hr) 48)(hr 00101.0(Aln-ln(3.0)
k tAlnAlnk tA
Aln
1-
00
unreacted 97%or g 9.2g86.2eA
1.0521.1)--(0.048Aln
0.048Aln-1.1
hr) 48)(hr 00101.0(Aln-ln(3.0)
k tAlnAlnk tA
Aln
1.052
1-
00
49
Concentration vs. Time: The Integrated Rate Equation
For reactions that are second order with respect to a particular reactant and second order overall, the rate equation is:
Where:[A]0= mol/L of A at time t=0. [A] = mol/L of A at time t.
k = specific rate constant. t = time elapsed since beginning of reaction.
a = stoichiometric coefficient of A in balanced overall equation.
k t aA
1
A
1
0
50
Concentration vs. Time: The Integrated Rate Equation
Second order reactions also have a half-life. Using the second order integrated rate-law as a starting
point.
At the half-life, t1/2 [A] = 1/2[A]0.
0
1/200
A ofr denominatocommon a haswhich
k t aA
1
A2/1
1
1/20
1/200
k t aA
1
or k t aA
1
A
2
51
Concentration vs. Time: The Integrated Rate Equation
If we solve for t1/2:
Note that the half-life of a second order reaction depends on the initial concentration of A.
01/2 Ak a
1t
52
Concentration vs. Time: The Integrated Rate Equation
Example 16-7: Acetaldehyde, CH3CHO, undergoes gas phase thermal decomposition to methane and carbon monoxide.
The rate-law expression is Rate = k[CH3CHO]2, and k = 2.0 x 10-2 L/(mol.hr) at 527oC. (a) What is the half-life of CH3CHO if 0.10 mole is injected into a 1.0 L vessel at 527oC?
CH CHO CH + CO3 g 4 g g
53
Concentration vs. Time: The Integrated Rate Equation
tk A
hr
hr
1/2
-1
1
1
2 0 10 010
5 0 10
0
2 1
2
. .
.
M M
54
Concentration vs. Time: The Integrated Rate Equation
(b) How many moles of CH3CHO remain after 200 hours?
1 1
1 1010
2 0 10 200
110 4 0
0
2 1
1 1
A Ak t
A hr hr
A
-1
..
.
MM
M M
114
1
14
0 071
0 071 mol
11A
A
A
mol = 1.0 L x 0.071 molL
M
M
M.
? .
55
Concentration vs. Time: The Integrated Rate Equation
(c) What percent of the CH3CHO remains after 200 hours?
reacted 29% and unreacted %71
%100mol 0.10
mol 0.071= unreacted %
56
Concentration vs. Time: The Integrated Rate Equation
Example 16-8: Refer to Example 16-7. (a) What is the half-life of CH3CHO if 0.10 mole is injected into a 10.0 L vessel at 527oC? Note that the vessel size is increased by a factor
of 10 which decreases the concentration by a factor of 10!
You do it!
57
Concentration vs. Time: The Integrated Rate Equation
tk A
hr
hr
note the time has increased by 10
over Example 16 - 7:
1/2
-1
1
1
2 0 10 0 010
5 0 10
0
2 1
3
. .
.
M M
58
Concentration vs. Time: The Integrated Rate Equation
(b) How many moles of CH3CHO remain after 200 hours?
You do it!
59
Concentration vs. Time: The Integrated Rate Equation
1 1
1 10 010
2 0 10 200
1100 4 0
0
2 1
1 1
A Ak t
A hr hr
A
-1
..
.
MM
M M
1104
1
104
0 0096
0 096 mol
11A
A
A
mol = 10.0 L x 0.0096 molL
M
M
M.
? .
60
Concentration vs. Time: The Integrated Rate Equation
(c) What percent of the CH3CHO remains after 200 hours?
You do it!
61
Concentration vs. Time: The Integrated Rate Equation
% unreacted =0.096 mol0.100 mol
unreacted & 4% reacted
100%
96%
62
Concentration vs. Time: The Integrated Rate Equation
Let us now summarize the results from the last two examples.
Initial Moles
CH3CHO
[CH3CHO]0
(M)
[CH3CHO]
(M)
Moles of CH3CHO at 200 hr.
% CH3CHO remaining
Ex. 16-7 0.10 0.10 0.071 0.071 71%
Ex. 16-8 0.010 0.010 0.0096 0.096 96%
63
Enrichment - Derivation of Integrated Rate Equations
For the first order reaction
a A products
the rate can be written as:
t
A
a
1-=Rate
64
Enrichment - Derivation of Integrated Rate Equations
For a first-order reaction, the rate is proportional to the first power of [A].
-1a
At
k A
65
Enrichment - Derivation of Integrated Rate Equations
In calculus, the rate is defined as the infinitesimal change of concentration d[A] in an infinitesimally short time dt as the derivative of [A] with respect to time.
-1a
At
k Ad
d
66
Enrichment - Derivation of Integrated Rate Equations
Rearrange the equation so that all of the [A] terms are on the left and all of the t terms are on the right.
-A
Aa k t
dd
67
Enrichment - Derivation of Integrated Rate Equations
Express the equation in integral form.
-
AA
a k tA
A tdd
0 0
68
Enrichment - Derivation of Integrated Rate Equations
This equation can be evaluated as:
-ln A a k t or
-ln A A a k t - a k 0
which becomes
-ln A A a k t
t0t
t
t
0
0
0
ln
ln
69
Enrichment - Derivation of Integrated Rate Equations
Which rearranges to the integrated first order rate equation.
k t aA
Aln
t
0
70
Enrichment - Derivation of Integrated Rate Equations
Derive the rate equation for a reaction that is second order in reactant A and second order overall.
The rate equation is:
2Ak t a
A
d
d
71
Enrichment - Derivation of Integrated Rate Equations
Separate the variables so that the A terms are on the left and the t terms on the right.
tk A a
A2 d
d
72
Enrichment - Derivation of Integrated Rate Equations
Then integrate the equation over the limits as for the first order reaction.
t
0
A
A2 tk a
A
A
0
dd
73
Enrichment - Derivation of Integrated Rate Equations
Which integrates the second order integrated rate equation.
k t aA
1
A
1
0
74
Enrichment - Derivation of Integrated Rate Equations
For a zero order reaction the rate expression is:
k
t a
A
d
d
75
Enrichment - Derivation of Integrated Rate Equations
Which rearranges to:
tk aA dd
76
Enrichment - Derivation of Integrated Rate Equations
Then we integrate as for the other two cases:
t
0
A
A
tk aA0
dd
77
Enrichment - Derivation of Integrated Rate Equations
Which gives the zeroeth order integrated rate equation.
k t a-AA
or
k t -aAA
0
0
78
Enrichment - Rate Equations to Determine Reaction Order
Plots of the integrated rate equations can help us determine the order of a reaction.
If the first-order integrated rate equation is rearranged. This law of logarithms, ln (x/y) = ln x - ln y, was applied to the
first-order integrated rate-equation.
0
0
Alnk t aAln
or
k t aAlnAln
79
Enrichment - Rate Equations to Determine Reaction Order
The equation for a straight line is:
Compare this equation to the rearranged first order rate-law.
bmy x
80
Enrichment - Rate Equations to Determine Reaction Order
b m y x
Now we can interpret the parts of the equation as follows: y can be identified with ln[A] and plotted on the y-axis. m can be identified with –ak and is the slope of the line. x can be identified with t and plotted on the x-axis. b can be identified with ln[A]0 and is the y-intercept.
0Alnk t aAln
81
Enrichment - Rate Equations to Determine Reaction Order
Example 16-9: Concentration-versus-time data for the thermal decomposition of ethyl bromide are given in the table below. Use the following graphs of the data to determine the rate of the reaction and the value of the rate constant.
700Kat HBrHCBrHC gg42g52
82
Enrichment - Rate Equations to Determine Reaction Order
Time
(min) 0 1 2 3 4 5
[C2H5Br] 1.00 0.82 0.67 0.55 0.45 0.37
ln [C2H5Br] 0.00 -0.20 -0.40 -0.60 -0.80 -0.99
1/[C2H5Br] 1.0 1.2 1.5 1.8 2.2 2.7
83
Enrichment - Rate Equations to Determine Reaction Order
We will make three different graphs of the data.
1 Plot the [C2H5Br] (y-axis) vs. time (x-axis) If the plot is linear then the reaction is zero order
with respect to [C2H5Br].
2 Plot the ln [C2H5Br] (y-axis) vs. time (x-axis) If the plot is linear then the reaction is first order
with respect to [C2H5Br].
3 Plot 1/ [C2H5Br] (y-axis) vs. time (x-axis) If the plot is linear then the reaction is second
order with respect to [C2H5Br].
84
Enrichment - Rate Equations to Determine Reaction Order Plot of [C2H5Br] versus time.
Is it linear or not?
[C2H5Br] vs. time
0
0.20.4
0.60.8
11.2
0 1 2 3 4 5
Time (min)
[C2
H5
Br]
85
Enrichment - Rate Equations to Determine Reaction Order
Plot of ln [C2H5Br] versus time. Is it linear or not?
ln [C2H5Br] vs. time
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0 1 2 3 4 5
Time (min)
ln [
C2H
5B
r]
86
Enrichment - Rate Equations to Determine Reaction Order
Plot of 1/[C2H5Br] versus time. Is it linear or not?
1/[C2H5Br] vs. time
0
1
2
3
0 1 2 3 4 5
Time (min)
1/[C
2H5B
r]
87
Enrichment - Rate Equations to Determine Reaction Order Note that the only graph which is linear is the plot of ln[C2H5Br] vs. time.
Thus this is a first order reaction with respect to [C2H5Br]. Next, we will determine the value of the rate constant from the slope of
the line on the graph of ln[C2H5Br] vs. time.
Remember slope = y2-y1/x2-x1.
1-
12
12
min 20.0min 3
60.0slope
min 14
)20.0(80.0
x-x
y-y slope
88
Enrichment - Rate Equations to Determine Reaction Order
From the equation for a first order reaction we know that the slope = -a k. In this reaction a = 1.
.min 0.20kconstant rate theThus
-k-0.20slope1-
89
Enrichment - Rate Equations to Determine Reaction Order
The integrated rate equation for a reaction that is second order in reactant A and second order overall.
This equation can be rearranged to:
k t aA
1
A
1
0
0A
1k t a
A
1
90
Enrichment - Rate Equations to Determine Reaction Order
Compare the equation for a straight line and the second order rate-law expression.
Now we can interpret the parts of the equation as follows: y can be identified with 1/[A] and plotted on the y-axis. m can be identified with a k and is the slope of the line. x can be identified with t and plotted on the x-axis b can be identified with 1/[A]0 and is the y-intercept.
b m y x
0A
1k t a
A
1
91
Enrichment - Rate Equations to Determine Reaction Order
Example 16-10: Concentration-versus-time data for the decomposition of nitrogen dioxide are given in the table below. Use the graphs to determine the rate of the reaction and the value of the rate constant
500Kat ONO 2NO 2 g2gg2
92
Enrichment - Rate Equations to Determine Reaction Order
Time
(min) 0 1 2 3 4 5
[NO2] 1.0 0.53 0.36 0.27 0.22 0.18
ln [NO2] 0.0 -0.63 -1.0 -1.3 -1.5 -1.7
1/[NO2] 1.0 1.9 2.8 3.7 4.6 5.5
93
Enrichment - Rate Equations to Determine Reaction Order
Once again, we will make three different graphs of the data.
1. Plot [NO2] (y-axis) vs. time (x-axis). If the plot is linear then the reaction is zero order with respect
to NO2.
2. Plot ln [NO2] (y-axis) vs. time (x-axis).• If the plot is linear then the reaction is first order with respect
to NO2.
3. Plot 1/ [NO2] (y-axis) vs. time (x-axis). If the plot is linear then the reaction is second order with
respect to NO2.
94
Enrichment - Rate Equations to Determine Reaction Order
Plot of [NO2] versus time. Is it linear or not?
[NO2] vs. time
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
Time (min)
[NO
2]
95
Enrichment -Rate Equations to Determine Reaction Order
Plot of ln [NO2] versus time. Is it linear or not?
ln [NO2] vs. time
-2
-1.5
-1
-0.5
0
0 1 2 3 4 5
Time (min)
ln [
NO
2]
96
Enrichment - Rate Equations to Determine Reaction Order
Plot of 1/[NO2] versus time. Is it linear or not?
1/[NO2] vs.time
01
23
45
6
0 1 2 3 4 5
Time (min)
1/[
NO
2]
97
Enrichment - Rate Equations to Determine Reaction Order
Note that the only graph which is linear is the plot of 1/[NO2] vs. time.
Thus this is a second order reaction with respect to [NO2].
Next, we will determine the value of the rate constant from the slope of the line on the graph of 1/[NO2] vs. time.
98
Enrichment - Rate Equations to Determine Reaction Order
From the equation for a first order reaction we know that the slope = a k In this reaction a = 2.
1-1 min 0.45kconstant rate theThus
k 20.90slope
M
min 1
1
1
12
12
90.0min 4
60.3slope
min 15
)90.1(50.5
x-x
y-y slope
MM
M
99
Collision Theory of Reaction Rates
Three basic events must occur for a reaction to occur the atoms, molecules or ions must:
1. Collide.
2. Collide with enough energy to break and form bonds.
3. Collide with the proper orientation for a reaction to occur.
100
Collision Theory of Reaction Rates
One method to increase the number of collisions and the energy necessary to break and reform bonds is to heat the molecules.
As an example, look at the reaction of methane and oxygen:
We must start the reaction with a match. This provides the initial energy necessary to break the
first few bonds. Afterwards the reaction is self-sustaining.
kJ 891 OH CO O CH (g)22(g)2(g)4(g)
101
Collision Theory of Reaction Rates
Illustrate the proper orientation of molecules that is necessary for this reaction.
X2(g) + Y2(g) 2 XY(g)
Some possible ineffective collisions are :
X
X
Y YY
Y
X X X X Y Y
102
Collision Theory of Reaction Rates
An example of an effective collision is:
X Y
X Y
X Y
X Y
X Y +
X Y
103
Collision Theory of Reaction Rates
This picture illustrates effective and ineffective molecular collisions.
104
Transition State Theory
Transition state theory postulates that reactants form a high energy intermediate, the transition state, which then falls apart into the products.
For a reaction to occur, the reactants must acquire sufficient energy to form the transition state. This energy is called the activation energy or Ea.
Look at a mechanical analog for activation energy
105
Transition State Theory
Epot = mgh
Cross section of mountain
Boulder
Eactivation
h
h2
h1
Epot=mgh2
Epot=mgh1
Height
106
Transition State Theory
PotentialEnergy
Reaction Coordinate
X2 + Y2
2 XY
Eactivation - a kinetic quantity
E Ha thermodynamic quantity
Representation of a chemical reaction.
107
Transition State Theory
108
Transition State Theory
The relationship between the activation energy for forward and reverse reactions is Forward reaction = Ea
Reverse reaction = Ea + E difference = E
109
Transition State Theory
The distribution of molecules possessing different energies at a given temperature is represented in this figure.
110
Reaction Mechanisms and the Rate-Law Expression
Use the experimental rate-law to postulate a molecular mechanism.
The slowest step in a reaction mechanism is the rate determining step.
111
Reaction Mechanisms and the Rate-Law Expression
Use the experimental rate-law to postulate a mechanism.
The slowest step in a reaction mechanism is the rate determining step.
Consider the iodide ion catalyzed decomposition of hydrogen peroxide to water and oxygen.
g22I
22 O + OH 2 OH 2-
112
Reaction Mechanisms and the Rate-Law Expression
This reaction is known to be first order in H2O2 , first order in I- , and second order overall.
The mechanism for this reaction is thought to be:
-22
2222
-2222
-
2--
22
IOHk=R law rate alExperiment
O+OH 2OH 2reaction Overall
I+O+OHOH+ IO stepFast
OH+IOI+OH step Slow
113
Reaction Mechanisms and the Rate-Law Expression
Important notes about this reaction:1. One hydrogen peroxide molecule and one
iodide ion are involved in the rate determining step.
2. The iodide ion catalyst is consumed in step 1 and produced in step 2 in equal amounts.
3. Hypoiodite ion has been detected in the reaction mixture as a short-lived reaction intermediate.
114
Reaction Mechanisms and the Rate-Law Expression
Ozone, O3, reacts very rapidly with nitrogen oxide, NO, in a reaction that is first order in each reactant and second order overall.
NOOk=Rate is law-rate alExperiment
O+NONO+O
3
g2g2gg3
115
Reaction Mechanisms and the Rate-Law Expression
One possible mechanism is:
223
223
33
O+NONO+Oreaction Overall
O+NONO+O stepFast
O+NONO+O step Slow
116
Reaction Mechanisms and the Rate-Law Expression
A mechanism that is inconsistent with the rate-law expression is:
correct. becannot mechanism thisproveswhich
Ok=Rate is mechanism thisfrom law-rate The
ONONO+Oreaction Overall
NONO+O stepFast
O+OO step Slow
3
223
2
23
117
Reaction Mechanisms and the Rate-Law Expression
Experimentally determined reaction orders indicate the number of molecules involved in:
1. the slow step only or
2. the slow step and the equilibrium steps preceding the slow step.
118
Temperature: The Arrhenius Equation
Svante Arrhenius developed this relationship among (1) the temperature (T), (2) the activation energy (Ea), and (3) the specific rate constant (k).
k = Ae
or
ln k = ln A -ERT
-E RT
a
a
119
Temperature: The Arrhenius Equation
This movie illustrates the effect of temperature on a reaction.
120
Temperature: The Arrhenius Equation
If the Arrhenius equation is written for two temperatures, T2 and T1 with T2 >T1.
ln k ln A -ERT
and
ln k ln A -E
RT
1a
1
2a
2
121
Temperature: The Arrhenius Equation
1. Subtract one equation from the other.
ln k k A - ln A -E
RTERT
ln k kERT
-E
RT
2 1a
2
a
1
2 1a
1
a
2
ln ln
ln
122
Temperature: The Arrhenius Equation
2. Rearrange and solve for ln k2/k1.
ln kk
ER T T
or
ln kk
ER
T - TT T
2
1
a
1 2
2
1
a 2 1
2 1
1 1
123
Temperature: The Arrhenius Equation
Consider the rate of a reaction for which Ea=50 kJ/mol, at 20oC (293 K) and at 30oC (303 K). How much do the two rates differ?
lnkk
ER
T - TT T
lnkk
8.314
K
lnkk
kk
e
2
1
a 2 1
2 1
2
1
Jmol
JK mol
2
1
2
1
0.677
50 000 303 293303 293
0 677
197 2
,
.
.
124
Temperature: The Arrhenius Equation For reactions that have an Ea50 kJ/mol, the rate
approximately doubles for a 100C rise in temperature, near room temperature.
Consider:
2 ICl(g) + H2(g) I2(g) + 2 HCl(g) The rate-law expression is known to be R=k[ICl][H2].
At 230 C, k = 0.163 s
At 240 C, k = 0.348 s
k approximately doubles
0 -1 -1
0 -1 -1
M
M
125
Catalysts
Catalysts change reaction rates by providing an alternative reaction pathway with a different activation energy.
126
Catalysts
Homogeneous catalysts exist in same phase as the reactants.
Heterogeneous catalysts exist in different phases than the reactants. Catalysts are often solids.
127
Catalysts
Examples of commercial catalyst systems include:
systemconverter catalytic Automobile
ONNO 2
CO 2O+CO 2
OH 18CO16O 25+HC
g2g2Pt and NiO
g
g2Pt and NiO
g2g
g2g2Pt and NiO
g2g188
128
Catalysts
This movie shows catalytic converter chemistry on the Molecular Scale
129
Catalysts
A second example of a catalytic system is:
npreparatio acid Sulfuric
SO 2OSO 2 g3NiO/Ptor OV
g2g252
130
Catalysts
A third examples of a catalytic system is:
ProcessHaber
NH 2H 3 N g3OFeor Fe
g2g232
131
Catalysts Look at the catalytic oxidation of CO to CO2
Overall reaction
2 CO(g)+ O2(g) 2CO2(g)
Absorption
CO(g) CO(surface) + O2(g)
O2(g) O2(surface)
Activation
O2(surface) O(surface)
Reaction
CO(surface) +O(surface) CO2(surface) Desorption
CO2(surface) CO2(g)
132
Synthesis Question
The Chernobyl nuclear reactor accident occurred in 1986. At the time that the reactor exploded some 2.4 MCi of radioactive 137Cs was released into the atmosphere. The half-life of 137Cs is 30.1 years. In what year will the amount of 137Cs released from Chernobyl finally decrease to 100 Ci? A Ci is a unit of radioactivity called the Curie.
133
Synthesis Question
Ci 100 reaches Chernobylat emitted Csfrom
ity radioactiv the when2426 440 1986
years440 years439 y0230.0
10.1t
t y0230.010.1
t y0230.0Ci 100
Ci 102.4ln
decay eradioactiv for this 1a andk t a A
Aln
Ci 102.4 MCi2.4
y0230.0 y1.30
693.0
t
693.0k
k
693.0t
137
1-
1-
1-6
0
6
1-
21
21
134
Group Question
99mTc has a half-life of 6.02 hours and is often used in nuclear medical diagnostic tests. Patients are injected with approximately 10 mCi of 99mTc that is then directed to specific sites in the patient’s body to detect gallstones, brain tumors and function, and other medical conditions. How long will the patient have a higher than normal radioactivity level after they have been injected with 10 mCi of 99mTc?
135
End of Chapter 16
A great deal of chemistry is a competition between Thermodynamics (Chapter 15) and Kinetics (Chapter 16).