Chemical Kinetics
Chapter 12
Unit 7 - Chemical Kinetics
AP Chemistry
Reaction Rates
Factors that Affect Reaction Rates
1.The physical state of the reactants
Reaction is limited to area of contact when in different phases
✦ Increase surface area are of solids to increase rate
2.The concentration of the reactants
✦ For most, as concentration increases, rate increases
3.The temperature at which the reaction occurs
✦ As temperature increases, the rate increase
✦
Reaction Rates
Factors that Affect Reaction Rates
4.The presence of a catalyst
5.On a molecular level, depends on the frequency of collisions.
✦ As collisions increase, the rate increases
✦ Collisions must occur with sufficient energy and with correct
orientation
Reaction Rates
Reaction Rates
✦
A rate is change over time
concentration of A at time t 2 - concentration of A at time t1
Rate =
t 2 - t1
✦
Δ [ A]
=
Δt
units are M/s
Reaction Rates
Reaction Rates
Sample Problem A
Consider the following reaction
N 2 ( g ) + 3H 2 ( g ) ⎯⎯
→ 2NH 3 ( g )
What happens to each of the reactants as the reaction progresses?
Reaction Rates
Reaction Rates
Sample Problem A
As the reaction progresses, the concentration of H2 goes down.
Concentration
✦
[H2]
Time
Reaction Rates
Reaction Rates
Sample Problem A
As the reaction progresses, the concentration of N2 goes down 1/3 as
fast.
Concentration
✦
[N2]
[H2]
Time
Reaction Rates
Reaction Rates
Sample Problem A
As the reaction progresses, the concentration of NH3 goes up.
Concentration
✦
[N2]
[H2]
[NH3]
Time
Reaction Rates
Reaction Rates and Stoichiometry
✦
✦
✦
In general, for a reaction
aA + bB ⎯⎯
→ cC + dD
The rate is given by
1 Δ [ A]
1 Δ [ B]
1 Δ [C ]
1 Δ[ D]
Rate = −
=−
=−
=−
a Δt
b Δt
c Δt
d Δt
So for the previous reaction, what does the rate equal?
Rate = −
Δ [ N2 ]
Δt
1 Δ[ H2 ]
1 Δ [ NH 3 ]
=−
=−
3 Δt
2 Δt
Reaction Rates
Reaction Rates and Stoichiometry
Sample Problem B
a.How is the rate at which ozone disappears related to the rate at
which oxygen appears in the reaction
2O3 ( g ) ⎯⎯
→ 3O2 ( g )
-5
b.If the rate at which O2 appears, Δ[O2]/Δt, is 6.0 x 10 M/s at a
particular instant, at what rate is O3 disappearing at this same time, Δ[O3]/Δt?
Reaction Rates
Change of Rate with Time
✦
✦
Average rates are taken over long intervals
Instantaneous rates are determined by finding the slope of a line
tangent to the curve at any given point because the rate can change
over time.
Concentration
Average Slope Method
D[H2]
Dt
Time
Concentration
Instantaneous Slope Method
Reaction rates are not constant
if the reaction depends on
concentration
Δ[ H2 ]
Δ (t )
Time
Rate Laws
Types of Rate Laws
1.Differential Rate Law - looks at the effect of concentration on the
reaction rate.
✦ Usually just referred to as the rate law
✦ Must come from a set of data
2.Integrated Rate Law - looks at how the concentration of reactants
change over time
Rate Laws
Forming the Rate Law
aA + bB ⎯⎯
→ cC + dD
Rate = k [ A ] [ B ]
k = rate constant (units vary)
m, n = reaction orders (usually small whole numbers)
[ ] = concentration of reactants
m + n = overall reaction order
m
✦
✦
✦
✦
n
Rate Laws
Forming the Rate Law
Example
Rate = k ⎡⎣ NH ⎤⎦ ⎡⎣ NO ⎤⎦
1+
4
1−
2
m = 1, n = 1
✦ we say the reaction is 1st order in NH41+ or 1st order in NO21-.
✦ The reaction is 2nd order overall.
✦ This means that because the rate at which NH41+ reacts with
11+
NO2 depends on [NH4 ] raised to the 1st power, the rate
1+
doubles when [NH4 ] doubles (triples when tripled, etc...). And
1the same goes for [NO2 ].
✦
Rate Laws
Forming the Rate Law
Example
Rate = k ⎡⎣ NH ⎤⎦ ⎡⎣ NO ⎤⎦
If a rate law is 2nd order with respect to a reaction, [A]2, doubling
the concentration of that substance will quadruple the reaction
rate.
The values of the exponents are NOT determined by the balanced
equation. They are determined experimentally!
1+
4
✦
✦
2N 2O5 ⎯⎯
→ 4NO2 + O2
H 2 + I 2 ⎯⎯
→ 2HI
CHCl3 + Cl2 ⎯⎯
→ CCl4 + HCl
1−
2
Rate = k [ N 2O5 ]
Rate = k [ H 2 ][ I 2 ]
Rate = k [ CHCl3 ][ Cl2 ]
1
2
Rate Laws
Forming the Rate Law
✦
✦
The RATE of a reaction depends on concentration, but the RATE
CONSTANT does not.
The rate constant is only affected by the temperature change and the
presence of a catalyst.
Rate Laws
Determining Rate Law
Sample Problem C
The initial rate of a reaction A + B → C was measured for several
different starting concentrations. Using the datas below, find
a.the rate law
b.the rate constant
c.the rate of reaction when [A] = 0.500 M and [B] = 0.100 M
Experiment
1
2
3
[A] (M)
0.1
0.1
0.2
[B] (M)
0.1
0.2
0.1
Initial Rate (M/s)
-5
4.0 x 10
-5
4.0 x 10
-5
16.0 x 10
Rate Laws
Determining Rate Law
Sample Problem D
2NO + 2H 2 ⎯⎯
→ N 2 + 2H 2O
Experiment
1
2
3
[NO] (M)
0.1
0.1
0.2
[H2] (M)
0.1
0.2
0.1
Initial Rate (M/s)
-3
1.23 x 10
-3
2.46 x 10
-3
4.92 x 10
a.Find the rate law.
b.Find the rate constant (with units).
c.Calculate the rate when [NO] = 0.050 M and [H2] = 0.150 M
Rate Laws
Determining Rate Law
Sample Problem E
Rate Data for the Reaction of Ammonia and Nitrate Ions in Water
Experiment
[NH41+] (M)
[NO21-] (M)
Initial Rate (M/s)
1
0.01
0.2
5.4 x 10-7
2
0.02
0.2
10.8 x 10-7
3
0.04
0.2
21.5 x 10-7
4
0.06
0.2
32.2 x 10-7
5
0.2
0.0202
10.8 x 10-7
6
0.2
0.0404
21.5 x 10-7
7
0.2
0.0606
32.2 x 10-7
8
0.2
0.0808
43.3 x 10-7
a.Determine the rate law.
b.Calculate the rate constant.
Rate Laws
Change of Concentration with Time (Integrated Rate Law)
✦
✦
Converts the rate law into an equation that tells what the
concentration is at a particular point in time.
If you memorize and can use the following table, you will know 90%
of the kinetics information on the AP Exam!
Rate Laws
Kinetics Table
Order
Rate Law
Integrated Rate Law
Straight Line Plot
Rate Constant and Slope
Half-Life
Zeroth
First
Second
Rate = k
Rate = k [ A ]
Rate = k [ A ]
ln [ A ] = −kt + ln [ A ]0
1
1
= kt +
[ A]
[ A ]0
[ A ] vs t
ln [ A ] vs t
1
vs t
[ A]
slope = −k
slope = −k
slope = k
0.693
t 12 =
k
1
t 12 =
k [ A ]0
[ A ] = −kt + [ A ]0
t 12
A ]0
[
=
2k
2
Rate Laws
AP Exam Practice
Sample Problem F
Answer the following questions related to the kinetics of chemical
reactions.
I
−
→ IO ( aq ) + Cl ( aq )
( aq ) + ClO ( aq ) ⎯⎯⎯
I,
−
OH
−
−
−
IO ,
Iodide ion, is oxidized by hypoiodite ion,
by hypochlorite,
ClO , in basic solution according to the equation above. Three
initial-rate experiments were conducted; the results are shown in the
following table.
Rate Laws
AP Exam Practice
Sample Problem F
Experiment
1
2
3
[I ]
(mol/L)
0.017
0.052
0.016
[ClO ]
(mol/L)
0.015
0.015
0.061
Initial Rate of Formation of
(mol/L*s)
0.156
0.476
0.596
IO
a.Determine the order of the reaction with respect to each reactant
listed below. Show your work.
i. I (aq)
ii.ClO (aq)
Rate Laws
AP Exam Practice
Sample Problem F
Experiment
1
2
3
[I ]
(mol/L)
0.017
0.052
0.016
[ClO ]
(mol/L)
0.015
0.015
0.061
Initial Rate of Formation of
(mol/L*s)
0.156
0.476
0.596
IO
b.For the reaction,
i. write the rate law that is consistent with the calculations in part
(a);
ii.calculate the value of the specific rate constant, k, and specify
units.
Rate Laws
AP Exam Practice
Sample Problem F
The catalyzed decomposition of hydrogen peroxide, H2O2(aq), is
represented by the following equation.
catalyst
2H 2O 2 ( aq ) ⎯⎯⎯→ 2H 2O ( l ) + O2 ( g )
The kinetics of the decomposition reaction were studied and the
analysis of the results show that it is a first-order reaction. Some of
the experimental data are shown in the table below.
[H2O2]
Time (min)
1
0
0.78
5
0.61
10
AP* Chemistry: Kinetics
Rate Laws
Name: ______________________________
Period:_____________
AP Exam Practice
(c) During the analysis of the data, the graph below was produced.
Sample Problem F
c.During the analysis of the data, the graph below was produced.
i. Label the vertical axis of the graph.
(i) Label the vertical axis of the graph that is repeated on your student answer pages.
ii.What are the units of the rate constant, k, for the decomposition
(ii) What are the units of the rate constant, k , for the decomposition of H O (aq) ?
of H2O2(aq)?
(iii) On the graph repeated on your student answer pages, draw the line that represents the plot of the
uncatalyzed
decomposition of 1.00
O (aq)of
. the uncatalyzed firstiii.Draw the
line first-order
that represents
theM Hplot
order decomposition of 1.00 M H2O2(aq).
2
2
2
NO CALCULATORS MAY BE USED
2
Rate Laws
Half-Life
Sample Problem G
The decomposition of a certain insecticide in water follows 1st order
-1
kinetics with a rate constant of 1.45 yr . A quantity of the
insecticide is washed into a lake on June 1, leading to a
-7
3
concentration of 5.0 x 10 g/cm .
a.What is the concentration of insecticide on June 1 of the following
year?
b.How long will it take for the concentration of the insecticide to
-7
3
drop to 3.0 x 10 g/cm ?
A Model for Chemical Kinetics
Activation Energy
A Model for Chemical Kinetics
Endothermic vs. Exothermic
A Model for Chemical Kinetics
Determining Activation Energy
✦
✦
Use Arrhenius equation
Ea
ln k = −
+ ln A
RT
Graphically the equation shows that a graph of ln k vs. 1/T will have
the slope equal to -Ea/R with a y-intercept at ln A.
Reaction Mechanisms
Reaction Mechanisms
✦
✦
A balanced chemical reaction only shows what happens at the
beginning and the end.
Mechanism shows what happens at all points during the reaction by
showing the elementary steps in the reaction.
✦ Each step should add together to form the balanced chemical
equation.
✦ The mechanism must agree with the given rate law.
Reaction Mechanisms
Rate Determining Step
✦
✦
In a multi-step mechanism, the slowest step is the rate-determining
step. The rate-determining step therefore determines the rate of the
reaction.
The experimental rate law must agree with the rate determining
step.
Reaction Mechanisms
Rate Determining Step
Sample Problem H
2NO ( g ) + Br2 ( g ) ⎯⎯
→ 2NOBr ( g )
a.Identify the rate determining step.
Step 1 NO ( g ) + Br2 ( g ) ←⎯
→ NOBr2 ( g )
Step 2 NOBr2 ( g ) + NO ( g ) ⎯⎯
→ 2NOBr ( g )
b.Identify the rate law.
c.Identify any intermediates.
(slow )
( fast )
Catalysts
Catalysts
✦
Catalyst - a substance that speeds up a reaction without being
consumed (this does not mean that it can be changed during the
process)
✦ lowers activation energy
✦ increases the number of collisions
✦ Homogeneous catalyst - in the same phase as the reactants
✦ Heterogeneous catalyst - in a different phase
✦ Enzyme - type of biological catalyst
Rate Laws
AP Exam Practice
Sample Problem I
An environmental concern is the depletion of the O3 in Earth’s upper
atmosphere, where O3 is normally in equilibrium with O2 and O. A
proposed mechanism for the depletion of O3 in the upper
atmosphere is shown below.
Step I
O3 + Cl ⎯⎯
→ O2 + ClO
Step II
ClO + O ⎯⎯
→ Cl + O2
a.Write a balanced equation for the overall reaction represented by
Step I and Step II above.
Rate Laws
AP Exam Practice
Sample Problem I
An environmental concern is the depletion of the O3 in Earth’s upper
atmosphere, where O3 is normally in equilibrium with O2 and O. A
proposed mechanism for the depletion of O3 in the upper
atmosphere is shown below.
Step I
O3 + Cl ⎯⎯
→ O2 + ClO
Step II
ClO + O ⎯⎯
→ Cl + O2
b.Clearly identify the catalyst in the mechanism above. Justify your
answer.
Rate Laws
AP Exam Practice
Sample Problem I
An environmental concern is the depletion of the O3 in Earth’s upper
atmosphere, where O3 is normally in equilibrium with O2 and O. A
proposed mechanism for the depletion of O3 in the upper
atmosphere is shown below.
Step I
O3 + Cl ⎯⎯
→ O2 + ClO
Step II
ClO + O ⎯⎯
→ Cl + O2
c.Clearly identify the intermediate in the mechanism above. Justify
your answer.
Rate Laws
AP Exam Practice
Sample Problem I
Step I
O3 + Cl ⎯⎯
→ O2 + ClO
Step II
ClO + O ⎯⎯
→ Cl + O2
d.If the rate law for the overall reaction is found to be
rate=k[O3][Cl], determine the following.
i. The overall order of the reaction.
ii.Appropriate units for the rate constant, k
iii.The rate-determining step of the reaction, along with justification
for your answer.
Daily Objectives
Chemistry II Honors
Today, I will be able to
use kinetic experiment data to calculate the rate law, rate law
constant, and the units of the rate law constant.
•
LO 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9
Rate Laws
AP Exam Practice
Sample Problem J
Consider the following general equation for a chemical reaction.
0
A ( g ) + B ( g ) ⎯⎯
→ C ( g) + D ( g)
ΔH rxn = −10 kJ
a.Describe the two factors that determine whether a collision
between molecules of A and B results in a reaction.
b.How would a decrease in temperature affect the rate of reaction
shown above? Explain your answer.
Rate Laws
AP Exam Practice
Sample Problem J
Consider the following general equation for a chemical reaction.
0
A ( g ) + B ( g ) ⎯⎯
→ C ( g) + D ( g)
ΔH rxn = −10 kJ
c.Write the rate law expression that would result if the reaction
proceeded by the mechanism shown below.
A + B ⎯⎯
→ [ AB ]
( fast )
→C + D
[ AB ] + B ⎯⎯
(slow )
d.Explain why a catalyst increases the rate of a reaction but does not
change the value of the equilibrium constant for that reaction.
Rate Laws
AP Exam Practice
Sample Problem K
A ( aq ) + 2B ( aq ) ⎯⎯
→ 3C ( aq ) + D ( aq )
For the reaction above, carried out in a solution of 30ºC, the
following kinetic data were obtained:
Experiment
1
Initial Conc. of Reactants Initial Rate of
Reaction
A0
B0
0.24
0.48
8
2
0.24
0.12
2
3
0.36
0.24
9
4
0.12
0.12
0.5
5
0.24
0.06
1
6
0.014
1.35
?
Rate Laws
AP Exam Practice
Sample Problem K
A ( aq ) + 2B ( aq ) ⎯⎯
→ 3C ( aq ) + D ( aq )
Experiment
1
Initial Conc. of Reactants Initial Rate of
Reaction
A0
B0
0.24
0.48
8
2
0.24
0.12
2
3
0.36
0.24
9
4
0.12
0.12
0.5
5
0.24
0.06
1
6
0.014
1.35
?
a.Write the rate-law expression for this reaction.
b.Calculate the value of the specific rate constant k at 30ºC and specify
its units.
Rate Laws
AP Exam Practice
Sample Problem K
A ( aq ) + 2B ( aq ) ⎯⎯
→ 3C ( aq ) + D ( aq )
Experiment
1
Initial Conc. of Reactants Initial Rate of
Reaction
A0
B0
0.24
0.48
8
2
0.24
0.12
2
3
0.36
0.24
9
4
0.12
0.12
0.5
5
0.24
0.06
1
6
0.014
1.35
?
c.Calculate the value of the initial rate of this reaction at 30ºC for the
initial concentrations shown in experiment 6.
d.Assume that the reaction goes to completion. Under the conditions
specified for experiment 2, what would be the final molar
concentration of C?
Rate Laws
AP Exam Practice
Sample Problem L
2ClO2 ( g ) + F2 ( g ) ⎯⎯
→ 2ClO2 F ( g )
The following results were obtained when the reaction represented
above was studied at 25ºC.
Experiment
Initial Conc. of Reactants Initial Rate of
Reaction of
[ClO2]
[F2]
[ClO2F]
1
0.01
0.1
2.4 x 10-3
2
0.01
0.4
9.6 x 10-3
3
0.02
0.2
9.6 x 10-3
Rate Laws
AP Exam Practice
Sample Problem L
2ClO2 ( g ) + F2 ( g ) ⎯⎯
→ 2ClO2 F ( g )
Experiment
Initial Conc. of Reactants Initial Rate of
Reaction of
[ClO2]
[F2]
[ClO2F]
1
0.01
0.1
2.4 x 10-3
2
0.01
0.4
9.6 x 10-3
3
0.02
0.2
9.6 x 10-3
a.Write the rate law expression for the reaction above.
b.Calculate the numerical value of the rate constant and specify the
units.
Rate Laws
AP Exam Practice
Sample Problem L
2ClO2 ( g ) + F2 ( g ) ⎯⎯
→ 2ClO2 F ( g )
Experiment
Initial Conc. of Reactants Initial Rate of
Reaction of
[ClO2]
[F2]
[ClO2F]
1
0.01
0.1
2.4 x 10-3
2
0.01
0.4
9.6 x 10-3
3
0.02
0.2
9.6 x 10-3
c.In experiment 2, what is the initial rate of decrease of [F2]?
Rate Laws
AP Exam Practice
Sample Problem L
d.Which of the following reaction mechanisms is consistent with the
rate law developed in (a). Justify your answer.
I.
⎯⎯
⎯
→
ClO2 + F2 ←
⎯ ClO2 F2
ClO2 F2 ⎯⎯
→ ClO2 F + F
ClO2 + F ⎯⎯
→ ClO2 F
⎯⎯
⎯
→
II. F2 ←
⎯ 2F
(
2 ClO2 + F ⎯⎯
→ ClO2 F
)
( fast )
( slow )
( fast )
( slow )
( fast )
Rate Laws
AP Exam Practice
Sample Problem M
2H 2O2 ( aq ) ⎯⎯
→ 2H 2O ( l ) + O2 ( g )
Hydrogen peroxide decomposes according to the equation above.
a.An aqueous solution of H2O2 that is 6.00 percent H2O2 by mass
has a density of 1.03 g/mL. Calculate each of the following.
i. The original number of moles of H2O2 in a 125 mL sample of the
6.00 percent H2O2 solution.
ii.The number of moles of O2(g) that are produced when all of the
H2O2 in the 125 mL sample decomposes.
2 H2O2(aq)
2 H2O(l) + O2(g)
Hydrogen peroxide decomposes according to the equation above.
Rate Laws
(a) An aqueous solution of H2O2 that is 6.00 percent H2O2 by mass has a density of 1.03 g mL–1. Calculate
each of the following.
(i) The original number of moles of H2O2 in a 125 mL sample of the 6.00 percent H2O2 solution
(ii) The number of moles of O2(g) that are produced when all of the H2O2in the 125 mL sample
AP Exam Practice
decomposes
Sample Problem
M
(b) The graphs below show results from a study of the decomposition of H O .
2
2
b.The graphs below show results from a study of the decomposition
of H2O2.
i. Write the rate law for the reaction. Justify your answer.
(i) Write the rate law for the reaction. Justify your answer.
(ii) Determine
the half-life of the
reaction.
ii.Determine
the
half-life
of
the
reaction.
(iii) Calculate the value of the rate constant, k. Include appropriate units in your answer.
(iv) Determine [H2O2] after 2,000 minutes elapse from the time the reaction began.
2 H2O2(aq)
2 H2O(l) + O2(g)
Hydrogen peroxide decomposes according to the equation above.
Rate Laws
(a) An aqueous solution of H2O2 that is 6.00 percent H2O2 by mass has a density of 1.03 g mL–1. Calculate
each of the following.
(i) The original number of moles of H2O2 in a 125 mL sample of the 6.00 percent H2O2 solution
(ii) The number of moles of O2(g) that are produced when all of the H2O2in the 125 mL sample
AP Exam Practice
decomposes
Sample Problem
M
(b) The graphs below show results from a study of the decomposition of H O .
2
2
b.The graphs below show results from a study of the decomposition
of H2O2.
iii.Calculate the value of the rate constant, k. Include appropriate
(i) Write the rate law for the reaction. Justify your answer.
units in your
answer.
(ii) Determine
the half-life of the reaction.
(iii) Calculate the value of the rate constant, k. Include appropriate units in your answer.
(iv) Determine
[H 2
O]] after
2,000 minutes
elapse
from the time the
reaction began.
iv.Determine
[H2O
after
2000
minutes
elapse
from the time the
reaction begun.
2
2