Chemistry 102(001) Fall 2012
CTH 328 10:00-11:15 am
Instructor: Dr. Upali Siriwardane
e-mail: upali@latech.edu
Office: CTH 311 Phone 257-4941
Office Hours: M,W 8:00-9:00 & 11:00-12:00 am;
Tu, Th, F 8:00 - 10:00am..
Exams: 10:00-11:15 am, CTH 328.
September 25, 2012 (Test 1): Chapter 13
October 18, 2012 (Test 2): Chapter 14 &15
November 13, 2012 (Test 3): Chapter 16 &18
Optional Comprehensive Final Exam: November 15, 2012
:
Chapters 13, 14, 15, 16, 17, and 18
CHEM 102, Spring 2012, LA TECH
13-1
GHW# 2: Chapter 13
Chemical Kinetics: Rate Laws
CHEM 102, Spring 2012, LA TECH
13-2
Chapter 13. Chemical Kinetics
13.1
13.2
13.3
13.4
13.5
Reaction Rate
Effect of Concentration on Reaction Rate
Rate Law and Order of Reaction
A Nanoscale View: Elementary Reactions
Temperature and Reaction Rate: The Arrhenius
Equation
13.6 Rate Laws for Elementary Reactions
13.7 Reaction Mechanisms
13.8 Catalysts and Reaction Rate
13.9 Enzymes: Biological Catalysts
13-10Catalysis in Industry
CHEM 102, Spring 2012, LA TECH
13-3
Chemical Kinetics Definitions
and Concepts
a) rate of reations
b) rate law
b) rate constant
c) order
d) differential rate law
c) integral rate law
d) Half-life law
CHEM 102, Spring 2012, LA TECH
13-4
Rate Law
Every chemical reaction has a Rate Law
The rate law is an expression that relates
the rate of a chemical reaction to a constant
(rate constant-k) and concentration of
reactants raised to a power.
The power of a concentration is called the order
with respect to a particular reactant.
CHEM 102, Spring 2012, LA TECH
13-5
Rate Law
E.g.
aA + bB -----> cC
rate a [A]l[B]m
rate = -1/a d[A]/dt = k [A]l[B]m; k = rate constant
[A] = concentration of A
[B] = concentration of B
l = order with respect to A
m = order with respect to B
l & m have nothing to do with stoichiometric coefficients
CHEM 102, Spring 2012, LA TECH
13-6
Differential Rate Law
E.g.
2 N2O5(g) -----> 4 NO2 (g) + O2 (g)
rate= - ½ d[N2O5]/dt a [N2O5]1
rate = - ½ d[N2O5]/dt = k [N2O5]1
k = rate constant
[N2O5] = concentration of N2O5
1 = order with respect to N2O5
Rate and the order are obtained by experiments
CHEM 102, Spring 2012, LA TECH
13-7
Order
The power of the concentrations is the order with
respect to the reactant.
E.g.
a A + b B -----> c C
If the rate law: rate = k [A]1[B]2
The order of the reaction with respect to A is one (1).
The order of the reaction with respect to B is two (2).
Overall order of a chemical reaction is equal to the
sum of all orders (3).
CHEM 102, Spring 2012, LA TECH
13-8
Graphical method
Rate
Integrated Rate Law
Graph
X vs. time
Slope
[A] = -kt + [A]
[A]t
-k
ln[A]t
-k
Order Law
0
rate = k
1
rate = k[A]
t
0
ln[A]t = -kt + ln[A]0
2
rate=k[A]2
CHEM 102, Spring 2012, LA TECH
1
[A]t
= kt +
1
[A]0
1
[A]t
k
13-9
Differential and Integral Rate Law
Rate Law
rate = k [A]0
rate = k [A]1
rate = k [A]2
CHEM 102, Spring 2012, LA TECH
Differential Rate Law Integral Rate
-D [A]/Dt = k ; ([A]0=1) [A]f-[A]0 = -kt
- d [A]/dt = k ; ([A]0=1 [A]f= -kt + [A]0
[A]f- [A]0= -kt
- D [A]/ D t = k [A]
ln [A]t/[A]0= - kt
d [A]/dt = - k [A]
-D [A]/Dt = k [A]2 1/ [A]f - 1/[A]0 = kt
d [A]/dt = - k [A]2
1/ [A]f = kt - 1/[A]0
13-10
Integral and Half-life forms
Integral Law
t½ Law
[A]f-[A]0 = -kt
t½ = [A] o / 2k
First order
ln [A]t/[A]0 = -kt
t½ = 0.693 / k
Second order
1/[A]f = kt + 1/[A]0
Zero order
CHEM 102, Spring 2012, LA TECH
t½ = 1 / k [A]o
13-11
1) The reaction A ---> B + C is known to follow the
rate law: rate = k [A]1
What are the differential, integral and half-life (t½)
form of this rate law?
CHEM 102, Spring 2012, LA TECH
13-12
First-order, Second-order,
and Zeroth-order Plots
CHEM 102, Spring 2012, LA TECH
13-13
Comparing graphs
This plot of ln[cis-platin] vs.
time produces a straight line,
suggesting that the reaction
is first-order.
CHEM 102, Spring 2012, LA TECH
13-14
2. Using graphical method, show that
2 N2O5 ---> 4 NO2 + O2, is a first order reaction.
Time / min
[N2O5] / moldm-3
0
20
40
60
80
100
160
0.01756
0.00933
0.00531
0.00295
0.00167
0.00094
0.00014
CHEM 102, Spring 2012, LA TECH
ln N2O5]
13-15
Finding rate laws by Initial rates
Method of initial rates
The order for each reactant is found by:
• Changing the initial concentration of that reactant.
• Holding all other initial concentrations and
conditions constant.
• Measuring the initial rates of reaction
The change in rate is used to determine the order for
that specific reactant. The process is repeated for
each reactant.
CHEM 102, Spring 2012, LA TECH
13-16
Decomposition Reaction
CHEM 102, Spring 2012, LA TECH
13-17
Graphical Ways to get Order
CHEM 102, Spring 2012, LA TECH
13-18
Initial rate
CHEM 102, Spring 2012, LA TECH
13-19
How do get order of reactants
E.g.
a A + b B -----> c C
Hold [B] constant and change (double) [A]
a A + b B -----> c C
If the rate law: rate = k [A]x[B]y
rate
= k [A]1 k1
First order:
1 x rate = k [2A]1 k1 = k 21[A]1 k1
rate1
= k [A ]1 k1
rate1
= 1
rate2
= k 21[A ]1 k1
rate2
= 21 (doubles)
Second order: 2 x rate = k [2A]1 k1 = k 22[A]2 k1
rate1
= k [A ]2 k1
rate1
= 1
2[A ]2 k
2 (quadruples)
rate
=
k
2
rate
=
2
2
1
2
CHEM 102, Spring 2012, LA TECH
13-20
How do you find order?
A + B -----> C
rate = k [A]l[B]m;
Hold concentration of other reactants constant
If [A] doubled, rate doubled
• 1st order, [2A]1 = 2 1 x [A]1 , 2 1 = 2
b) If [A] doubled, rate quadrupled
• 2nd order, [2A]2 = 2 2 x [A]2 , 2 2 = 4
c) If [A] doubled, rate increased 8 times
• 3rd order, [2A]3 = 2 3 x [A]3 , 2 3 = 8
CHEM 102, Spring 2012, LA TECH
13-21
Rate data
CHEM 102, Spring 2012, LA TECH
13-22
3. For the reaction: A ---> D, Find the order of [A]
for each case.
It was found in separate experiments that
a) The rate doubled when [A] doubled
b) The rate tripled when [A] tripled
c) The rate quadrupled when [A] doubled
d) The rate increased 8 times when [A] doubled
CHEM 102, Spring 2012, LA TECH
13-23
Units of the Rate Constant (k)
1
first order: k = ─── =
s-1
s
L
second order k =
───
mol s
third order k =
CHEM 102, Spring 2012, LA TECH
L2
───
mol2 s
13-24
4. For the chemical reaction: A + B ----> C
Using the following initial data to deduce:
a) Order of each reactant
b) Rate constant
[A],mol/L [B],mol/L rate,mol/Ls
_____________________________
2.0
3.0
0.10
6.0
3.0
0.90
6.0
6.0
0.90
CHEM 102, Spring 2012, LA TECH
13-25
Overall order
CHEM 102, Spring 2012, LA TECH
13-26
Rate Constant
E.g.
a A + b B -----> c C
rate a [A]l[B]m
rate = k [A]l[B]m;
k = rate constant
proportionality constant of the rate law
Larger the k faster the reaction
It is related inversely to t½
CHEM 102, Spring 2012, LA TECH
13-27
Determining K, Rate Constant
CHEM 102, Spring 2012, LA TECH
13-28
First Order Reactions
and t½
A ----> B
CHEM 102, Spring 2012, LA TECH
13-29
Radio Activity and Nuclear Kinetics
Nuclear reactions?
Fusion
Fission
What kinetics fission follow?
CHEM 102, Spring 2012, LA TECH
13-30
Half-life t½
Radioisotope
Polonium-215
Bismuth-212
Sodium-24
Half-life
0.0018 seconds
60.5 seconds
15 hours
Iodine-131
Cobalt-60
8.07 days
5.26 years
Carbon-14
5730 years
Radium-226
1600 years
Uranium-238
4.5 billion years
CHEM 102, Spring 2012, LA TECH
13-31
Nuclear Reactions : First order kinetics
CHEM 102, Spring 2012, LA TECH
13-32
t1/2 equation
0.693 =
t1/2 =
CHEM 102, Spring 2012, LA TECH
k t1/2
0.693
---k
13-33
Half-life -
t1/2
The half-life and the rate constant are related.
t1/2 =
0.693
k
Half-life can be used to calculate the first order rate
constant.
For our N2O5 example, the reaction took 1900 seconds to
react half way so:
k
=
0.693
t1/2
CHEM 102, Spring 2012, LA TECH
=
0.693
1900 s
=
-4 -1
3.65 x 10 s
13-34
5. The rate constant for the first-order conversion of
A to B is 2.22 hr-1. How much time will be required
for the concentration of A to reach 75% of its
original value?
CHEM 102, Spring 2012, LA TECH
13-35
6) The half-life of a radioactive (follows first order
rate law) isotope is 10 days. How many days
would be required for the isotope to degrade to
one eighth of its original radioactivity?
CHEM 102, Spring 2012, LA TECH
13-36
7) The rate constant for the first order
decomposition of SO2Cl2 (SO2Cl2  SO2 +Cl2) at
very high temperature is 1.37 × 10-3 min-1. If the
initial concentration is 0.500 M, predict the
concentration after five hours (300 min).
CHEM 102, Spring 2012, LA TECH
13-37