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13-1CHEM 102, Spring 2012, LA TECH
CTH 328 10:00-11:15 am
Instructor: Dr. Upali Siriwardane
e-mail: [email protected]
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
Chemistry 102(001) Fall 2012
13-3CHEM 102, Spring 2012, LA TECH
Chapter 13. Chemical Kinetics
13.1 Reaction Rate 13.2 Effect of Concentration on Reaction Rate 13.3 Rate Law and Order of Reaction
13.4 A Nanoscale View: Elementary Reactions
13.5 Temperature and Reaction Rate: The
Arrhenius Equation13.6 Rate Laws for Elementary Reactions13.7 Reaction Mechanisms13.8 Catalysts and Reaction Rate13.9 Enzymes: Biological Catalysts13‑10 Catalysis in Industry
13-4CHEM 102, Spring 2012, LA TECH
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
13-5CHEM 102, Spring 2012, LA TECH
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.
Rate Law
13-6CHEM 102, Spring 2012, LA TECH
Rate LawE.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
13-7CHEM 102, Spring 2012, LA TECH
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
13-8CHEM 102, Spring 2012, LA TECH
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).
13-9CHEM 102, Spring 2012, LA TECH
Graphical methodOrder
RateLaw
Integrated Rate Law GraphX vs. time
Slope
0 rate = k [A]t = -kt + [A]0 [A]t -k
1 rate = k[A]ln[A]t = -kt + ln[A]0
ln[A]t -k
2 rate=k[A]2 = kt + k1
[A]0
1
[A]t
1
[A]t
13-10CHEM 102, Spring 2012, LA TECH
Rate Law Differential Rate Law Integral Rate
rate = k [A]0 - 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
rate = k [A]1 - D [A]/ D t = k [A] ln [A]t/[A]0= - kt
d [A]/dt = - k [A]
rate = k [A]2 - 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
Differential and Integral Rate Law
13-11CHEM 102, Spring 2012, LA TECH
Integral Law
[A]f-[A]0 = -kt
ln [A]t/[A]0 = -kt
1/[A]f = kt + 1/[A]0
Integral and Half-life forms
First order
Zero order
Second order
t½ Law
t½ = [A] o / 2k
t½ = 0.693 / k
t½ = 1 / k [A]o
13-12CHEM 102, Spring 2012, LA TECH
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?
13-14CHEM 102, Spring 2012, LA TECH
This plot of ln[cis-platin] vs.
time produces a straight line,
suggesting that the reaction
is first-order.
Comparing graphs
13-15CHEM 102, Spring 2012, LA TECH
Time / min [N2O5] / moldm-3 ln N2O5]
0 0.0175620 0.0093340 0.0053160 0.0029580 0.00167
100 0.00094160 0.00014
2. Using graphical method, show that
2 N2O5 ---> 4 NO2 + O2, is a first order reaction.
13-16CHEM 102, Spring 2012, LA TECH
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.
Finding rate laws by Initial rates
13-20CHEM 102, Spring 2012, LA TECH
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
rate2 = k 22[A ]2 k1 rate2 = 22 (quadruples)
13-21CHEM 102, Spring 2012, LA TECH
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
13-23CHEM 102, Spring 2012, LA TECH
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
13-24CHEM 102, Spring 2012, LA TECH
Units of the Rate Constant (k) 1first order: k = ─── = s-1
s L second order k = ─── mol s
L2 third order k = ─── mol2 s
13-25CHEM 102, Spring 2012, LA TECH
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
13-27CHEM 102, Spring 2012, LA TECH
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
13-30CHEM 102, Spring 2012, LA TECH
Radio Activity and Nuclear KineticsNuclear reactions?
Fusion
Fission
What kinetics fission follow?
13-31CHEM 102, Spring 2012, LA TECH
Half-life t½
Radioisotope Half-life
Polonium-215 0.0018 seconds
Bismuth-212 60.5 seconds
Sodium-24 15 hours
Iodine-131 8.07 days
Cobalt-60 5.26 years
Carbon-14 5730 years
Radium-226 1600 years
Uranium-238 4.5 billion years
13-34CHEM 102, Spring 2012, LA TECH
The half-life and the rate constant are related.
t1/2 =
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 = = = 3.65 x 10-4
s-1
0.693
k
0.693
t1/2
0.693
1900 s
Half-life - t1/2
13-35CHEM 102, Spring 2012, LA TECH
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?
13-36CHEM 102, Spring 2012, LA TECH
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?