1. Chemistry 102(001) Fall 2012 CTH 328 10:00-11:15 am
Instructor: Dr. Upali Siriwardane
Office: CTH 311 Phone
Office Hours: M,W 8:00-9:00 & 11:00-12:00 am; Tu, Th, F 8: :00am..
Exams: 10:00-11:15 am, CTH 328.
September 25,  2012 (Test 1): Chapter 13
October 18, (Test 2): Chapter 14 &15
November 13, (Test 3): Chapter 16 &18
Optional Comprehensive Final Exam: November 15, :
Chapters 13, 14, 15, 16, 17, and 18

2. Chemical Kinetics: Rate Laws
GHW# 2: Chapter 13
Chemical Kinetics: Rate Laws

3. 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
Equation
13.6 Rate Laws for Elementary Reactions
13.7 Reaction Mechanisms
13.8 Catalysts and Reaction Rate
13.9 Enzymes: Biological Catalysts
13‑10 Catalysis in Industry

4. 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

5. 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.

6. 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

7. 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

8. 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).

9. = kt + Graphical method k rate = k 1 ln[A]t 2 [A]t -k Rate
Order
Rate
Law
Integrated Rate Law
Graph
X vs. time
Slope
rate = k
[A]t = -kt + [A]0
[A]t -k 1
rate = k[A]
ln[A]t = -kt + ln[A]0
ln[A]t 2
rate=k[A]2
= kt + k 1
[A]t 1
[A]t 1
[A]0

10. Differential and Integral Rate Law
Rate Law Differential Rate Law Integral Rate
rate = k [A] 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] 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

11. Integral and Half-life forms
t½ Law
t½ =  [A] o / 2k
t½ = / k
t½ = 1 / k [A]o
Integral Law
[A]f-[A]0 = -kt
ln [A]t/[A]0 = -kt
1/[A]f = kt + 1/[A]0
Zero order
First order
Second order

12. 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. First-order, Second-order, and Zeroth-order Plots

14. Comparing graphs This plot of ln[cis-platin] vs.
time produces a straight line,
suggesting that the reaction
is first-order.

15. 2. Using graphical method, show that
2 N2O5 ---> 4 NO2 + O2, is a first order reaction.
Time / min
[N2O5] / moldm-3
ln N2O5] 20 40 60 80
100
160

16. 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.

17. Decomposition Reaction

18. Graphical Ways to get Order

19. Initial rate

20. 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: x rate = k [2A]1 k1 = k 21[A]1 k1
rate = k [A ] k1 rate = 1
rate = k 21[A ]1 k1 rate = 21 (doubles)
Second order: 2 x rate = k [2A]1 k1 = k 22[A]2 k1
rate = k [A ] k1 rate = 1
rate = k 22[A ]2 k1 rate = 22 (quadruples)

21. 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

22. Rate data

23. 3. For the reaction: A ---> D, Find the order of [A] for each case
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

24. Units of the Rate Constant (k)1
first order: k = ─── = s-1 s L
second order k = ───
mol s L2
third order k = ───
mol2 s

25. 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 _____________________________

26. Overall order

27. 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

28. Determining K, Rate Constant

29. First Order Reactions and t½
A ----> B

30. Radio Activity and Nuclear Kinetics
Nuclear reactions? Fusion Fission What kinetics fission follow?

31. Half-life t½ Carbon-14 Radioisotope Half-life Polonium-215
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

32. Nuclear Reactions : First order kinetics

33. t1/2 equation
0.693 = k t1/2
0.693
t1/2 = ---- k

34. t1/2 = Half-life - t1/2 0.693 k k = = = 3.65 x 10-4 s-1
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

35. 5. The rate constant for the first-order conversion of A to B is 2
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?

36.  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?

37.  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 M, predict the concentration after five hours (300 min).