1. 13.2 0th, 1st and 2nd Order Reaction Factors Affecting Reaction Rates
Fred Omega Garces
Chemistry 201
Miramar College

2. Outline Rate Laws: Differential Rate Law Integrated Rate Law
0th Order: Rate = k[A]0 = k [A] = -kt + [Ao]
1st Order: Rate = k[A] ln[A] = -kt + ln[Ao]
2nd Order: Rate = k[A] / [A] = kt + 1 / [Ao]

3. Evaluation of Rate Constant and Half-lives
Oth Order:
2N2O (g)  2N2 (g) + O2 (g)
Rate = k[A]0 = k
1st Order:
14C  14N e
Rate = k [A] 1
2nd Order:
NO2 (g)  NO (g) + 1/2 O2 (g)
CH3Cl + OH- CH3OH + Cl- Rate = k[A]2

4. Zeroth Order A Decomposition: 2N2O  2N2 + O2 t
Some reactions are independent on concentrations.
rxn rate = k [A]0 = k
[A] - [A o] = -kt
or [A] = -k t + [A o]
y = mx + b
Slope =  [A] = -k t
Data :
[A] Rates
1 1
4 1
8 1 A
@ t  te
[A] = 0 t
plot of [A] vs t (time)
straight line

5. Half-Life
Half-life (t1/2) Time for the concentration of a reactant to decrease to half its original concentration.
Ao - original concentration
@ t1/2 A = Ao/2
The time it takes for the concentration of the original sample to decrease to half its original value.
Consider, t1/2 = 1 hr
hr hr hr
st t1/ nd t1/2 3rd t1/2

6. Zeroth Order: Half-life
Data :
[A] Rates
1 1
4 1
8 1
Metabolism of Alcohol
Rate: 1 oz / 5 hr
or oz /hr
Oth order reaction seldom occurs except for reactions which are catalyzed by enzymes

7. First Order y = mx + b ln[A] = - kt + ln[A]o Slope =  ln [A] = -k t
Radioactivity: 14C  14N e
rxn rate = -dA/dt = k[A]  dA / [A] = - k dt
Separate:
Integrate:
ln[A] = - kt + ln[A]o
y = mx + b
Data :
[A] Rates m/s
1 1
4 4
8 8
ln [A]o
Slope =  ln [A] = -k t
ln [A]
plot of ln[A] vs t
straight line t

8. First Order: Half-life
Data :
[A] Rates m/s
1 1
4 4
8 8
Carbon Dating: Half-life is independent of reactant conc.
14N  14C + 1H
ln[A] = - kt + ln[A]o 1n O2
*CO2
14C - Carbon dating
t1/2 = 5730 yr.
*CO2
ln 2 = + k t1/2
*CO2 *C
 Half-life is not function of conc.

9. Radioisotope Dating ln[A] = - kt + ln[A]o
For 1st Order Reaction: Half-life is independent of concentration of reactant.
C-14 dating is accurate only up to 50,000yr.
14C  14N e (-emission)
U-238 accurate up to 4.5•109 yr.
Based on data, Earth is Billion yrs. old.
Otzi The Iceman
ln[A] = - kt + ln[A]o
3300 BC or 5300 years ago

10. Calculation of Age Based on t1/2
TURIN, Italy -- Almost everything about the Shroud of Turin is mysterious- its age, its authenticity, and the identity of the bearded man with deep-set eyes whose image is imprinted on the 14-foot length of yellowing linen, still believed by many Christians to be the burial cloth of Jesus as carbon testing done on tiny swatches of the shroud concluded in or to the time of Jesus, the centuries-old fascination with the shroud....
The Shroud of Turin is a linen cloth over 4 m long. It bears a faint, straw-colored image of an adult male of average build who had apparently been crucified. Reliable records of the shroud date to about 1350, but for these past 600 years it has been alleged to be the burial shroud of Jesus Christ. Numerous chemical and other tests have been done on tiny fragments of the shroud in recent years. The general conclusion has been that the image was not painted on the cloth by any traditional method, but no one could say exactly how the image had been created. Re-cent advances in radiochemical dating methods, however, led to a new effort in 1987–1988 to estimate the age of the cloth. Using radioactive 14 C, the flax from which the linen was made was shown to have been grown between 1260 and 1390 A.D. There is no chance that the cloth was made at the time of Christ.

11. Second Order Decomposition: NO2 (g)  NO (g) + 1/2 O2 (g)
rxn rate = -dA/dt = k[A]2  dA / [A]2 = - k dt
Separate:
Integrate:
y = m x b
Slope =  1/ [A] = k t
1/[A]
plot of 1/[A] vs t
straight line
[A] t
1/ [A]o t

12. Second Order: Half-life
Data :
[A] Rates m/s
1 1
4 16
8 64
Decomposition of NO2:
NO2 (g)  NO (g) + 1/2O2 (g)
In a second-order reaction each successive half-life is double the preceding one. Furthermore, the half-life for a second order reaction is inversely related to the initial concentration of reactant.
 Half-life is a function of conc. & k

13. In Class Exercise
N2O5 can decomposes to nitrogen dioxide and oxygen gases.
Here are some data for the decomposition reaction:
Time (min)
[N2O5] • 10-2M
Determine the order and the rate constant by constructing
appropriate graphs using the data.
What is the rate constant for this reaction?
What is the overall rate law for this reaction?
What is the half-life of this reaction?

14. Analysis

15. Summary Order Order Order Zero First Second
Rate Law R = k R=k[A] R = k[A]2
Integrated rate law A = -kt + [A]o ln[ A] = -kt + ln[A]o 1/[A]=kt +1/[A]o
Plot (straight line) [A] vs. t ln[A] vs. t 1/[A] vs. t
slope m = -k m = -k m = k
Half-life t1/2 = [A]0/2k t1/2 =0.693/k t1/2 =1/k[A]0