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![Recall: Differential Rate Laws
RECALL: (Differential) Rate Laws for 3 common
reaction orders:
First Order: Rate = k [A]1
Second Order: Rate = k [A]2
Zero Order: Rate = k [A]0
(No dependence of reaction rate on [A].)](https://image.slidesharecdn.com/unit14kinteticspt5secordfinal-160601162250/75/Chem-2-Chemical-Kinetics-V-The-Second-Order-Integrated-Rate-Law-2-2048.jpg)
![Second-Order Integrated Rate Law
Using calculus to integrate the differential rate
law for a second-order process gives us
1
A t
= 𝑘t +
1
A 0
Where,
[A]0 is the initial concentration of A, and
[A]t is the concentration of A at some time, t, during the
course of the reaction.](https://image.slidesharecdn.com/unit14kinteticspt5secordfinal-160601162250/75/Chem-2-Chemical-Kinetics-V-The-Second-Order-Integrated-Rate-Law-4-2048.jpg)
![Determining Reaction Order using
Integrated Rate Laws
Step 1: Collect
concentration versus
time data.
Step 2: Calculate
the reciprocal for
each concentration
measured. (1/[A])
Time [A] 1/[A]
0 0.0400 25.000
10 0.0303 33.003
20 0.0244 40.984
30 0.0204 49.020
40 0.0175 57.143](https://image.slidesharecdn.com/unit14kinteticspt5secordfinal-160601162250/75/Chem-2-Chemical-Kinetics-V-The-Second-Order-Integrated-Rate-Law-7-2048.jpg)
![Determining Rxn Order using Integrated Rate Laws
Step 3: Graph 1/[A] vs. time
The plot shows
a straight line.
The reaction
fits 2nd order
kinetics.](https://image.slidesharecdn.com/unit14kinteticspt5secordfinal-160601162250/75/Chem-2-Chemical-Kinetics-V-The-Second-Order-Integrated-Rate-Law-8-2048.jpg)
![Half-Life for a Second-Order Process
Deriving the half life for a second order process:
Let [A]t = 0.5[A]0
1
0.5 A 0
= 𝑘t +
1
A 0
2
A 0
= 𝑘t +
1
A 0
Subtract 𝟏
A
0
from both sides…](https://image.slidesharecdn.com/unit14kinteticspt5secordfinal-160601162250/75/Chem-2-Chemical-Kinetics-V-The-Second-Order-Integrated-Rate-Law-10-2048.jpg)
![Half-Life for a Second-Order Process
𝒕 𝟏
𝟐
=
𝟏
𝒌 𝑨 𝟎
Note that the half life for a second-order
process DOES depend on the initial
concentration [A]0](https://image.slidesharecdn.com/unit14kinteticspt5secordfinal-160601162250/75/Chem-2-Chemical-Kinetics-V-The-Second-Order-Integrated-Rate-Law-12-2048.jpg)
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Chem 2 - Chemical Kinetics V: The Second-Order Integrated Rate Law
This document discusses chemical kinetics for second-order reactions. It explains that for a second-order reaction, the rate is proportional to the concentration of the reactant squared. The integrated rate law for a second-order reaction is derived as 1/[A]t = kt + 1/[A]0, where [A]t is the concentration at time t, k is the rate constant, and [A]0 is the initial concentration. If a plot of 1/[A] versus time is linear, then the reaction is second-order. The half-life of a second-order reaction depends on the initial concentration and is calculated as t1/2 = 1/k[A]0.
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Chem 2 - Chemical Kinetics V: The Second-Order Integrated Rate Law
- 1. Chemical Kinetics (Pt.5) The Second-Order Integrated Rate Law By Shawn P. Shields, Ph.D. This work is licensed by Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
- 2. Recall: Differential RateLaws RECALL: (Differential) Rate Laws for 3 common reaction orders: First Order: Rate = k [A]1 Second Order: Rate = k [A]2 Zero Order: Rate = k [A]0 (No dependence of reaction rate on [A].)
- 3. Determining Reaction Orderwith Integrated Rate Laws 1) Collect concentration data versus time. 2) To determine if the reaction is second order, calculate the value of 𝟏 𝐀 for each concentration. 3) Plot 𝟏 𝐀 versus time. If it’s a straight line, it’s second order!
- 4. Second-Order Integrated RateLaw Using calculus to integrate the differential rate law for a second-order process gives us 1 A t = 𝑘t + 1 A 0 Where, [A]0 is the initial concentration of A, and [A]t is the concentration of A at some time, t, during the course of the reaction.
- 5. Second-Order Integrated RateLaw Plotting versus time will yield a line if the process is second order. 1 A t = 𝑘t + 1 A 0 Y = mx + b
- 6. Second-Order Plots Graphs fora Second Order Reaction from http://2012books.lardbucket.org/books/principles-of-general-chemistry- v1.0m/s18-03-methods-of-determining-reactio.html 1 A t = 𝑘t + 1 A 0 plot of A vs time
- 7. Determining Reaction Orderusing Integrated Rate Laws Step 1: Collect concentration versus time data. Step 2: Calculate the reciprocal for each concentration measured. (1/[A]) Time [A] 1/[A] 0 0.0400 25.000 10 0.0303 33.003 20 0.0244 40.984 30 0.0204 49.020 40 0.0175 57.143
- 8. Determining Rxn Orderusing Integrated Rate Laws Step 3: Graph 1/[A] vs. time The plot shows a straight line. The reaction fits 2nd order kinetics.
- 9. Plot for aSecond Order Reaction 𝟏 𝑨 𝒕 = 𝒌𝒕 + 𝟏 𝑨 𝟎 k is the “rate constant” The slope of the line is k. k = 0.803 M1 s1
- 10. Half-Life for aSecond-Order Process Deriving the half life for a second order process: Let [A]t = 0.5[A]0 1 0.5 A 0 = 𝑘t + 1 A 0 2 A 0 = 𝑘t + 1 A 0 Subtract 𝟏 A 0 from both sides…
- 11. Half-Life for aSecond-Order Process Subtract 𝟏 A 0 from both sides… 2 A 0 = 𝑘t + 1 A 0 2 A 0 − 1 A 0 = 𝑘t1 2 1 A 0 = 𝑘t1 2 1 𝑘 A 0 = t1 2 Time is now labeled for half life with a subscript (t1/2)
- 12. Half-Life for aSecond-Order Process 𝒕 𝟏 𝟐 = 𝟏 𝒌 𝑨 𝟎 Note that the half life for a second-order process DOES depend on the initial concentration [A]0
- 13. Example Problems will beposted separately. Next up, Microscopic Aspects of Kinetics- Chemical Reaction Mechanisms (Pt 6)