Chem 2 - Chemical Kinetics V: The Second-Order Integrated Rate Law

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 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] ( No dependence of reaction rate on [A].)

3. Determining Reaction Order with Integrated Rate Laws Collect concentration data versus time. To determine if the reaction is second order, calculate the value of for each concentration . Plot versus time. If it’s a straight line, it’s second order!   

4. Second-Order Integrated Rate Law Using calculus to integrate the differential rate law for a second-order process gives us Where, [ A] 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 Rate Law Plotting versus time will yield a line if the process is second order. Y = mx + b  

6. Second-Order Plots Graphs for a Second O rder R eaction from http :// 2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0m/s18-03-methods-of-determining-reactio.html    

7. 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 ] 0.0400 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 Order using Integrated Rate Laws Step 3: Graph 1/[ A ] vs. time The plot shows a straight line. The reaction fits 2 nd order kinetics.

9. Plot for a Second Order Reaction   k is the “rate constant” The slope of the line is k. k = 0.803 M  1 s  1

10. Half-Life for a Second-Order Process Deriving the half life for a second order process: Let [A] t = 0.5[A] Subtract from both sides…  

11. Half-Life for a Second-Order Process Subtract from both sides…   Time is now labeled for half life with a subscript ( t 1/2 )

12. Half-Life for a Second-Order Process Note that the half life for a second-order process DOES depend on the initial concentration [A]  

13. Example Problems will be posted separately. Next up, Microscopic Aspects of Kinetics- Chemical Reaction Mechanisms (Pt 6)