Chem 2 - Chemical Kinetics IV: The First-Order Integrated Rate Law

Chem 2 - Chemical Kinetics IV: The First-Order Integrated Rate Law

1. Chemical Kinetics (Pt. 4) The First-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. Differential Rate Laws ( 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. Integrated Rate Laws Use calculus to integrate the (differential) rate law for each of three common reaction orders. Now, we have a practical way to determine the order of a reaction .

4. Determining Reaction Order using Integrated Rate Laws In an experiment, collect concentration data versus time. To determine if the reaction is first order, calculate the ln[A] of each concentration . Plot ln[A] versus time. If it’s a straight line, it’s first order! 

5. First-Order Integrated Rate Law Using calculus to integrate the differential rate law for a first-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.  

6. First-Order Integrated Rate Law Rearrange this equation… This is a linear equation!   Use log rule:  

7. First-Order Integrated Rate Law A first-order reaction is an exponential decay (in terms of reactant). The concentration of reactant A decreases exponentially over time.  

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

9. Determining Reaction Order using Integrated Rate Laws Step 1: Collect concentration versus time data. Step 2: Calculate the natural log for each concentration measured. (ln [A ]) Time [A] ln[A] 0.25 -1.38629 60 0.218 -1.52326 90 0.204 -1.58964 120 0.19 -1.66073 180 0.166 -1.79577

10. Determining Rxn Order using Integrated Rate Laws Step 3: Graph ln [A ] vs. time The plot shows a straight line. The reaction fits 1 st order kinetics.

11. Determining Rxn Order using Integrated Rate Laws   k is the “rate constant” The slope of the line is  k. k = 0.0023 s  1

12. Half Life for First-Order Reactions Half-life is defined as the time required for one-half of a reactant to react. Because [A] at t 1/2 is one-half of the original concentration of A, [ A] t = 0.5 [ A] The Half L ife of a First O rder R eaction from http:// 2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0m/s18-05-half-lives-and-radioactive-dec.html

13. Half-Life for a First Order Process Deriving an expression for the half-life of a first-order process: Let [A] t = 0.5[A] Use log rule:  

14. Half-Life for a First Order Process   Time is now labeled for half life with a subscript ( t 1/2 )

15. Half-Life for a First Order Process Cancel negative signs and solve for t 1/2   Ln 0.5 is just a number (put it in your calculator!)

16. Half-Life for a First Order Process Note that the half life for a first-order process does not depend on the initial concentration [A]  

17. Example Problems will be posted separately. Next up, The Second Order Integrated Rate Law (Pt 5)