Successfully reported this slideshow.
Upcoming SlideShare
×

8

Share

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

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

• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

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

1. 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. 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]0 (No dependence of reaction rate on [A].)
3. 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. 4. Determining Reaction Order using Integrated Rate Laws 1) In an experiment, collect concentration data versus time. 2) To determine if the reaction is first order, calculate the ln[A] of each concentration. 3) Plot ln[A] versus time. If itβs a straight line, itβs first order! ο
5. 5. First-Order Integrated Rate Law Using calculus to integrate the differential rate law for a first-order process gives us ln A t A 0 = βπt 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.
6. 6. First-Order Integrated Rate Law Rearrange this equationβ¦ ln A t A 0 = βπt ln A t β ln A 0 = βπt ln A t = βπt + ln A 0 This is a linear equation! Use log rule: π₯π§ π± π² = π₯π§ π± β π₯π§ π²
7. 7. First-Order Integrated Rate Law A first-order reaction is an exponential decay (in terms of reactant). A t = A 0 πβπt The concentration of reactant A decreases exponentially over time.
8. 8. First-Order Plots Graphs for a first-order reaction: Graphs for a First Order Reaction from http://2012books.lardbucket.org/books/principles-of-general-chemistry- v1.0m/s18-03-methods-of-determining-reactio.html π¨ π = π¨ π πβππ­ π₯π§ π¨ π = βππ­ + π₯π§ π¨ π
9. 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 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. 10. Determining Rxn Order using Integrated Rate Laws Step 3: Graph ln [A] vs. time The plot shows a straight line. The reaction fits 1st order kinetics.
11. 11. Determining Rxn Order using Integrated Rate Laws π₯π§ π¨ π = βππ­ + π₯π§ π¨ π k is the βrate constantβ The slope of the line is ο­k. k = 0.0023 sο­1
12. 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 t1/2 is one-half of the original concentration of A, [A]t = 0.5 [A]0 The Half Life of a First Order Reaction from http://2012books.lardbucket.org/books/principles-of-general-chemistry- v1.0m/s18-05-half-lives-and-radioactive-dec.html
13. 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]0 ln 0.5 A 0 = βπt + ln A 0 ln 0.5 A 0 β ln A 0 = βπt Use log rule: π₯π§ π± π² = π₯π§ π± β π₯π§ π²
14. 14. Half-Life for a First Order Process ln 0.5 A 0 β ln A 0 = βπt ln 0.5 A 0 A 0 = βπt1 2 ln 0.5 A 0 A 0 = βπt1 2 π₯π§ π. π = βππ­ π π Time is now labeled for half life with a subscript (t1/2)
15. 15. Half-Life for a First Order Process π₯π§ π. π = βππ­ π π β0.693 = βπt1 2 Cancel negative signs and solve for t1/2 π π π = π. πππ π Ln 0.5 is just a number (put it in your calculator!)
16. 16. Half-Life for a First Order Process π π π = π. πππ π Note that the half life for a first-order process does not depend on the initial concentration [A]0
17. 17. Example Problems will be posted separately. Next up, The Second Order Integrated Rate Law (Pt 5)

### Be the first to comment

Oct. 1, 2016

Oct. 8, 2016

Dec. 5, 2018

Dec. 3, 2019
• #### Elibarikissa

Dec. 20, 2019

Feb. 28, 2020
• #### KathirKing2

Jun. 24, 2020
• #### MarionAkiri

Jan. 29, 2021

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

Total views

5,337

On Slideshare

0

From embeds

0

Number of embeds

365

146

Shares

0