1. Chemical Kinetics The area of chemistry that concerns reaction rates and reaction mechanisms.

2. Reaction Rate The change in concentration of a reactant or product per unit of time

3. Rate Laws Differential rate laws express (reveal) the relationship between the concentration of reactants and the rate of the reaction. Integrated rate laws express (reveal) the relationship between concentration of reactants and time The differential rate law is usually just called “the rate law.”

4. Determining Order with Concentration vs. Time data (the Integrated Rate Law) Zero Order: First Order: Second Order:

5. Solving an Integrated Rate Law Time (s) [H 2 O 2 ] (mol/L) 01.00 1200.91 3000.78 6000.59 12000.37 18000.22 24000.13 30000.082 36000.050 Problem: Find the integrated rate law and the value for the rate constant, k A graphing calculator with linear regression analysis greatly simplifies this process!! (Click here to download my Rate Laws program for theTi-83 and Ti-84)

6. Time vs. [H 2 O 2 ] Time (s) [H 2 O 2 ] 01.00 1200.91 3000.78 6000.59 12000.37 18000.22 24000.13 30000.082 36000.050 y = ax + b a = -2.64 x 10 -4 b = 0.841 r 2 = 0.8891 r = -0.9429 Regression results:

7. Time vs. ln[H 2 O 2 ] Time (s) ln[H 2 O 2 ] 00 120-0.0943 300-0.2485 600-0.5276 1200-0.9943 1800-1.514 2400-2.04 3000-2.501 3600-2.996 Regression results: y = ax + b a = -8.35 x 10 -4 b = -.005 r 2 = 0.99978 r = -0.9999

8. Time vs. 1/[H 2 O 2 ] Time (s) 1/[H 2 O 2 ] 01.00 1201.0989 3001.2821 6001.6949 12002.7027 18004.5455 24007.6923 300012.195 360020.000 y = ax + b a = 0.00460 b = -0.847 r 2 = 0.8723 r = 0.9340 Regression results:

9. And the winner is… Time vs. ln[H 2 O 2 ] 1. As a result, the reaction is 1 st order 2. The (differential) rate law is: 3. The integrated rate law is: 4. But…what is the rate constant, k ?

10. Finding the Rate Constant, k Method #1: Calculate the slope from the Time vs. ln[H 2 O 2 ] table. Time (s) ln[H 2 O 2 ] 00 120-0.0943 300-0.2485 600-0.5276 1200-0.9943 1800-1.514 2400-2.04 3000-2.501 3600-2.996 Now remember:  k = -slope k = 8.32 x 10 -4 s -1

11. Finding the Rate Constant, k Method #2: Obtain k from the linear regresssion analysis. Now remember:  k = -slope k = 8.35 x 10 -4 s -1 Regression results: y = ax + b a = -8.35 x 10 -4 b = -.005 r 2 = 0.99978 r = -0.9999

12. Rate Laws Summary Zero Order First Order Second Order Rate Law Rate = kRate = k[A]Rate = k[A] 2 Integrated Rate Law [A] = -kt + [A] 0 ln[A] = -kt + ln[A] 0 Plot the produces a straight line [A] versus tln[A] versus t Relationship of rate constant to slope of straight line Slope = -k Slope = k Half-Life