Previously in Chem 104: How to determine Rate Law

1. Previously in • Chem 104: • How to determine Rate Law • TODAY • How to determine rate constant, k • Recognizing Plots • Using Integrated Rate Laws to determine concentrations vs time • Using the Arrhenius Eqn to find k at new Temp

2. 2X 2X 4.1 X 4.1 X Data on how the rate of H2O2 decomposition is affected by varying the Initial [I-] values.

3. So Rate depends on [H2O2]o : Raterxn = k [H2O2]o AND Rate depends on [KI] o : Raterxn = k* [KI]o Overall, Rate depends on two parameters: Raterxn = k’ [H2O2]o [KI]owhere k’= k k* And we saythe overall reaction is Second Order, 2o, First order, 1o, in H2O2 and First order, 1o, in KI

4. This expression where both dependences are written: Raterxn = k’ [H2O2]o [KI]o is the Rate law. The Rate Law is the reason Kinetics studies are done: It shows us the slowest step in reaction sequence: the Rate Determining Step, r.d.s.

5. Obtaining Rate Constants from Kinetic Data

6. Examples of Plots of Different Reaction Orders

7. Integrated Rate Laws

8. [rgt]o [rgt] t½ = ½ [rgt]o [rgt] t¼= ¼ [rgt]o t ½ t¼ Time, sec

9. Radioactive Decay and Half Lives Technetium Radiopharmaceuticals, Tc

10. The Collision Theory of Reactions • Reactions result when atoms/molecules collide with • sufficient energy to break bonds • - Molecules must collide in an orientation that leads to • productive bond cleavage and/or formation Collision Theory Connects Macroscopic and Microscopic Perspectives of Kinetics • The more molecules in a volume, the more collisions, or, the reaction occurrence depends on concentration

11. Collision Theory and: The Rate Law: the Macroscopic View Rate = k[H2O2][I-] [H2O2]o Why concentrations affect rate Time, sec

12. The Collision Theory: why higher temperatures help • Reactions result when atoms/molecules collide with • sufficient energy to break bonds • Molecules at a higher temperature move faster— • have a greater energy (energy distribution increases)

13. Energetics of a Reaction are Summarized in a Reaction Coordinate Ex. 1: For a single step reaction: A + A  B energy Ea : the “sufficient energy” in collision 2A rgts DHf : net reaction enthalpy B prdt Reaction progress

14. Collision Theory and: The Rate Law: the Macroscopic View Rate = k[H2O2][I-] Why concentrations affect rate [H2O2]o Time, sec The Rate Law: the Microscopic View

15. The Importance of the Rate Law The Rate Law specifies the the molecularity of the Rate-Determining Step, it specifies which collisions most affect rate. The Rate Determining Step is the process (collision) that has Ea, the energy of activation, the most energetic step of reaction.

16. Connecting Hoses to Water the Garden ½ inch, 4 gal/min 3/4 inch, 8 gal/min 1 inch, 16 gal/min How do you connect these 3 hoses to deliver water at the fastest rate? All will have same rate— Limited by the 4 gal/min, ½ inch hose

17. The rate determining step at the Burgmayer’s: Andrew…

18. In the reaction: 2 H2O2 O2 + 2 H2O the Rate Law is: Raterxn = k’ [H2O2]o [I-]o And so the r.d.s. involves one H2O2 and one I- Maybe like this?

19. If this is the slow step, how do we get to products? Step 1: H2O2 + I- H-O-I + OH-slow Step 2: H-O-I + H2O2 O2 + H2O + I- + H+ fast Step 3: H+ + OH- H2O v. fast Net reaction: 2 H2O2 O2 + 2 H2O the Rate Law is: Raterxn = k’ [H2O2]o [KI]o

20. These steps are called Elementary Reaction Steps. Here, all are bi-molecular (involve 2 species) Step 1: H2O2 + I- H-O-I + OH-k = 10-3 sec-1 Step 2: H-O-I + H2O2 O2 + H2O + I- + H+ k = ?sec-1 Step 3: H+ + OH- H2O k = 1013 sec-1 Net reaction: 2 H2O2 O2 + 2 H2O k = 10-3 sec-1 the Rate Law is: Raterxn = k’ [H2O2]o [KI]o

21. The Arrhenius Equation What is this? k = Ae-Ea/RT Activation energy: We now understand what that is

23. H2O2 I-

24. Bad orientation: no productive reaction occurs

25. If collision orientation is favorable, a reaction occurs OH- I-O-H

26. There may be several good collision orientations

27. The Arrhenius Equation Orientation Factor k = Ae-Ea/RT Activation energy: We now understand what that is

28. Energetics of a Reaction Summarized in a Reaction Coordinate Ex. 2: For a multi step reaction: 2 H2O2 O2 + 2 H2O energy 2 H2O2 DHf 2H2O+ O2 Reaction progress

29. Energetics of a Reaction Summarized in a Reaction Coordinate Ex. 2: For a multi step reaction: 2 H2O2 O2 + 2 H2O Transition state Step 2 energy Step 1: + I- Ea H-O-I + OH- intermediates - I- Step 3 2 H2O2 DHf 2H2O+ O2 Reaction progress