Kinetics

1. Kinetics Integrated rate law

2. TWO TYPES OF RATE LAWS • differential rate law--expresses how the rate depends on concentration (most common & what we’ve been doing!) • integrated rate law--expresses how the concentrations depend on time Choice: Depends on reaction and what is more convenient to measure

3. 12.4 INTEGRATED RATE LAW -CONCENTRATION/TIME RELATIONSHIPS When we wish to know how long a reaction must proceed to reach a predetermined concentration of some reagent, we can construct curves or derive an equation that relates concentration and time.

4. Graphical methods fordistinguishing FIRST, SECOND and ZERO order reactions First order: ln[A] = -kt + ln[A]o (y = ax + b) ln[reactant] vs. time straight line for first order in that reactant & since a = -k the slope of the line is negative. ln[A] t

5. Second order: 1/[A] = kt + 1/[A]o (y = ax + b) 1/[reactant] vs. time straight line for second order in that reactant since a = k the slope is positive. 1 [A] t

6. Zero order: [A] = -kt + [A]o (y = ax + b) [A] vs. time straight line for zero order in that reactant & since a = -k the slope of the line is negative [A] t

7. Half-life and reaction rate for ZERO-ORDER REACTIONS, t1/2 t1/2 = time required for one half of one of the reactants to disappear rate = k[A]0 = k (1) = k integrated rate law is: [A] = -kt + [A]o k = [A]o or t1/2 = [A]o 2t1/2 2k

8. Half-life and reaction rate for FIRST-ORDER REACTIONS, t1/2 rate = k[A]1 integrated rate law is: ln[A] = -kt + ln[A]o k = ln2 t ½ = .693 t ½ k

9. Half-life and reaction rate for SECOND-ORDER REACTIONS, t1/2 Rate = k[A]2 Integrated rate law is 1 = kt + 1 [A] [A]o k = 1 or t1/2 = 1 t1/2 [A]o k[A]o

10. Formula Sheets • On the AP test you will be given the integrated rate law for 1st and 2nd order reactions and that t ½ formula for a 1st order reaction. • On your test you will have to remember zero order (and what 1st and 2nd order look like as they are not labeled).