Why do some reactions happen and others don’t? Are the products more stable than the reactants? Thermodynamics Does the reaction go at a reasonable rate? Kinetics Chapter 14: Chemical Kinetics Rates of Reactions

Control of Reactivity

Collision Theory Consider: NO + O3  NO2 + O2 For a reaction to take place: - Molecules must collide - They must do so in the correct orientation - They must collide with an energy greater than the “activation” energy Consider: NO + O3  NO2 + O2 product molecules separate Molecules collide Bonds are formed and break

What would control how fast a reaction happens?

So, what controls the rate of a reaction? Number of collisions How often they collide in a shape that allows new bonds to form The energy of the colliding reactant molecules We’ll consider dependence on: Concentration a. Rate laws b. Concentration vs. time relationships Temperature and activation energy Mechanism

Concentration Dependence It makes sense that as concentration increases, the number of collisions per second will increase Therefore, in general, as concentration increases, rate increases But, it depends on which collisions control the rate So, you can’t predict concentration dependence- it must be measured experimentally

Types of measured rates: Rate over time: Instantaneous rate: Initial rate:

Example of rate measurement:

Rate Laws (also called Rate Equations) first order reaction For the reaction: 2 N2O5  4 NO + O2 Rate = k[N2O5] For the reaction: NO2  NO + ½ O2 Rate = k[NO2]2 For the reaction: CO + NO2  CO2 + NO Rate = k[CO][NO2] second order reaction first order in CO and in NO2; second order overall

Determining a Rate Law Method of Initial Rates Determining the rate law must be done by experiment; the reaction equation does not tell you the rate law Two methods: Initial Rates and the Graphical Method Method of Initial Rates Measure the rate of the reaction right at the start. Vary the starting concentrations Compare initial rates to initial concentrations

Determining a Rate Law: Initial Rate Method Isolation of variables: Vary only one concentration at a time and keep temperature constant If concentration doubles and: Rate does not change, then zero order Rate doubles, then first order Rate quadruples, then second order General Rule:

Initial Rate Method: Example 1 What is the rate law?

Initial Rate Method: Example 2

Concentration-Time Relationships

Example 1

Example 2 The decomposition of nitrous oxide at 565 oC, 2 N2O  2 N2 + O2 is second order in N2O. If the reaction is initiated with [N2O] equal to 0.108 M, and drops to 0.940 M after 1250 s have elapsed, what is the rate constant?

Graphical Method for Determining Rate Laws A plot of concentration vs. Time will be linear. A plot of ln[R] vs. Time will be linear. A plot of 1/[R] vs. Time will be linear.

Graphical Method for Determining Rate Laws How it works: 1. Collect [R] over an interval of times. 2. Make plots of [R] vs. time ln[R] vs. time 1/R vs. time Only one will be linear. That tells you the reaction order. The slope of the linear plot is the rate constant.

Graphical Method for Determining Rate Laws Example: 2 H2O2  2 H2O + O2 Time(min) [H2O2](mol/L) 0 0.0200 200 0.0160 400 0.0131 600 0.0106 800 0.0086 1000 0.0069

Graphical Method for Determining Rate Laws: Order Example: 2 H2O2  2 H2O + O2 Time(min) [H2O2](mol/L) 0 0.0200 200 0.0160 400 0.0131 600 0.0106 800 0.0086 1000 0.0069

Graphical Method for Determining Rate Laws: k

Half-Life: t1/2 the time it takes for half the reactant concentration to drop to half of its original value First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1.05 x 10-3/min

Cool things about half-life:

Calculations involving Half-Life For a first order reaction: What is the relationship between t1/2 and k? What is the relationship between t1/2 and k for a second order reaction?

Radioactive Decay All radioisotopes decay via first order reactions. Instead of concentrations, amounts are used. Measured as radioactive activity, in counts per minute (cpm) using a detector.

Radioactive Decay: Example 1 Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.7 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 1.0 day?

Radioactive Decay: Carbon Dating In living thing Sunlight + Nitrogen Atmospheric C-14 C-14 Dead thing Sunlight + Nitrogen Atmospheric C-14

Radioactive Decay: Example 2 The Carbon-14 activity of an artifact in a burial site is found to be 8.6 counts per minute per gram. Living material has an activity of 12.3 counts per minute per gram. How long ago did the artifact die? t1/2 = 5730 years