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 KineticsRates of Reactions

Control of Reactivity

Consider: NO + O3 NO2 + O2

Molecules collide Bonds are formed and break

product molecules separate

Collision Theory

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

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:1. Concentration

a. Rate laws

b. Concentration vs. time relationships

2. Temperature and activation energy

3. 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:

concentrationrate =

time

Example of rate measurement:

Rate Laws (also called Rate Equations)

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]

first order reaction

second order reaction

first order in CO and in NO2; second order overall

Determining a Rate Law

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

-ktt o[R] = [R] e

Example 1

-ktt o[R] = [R] e

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?

Example 2

Graphical Method for Determining Rate Laws

A plot of concentrationvs. 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. timeln[R] vs. time1/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 0.0200200 0.0160400 0.0131600 0.0106800 0.00861000 0.0069

Graphical Method for Determining Rate Laws: Order

Example: 2 H2O2 2 H2O + O2

Time(min) [H2O2](mol/L)0 0.0200200 0.0160400 0.0131600 0.0106800 0.00861000 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:

ktt

t oo

Rln = -kt R = R e

R

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.

kttt o

o

Nln = -kt N = N e

N

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?

kttt o

o

Nln = -kt N = N e

N

Radioactive Decay: Carbon Dating

C-14In living thing Atmospheric C-14

Sunlight + Nitrogen

C-14Dead thing Atmospheric C-14

Sunlight + Nitrogen

Radioactive Decay: Example 2The 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

kttt o

o

Nln = -kt N = N e

N