Outline: 1/31/07 Turn in Research Symposium

Seminar reports – to me Exam 1 – two weeks from Friday…

Today: Start Chapter 15: Kinetics Kinetics & Reaction mechanisms

Chapters 6 and 14 introduced Thermodynamics:

heat, work, energy, 1st , 2nd laws, state vs. path variables, spontaneity, etc. as related to chemical reactions….

Chapter 15 introduces: the rate of reactions (kinetics) the mechanisms of reactions

These two concepts are closely related on a molecular level!

Is the rate of a reaction important? e.g. airbags….

Both rate of reaction and mechanism are vital to understanding this problem!

Is the exact mechanism important?

e.g. Ozone destruction

(i) O3 + Cl O2 + ClO

(ii) O + ClO O2 + Cl

O3 + O 2 O2

CFC + ultraviolet light free Cl atoms

h

• Speed of a reaction is measured by the change in concentration with time.

• For a reaction A B

Reaction RatesReaction Rates

t

B of moles

in time changeB of moles ofnumber in change

rate Average

t

A of molesA respect to with rate Average

Consider:

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

Most useful units for this rate = molarity/time.

(Since volume is constant, molarity and moles are directly proportional.)

Reaction RatesReaction Rates

The average rate decreases with time?

How do we get a useful number?Plot [C4H9Cl] versus time:

The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve.

Instantaneous rate is different from average rate.

Reaction RatesReaction Rates

All reaction “rates” slow down when viewed this way…

What is the “rate” of a reaction? = the number of reactions/unit time= the number of reactions/unit time

Why does the reaction slow down?

Go back to a molecular picture…

Answer: Per molecule it doesn’t !!!

6/12 = 50% 3/6 = 50%

(For some reactions…)

In general:

rates decrease as concentrations decrease...

there are stoichiometric factors…

For a reaction (in general):

aA + bB cC + dD

Reaction RatesReaction Rates

tdtctbta

D1C1B1A1Rate

(if rate is not specified for a particular substance!)

For example:

NH4+

(aq) + NO2(aq) N2(g) + 2H2O(l)

Concentration and RateConcentration and Rate

• For the reaction

NH4+(aq) + NO2

-(aq) N2(g) + 2H2O(l)

– as [NH4+] doubles, the rate doubles...

– as [NO2-] doubles, the rate doubles...

– rate [NH4+][NO2

-].

• Rate law:

• The constant k is the rate constant.

Concentration and RateConcentration and Rate

]NO][NH[Rate 24k

Rate = k [A]x[B]y

where: k is the rate constant [A],[B] are the concentrations of A,B x,y exponents are the reaction “order”

Rate LawsRate Laws

For a general reaction with rate law

the reaction is mth order in reactant 1 and nth order in reactant 2.

• The overall order of reaction is m + n

• A reaction can be zeroth order if m, n, are zero.

• Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry.

nmk ]2reactant []1reactant [Rate

• A reaction is zero order in a reactant if the change in concentration of that reactant produces no effect.

• A reaction is first order if doubling the concentration causes the rate to double.

• A reaction is nth order if doubling the concentration causes an 2n increase in rate.

• Note that the rate constant (k) does not depend on concentration.

Examples of reaction order: 1st order: x = 1 or y = 1 e.g. Rate = k [A]

2nd order: x = 2 or y = 2 or (x = 1, y = 1) e.g. Rate = k[A]2 or Rate = k[A][B]

3rd order: x = 3 or (x = 2 , y = 1) etc. e.g. Rate = k[A]3 or Rate = k[A]2[B]

Determining the Reaction Rate:

Two proposed mechanisms for2 NO2 2 NO + O2

A) step 1: NO2 NO + O (slow) step 2: NO2 + O NO + O2 (fast)

B) step 1: 2 NO2 NO3 + NO (slow) step 2: NO3 NO + O2 (fast)

Which is correct???

Determining the Reaction Rate:

Two proposed mechanisms for2 NO2 2 NO + O2

A) step 1: NO2 NO + O (slow) step 2: NO2 + O NO + O2 (fast)

B) step 1: 2 NO2 NO3 + NO (slow) step 2: NO3 NO + O2 (fast)

Unimolecular, so Rate = k[NO2]

Bimolecular, so Rate = k[NO2]2

Kinetics tells us about the mechanism!

0.20 0.12 0.08 M/s

Rate = k [NO2]x

0.20 M/s = k [4.1]x

0.08 M/s = k [2.5]x

2.5 = [1.6]x

x = 2

B) step 1: 2 NO2 NO3 + NO (slow) step 2: NO3 NO + O2 (fast)

Bimolecular, so Rate = k[NO2]2

Determining the Reaction Rate:

Find the rate limiting step and use the reactant(s) and coefficient(s) in the rate law.

Rate = k [NO2]2 Rate-determining step

The rate equation cannot be predicted, it can only be measured empirically.

Bottom line: Rate Law is related to the mechanism

of the rate-determining step!

The rate equation cannot be predicted, it can only be measured empirically.

Calculate k from initial rates Use the integrated form of the rate eqn.

to solve for concentration (Section 15.4)

There are two forms to know:

First order: ln[A] = ln[A]o k t

Second order: 1/[A] = 1/[A]o k t

15-3

15-5

Can use data to find kk and reaction order

How do you find

the reaction order?

Plot both….1st Order Plot

R2 = 0.8389-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

0 100 200 300

Time (s)

Ln

[NO

2]

Series2

Linear(Series2)

2nd Order Plot

R2 = 0.9949

0.0

100.0

200.0

300.0

400.0

0 100 200 300

Time (s)

1/[N

O2]

Series2

Linear(Series2)

ln[A] = ln[A]o k t

1/[A] = 1/[A]o k t

Only one will be truly linear….

Rate = k [NO2]2

slope