Introduction to Kinetics - PowerPoint Presentation

Slide1

Introduction to Kinetics

Lecture 14 Slide2

Reading in Chapter 5

Read sections 5.1 through 5.5.4 (p.160 to p. 199) and section 5.7 (p. 207-211).

We will probably skip the intervening sections – or cover them briefly.

Book

errata

:

http://

bcs.wiley.com

/he-

bcs

/

Books?action

=

index&itemId

=0470656670&bcsId=8017 Slide3

Kinetics

Whereas thermodynamics concerns itself with equilibrium and the distribution of components between species and phases at equilibrium, kinetics concerns itself with the

pathway

to equilibrium, including the

rates

and

mechanisms

of reaction.

Rates depend on temperature and at the surface of the Earth reaction rates are often so slow that equilibrium is never achieved. This can also be true at higher temperature - and we have mentioned one example (the

spinodal

).

The microscopic perspective becomes somewhat more important in kinetics than it was in thermodynamicsSlide4

Overall & Elementary Reactions

The reaction:

CaAl

2

Si

2

O

8

+ 3H

2

O + CO

2

= CaCO

3

+ 2Al(OH)

3

+ 2SiO

2

describes a key process at the surface of the Earth, namely weathering igneous minerals (plagioclase) to form common sedimentary ones (calcite, gibbsite, and quartz). But does this

overall reaction

describe what actually happens?

NO.

In thermodynamics ,we might not care, but in kinetics, we do. The first step in understanding reaction pathways and reaction mechanics is to breakdown overall reactions such as this into the

elementary reactions

.

An

elementary reaction

is one that involves only one step a describes what occurs on the microscopic level.Slide5

Reaction Mechanisms

We can begin to breakdown the overall reaction. Some steps are:

CO

2(g) + H

2

O = CO

2(

aq

)

+ H

2

O

CO

2(

aq

)

+ H

2

O = H

2

CO

3

H

2

CO

3

= H

+

+ HCO

3

–

Producing acidity necessary for weathering.

Next step is likely absorption of H

+

to the surface:

CaAl

2

Si

2

O

8

+ 2H

+

= H

2

CaAl

2

Si

2

O

8

2+

Followed by replacement of the

Ca

by H:

H

2

CaAl

2

Si

2

O

8

2

+

= H

2

Al

2

Si

2

O

8

+ Ca

2+

etc.Slide6

Defining Reaction Rates

For a reaction such as:

Ca

2+

+ Mg

2+

+ 2CO

3

2–

=

CaMg

(CaO

3)2 We define the rate of reaction as the rate of production of the products, or equivalently, the rate of consumption of the reactants divided by the stoichiometric coefficient:Equivalently:The equation tell us nothing about what the reaction rate is, we are just defining what it means.We’ll shortly see that rates generally do depend on concentrations or reactants and products, so don’t be confused.Slide7

Reaction Rates & Concentration

Consider the gas phase reaction:

N

0

+ O

2

= NO + O

0

First thing that must happen is we must bring the reactants together.

We can imagine a reference frame in which the N atom sweeps out a volume

v × t

(velocity times time).Whether a reaction will occur in that time will depend on whether or not the center of an oxygen molecule is present within that volume.Number of collisions (per N)will be:Overall collision rate will be:Slide8

For an elementary reaction, we expect the rate of reaction to depend on the concentration of reactants

Bottom Line:Slide9

Dependence on Temperature

Just because two people meet on a date, doesn’t mean they will tie the knot.

Kinda

depends on how ‘hot’ the date was!

Similarly, just because two atoms or molecules collide, doesn’t mean they will react.

Depends on whether the collision is energetic enough to overcome coulomb repulsion

and the

electron orbits can reorganize.

An energy barrier,

E

B

, must

be overcome.That means it depends on temperature.Hence the date analogy!Slide10

Temperature and Barrier Energy

Since energy levels are closely spaced, we can integrate, so

the

probability

of

a molecule

having E ≥ E

B

is:

Our reaction rate is now:

Maxwell-Boltzmann Law gives

ave.

velocity in a gas as:where µ is reduced mass of gas:µ = mNmO2/(mN + mO2)

We suppose that a reaction will proceed if the N atom has at least certain energy, E ≥ EB.What function tells us how energy is distributed among molecules?

Boltzmann Distribution Function.Slide11

Arrhenius Relation

Our equation now is:

Let:

A

describes the frequency of opportunity for reaction and is called the

frequency factor

.

W

e can express the temperature dependence of the reaction rate as:

This is known as the

Arrhenius relation

and describes the dependence of reaction rates on temperature.Slide12

The Rate Constant

Arrhenius Relation

k

is known as the rate constant.

So many K’s!

We’ll use upper case roman K for the equilibrium constant

Lower case roman k for Boltzmann’s constant

Lower case italic

k

for the rate constant.

We can now write the rate of our N+O

2

reaction as:R = knN nO2Slide13

Reaction Rates and Temperature

The Arrhenius Relation tells us that reaction rates depend exponentially on temperature (fits everyday experience).

This is reason high-T rocks survive at the surface of the Earth

out of equilibrium

.

In the gas phase reaction,

A

depended on square root of

T

- much weaker than the exponential factor.

Other kinds of reactions show difference dependence of

A

on T.In many cases we can view A as a constant independent of T.Slide14

General Form of Rate Equation

We may now write a general form of the rate equation for a reaction such as:

aA

+

bB

=

cC

+

dD

(don’t confuse this with the definition of the rate).

In the general case of overall reactions,

the exponents can be any number (including 0)

.For the special case of elementary reactions, the exponents of the reactants are the stoichiometric coefficients and the exponents of the products are 0; i.e., rates of elementary reactions are independent of the concentrations of products.Hence if the above is elementary:Slide15

Order of the Reaction

The order of the reaction is the sum of the exponents of the activities in the rate equation.

For example, formation of carbonic acid

CO

2

+ H

2

O = H

2

CO

3

Rate should be (assuming ideality, and an elementary reaction):

So this is a second order reaction.In this case, however, concentration of water will not change appreciably, so it is a pseudo-first order reaction:Slide16

Rates and Concentrations

Knowing the rate constant (usually empirically determined), we can compute rate.

Integrating rate of first order reaction gives:

Graph shows how CO

2

concentration changes in the reaction

CO

2

+ H

2

O = H

2

CO3Slide17

Distinguishing Elementary from Complex ReactionsSlide18

Elementary or Not?

Can’t always predict whether a reaction is elementary or not just by looking at it. The earlier rules about order of reaction provide a test.

For example, 2NO

2

–> 2NO +O

2

Rate of reaction turns out to be

What does does this tell us?

The reaction is elementary.Slide19

Elementary or Not?

Now consider 2O

3

–> 3O2

Rate of this reaction turns out to be:

Since it depends on the concentration of a reactant, it is not an elementary reaction.

Indeed, it is a fairly complex one involving a

reactive intermediate

, O˚, which does not appear in the reaction

.

For example, in the stratosphere: