In the previous concept development studies, we began our understanding

of chemical reaction rates just from an empirical point of view.

Could we write down equations which related the rate

of the chemical reaction to, for example, the concentrations

of the reactants and to figure out, how then,

the concentration of the reactants would vary with time?

And the current concept development study over the course of the next

couple of lectures, we want to develop a model that helps us understand

why the reaction rate depends upon the concentrations in the way that it does.

Let's go back and take a look at that data again

on the experimentally observed rate laws for a whole collection of reactions.

You'll remember these data from before, where we

discovered, in fact, that there could be a

relationship between the stoichiometric coefficient of the materials

reacting, say, two nitric oxides reacting with a single

oxygen, and the exponents or the orders in the rate law for that reaction.

So for example, in this same reaction.

The exponent two on the nitric oxide matches the Stoichiometric

coefficient, two on the nitric oxide in the balanced equation.

And, an exponent on the oxygen one,

matches the Stoichiometric coefficient one on the oxygen.

But that doesn't always seem to be the case.

For example.

Two

ICLs reacting with one hydrogen, we'll notice that there isn't an alignment

between the stoichiometric coefficients on the ICL and the exponent on the ICL.

in a similar way, and a particularly complicated one, the reaction

of hydrogen and bromine even produces And a half integer, exponent.

But on some occasions, again, the last one here between ozone and chlorine,

there does seem to be an alignment between the stoichiometric coefficients

and the balanced equation, and the exponents in the rate law.

What we want to do is use this experimental data, to develop

a model that helps us understand, where do those variations come from.

And our first step in this process is to try

to begin to understand, how does a chemical reaction take place.

At the very lowest level, it seems pretty clear,

that if two molecules are to react with each other they have to collide.

They need to be in close proximity to one another for the atoms to be exchanged.

From one molecule to another. That seems straightforward.

So let's think about the probabilities of that event occurring.

We actually have looked at this before, for the case of an ideal

gas of say, molecules, A, flying about in random motion, in random directions.

We've studied this before.

And, we're asking the question, as these molecules

randomly move about, what is the probability that two

of them would essentially wind up in the

same time at a such that a collision occurs?

If they are confined to some space here, it's pretty clear that they are going to

run into each more frequently when there are

more of them, confine to a smaller space.

This is our own experience to sort of walking around in crowded venue

like a sports arena or walking around in uncrowded arenas like maybe a park.

The higher density of the people in the area,

the more likely you are to run into each other.

So the probability of a collision.

Depends upon how many particles are there in what volume.

The more particles there are per volume,

the greater will be the collision probability.

And in fact, since that is the

concentration, then the collision

probability depends upon the concentration.

Furthermore, It depends upon it in a way

which is slightly more complicated than just proportional.

Back when we studied the ideal gas law and the kinetic molecular theory, we came up

with an equation which actually described the rate

of collisions of A molecules with each other.

And notice the the things that it, that show up here.

There is the size

of the molecule, the d squared Tells us d is the diameter of the molecule.

This term here is the, essentially, average speed of the molecules.

It makes sense that the faster the molecules are

going, the more frequently they'll run into each other.

But mostly, and very importantly, notice that the dependence

upon the concentration depends upon the A particle's square.

That's because in order to have a collision say at

this particular point, I need to have two events occur simultaneously.

I need to have the probability of the A

molecule being here and a second A molecule being here.

So the concentration, I'm sorry, the the, collision probability goes up not

as the concentration of A, but as the concentration of A squared.

What if we want to have a reaction say

of A plus B running into each other. Now instead, I've got a container in which

I have mixed together B molecules and A molecules in some random fashion.

And the probability that an A molecule and

a B molecule in travelling intercept at some

particular point and have a collision, then depends

both upon the concentration of the A molecules and

the concentration of the B molecules.

The higher the density of B molecules, the more frequently they'll run into As.

But it also depends upon how many As there

are, the higher the concentration of the A molecules.

Now, we've already seen a little while ago that if we

had a reaction in which we were reacting, say, 2A molecules with

each other, the rate at which the reaction could occur could

not be any faster than the rate at which the A molecules

run into each other.

And we've already seen on the previous slide that that rate goes like A squared.

Notice an interesting trend here, that is, when the stoichiometric coefficient

on A and B is just 1, each of A and B are raised to the first power.

when the stoic humetric coefficient on A is 2, A is raised to the second power.

That actually suggests overall

that there's some kind of a relationship here, that the stoichiometry is related to

the order of the reaction rates, and

in particular the exponent of the reaction rate.

The rate law appears to be related to the stoichiometry of the collisions.

Sorry.

Is related to the stoichiometry of the collisions.

That's what comes

out of this collision theory model that we're developing here.

But now we go back and look at that data again.

Here are stoichiometry equations and here are rate laws.

And we've already observed earlier in this lecture that

they don't seem to be cleanly related to one another.

What that tells us is there must be something more to the story.

There must be something else going on

other than just molecules running into each other.

Apparently, other complexities must come in to play.

Let's consider then.

That what we've observed from our collision model is that if the

reaction occurs in a single step, say, A molecules must col, collide

with B molecules, or A molecules must collide with A molecules, then

the order of reaction is determined by the stoichiometry of the reaction.

But, since in many

cases, the order of the reaction does not

seem related to the stoichiometry of the collision,

we can conclude that the reaction then will

not occur, does not occur in a single collision.

If there's a single collision, the order in the stoichiometry are the same.

If the order in the stoichiometry are not the same,

then there isn't a single collision that produces the chemical reaction.

Let's do a specific example to make it clear what we are talking about here.

A specific example is going to be the reaction of nitrogen

dioxide with carbon monoxide to form nitric oxide and carbon dioxide.

The question is, does this reaction occur in a single collision?

Do we have, for example her, nitric

oxide molecules running into carbon dioxide molecules

in a single step?

It would seem like that would make sense, that

in order to exchange the oxygen from one molecule to

the other, All we would need to do is have

the nitrogen dioxide and the carbon monoxide get close together.

Let's test that model by looking at the rate law.

The experimentally observe rate law for this reaction does not depend upon

the concentration of the carbon monoxide molecules, and it depends doubly,

quadratically on the nitrogen dioxide molecule concentration.

So immediately you can conclude from the model we've

just developed, this reaction cannot occur in a single collision,

because if it did, the rate would depend upon

the concentration of the nitrogen dioxide to the first power.

And the concentration of the carbon monoxide to the

first power, and that's not what we observed experimentally.

Something else is going on,

so we can conclude that the reaction occurs in more than one step.

That leads us to the concept of a reaction mechanism.

A reaction mechanism is a series of

reactions, which lead to the overall reaction.

Each reaction in the series is a single collision, two molecules

running into each other and reacting

to produce some, perhaps, intermediate product.

And a series of these reactions were

collisions occurring in sequence, produces the overall reaction.

Let's give, let's see, an example of what this might look like.

So, since the rate law depends on the

nitrogen dioxide concentration squared, and in a single

collision, the rate will be given by the

concentrations of the products, or of the reactants together.

It must be true, in order to have this rate law, somewhere along the

line, the mechanism must include a reaction

step in which nitrogen dioxide molecules are running

into nitrogen dioxide molecules.

The rate of a process in which nitrogen dioxide molecules run into each other

would be nitrogen dioxide concentration squared times a proportionality constant.

And therefore we expect to have a mechanism in which that reaction occurs.

Here is a possible mechanism.

Imagine, what happens is first, two nitrogen

Dioxide molecules run into each other, producing two new materials here.

Notice what we wind up with is a NO3.

And in NO.

NO is in fact one of the products of the overall reaction.

NO3 is not.

So before the reaction is over, that NO3 is going to have to go away somewhere.

But we also have not yet used our carbon monoxide reactant, so perhaps

what happens is that the nitren nitrogen, the NO3.

Reacts with the carbon monoxide to produce finally

products of the reaction in O2 and CO2.

Notice that NO2 is produced, recreating one of

the reactants that could go back and can

participate in for the reaction, and the two

steps together, produce the two products of this reaction.

Nitric oxide and carbon dioxide.

Now, how would this mechanism be related to the overall rate law?

We know that the rate law has nitrogen dioxide

squared as its concentration, or, as its rate law.

And as a consequence, apparently that first step in

the process is more important then the second step.

As a consequence, we create a new model now in

which we say two steps take place here, but one

of those steps is much slower than the other step.

That's an interesting argument because it says I

have to accomplish two things before the reaction occur.

One of those things is very slow.

In fact I can go no faster than the slowest step in my process.

The slowest step in the process determines

my overall reaction rate, and as a consequence, we actually

refer to that slow step as the rate determining step.

That the rate of the reaction that must take place in the first step

of our overall reaction, that first step must determine the overall reaction rate.

And what is the speed of that first reaction?

Well, according to what we have done, it must be the

rate at which one nitrogen dioxide

collides with another dioxide, nitrogen dioxide.

That's exactly what we have done back over here

when we talked about A molecules running into one another.

Instead what we need, is nitrogen dioxide molecules running into each other.

And the rate in which nitrogen dioxide molecules run into each other, is going to

depend upon how many nitrogen dioxide molecules

there are per volume in this particular container.

That means it depends upon the concentration.

Of the nitrogen dioxide squared because the collision

rate of nitrogen dioxides with each other depends

upon the nitrogen dioxide squared.

Therefore, the rate of step one is k times NO2 squared.

And if step one is the slow step, the rate-determining step in the, in this

whole reaction, the overall rate of the reaction

is the rate of the slow moving step.

The other step occurs so rapidly that once the first step has

occurred, the second step immediately clicks in.

This, then, is an example of how a multi-step process can give rise

to an overall reaction and the slow step in that multi-step process determines what

the rate law is by determining what the stoichiometric coefficients in the rate

determining step are and thereby determining what

the rate is of the collisions in

that rate determining step.

We could develop mechanisms for a variety of different reactions, and each of

those mechanisms will help account for the

overall reaction rate law for that reaction.

There are other things that have to happen

besides collisions of molecules for reactions to take place.

We're going to consider those other characteristics in the next lecture.

CSD 21 Reaction Kinetics I

普通化学：基本概念与应用

与讲师见面