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In the previous lecture we began to develop

a model by which we could understand how chemical

reaction rates depend upon the concentrations of the reactant

materials and we actually developed a couple of concepts.

First, in the case that the reaction occurs via a

single collision between molecules of the same type or different types.

Then the order of the reaction, and by

order of the reaction, we're referring to the exponents

on the concentrations and the rate law.

Is determined by the stoichiometry of the collision, in other words,

the coefficients in the re, in the balanced overall chemical equation.

But we also observed in many cases that the

rate law did not obey the stoichiometry of the reaction.

And what we concluded from that, was that, under those

circumstances the reaction does not occur in a single collision.

Instead, we developed this idea of a mechanism, a

series of reactions which occurs to build the overall reaction.

And we also developed the idea that the slowest step in

that process, is the process which determines the overall reaction rate.

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Let's focus for the time being on this first

idea now, this idea of a single collision reaction.

The implication here is that every time two molecules react,

or, or collide, that they will react.

But actually what we are going to now observe is that the rate at

which molecules collide, is not equal to the rate at which they react.

The reaction rate can be no faster than

the collision rate because the molecules have to collide

to react, but it might be much, much slower

than the collision rate if other characteristics are required.

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Let's look

[INAUDIBLE],

look at some experimental data that might help reveal that to us.

In particular, we're going to look now at the temperature dependence of the

reaction rate as well as the temperature dependence of the collision rate.

Here's our equation that describes the

collision rate from kinetic molecular theory.

Where is the temperature buried in this equation?

Well, one place that it's locking is right here in the average

speed of the molecules.

We know that the average speed of the molecules

will vary like, the square root of the temperature.

So, as the temperature increases, we expect the collision rate to

increase, because the molecules are moving more rapidly towards one another.

But notice it increases relatively slowly like the square root

of the temperature not like say the square of the temperature.

There's also possibly a temperature dependence in

the density of the part, particles, the number of particles per volume.

But, if we think about that number actually for a

constant pressure increasing the temperature

actually decreases the particle density.

Suggesting that the reaction would actually slow down

because there would be fewer collisions of higher temperature.

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Those would be our predictions based upon a collision model.

What are the experimental data actually look like?

Well, we're going to take a specific

case of a reaction hydrogen molecules reacting with iodine molecules.

To form two hydrogen iodide molecules, all

of these molecules are gas phased diatomic molecules.

Let's see how the temperature changes the rate of this chemical reaction.

Actually it will show up in the rate constant for this reaction.

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And so what we're going to measure

is the variation of the rate constant. As a function of the

temperature for this particular reaction. The y axis here shows the rate constant.

Temperature in degrees Calvin increasing. Notice what we see is a very

precipitous rise in the rate as when the temperature increases.

Much, much greater than, for example,

might have been expected on the basis of this square root

temperature dependence buried in here. We go back and look at this, this

[INAUDIBLE]

k is increasing much, much more rapidly than

would be anticipated just by the collision rate.

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This curve actually looks like it's growing exponentially.

So, we might be interested in whether

k goes as the exponential of the temperature.

And to check that out we'll draw a slightly

different graph where we can get a straight line.

Here's the slightly different graph.

Here we've plotted the logarithm of the

[INAUDIBLE],

of the rate constant.

As a function not of the temperature but as one over the temperature.

Notice that we get a very, very nice straight line of the data

when we draw it in terms of logarithm acay versus one over the temperature.

Let's stare at this graph for just a minute and make

sure that we understand how these two graphs correspond to each other.

Clearly k increases with the temperature.

The graph

on the right makes it look like k is

decreasing with the temperature, but remember, the x axis

here is one over the temperature, so high temperature

is over here, and low temperature is over here.

So, when the temperature increase, we increase the logarithm of the

rate constant and there by increase the rate constant as well.

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Because we get a straight line on this

particular graph, we can actually use the usual Y=mx+b to describe this equation.

And we wind up with the following results. It says the logarithm of k.

Is linear and one over the temperature with a linear slope of

A and a Y intercept of B. Now, one of the things that we could

actually do is rewrite that equation if we have the logarithm of k,

is equal to a over T plus b and we'll remember a is,

in fact, a negative number, because the slope of that line is negative.

We could take the exponential of both sides of that equation.

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And that's going to look like e to the a over T times e to the b, and e to

the b is just a constant in and of itself. We'll rewrite that equation then as

is shown here in a somewhat more familiar form that says, the

temperature dependence of the rate constant is given by a constant,

multiplied the exponential of another constant, divided by T.

Well we'll remember that a has to be a number less than 0.

Because the slope of this line over here is negative and a is

the slope of the line.

So a is a number less than 0 in this equation.

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This is a form that in fact shows up to

be rather common form for the temperature dependence of chemical reactions.

So we refer to it as the Arrhenius

equation after Svante Arrhenius, who first described it.

Turns out that in most cases, the

chemical reaction rate constant increases in this form.

One of the things we'd like to understand

is, what are these constants here? What do they have to do with?

We've not seen those before.

And in addition, what we'll do, is try to understand why

the reaction rate depends upon something other than just the collision rate.

because clearly the collision rate does not increase nearly

as rapidly as this exponential form and the Arrhenius equation.

So what else has to happen in order for a reaction to take place?

Let's illustrate by considering a reaction of hydrogen molecules

with fluorine atoms to form hydrogen fluoride molecules plus.

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Furthermore, this is only going to happen if the

fluorine hits one or the other of the hydrogens.

Imagine that the collision occurred instead by the

fluorine hittings or the perpendicular to the H2 molecule.

We slided up here.

If that were the circumstance, we're probably

not going to get a reaction because the

fluorine won't be able to pull either of the hydrogens away from the H2 molecule.

What that tells us then,

is that amongst the things that are required for

a reaction to occur are, a sufficient amount of energy.

We need to actually be able to pull some atoms slightly apart from each other.

To begin the formation of new bonds.

We have to have the appropriate orientation.

In this particular case, we need the flourine to attack

the hydrogen from the end and not perpendicularly to it.

And it turns out, even if we

have the appropriate orientation, we have sufficient energy,

there's a certain amount of luck involved in the chemical reaction.

The molecules are actually vibrating and oscillating, and they have to align and

time up their oscillations just exactly right to get the reaction to take place.

Given all of these factors, it seems like it might

be challenging to understand this Arrhenius Equation here that accounts for.

The temperature dependence.

But that temperature dependence is almost certainly mostly dependent upon

the energy, because we know from our kinetic molecular theory that

the temperature has something to do with the energies of the molecules.

The higher the temperature, the more energy they have.

If a sufficient amount of energy is required for the reaction to take place.

Then perhaps, we can account for the

temperature dependence through that sufficiency ener, energy.

That leads us to draw a diagram, typically called a reaction energy diagram.

It shows the energy is a function

of the progress through the reaction.

Over here, we might have for example, the reactants.

And over here we have the products.

Notice that this is an energy axis here, so the difference that we are seeing here

is in fact the increase in energy, delta E, required

for the reaction to take place. However, notice that we don't

just shortcut from the reactants to the products.

We actually have to go over a hill to have sufficient

amount of energy to be able to get the reaction to occur.

That's similar to what we were describing here

when we have to increase the energy of the

H2, as the fluorine approaches, in order to be able to begin to form a new HF bond.

The amount of energy which is

required for the reaction to take place, this amount here, is actually referred to

as the activation energy, a term that I'll write down over here on the page.

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EA. Is the energy required

to make it from reactants to products over

a barrier called the activation energy.

It turns out in the model for activation energy, according to what

we learned from Arrhenius and without us attempting to derive what that means.

We can actually relate a to this a in the

Arrhenius equation. We can actually relate

it to the activation energy such that in fact the temperature

dependence of the rate constant. Is given by

that same old constant capital A, multiplied by the exponential

of the negative. Remember A is negative.

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As you can see.

And in fact, that equation describes the temperature dependence

of the rate constant for a variety of chemical reactions.

Now, the original curve that I drew on the previous slide.

Indicates that we rise up to a barrier and then fall

to an energy which is in fact, above the original energy.

And according to what we learned in the first

semester that means that this is an endothermic reaction

on this graph but, of course, not all equations are endothermic.

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Exothermic reactions mean that a certain amount of energy has

been reduced as we have gone from reactants to products.

We might imagine that if we lower the energy going from reactants to products,

that there would be no activation energy

because we're simply releasing energy during the reaction.

But in fact that's not true.

In fact, even for exothermic reactions, a barrier must be surmounted

a certain amount of energy before we can make our way from reactant to product.

That means there is also an activation energy here for the endothermic reaction.

I'm sorry, the exothermic reaction, just like there is an

activation energy for the endothermic case as well.

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Now you recall, it's also necessary that we get an appropriate

orientation for the reactants and that there's some luck involved as well.

Those factors are buried here in this pre-exponential, deter, factor, that has

some buried things in it that have to be measured experimentally as well.

We can actually get that factor A also from the equation

from this straight line, since the equation for that real

straight line relates to the y intercept of this particular graph.

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All in all then we have a good model by which we can

describe the probability for reaction being

depended upon the concentration of the reaction.

And the rate of success of the collisions that occur as being

related to the temperature, because the temperature increases will give us more

energy by which we can surmount the activation barrier.

We're now going to use this material to begin

to understand reactions as they occur and create equilibria.

And those equilibria will be important in understanding general chemical reactions.