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PROFESSOR: So, let's finish
up new material today, new

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material Monday, and then we're
done with the kinetics unit.

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So, we're going to talk about
temperature, collision theory,

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and activated complex
theory today.

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So on the first day, we talked
about kinetics, we talked about

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factors affecting the rates,
and this was in your handout on

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that first lecture, but just to
kind of review for a minute

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what we have talked about so
far and where we're going.

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So these are some of the things
we came up with are factors

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affecting the rates
of reaction.

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People said mechanism affects
the rate of reaction, so

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we talked about mechanism.
 

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Concentration of material,
nature of material -- that

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pretty much fits in
in every lecture.

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We've been talking some about
that, say, if it's first order

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or second order, if you have a
concentration term in there, or

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if you don't have a
concentration term.

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The nature of the material,
we're going to talk

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more about that today.
 

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Temperature is going to be the
number one topic for today, and

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on Monday the number one topic
is the use of catalysts

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to speed up reactions.
 

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So, by Monday we'll be
done with this list.

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So, what about temperature.
 

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So temperature, when I said
what affects the rate of

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reaction, temperature was one
of the things that you yelled

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out at me, and that's very much
true, it has one of the biggest

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effects on the rate
of reactions.

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So when we were talking about
the gas phase, there was an

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observation made that the
reaction rates tend to increase

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as the temperature increases.
 

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And most of you can think about
this and are aware of it, and

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today we're going to talk more
about the quantitative affect

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of this, how much does the rate
of a reaction increase when the

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temperature increases,
how do you know what

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equation do you use.
 

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So, this idea has been
around for awhile.

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So in 1889, Arrhenius plotted
rate constants versus

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temperature, and he found that
if he plotted the natural log

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of those rate constants versus
inverse temperature, then he

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would get a straight line.
 

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So let's look at the
plot that he had.

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So, he found that if he plotted
natural log of the rate

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constants versus 1 over
temperature, so units or kelvin

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to the minus 1, that he
got a straight line.

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Which means that the rate
constants are varying

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exponentially with
inverse temperature.

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So you have to use a natural
log to get a straight line,

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if you don't use natural
log, you wouldn't get

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a straight line here.
 

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So, let's look at some of these
terms that we have here, and

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here's our equation for the
straight line, the natural log

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of k equals minus e a -- e a is
activation energy, which we're

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going to talk a lot about today
-- over r t, r is our friend

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the gas constant, and t is
temperature, plus

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natural log of a.
 

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So what is a?
 

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A is called factor a or
sometimes it's called

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pre-exponential factor, and had
has the same units as k, k

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being the rate constant.
 

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So, let's think about this
equation and this plot, and

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about factor A and this other
term, activation energy.

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So, factor A and activation
energy depend on the

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reaction being studied.
 

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So, it depends on the nature
of the materials involved.

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So I said we'd talk again
about nature of the material.

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So one kind of reaction's going
to have one activation energy,

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another one will have
a different one.

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So, let's think about
this term, factor A.

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What is it exactly?
 

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Do you think it would be
temperature dependent?

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What do you think?
 

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How many people think yes, it
would be temperature dependent?

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How many people think no?
 

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Some people are not
going to commit.

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The answer is no.
 

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So, let's think about
what factor A is.

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So, factor A is the rate
constant at some really,

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really large temperature.
 

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So, if we look at this plot,
the natural log of k equals the

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natural log of A, or k equals A
if you're along this axis here.

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If you're along that axis here,
that's at zero, so that's when

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1 over temperature equals zero,
then the rate constant

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equals factor A.
 

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What would be true about the
temperature for 1 over

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temperature to equal zero?
 

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Very big.
 

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So, at the biggest, hugest
temperature you can imagine,

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the rate constant's
going to equal A.

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And so, factor A depends on the
nature of the material being

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studied and you would have to
determine what that value is.

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But it's definitely not
temperature dependent.

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It's the value of the
rate constant at an

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enormous temperature.
 

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So, what about
activation energy?

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Do you think that's
temperature dependent?

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Why don't you tell
me what you think.

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All right, let's take
10 more seconds.

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All right, so I'd like you to
discuss this amongst yourselves

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and see whether you're
happy with this answer.

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All right, go ahead
and vote again.

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All right, 10 more seconds.
 

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And the correct answer is?
 

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So, I think most of you
will remember this answer.

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So the activation energy is
not temperature dependent.

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You can calculate what the
activation energy is by

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plotting the rate constants
versus 1 over temperature,

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and then you get it from
the slope of the line.

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So, activation energy depends
on the nature of the

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material, but it isn't
temperature dependent.

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So, we're going to talk a
lot more about that today.

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Before we leave this, I
just want to say one thing

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about a clicker question.
 

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So, at the end of last time, we
had our first repeat winner

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for a clicker competition.
 

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So, we thought that we might
have an opportunity for

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recitations to see if they can
-- if some other recitation

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can get a second win.
 

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So on Monday we're going to
have our final clicker

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competition, and if somebody
else does tie, one section,

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that we'll have a final
one-time clicker question

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that'll be a run-off.
 

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And whatever recitation wins,
we have special prizes for the

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members of that recitation.
 

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So that's on Monday.
 

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So you may want to review
catalysis on Monday, if you

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feel that you're in the running
for the grand champion

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clicker recitation.
 

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All right, so let's
go back to this.

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So we found out that no,
activation energy is not

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temperature dependent.
 

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All right, so what are you
going to see on your equation

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sheet on the final, you may see
a couple of different forms

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that are all equivalent
to each other.

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So here is the plot
of a straight line.

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It will often be written with
just natural log of a and e

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a over r t terms reversed.
 

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So that's as a straight line,
and this is often what you see

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for the Araneus equation.
 

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You can also get rid of the
natural logs and have the term

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here exponential, so you have k
equals factor A times e

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to the minus, activation
energy divided by r t.

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So, those are the equations,
they're all equivalent to each

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other that you might see
on your equation sheet.

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So, it's also true that
non-gases can exhibit this kind

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of behavior, and let me just
give you one example of a

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non-gas that exhibits this
kind of behavior and you

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tell me what this is.
 

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What is that?
 

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Crickets.
 

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So crickets exhibit
Arrhenius behavior.

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They will chirp faster as the
temperature gets hotter.

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So if you're out camping,
sometimes it can be in the

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summer, it can be actually be
quite deafening, and you were

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very happy to go back to the
city where you only have

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ambulances and cars going,
and you don't have this

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incredible racket at night.
 

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You can actually calculate what
the temperature is by counting

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the number of chirps of the
crickets and using

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a little equation.
 

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I think it's you count for 14
seconds and add 40 and that's

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the temperature in fahrenheit
or something like that.

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So, not only gases do
this kind of behavior.

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All right, so activation
energy, we're going to be

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talking a lot about this today.
 

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So, what is it exactly.
 

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So let's think about two
molecules coming together.

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So when two molecules come
together, you have this

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bimolecular process going on,
but every time two molecules

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come together, they're not
going to go on and

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form a product.
 

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You're only going to form
a product when those

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molecules have a critical
amount of energy.

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When they have the energy
which allows them to react,

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that activation energy.
 

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If they have enough energy when
they come together, they will

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go on and form products.
 

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So, that's what activation
energy is, it's this critical

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amount of energy that they need
to react with each other.

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All right, so let's just think
about what affects that

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critical amount of energy, and
of course, temperature is

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going to be involved.
 

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So let's think about that.
 

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So if we have fraction of
molecules on one side, and we

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have kinetic energy down here,
let's think about

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how temperature is
involved in this.

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So, at a low temperature, the
fraction of molecules that are

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going to have enough energy to
react is going to be less.

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And let's think about at a
higher temperature, go like

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this, so this is high
temperature, and we have

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low temperature up here.
 

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And then over here we would
have our activation energy, the

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energy needed for a reaction.
 

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And you see, if you're at low
temperature, only a small

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number of molecules are going
to have enough energy to react,

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but if you're at higher
temperature, a large number of

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molecules are going to have
that critical energy to react.

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So, at low temperature, not
many can react, at higher

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temperature, many more will
have that energy -- will be

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able to overcome that
activation energy, will have

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it and they can react.
 

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So, temperature plays
a big role here.

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So we can use this idea
of activation energy to

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predict a rate constant.
 

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Let's look at an example.
 

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So, often people have sucrose
in their diet, and the

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hydrolysis of sucrose will form
glucose and fructose as part of

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this digestive process.
 

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And we can think about the
rates at which that would

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happen in the body.
 

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So normally, we're at 37
degrees, that's normal body

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temperature, and we have the
observed rate constant

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for that is 1 .
 

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0 times 10 to the minus
3 per molar per second.

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But what happens if your body
temperature is lowered, what

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happens if it was at 35
degrees, and to be able to

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answer that question, you need
to know what the activation

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energy is for this process,
and here it's 108

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kilojoules per mole.
 

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So, we want to ask the
question, what is the new

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rate constant at 35 degrees?
 

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So, we can take our Arrhenius
equations, and we can put a

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00:14:51 --> 00:14:55
1 by the rate constant for
temperature 1, and a 2 for the

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rate constant at temperature 2.
 

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Now we can combine
these equations.

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Natural log of a cancels out,
it's not temperature dependent

235
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so it doesn't stay in here.
 

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And so we can solve, we can
subtract these two, or that's

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equivalent to dividing them,
and so natural log of rate

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constant 2 over rate constant 1
equals minus the activation

239
00:15:20 --> 00:15:25
energy over the gas constant
times this temperature term.

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Does this look at all familiar?
 

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Does this look like some
other equation you

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saw once upon a time?
 

243
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Do you remember what that
equation was called?

244
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Van't Hoff equation, right.
 

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And there we were comparing
what instead of rate constants?

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Equilibrium constants,
and instead of e a, what

247
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term did we have here?
 

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Delta h, right.
 

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And it's good you remember
that because we're going to

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come back to that at the
end of today's class.

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So, we can use this equation
and plug in the values.

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We put in our activation
energy, and remember to pay

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attention to units, because if
you're going to cancel your

254
00:16:03 --> 00:16:06
joules with a gas constant, you
want to make sure you've

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converted your kilojoules to
joules, and then we can plug

256
00:16:10 --> 00:16:14
everything in and
solve for k 2.

257
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So, here k 2 is 7 .
 

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6 times 10 to the minus
4 per molar per second,

259
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so it's slower.
 

260
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And this is one reason why it's
really nice to have your body

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temperature stay the
normal temperature.

262
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If you get too cold, your body
processes, your enzymes are not

263
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functioning, everything
is slowed down.

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And if you get too hot,
that's not good either.

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00:16:35 --> 00:16:38
So you really want to maintain
it, and so for some of you who

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come to MIT from warmer
climates, let me introduce

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you to the L.L.
 

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Bean catalog, they sell
coats, they sell boots,

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00:16:46 --> 00:16:47
and all sorts of things.
 

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So, this winter, when you come
back for IAP, or for the term,

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you're well-prepared, and you
don't have to prove that it's

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00:16:56 --> 00:16:58
not good if your body
temperature goes

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below 37 degrees.
 

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00:17:03 --> 00:17:06
All right, let's think about
what else this equation tells

275
00:17:06 --> 00:17:10
us, and the other thing it
tells us is that if you have a

276
00:17:10 --> 00:17:16
very large activation energy,
if this e a is a very, very big

277
00:17:16 --> 00:17:20
number, that means that your
rate constants will be very

278
00:17:20 --> 00:17:22
sensitive to temperature.
 

279
00:17:22 --> 00:17:25
So if this is really, really
big, there's going to be a big

280
00:17:25 --> 00:17:28
change in your rate constants
as temperature changes.

281
00:17:28 --> 00:17:30
And keep that in mind,
we're going to come

282
00:17:30 --> 00:17:34
back to that later.
 

283
00:17:34 --> 00:17:38
So, what do you think happens
to the rate of an enzymatic

284
00:17:38 --> 00:17:40
reaction at liquid
nitrogen temperatures?

285
00:17:40 --> 00:17:44
We looked at going from
37 degrees to 35, liquid

286
00:17:44 --> 00:17:47
nitrogen is pretty cold.
 

287
00:17:47 --> 00:17:51
So, not a whole lot happens at
liquid nitrogen temperatures as

288
00:17:51 --> 00:17:56
far as enzymes go, and I'll
just mention, so it slows way

289
00:17:56 --> 00:18:00
down, that this is a trick
that I use in my research.

290
00:18:00 --> 00:18:05
So we have crystals of enzymes,
and we can try to get

291
00:18:05 --> 00:18:10
structures in particular states
by taking the crystals that

292
00:18:10 --> 00:18:13
have enzyme in it, and starting
a reaction, and then dunking

293
00:18:13 --> 00:18:16
the crystals in liquid nitrogen
to kind of stop it at a

294
00:18:16 --> 00:18:18
particular stage, and then
you look at what the

295
00:18:18 --> 00:18:20
structure looks like.
 

296
00:18:20 --> 00:18:21
So that's one use.
 

297
00:18:21 --> 00:18:24
So, we're going to also take a
look at other reactions, we

298
00:18:24 --> 00:18:27
don't have any enzymes here,
but some other things, and look

299
00:18:27 --> 00:18:32
at what happens when we get
things to be very cold.

300
00:18:32 --> 00:18:50
[EXPERIMENTING]
 

301
00:18:50 --> 00:18:53
So, Dr. Taylor is pouring
out some liquid nitrogen.

302
00:18:53 --> 00:19:04
PROFESSOR: All right, so what
we're going to look at is a

303
00:19:04 --> 00:19:07
reaction that we can see
pretty easily here.

304
00:19:07 --> 00:19:11
Have any of you used glow
sticks before, maybe trick or

305
00:19:11 --> 00:19:13
treating or some other point.
 

306
00:19:13 --> 00:19:17
So basically, you may or may
not know how they work.

307
00:19:17 --> 00:19:19
There's two compartments in
glow sticks that have two

308
00:19:19 --> 00:19:22
different chemicals in them,
and they're trade secrets so we

309
00:19:22 --> 00:19:23
can't put them on the board.
 

310
00:19:23 --> 00:19:26
But basically, what we
have here is a reaction.

311
00:19:26 --> 00:19:28
A lot of reactions we know
give off heat, or they

312
00:19:28 --> 00:19:30
give infrared light.
 

313
00:19:30 --> 00:19:33
Here we have a reaction
that gives off energy

314
00:19:33 --> 00:19:35
as visible light.
 

315
00:19:35 --> 00:19:37
So would you call this
an endothermic or an

316
00:19:37 --> 00:19:39
exothermic reaction here?
 

317
00:19:39 --> 00:19:42
Yeah, so this is an
exothermic reaction.

318
00:19:42 --> 00:19:45
So just as Professor Drennan
was talking about with slowing

319
00:19:45 --> 00:19:48
down enzymatic reactions we
can think about if we can

320
00:19:48 --> 00:19:50
slow down this reaction.
 

321
00:19:50 --> 00:20:01
So, we're just going to put it
in the liquid nitrogen -- so,

322
00:20:01 --> 00:20:04
keep an eye on this, we'll
do several controls of

323
00:20:04 --> 00:20:05
different colors here.
 

324
00:20:05 --> 00:20:09
So, see if an orange glow
stick works the same.

325
00:20:09 --> 00:20:12
What we're looking to see is if
we can slow down this reaction.

326
00:20:12 --> 00:20:14
What would we see if we
slowed it down or even

327
00:20:14 --> 00:20:17
if we stopped it?
 

328
00:20:17 --> 00:20:19
Yeah, we're not going
to see anymore color.

329
00:20:19 --> 00:20:21
So are you starting to
see color loss in this

330
00:20:21 --> 00:20:28
first reaction here?
 

331
00:20:28 --> 00:20:39
So, we'll try
green, and yellow.

332
00:20:39 --> 00:20:42
So, it looks like this first
one might have stopped

333
00:20:42 --> 00:20:45
already, you see there's
no color anymore here.

334
00:20:45 --> 00:20:47
What would you expect
if this heated back up

335
00:20:47 --> 00:20:49
to room temperature?
 

336
00:20:49 --> 00:20:53
Yeah, so hopefully, if you just
keep your eye on this, we'll

337
00:20:53 --> 00:20:55
continue on with the lecturing,
because I don't know how long

338
00:20:55 --> 00:20:58
it will take for it to warm
back up the room temperature.

339
00:20:58 --> 00:21:02
But keep an eye and we'll see
if we get the temperature back

340
00:21:02 --> 00:21:05
high enough to see
the glow again.

341
00:21:05 --> 00:21:08
And since we do have a liquid
nitrogen here, it's too hard

342
00:21:08 --> 00:21:10
to resist freezing a flower.
 

343
00:21:10 --> 00:21:14
This has nothing to do with
kinetics -- we can't even

344
00:21:14 --> 00:21:17
try that connection.
 

345
00:21:17 --> 00:21:20
But we will be freeze a flower.
 

346
00:21:20 --> 00:21:28
OK, she will try making --
good catharsis pre-exam.

347
00:21:28 --> 00:21:37
PROFESSOR: So, has anyone
had liquid nitrogen

348
00:21:37 --> 00:21:41
applied to them?
 

349
00:21:41 --> 00:21:45
It's used in doctor's offices,
if you want a little something

350
00:21:45 --> 00:21:47
removed perhaps, put a little
liquid nitrogen on

351
00:21:47 --> 00:21:48
and burn it off.
 

352
00:21:48 --> 00:21:52
Good premed training for you.
 

353
00:21:52 --> 00:21:54
I think we're pretty
frozen here.

354
00:21:54 --> 00:22:06
So it looks the same, but as
you can see -- [INAUDIBLE]

355
00:22:06 --> 00:22:14
-- So I think that's all
we can do [LAUGHTER]

356
00:22:14 --> 00:22:25
[APPLAUSE]
 

357
00:22:25 --> 00:22:30
PROFESSOR: So I actually heard
something interesting on NPR

358
00:22:30 --> 00:22:33
about liquid nitrogen removing
warts and things like that, and

359
00:22:33 --> 00:22:35
they were talking about how
there was something that was

360
00:22:35 --> 00:22:38
actually better than liquid
nitrogen for doing that.

361
00:22:38 --> 00:22:41
Did anyone hear the story about
what the thing was that was

362
00:22:41 --> 00:22:44
better than liquid nitrogen?
 

363
00:22:44 --> 00:22:47
It was duct tape.
 

364
00:22:47 --> 00:22:49
And so some scientists had
looked at what all the

365
00:22:49 --> 00:22:51
uses of duct tape are.
 

366
00:22:51 --> 00:22:54
And since most of you are
planning on being scientists

367
00:22:54 --> 00:22:57
or engineers, duct tape will
probably be an important part

368
00:22:57 --> 00:22:59
of your life in the future.
 

369
00:22:59 --> 00:23:03
And so, duct tape worked
better than liquid nitrogen

370
00:23:03 --> 00:23:04
for removing warts.
 

371
00:23:04 --> 00:23:07
And they found that duct
tape worked really well

372
00:23:07 --> 00:23:08
for a lot of things.
 

373
00:23:08 --> 00:23:11
There was only one thing
they tried that it did

374
00:23:11 --> 00:23:12
not work well for.
 

375
00:23:12 --> 00:23:15
Anyone want to guess
what that was?

376
00:23:15 --> 00:23:19
Repairing ducts, yes.
 

377
00:23:19 --> 00:23:22
Not really good -- there were
many, many, many better ways to

378
00:23:22 --> 00:23:26
repair ducts than with duct
tape, but I guess they decided

379
00:23:26 --> 00:23:30
that calling it wart removal
tape was just not quite as

380
00:23:30 --> 00:23:38
catchy as duct tape, so it's
still referred to as duct tape.

381
00:23:38 --> 00:23:44
OK, so when you lower
the temperature, things

382
00:23:44 --> 00:23:46
tend to slow down.
 

383
00:23:46 --> 00:23:51
But if molecules are going to
react, they need to have enough

384
00:23:51 --> 00:23:54
energy, they need to have a
high enough temperature

385
00:23:54 --> 00:23:58
to overcome this
activation energy.

386
00:23:58 --> 00:24:02
So that critical amount.
 

387
00:24:02 --> 00:24:06
So again, when the molecules
come together, and let's just

388
00:24:06 --> 00:24:08
look at these for a minute,
when they're coming together to

389
00:24:08 --> 00:24:13
react, and if they're going to
react, there needs to be some

390
00:24:13 --> 00:24:15
energy associated with this,
because you're probably going

391
00:24:15 --> 00:24:19
to have to break a bond, and
that's going to take something,

392
00:24:19 --> 00:24:22
and then you may have to form
a new bond, for example.

393
00:24:22 --> 00:24:26
So there needs to be a critical
amount of energy, you need to

394
00:24:26 --> 00:24:29
be able to overcome that
activation energy barrier

395
00:24:29 --> 00:24:32
for the molecules to react.
 

396
00:24:32 --> 00:24:35
So it always takes some energy
for things to react and so you

397
00:24:35 --> 00:24:37
need to have enough energy.
 

398
00:24:37 --> 00:24:42
And so, if those molecules have
that energy, they'll come

399
00:24:42 --> 00:24:44
together, react, and
you'll form products.

400
00:24:44 --> 00:24:46
If they don't have that energy,
they're just going to go

401
00:24:46 --> 00:24:52
back to what they were,
unchanged reactants.

402
00:24:52 --> 00:24:56
So you need to have sufficient
energy to overcome that

403
00:24:56 --> 00:24:59
activation energy barrier.
 

404
00:24:59 --> 00:25:02
So, this is just a little movie
that shows two molecules coming

405
00:25:02 --> 00:25:06
together, and if they have
enough energy to react, you

406
00:25:06 --> 00:25:11
will see a spark, and then
the molecules will react.

407
00:25:11 --> 00:25:13
So, here we go.
 

408
00:25:13 --> 00:25:15
Molecule in red, in
green, they're checking

409
00:25:15 --> 00:25:16
each other out.
 

410
00:25:16 --> 00:25:19
Do they have enough --
they had enough energy,

411
00:25:19 --> 00:25:25
and they reacted, and
went on to product.

412
00:25:25 --> 00:25:30
All right, so let's talk about
this activation energy barrier

413
00:25:30 --> 00:25:38
and these activated complexes.
 

414
00:25:38 --> 00:25:53
OK, so in this example, you
have n o 2 plus c o, and

415
00:25:53 --> 00:25:58
they can come together
and form n o plus c o 2.

416
00:25:58 --> 00:26:02
And that's going to take some
amount of energy to react.

417
00:26:02 --> 00:26:05
And so, I'm drawing something
that's called an activated

418
00:26:05 --> 00:26:16
energy diagram, and we have
potential energy on one axis,

419
00:26:16 --> 00:26:28
and on the other we have what's
called a reaction coordinate.

420
00:26:28 --> 00:26:31
And so, the reactants are going
to have a certain amount of

421
00:26:31 --> 00:26:36
energy, so our reactants are
going to have some amount of

422
00:26:36 --> 00:26:45
energy, and our products will
have some amount of energy.

423
00:26:45 --> 00:26:51
But even though in this case
the change, the products are

424
00:26:51 --> 00:26:56
lower in energy, and you have
a delta e for the difference

425
00:26:56 --> 00:26:59
between the reactants and the
products, they can't go

426
00:26:59 --> 00:27:01
directly to products.
 

427
00:27:01 --> 00:27:05
They have to overcome an
activation energy barrier.

428
00:27:05 --> 00:27:08
So they have to overcome
some kind of barrier

429
00:27:08 --> 00:27:12
before they can react.
 

430
00:27:12 --> 00:27:16
So, only ones that can overcome
that barrier, that have enough

431
00:27:16 --> 00:27:21
energy to overcome this
activation energy barrier, so

432
00:27:21 --> 00:27:25
the activation energy for the
forward reaction, only those

433
00:27:25 --> 00:27:27
will be able to react.
 

434
00:27:27 --> 00:27:31
There's also an activation
energy barrier for the reverse

435
00:27:31 --> 00:27:33
reaction on this side.
 

436
00:27:33 --> 00:27:37
So, if you go from products to
reactants, you have to overcome

437
00:27:37 --> 00:27:40
that activation energy barrier.
 

438
00:27:40 --> 00:27:48
And up here, this is called the
activated complex, so you have

439
00:27:48 --> 00:27:55
some kind of activated complex
or transition state, so the

440
00:27:55 --> 00:27:58
molecules will come together,
they'll form some kind of

441
00:27:58 --> 00:28:04
transition state up here, and
then go down into products.

442
00:28:04 --> 00:28:08
OK, so most of you are sort of
familiar with the concept, I

443
00:28:08 --> 00:28:10
think, of this activation
energy, we've been talking

444
00:28:10 --> 00:28:14
about it, but the idea of an
activation energy barrier, I

445
00:28:14 --> 00:28:16
think is something that
probably all of you can

446
00:28:16 --> 00:28:18
personally connect with.
 

447
00:28:18 --> 00:28:23
So, for me, one of the things
that I find really hard to do

448
00:28:23 --> 00:28:27
is get started writing a long
National Institutes

449
00:28:27 --> 00:28:28
of Health grant.
 

450
00:28:28 --> 00:28:34
They're about 25 pages long,
they're single spaced, font 11,

451
00:28:34 --> 00:28:39
and they have point 5 margins
on every side of the page, and

452
00:28:39 --> 00:28:42
it's really dense, and it takes
a long time to sort of

453
00:28:42 --> 00:28:43
get going on that.
 

454
00:28:43 --> 00:28:47
And so, there is deadlines, and
MIT is very particular, you

455
00:28:47 --> 00:28:51
need to have it to the Office
of Sponsored Research five full

456
00:28:51 --> 00:28:54
business days before it's due
at the National Institutes of

457
00:28:54 --> 00:28:57
Health, and then the Department
needs to sign off on it.

458
00:28:57 --> 00:29:00
And I'll be looking at my
calendar and I have those dates

459
00:29:00 --> 00:29:03
marked, and checking how
many days I have left, and

460
00:29:03 --> 00:29:06
eventually, just like getting
started, it's like oh, there's

461
00:29:06 --> 00:29:09
so much to do, I have to read
the literature, the new stuff

462
00:29:09 --> 00:29:11
that's come out on my topic.
 

463
00:29:11 --> 00:29:13
And I have to think about what
projects I'm going to do in the

464
00:29:13 --> 00:29:16
future, and I have to write
about the progress that I've

465
00:29:16 --> 00:29:19
made so far, which is not
really what I want it to be.

466
00:29:19 --> 00:29:23
And so, I think a lot about how
-- it's just overwhelming.

467
00:29:23 --> 00:29:25
But then eventually
something happens.

468
00:29:25 --> 00:29:29
Either it's tremendous fear
that there's so few days left

469
00:29:29 --> 00:29:31
and you just have to do it.
 

470
00:29:31 --> 00:29:34
Sometimes it's going and
getting an enormous cup of

471
00:29:34 --> 00:29:36
coffee and sitting down.
 

472
00:29:36 --> 00:29:38
You know, people have been
known to sort of chain

473
00:29:38 --> 00:29:41
themselves to their desk, like
they're not going to get to get

474
00:29:41 --> 00:29:45
up until they've written the
introduction to the grant.

475
00:29:45 --> 00:29:47
So, a lot you can
connect with this.

476
00:29:47 --> 00:29:50
That any new thing you start,
there's some barrier that

477
00:29:50 --> 00:29:53
you have to overcome to
get started with it.

478
00:29:53 --> 00:29:56
And often once you're started
it's not that bad, and some of

479
00:29:56 --> 00:30:00
you may be thinking, exam 1 was
a long time ago, I recall

480
00:30:00 --> 00:30:02
there was a lot of
material on exam 1.

481
00:30:02 --> 00:30:04
And it seems really scary.
 

482
00:30:04 --> 00:30:07
But then the fact that I
mention the final exam over and

483
00:30:07 --> 00:30:12
over in class is helping you
get that energy that you need

484
00:30:12 --> 00:30:16
to overcome that activation
energy barrier and start

485
00:30:16 --> 00:30:18
studying, because once you
start studying you go, Oh

486
00:30:18 --> 00:30:19
yeah, I remember this,
this wasn't so bad.

487
00:30:19 --> 00:30:23
So you just need to get over
that activation energy

488
00:30:23 --> 00:30:25
barrier and you're all set.
 

489
00:30:25 --> 00:30:28
So, molecules have to do the
same thing, and the ones that

490
00:30:28 --> 00:30:31
have higher temperature have
an easier time getting

491
00:30:31 --> 00:30:34
over that barrier.
 

492
00:30:34 --> 00:30:39
So, here we can talk about
this general process.

493
00:30:39 --> 00:30:42
We can look at the individual
numbers involved.

494
00:30:42 --> 00:30:45
So in this particular case,
there's an activation energy

495
00:30:45 --> 00:30:53
for the forward reaction of 132
kilojoules per mole, and there

496
00:30:53 --> 00:30:59
is an activation energy for the
reverse reaction of 358

497
00:30:59 --> 00:31:01
kilojoules per mole.
 

498
00:31:01 --> 00:31:05
And there's also a delta e for
the reaction, which is this

499
00:31:05 --> 00:31:09
line, from reactions to
products, which in this case is

500
00:31:09 --> 00:31:13
minus 226 kilojoules per mole.
 

501
00:31:13 --> 00:31:15
So do you think this reaction
is endothermic or exothermic?

502
00:31:15 --> 00:31:23
What do you think,
exothermic or endothermic?

503
00:31:23 --> 00:31:29
It's exothermic, and if you
look back in your notes, we

504
00:31:29 --> 00:31:32
talked a little bit about
the relationship between

505
00:31:32 --> 00:31:33
delta h and delta e.
 

506
00:31:33 --> 00:31:38
And they're actually
pretty similar.

507
00:31:38 --> 00:31:44
A delta h usually equals delta
e plus a change in p v.

508
00:31:44 --> 00:31:50
So, for gases it's about 1% or
2% difference, and for solids,

509
00:31:50 --> 00:31:52
there's really negligible
difference between

510
00:31:52 --> 00:31:54
delta e and delta h.
 

511
00:31:54 --> 00:31:58
So, they're pretty
similar types of values.

512
00:31:58 --> 00:32:01
So, we can we can think about
what delta e really is, and so

513
00:32:01 --> 00:32:05
delta e in terms of activation
energy is going to be equal to

514
00:32:05 --> 00:32:09
the activation energy for the
forward reaction minus the

515
00:32:09 --> 00:32:13
activation energy for
the reverse reaction.

516
00:32:13 --> 00:32:18
And in this particular case, we
have 226 kilojoules per mole is

517
00:32:18 --> 00:32:26
our delta e, and for our
forward reaction, we have 132

518
00:32:26 --> 00:32:33
kilojoules per mole, and for
the reverse reaction, the

519
00:32:33 --> 00:32:38
activation energy for the
reverse reaction is 358

520
00:32:38 --> 00:32:42
kilojoules per mole, and so
these should all equal

521
00:32:42 --> 00:32:44
up to each other.
 

522
00:32:44 --> 00:32:47
And so, if you know two
of these values, you can

523
00:32:47 --> 00:32:48
calculate the third.
 

524
00:32:48 --> 00:32:50
And this is one of the
equations that you have to

525
00:32:50 --> 00:32:53
memorize for the final, because
it has, its sort of a

526
00:32:53 --> 00:32:57
conceptual thing that you need
to understand what this diagram

527
00:32:57 --> 00:33:01
says, that this plus that is
equal to that, that these all

528
00:33:01 --> 00:33:02
add up to each other.
 

529
00:33:02 --> 00:33:05
And if you have a negative
value here, that means it's

530
00:33:05 --> 00:33:07
an exothermic reaction.
 

531
00:33:07 --> 00:33:12
So, this delta e is a change in
internal energy of the system,

532
00:33:12 --> 00:33:16
and you can determine that
value experimentally, say, with

533
00:33:16 --> 00:33:21
a calorimetry experiment.
 

534
00:33:21 --> 00:33:27
OK, so let's keep this in mind
and go on and take a look at

535
00:33:27 --> 00:33:31
how this connects back with
some other things that we have

536
00:33:31 --> 00:33:34
already talked about
in this course.

537
00:33:34 --> 00:33:38
So, for an elementary reaction,
and I think for all of us,

538
00:33:38 --> 00:33:42
there's always some activation
energy barrier to overcome.

539
00:33:42 --> 00:33:46
There's always some positive
activation energy to overcome.

540
00:33:46 --> 00:33:50
And because there's always this
activation energy to overcome,

541
00:33:50 --> 00:33:53
increasing the temperature is
always going to increase the

542
00:33:53 --> 00:33:56
rate of an elementary reaction.
 

543
00:33:56 --> 00:33:59
It's always going to make it
easier to get over that

544
00:33:59 --> 00:34:01
activation energy barrier.
 

545
00:34:01 --> 00:34:06
But for an overall reaction,
increasing the temperature

546
00:34:06 --> 00:34:09
may not increase the
rate of the reaction.

547
00:34:09 --> 00:34:14
So let's consider why
that would be true.

548
00:34:14 --> 00:34:17
So, here is a reaction that
we've talked about before, we

549
00:34:17 --> 00:34:20
talked about this proposed
mechanism where we have a fast

550
00:34:20 --> 00:34:26
reversible step and
a slow second step.

551
00:34:26 --> 00:34:29
So we learned last time that we
can write the rate of product

552
00:34:29 --> 00:34:33
formation from the second step,
there are two molecules of n o

553
00:34:33 --> 00:34:38
2 being formed, so we have 2
times k 2, the concentration

554
00:34:38 --> 00:34:43
of n 2 o 2, and the
concentration of o 2.

555
00:34:43 --> 00:34:45
But this is an intermediate,
so we need to solve

556
00:34:45 --> 00:34:49
for that intermediate.
 

557
00:34:49 --> 00:34:54
So, in this case, we have a
fast reversible first reaction

558
00:34:54 --> 00:34:56
and a slow second reaction.
 

559
00:34:56 --> 00:34:59
So this intermediate is going
to build up, and it's going to

560
00:34:59 --> 00:35:03
be more or less an equilibrium
with the reactants, because

561
00:35:03 --> 00:35:07
this is very fast, and only a
little bit of this is siphoned

562
00:35:07 --> 00:35:12
off to make product, and so
this creates an equilibrium

563
00:35:12 --> 00:35:13
type situation.
 

564
00:35:13 --> 00:35:17
So why don't you solve this
intermediate for me, this is a

565
00:35:17 --> 00:36:13
review from the last class.
 

566
00:36:13 --> 00:36:29
OK, let's just take
10 more seconds.

567
00:36:29 --> 00:36:33
Very good.
 

568
00:36:33 --> 00:36:37
So, we can solve for this,
equilibrium constant for the

569
00:36:37 --> 00:36:40
first step, products over
reactants, and then if you

570
00:36:40 --> 00:36:43
solved for this, the
intermediate here, which is the

571
00:36:43 --> 00:36:46
product in the first step, then
it would be equal to k

572
00:36:46 --> 00:36:50
1 times n o squared.
 

573
00:36:50 --> 00:36:55
We can take that term and we
can we can plug it in, so over

574
00:36:55 --> 00:37:00
here, we can substitute it into
this equation, and so we have 2

575
00:37:00 --> 00:37:08
k 2, big K 1 times n
o squared times o 2.

576
00:37:08 --> 00:37:10
All right, so here
is our rate then.

577
00:37:10 --> 00:37:13
And if you missed some of
this, this was in the

578
00:37:13 --> 00:37:15
notes from before.
 

579
00:37:15 --> 00:37:19
So now let's think about
the effect of temperature.

580
00:37:19 --> 00:37:23
So, k 2 is an elementary rate
constant, and so its

581
00:37:23 --> 00:37:26
temperature -- if you increase
the temperature, its

582
00:37:26 --> 00:37:29
rate will increase.
 

583
00:37:29 --> 00:37:35
So here again is our equation,
the activation energy is always

584
00:37:35 --> 00:37:37
positive, there's always
positive, there's always

585
00:37:37 --> 00:37:39
some barrier to overcome.
 

586
00:37:39 --> 00:37:41
So if you increase the
temperature, you're

587
00:37:41 --> 00:37:46
always going to increase
the elementary rate.

588
00:37:46 --> 00:37:49
Well, what about
equilibrium constant?

589
00:37:49 --> 00:37:53
So we've talked about this back
in chemical equilibrium that

590
00:37:53 --> 00:37:56
the effect of temperature on
the equilibrium constant

591
00:37:56 --> 00:38:01
depends on whether the reaction
is endothermic or exothermic.

592
00:38:01 --> 00:38:05
And you told me before, the
equation, and that's the Van't

593
00:38:05 --> 00:38:06
Hoff equation shown here.
 

594
00:38:06 --> 00:38:09
And so look how similar
those equations are.

595
00:38:09 --> 00:38:13
So for an elementary rate
constant, we had e a, and for

596
00:38:13 --> 00:38:18
equilibrium constant, we're
talking about delta h.

597
00:38:18 --> 00:38:23
So, if you have, here the
reaction is exothermic, and if

598
00:38:23 --> 00:38:26
you increase the temperature of
an exothermic reaction,

599
00:38:26 --> 00:38:33
what happens to k?
 

600
00:38:33 --> 00:38:36
It decreases.
 

601
00:38:36 --> 00:38:40
So, again, it would shift,
then, to the endothermic

602
00:38:40 --> 00:38:42
direction, decreasing k.
 

603
00:38:42 --> 00:38:44
So let's look at this then.
 

604
00:38:44 --> 00:38:47
So we have in this k obs term,
we have an elementary rate

605
00:38:47 --> 00:38:51
constant and an equilibrium
constant, so if you if you

606
00:38:51 --> 00:38:54
increase the temperature, the
rate constant increases, but

607
00:38:54 --> 00:38:59
the equilibrium constant
is going to decrease.

608
00:38:59 --> 00:39:03
So, the magnitude of the
increase or decrease depends on

609
00:39:03 --> 00:39:09
the size of the activation
energy or the size of delta h.

610
00:39:09 --> 00:39:13
So for this particular example,
there's no way that you would

611
00:39:13 --> 00:39:16
know this so I'm telling you,
that the activation energy is a

612
00:39:16 --> 00:39:18
small number, or you might be
able to look it up in your

613
00:39:18 --> 00:39:22
book, and delta h is a very
big number and it's negative,

614
00:39:22 --> 00:39:24
it's an exothermic reaction.
 

615
00:39:24 --> 00:39:28
So if you have a very small
number for e a, that means that

616
00:39:28 --> 00:39:30
the rate constant will increase
only a little bit, it's not

617
00:39:30 --> 00:39:33
that sensitive to a change
in temperature, because e

618
00:39:33 --> 00:39:35
a's a very small number.
 

619
00:39:35 --> 00:39:39
But if delta h is a big number,
then the equilibrium constant

620
00:39:39 --> 00:39:41
would decrease a lot with
temperature because this

621
00:39:41 --> 00:39:43
is a big number here.
 

622
00:39:43 --> 00:39:46
So in this particular example,
increasing the temperature

623
00:39:46 --> 00:39:51
actually decreases the observed
rate, because delta h is, in

624
00:39:51 --> 00:39:53
this particular example,
a much bigger thing.

625
00:39:53 --> 00:39:56
So if you were given either
numbers or some information

626
00:39:56 --> 00:39:59
like that, you should be able
to rationalize what might be

627
00:39:59 --> 00:40:04
true about the rate
of the reaction.

628
00:40:04 --> 00:40:07
so, a large activation energy
means that the rate constant

629
00:40:07 --> 00:40:10
is very sensitive to
changes in temperature.

630
00:40:10 --> 00:40:13
A large delta h means
equilibrium constant

631
00:40:13 --> 00:40:18
is very sensitive to
changes in temperature.

632
00:40:18 --> 00:40:22
And, as we've talked about, e a
is always positive, so the

633
00:40:22 --> 00:40:26
elementary rates always
increase with temperature,

634
00:40:26 --> 00:40:32
whereas delta h can be positive
or negative, so equilibrium

635
00:40:32 --> 00:40:38
constants can increase or
decrease with temperature.

636
00:40:38 --> 00:40:43
And here, the magnitude of
delta h indicates the magnitude

637
00:40:43 --> 00:40:45
of the change, how much k will
change, will it be a big change

638
00:40:45 --> 00:40:50
or a small change, whereas the
sign of delta h indicates the

639
00:40:50 --> 00:40:55
direction of the change.
 

640
00:40:55 --> 00:40:58
So, just want to review
one thing and then

641
00:40:58 --> 00:41:00
we'll stop for the day.
 

642
00:41:00 --> 00:41:04
So when a stress is applied to
a system, an equilibrium, the

643
00:41:04 --> 00:41:08
system tends to try to
minimize that stress.

644
00:41:08 --> 00:41:12
So we're back to
LeChatelier's principle.

645
00:41:12 --> 00:41:14
And so, just one more
clicker question and

646
00:41:14 --> 00:41:15
we'll stop for the day.
 

647
00:41:15 --> 00:41:21
So increasing the temperature
is going to do what again?

648
00:41:21 --> 00:41:36
Again, thinking back
to LeChatelier.

649
00:41:36 --> 00:41:51
And just 10 more seconds.
 

650
00:41:51 --> 00:41:52
Very good.
 

651
00:41:52 --> 00:41:56
So, we're going to finish
up these notes on Monday.

652
00:41:56 --> 00:41:59
We're going to think about
LeChatelier in a new way, we're

653
00:41:59 --> 00:42:02
going to think about it in
terms of activation energy,

654
00:42:02 --> 00:42:06
which is really fun, because we
tie back what we learned in the

655
00:42:06 --> 00:42:08
middle of course to what
we're seeing now in

656
00:42:08 --> 00:42:09
the end of the course.
 

657
00:42:09 --> 00:42:11
All right, have a great
weekend, everybody.

658
00:42:11 --> 00:42:12