WEBVTT

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Prof: Okay,
so last time we were talking

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about exponents,
and how statistics gives rise

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to them.

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And we looked last time at the
Boltzmann factor,

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that e^-H/RT^( )or
ΔH/RT,

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which tells you the temperature
dependence of the equilibrium

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constant.

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It gives you the equilibrium
constant;

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remember at room temperatures
3/4thsΔH in

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kilocalories.

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Right?

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And we saw last time that that
comes from counting arrangements

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of a fixed number of energy
bits.

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And the important thing is that
they're random,

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that all of them are equally
likely.

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<<Technical
adjustment>>

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That has interesting
philosophical implications I

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think.

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Do you remember at the start of
the course we were talking about

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types of authority,
and in particular,

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remember, in Hamlet,
Act V, Scene II,

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he says, "There's a
divinity that shapes our

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ends."

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So this was a traditional view
in society.

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But then this guy came along,
in 1859.

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Do you know who that is?

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Charles Darwin,
with The Origin of the

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Species.

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So there was conflict between
the religious fundamentalists

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and Darwinists that continues to
this day.

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But I think they really miss
the point, because Darwin had

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the idea that things were
developing and getting better

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all the time.

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Right?

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So there's a certain
compatibility between that and

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the sensibilities of the
fundamentalists.

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But also, not too long from
then, this guy came along,

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Boltzmann, and he said
everything is driven just by

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randomness.

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There's no goal for everything.

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That should be the real
conflict, between religious

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fundamentalists and science,
is Boltzmann.

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But so few people understand
what Boltzmann did that there's

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no reason for the conflict.

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At any rate,
we saw where the Boltzmann

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factor came from,
in terms of statistics.

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Then there's the entropy
factor, which we saw last time.

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And notice that,
as I've written it here,

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in the top equation,
the one with Boltzmann,

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there's an R,
and the one at the bottom has a

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k.

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Sometimes you see R's
and sometimes see k's.

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They're actually the same thing.

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The k is if you measure
the energy per molecule,

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and R is if you measure
the energy per mole.

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So all you have is Avogadro's
number is included in one of

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them and not the other.

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They're really the same thing,
these two exponentials.

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But at any rate,
we can cancel the T's

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and know that that
e^S/k^( )is a counting

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number, W;
the number of molecular

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structures being grouped.

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And we saw that at the end of
last time in terms of gauche-

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versus anti-butane.

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And remember that S = ln
k -- which is the same

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equation, just the log on each
side -- is on Boltzmann's tomb.

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But let's look at one more
example, in terms of

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cyclohexane.

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Do you remember the cyclohexane
conorformers --

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<<technical
adjustment>>

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-- remember the cyclohexane
conformers, if it's a chair,

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it's very rigid.

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Why is it rigid?

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Do you remember?

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Why is it hard to twist?

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With respect to the molecular
model, why is it hard to twist?

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Eric?

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Why does this particular model,
in which rotation around bonds

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is completely free,
why is it hard to rotate to go

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like this?

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Why is there a click?

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Student:
>.

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Prof: Pardon me?

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Student:  It has the
optimal bending angles,

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109.5.

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Prof: Ah,
it's the bending angle that has

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to flatten out when you do this.

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Remember we talked about that.

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But anyhow this one is very
rigid.

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But if you click it,
into the boat,

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then it's actually a twist-boat
and it turns to all sorts of

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structures ever so easily.

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So there are many more
accessible structures for a

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boat, than there are for a
chair.

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The chair, you have this one
and you have this one.

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Right?

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But for a boat,
or a twisted,

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or the "flexible"
form as it's often called,

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you have lots and lots of
accessible structures.

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What's that going to mean in
terms of entropy?

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That there are many more
structures you're going to count

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for the flexible form than you
count for the chair form,

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the rigid form.

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Okay?

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So if we look at -- this is a
picture of the energy with the

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chair at the minimum of energy.

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The twist-boat is 5.5
kilocalories above,

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but it has very small barriers
among different twist-boat

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forms.

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So we would say there are few
structures that are chair

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cyclohexane, but many structures
that are the boat.

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And furthermore,
if we look at it in terms of

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quantum mechanics,
which is the real way to do it,

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we notice that when there's a
steep,

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stiff valley,
there are very few energy

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levels that are accessible.

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Right?

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But if the barriers are low,
then there are many,

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many quantum levels.

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So you count many more quantum
levels for the flexible form

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than you do for the chair form.

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What that means is from,
whether the red classical view

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or the green quantum view,
there's a big statistical

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factor, an entropy factor,
which turns out to be about

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7-fold favoring the twist-boat
over the chair.

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The chair is still favored;
it's favored because of energy,

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that Boltzmann factor,
e^ΔH/kT.

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But this reduces that bias in
favor of the chair -- which

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would otherwise be 10^3/4ths of
5.5; right?

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-- it reduces it by about a
factor of 2000.

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So the equilibrium constant is
only 14,000 -- instead of

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14,000, it reduces by a factor
of 7, to make it 2000.

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Okay, so that's -- but so we've
been talking about entropy here

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in statistical terms.

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But remember earlier we talked
about the fact that physical

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chemists actually measure
entropy as something

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experimental,
not just a counting exercise,

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and they do it beginning with
something that's as close as

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possible to zero Kelvin.

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Because if you have a perfectly
ordered crystal,

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at zero Kelvin,
then there's only one structure

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you're talking about.

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Right?

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So the entropy is the log of
one, which is zero,

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or log of 1/R;
times R.

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Okay?

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So it's zero.

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But then as you warm it up,
as you put heat in,

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you measure the increase in
this thing called entropy by how

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much heat you put in,
at each temperature,

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as you warm up.

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And we talked about that
already.

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And you'll notice qualitatively
how this works is that floppy

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molecules,
like the flexible form of

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cyclohexane,
that have many closely spaced

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energy levels,
absorb more energy,

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and they absorb it at lower
temperatures,

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and thus they have more entropy
when they get warmed.

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So whether you do it
experimentally,

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by measuring the heat that gets
absorbed,

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or whether you measure it by
counting quantum states,

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you get the same result;
that a floppy molecule is

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favored in terms of entropy.

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We talked about that when we
were talking about the barrier

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to ethane rotation.

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Okay, so we've looked at the
Boltzmann factor and this

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entropy factor,
that come from counting.

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Notice that in the second case,
truly we should be counting not

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structures but quantum states;
how many states are there that

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count?

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And if you want to be really,
really picky,

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you say the weighted number of
quantum states;

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because ones that are higher in
energy are not as populated as

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ones that are lower in energy.

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But we don't have to worry
about that now.

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At any rate,
those two factors,

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taken together,
are what gives the equilibrium

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constant,
which as we said before is

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e^-ΔG,
free energy;

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that means it's both enthalpy,
heat, and entropy,

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this counting thing.

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But there's more to it than
that.

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There's also the statistics
involved in the Law of Mass

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Action.

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And that comes from counting
molecules per volume;

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that is, concentration.

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So you can count energy,
you can count quantum states,

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and you can count molecules per
volume.

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This is very easily understood.

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The way it developed
experimentally is that in the

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late 1700s there was an attempt
to assemble a hierarchy of

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affinities;
that some elements had more

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affinity than others.

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So if you had a compound that
involved one element,

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and mixed it with an element
that had higher affinity,

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that one with higher affinity
would take away molecules from

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the one with lower affinity.

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But then it was found,
in the early 1800s,

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that it doesn't always go in
that direction,

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because concentrations can
change and make things go the

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wrong way,
toward something that's a very

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low affinity,
if it has very high

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concentration.

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And by the middle 1800s,
this was formulated as an

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equilibrium constant,
K, which was understood

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as the balance between forward
reactions and reverse reactions.

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You've seen that k_1/k_-1
is the equilibrium constant.

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So concentration comes into it,
in this thing called the Law of

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Mass Action.

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If you have two A's that can go
to A_2,

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then you have this equilibrium
constant,

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written as the concentration of
A_2 divided by the concentration

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of A^2.

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Now why the exponent?

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Where does that exponent two
come from?

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And sometimes it's three.

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Remember?

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Again, it's statistical and
very, very easy to see.

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Here I used Excel to place a
bunch of circles randomly on a

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two-dimenstional plot.

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So it put 50 of these circles
down.

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And we're going to count as
dimers things where they

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overlap, where they touch one
another.

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Okay?

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So there's -- if you have 50
particles, this particular

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realization of randomness gave
one dimer.

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But suppose we add another 50.

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Right?

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Now, in addition to the
original dimer,

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there are 8 more.

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Okay?

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And now suppose I add another
50, now there are 19 dimers.

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Or another 50;
now there are 35 dimers.

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Or another 50,
and now there are 59 dimers.

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Now let's make a plot of how
many dimers there are,

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compared to how many particles
there are, undimerized ones.

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So there's the number of
particles and the number of

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dimers, plotted;
the data there.

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And you see what it is.

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It's a parabola;
that the number of dimers is

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proportional to the square of
the number of monomers.

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Now why should that be so?

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It's because as you increase
the concentration,

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you increase the number of
units there; obviously.

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That's by definition.

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But you also increase the
fraction of the units that have

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a near neighbor,
that are touching.

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So not only do you increase the
number that could be dimers,

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you increase the fraction that
are dimers.

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So there are two ways in which
increasing the concentration

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increases the dimer.

11:52.403 --> 11:53.003
Right?

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So it's a square.

11:54.298 --> 11:55.638
That's where the exponent comes
in.

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It's purely statistical,
for random distribution.

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And then, of course,
energy can enter in,

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entropy can enter in.

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That will change the K.

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But the exponent on P --
right?

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-- is due just to this counting
procedure.

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So you increase both the number
and the fraction that are

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dimers.

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Okay, so now we know about
equilibrium, statistics and

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exponents.

12:21.500 --> 12:25.580
We have particle distribution,
that's the law of mass action;

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that's that square we just
talked about.

12:27.340 --> 12:30.190
We have energy distribution,
ΔH,

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the Boltzmann factor.

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And we have counting of quantum
states, which has to do with

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entropy.

12:37.360 --> 12:42.770
Okay, so free energy determines
what equilibrium is,

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what can happen.

12:44.474 --> 12:45.434
Right?

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And that ΔG
remember includes both entropy

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and energy.

12:49.788 --> 12:53.728
But it doesn't tell you at all
how quickly it will happen,

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what the kinetics of the
reaction are.

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So for that purpose we're going
to try visualizing reactions,

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to see if we can get a picture
of what determines rates.

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And we're going to look at two
kinds of things.

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We're going to look at
classical trajectories,

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and at the potential energy
surface, and collective

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concepts.

13:12.889 --> 13:17.009
So first let's start with the
potential energy surface.

13:17.009 --> 13:19.279
Here's a very simple potential
energy surface.

13:19.278 --> 13:20.838
It's just a two-dimensional
diagram.

13:20.840 --> 13:22.700
So you've seen it before.

13:22.700 --> 13:24.980
We plot the distance between
two atoms, A-B,

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and the potential energy as a
function of the distance.

13:28.000 --> 13:29.920
So this is a Morse-type curve.

13:29.918 --> 13:35.758
Okay, so we put a ball on it,
and let that ball roll to map

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out different distances,
as it moves -- that's the

13:39.683 --> 13:42.413
horizontal axis --
and the energy corresponding to

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that distance.

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So it rolls back and forth --
right?

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-- mapping out the change in
geometry horizontally,

13:49.628 --> 13:51.928
and the change in energy
vertically.

13:51.928 --> 13:55.478
Now we're going to look at a
three-dimensional surface,

13:55.481 --> 13:58.181
or actually two geometrical
dimensions;

13:58.178 --> 14:02.048
plus the third dimension coming
out at you, the contours,

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have to do with potential
energy, of three particles now.

14:06.129 --> 14:09.039
But in order to describe the
position of three particles,

14:09.037 --> 14:11.997
you need three distances;
one to two, two to three,

14:12.000 --> 14:13.060
and three to one.

14:13.059 --> 14:13.559
Right?

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So that's too many dimensions
to plot this way.

14:15.750 --> 14:18.680
So we're going to assume that
they're all on a line.

14:18.678 --> 14:20.928
So we only have the distance
between one and two,

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and the distance between two
and three.

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So two coordinates will tell
you what the arrangement of

14:27.469 --> 14:31.159
those three atoms are,
if they're in just one

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dimension.

14:32.330 --> 14:35.860
Okay, so a linear triatomic,
A-B-C.

14:35.860 --> 14:39.140
On the horizontal distance we
have the distance A to B,

14:39.135 --> 14:42.165
on the vertical axis,
B to C, and the contours tell

14:42.169 --> 14:44.949
us how low the energy is;
the darker, the lower the

14:44.945 --> 14:45.265
energy.

14:45.269 --> 14:49.869
Okay, so this specifies the
structure.

14:49.870 --> 14:53.930
So the position of a point
specifies not the position of an

14:53.934 --> 14:56.674
atom but the position of a set
of atoms.

14:56.668 --> 14:57.368
Right?

14:57.370 --> 15:00.510
So as we move one point around,
we're moving two atoms,

15:00.510 --> 15:02.140
or changing two distances.

15:02.139 --> 15:05.759
But we can denote it with one
point here, in two geometric

15:05.763 --> 15:06.593
dimensions.

15:06.590 --> 15:08.750
Okay, so let's look at several
regions.

15:08.750 --> 15:10.950
Let's look at that valley on
the right.

15:10.950 --> 15:13.110
What is that valley?

15:13.110 --> 15:17.230
When a point is in that valley,
what's it describing?

15:17.230 --> 15:22.630
It says that the distance
between A and B is large.

15:22.625 --> 15:23.485
Right?

15:23.490 --> 15:25.610
So A is far away from B.

15:25.610 --> 15:28.550
What does it say about the BC
distance?

15:28.549 --> 15:31.309
It's short.

15:31.308 --> 15:34.428
It's the normal distance for a
BC molecule.

15:34.429 --> 15:38.239
So what is it;
when a point is in that valley,

15:38.238 --> 15:40.228
what geometry is it describing?

15:40.230 --> 15:44.150
It's describing a BC molecule,
with an A atom at a great

15:44.153 --> 15:47.513
distance from it,
depending on how far out we go

15:47.506 --> 15:48.716
to the right.

15:48.720 --> 15:50.440
Does everybody see that?

15:50.440 --> 15:54.830
One position of the point tells
us where both -- where all three

15:54.832 --> 15:57.552
atoms are, as long as they're on
a line.

15:57.552 --> 15:58.252
Right?

15:58.250 --> 16:00.890
Now how about up there,
on that plateau?

16:00.889 --> 16:03.129
What's happening there?

16:03.129 --> 16:04.999
What's the physical system?

16:05.000 --> 16:06.100
Maria, what do you say?

16:06.100 --> 16:09.140
Student:  All the atoms
are separate from each other.

16:09.139 --> 16:10.509
Prof: Yeah,
the atoms are all separate from

16:10.508 --> 16:10.898
one another.

16:10.899 --> 16:15.029
C is far from B and A is far
from B.

16:15.028 --> 16:16.588
So there the atoms are
separated.

16:16.590 --> 16:17.820
And it's high in energy.

16:17.820 --> 16:20.410
You're not surprised that it
takes energy to pull them apart.

16:20.409 --> 16:24.299
And there is a cliff. Right?

16:24.298 --> 16:27.118
If this were a hiking map,
that would be a cliff.

16:27.120 --> 16:28.340
What does that cliff mean?

16:28.340 --> 16:29.890
Why is there a cliff there?

16:29.889 --> 16:33.159
Greg, what do you say?

16:33.158 --> 16:37.418
Why is there a cliff shown
there?

16:37.418 --> 16:40.908
What's the geometry that points
in that region described?

16:40.908 --> 16:43.028
Student:  Closer
together.

16:43.029 --> 16:44.879
Prof: What's close
together?

16:44.879 --> 16:46.489
Is A close to B?

16:46.490 --> 16:47.960
Student:  Closer.

16:47.960 --> 16:49.590
Prof: Is A close to B?

16:49.586 --> 16:50.536
I couldn't hear.

16:50.538 --> 16:51.548
Student:  Closer maybe
to B.

16:51.548 --> 16:52.228
Prof: No.

16:52.225 --> 16:53.275
Here's the distance A-B.

16:53.279 --> 16:55.109
It's way out there,
where that cliff is.

16:55.113 --> 16:55.493
Right?

16:55.490 --> 16:56.550
So A's far away.

16:56.549 --> 16:57.719
But what's happening?

16:57.720 --> 17:01.770
B and C are getting very close
to one another.

17:01.769 --> 17:03.519
So that's a collision between B
and C;

17:03.519 --> 17:05.779
much shorter than their bond
distance.

17:05.780 --> 17:06.270
Right?

17:06.269 --> 17:08.079
They're being scrunched
together in that region,

17:08.080 --> 17:09.860
and that's why the energy goes
up very rapidly,

17:09.855 --> 17:11.585
because they're running into
one another;

17:11.589 --> 17:13.849
closer than they like to be.

17:13.849 --> 17:16.919
There's a ridge -- right?

17:16.920 --> 17:18.320
-- as you go down there.

17:18.318 --> 17:19.988
If you were hiking,
that would be a ridge.

17:19.990 --> 17:23.260
And there's a special point on
the ridge, which is marked by

17:23.261 --> 17:24.151
the red cross.

17:24.150 --> 17:26.230
What would you call that if you
were hiking?

17:26.230 --> 17:29.120
If you were in the valley
that's labeled yellow,

17:29.118 --> 17:31.028
and you were thinking of
getting to the other valley,

17:31.028 --> 17:34.558
what would you call that cross,
if you were hiking?

17:34.559 --> 17:35.639
Student:  A peak.

17:35.640 --> 17:39.770
Prof: Not a peak. Right?

17:39.769 --> 17:42.289
It comes -- it gets high as it
gets close to me here,

17:42.294 --> 17:44.144
and it gets high out on the
plateau.

17:44.140 --> 17:46.940
It's actually low,
as we go along the line,

17:46.943 --> 17:50.353
but it's high as we go
perpendicular to the line.

17:50.348 --> 17:52.108
What would you call that if you
were hiking?

17:52.109 --> 17:53.389
Some of you must hike.

17:53.390 --> 17:54.410
Student:  A pass.

17:54.410 --> 17:56.380
Prof: Pardon me?

17:56.380 --> 17:57.600
Student:  A pass.

17:57.598 --> 17:59.958
Prof: It's a pass,
between one valley and the

17:59.963 --> 18:00.663
other valley.

18:00.660 --> 18:03.540
That's the way you would go if
you were hiking -- right?

18:03.538 --> 18:04.678
-- so you don't have to climb
so high.

18:04.680 --> 18:07.260
Okay, so it's a pass.

18:07.259 --> 18:10.139
Or in chemistry we call it a
transition state,

18:10.144 --> 18:11.944
or a transition structure.

18:11.940 --> 18:14.860
And it's like a potato chip.

18:14.858 --> 18:15.588
Right?

18:15.588 --> 18:19.458
It's a minimum in one
direction, along the ridge,

18:19.463 --> 18:23.823
but it's a maximum in the path
between the two valleys.

18:23.823 --> 18:24.553
Okay?

18:24.549 --> 18:27.229
So it's a very special point.

18:27.230 --> 18:29.720
Okay, now let's look at this a
little closer.

18:29.720 --> 18:33.360
Suppose we sliced this surface,
we took a knife and sliced it

18:33.359 --> 18:35.869
along the red line there,
horizontally,

18:35.874 --> 18:39.264
and then folded it back to look
at the cross-section.

18:39.259 --> 18:40.729
Does everybody see what I'm
saying?

18:40.730 --> 18:42.830
What would the cross-section
look like?

18:42.828 --> 18:48.718
It's exactly that one we looked
at before.

18:48.720 --> 18:54.250
So that involves stretching A
and B, with C so far away that

18:54.253 --> 18:55.763
it's irrelevant.

18:55.755 --> 18:56.595
Right?

18:56.598 --> 18:58.328
So it's just stretching a
diatomic molecule.

18:58.328 --> 19:02.428
Or if we sliced -- so that's
vibration of AB,

19:02.425 --> 19:06.145
with a distant spectator of
C.***Okay?

19:06.150 --> 19:08.710
Now suppose we sliced it that
way and pulled it back.

19:08.710 --> 19:10.080
Now what is it?

19:10.078 --> 19:16.538
It's a vibrating BC molecule,
with A far away.

19:16.540 --> 19:17.690
Right?

19:17.690 --> 19:20.740
So again, by choosing points on
this, we can describe any

19:20.744 --> 19:24.134
geometry of these three points
we want, as long as they're on a

19:24.127 --> 19:24.617
line.

19:24.618 --> 19:26.578
But a single point is a whole
structure.

19:26.578 --> 19:33.578
Okay, now let's look at a
trajectory.

19:33.578 --> 19:36.678
We roll a ball on this surface,
and it rolls up toward the pass

19:36.684 --> 19:39.044
but doesn't make it and comes
back like that.

19:39.038 --> 19:42.408
So that's a trajectory that was
unreactive;

19:42.410 --> 19:46.030
it didn't make it into the
product valley,

19:46.027 --> 19:48.937
it didn't get across the ridge.

19:48.940 --> 19:53.810
And physically what it means is
that A gets closer to BC.

19:53.808 --> 19:56.428
While BC is vibrating,
it's moving up and down.

19:56.432 --> 19:56.892
Right?

19:56.890 --> 19:58.510
So BC is vibrating.

19:58.509 --> 20:02.549
A comes in and then bounces off
again.

20:02.547 --> 20:03.417
Right?

20:03.420 --> 20:08.640
So it was an unsuccessful
attempt of A to take B away from

20:08.643 --> 20:09.013
C.

20:09.009 --> 20:11.589
Or suppose we do this one.

20:11.588 --> 20:16.998
A approaches,
and now C flies away from

20:16.996 --> 20:19.126
vibrating AB.

20:19.130 --> 20:21.200
Does everybody see that?

20:21.200 --> 20:23.920
You want me to say it again?

20:23.920 --> 20:24.600
Right?

20:24.598 --> 20:27.418
So as it comes along,
B and C are standing still.

20:27.420 --> 20:28.740
It's not moving vertically,
right?

20:28.740 --> 20:31.650
So B and C are at their normal
distance, their standard

20:31.654 --> 20:32.254
distance.

20:32.250 --> 20:35.680
A comes in, whops into it,
gets really close,

20:35.676 --> 20:38.706
runs into that cliff,
really close to B,

20:38.714 --> 20:41.054
because it's the distance A-B.

20:41.053 --> 20:41.913
Right?

20:41.910 --> 20:46.310
And then it starts -- AB is
vibrating, and C is getting far

20:46.314 --> 20:49.584
away, as it goes down the
product valley.

20:49.578 --> 20:53.438
So that's a reactive
trajectory, where the first

20:53.440 --> 20:55.740
trajectory was unreactive.

20:55.740 --> 21:01.640
Notice that this is classical,
rolling a marble on the thing,

21:01.644 --> 21:06.274
because A was approaching a
non-vibrating BC.

21:06.269 --> 21:09.999
We know from quantum mechanics
that BC can't just sit there.

21:10.000 --> 21:11.020
BC vibrates.

21:11.019 --> 21:14.679
So that's not a realistic
trajectory, it's a classical

21:14.682 --> 21:17.382
model of a quantum mechanical
system.

21:17.380 --> 21:24.300
Now people have made surfaces
like that for real systems,

21:24.298 --> 21:27.918
like H_3, one hydrogen atom
attacking a hydrogen molecule

21:27.924 --> 21:30.454
and taking one of the hydrogens
away.

21:30.450 --> 21:31.170
Here it is.

21:31.170 --> 21:31.930
This was drawn.

21:31.930 --> 21:35.530
This is the first surface that
was drawn, that I know of,

21:35.525 --> 21:38.025
by Henry Eyring at Princeton in
1935.

21:38.029 --> 21:41.229
And it had some -- it has crazy
angles.

21:41.230 --> 21:44.660
And the reason it has that
angle is so that a marble

21:44.662 --> 21:48.432
rolling on it will behave
according to the way the masses

21:48.431 --> 21:51.661
of the thing --
so that the kinetics,

21:51.660 --> 21:54.440
the kinematics,
are exactly right,

21:54.440 --> 21:58.040
so that it really does do the
proper classical thing.

21:58.038 --> 22:03.168
If you roll a marble on here,
it will trace Newton's Laws of

22:03.171 --> 22:05.781
Motion, for this H_3 system.

22:05.778 --> 22:08.968
One thing that's unrealistic
about it is that there's a

22:08.971 --> 22:11.101
minimum near the transition
state.

22:11.099 --> 22:12.459
There's a little lake up there.

22:12.460 --> 22:15.470
That's just an artifact that
came from the equation he used

22:15.472 --> 22:16.982
to approximate the surface.

22:16.980 --> 22:17.870
It's not real.

22:17.868 --> 22:21.508
There actually is a potato
chip, not a lake up there at the

22:21.509 --> 22:21.949
pass.

22:21.950 --> 22:24.800
Some people have called it Lake
Eyring.

22:24.804 --> 22:25.334
Okay?

22:25.328 --> 22:30.358
But here's a more complicated
surface that was -- it says it

22:30.363 --> 22:33.523
was done by C. Parr,
in his Ph.D.

22:33.519 --> 22:36.109
thesis at Caltech in 1969.

22:36.109 --> 22:39.729
This is for H-H-Br;
again linear,

22:39.732 --> 22:44.142
but a hydrogen atom attacking
HBr to take away it's hydrogen.

22:44.140 --> 22:48.810
And this describes the
construction of a model based on

22:48.810 --> 22:52.270
that surface,
an actual physical model on

22:52.271 --> 22:54.611
which you can roll marbles.

22:54.607 --> 22:55.557
Right?

22:55.558 --> 22:57.648
So here it is,
and the dimensions,

22:57.646 --> 23:01.056
that one inch corresponds to
1.4 inches is an angstrom,

23:01.064 --> 23:01.954
and so on.

23:01.950 --> 23:05.550
So they actually constructed
physical models to do this.

23:05.548 --> 23:08.948
And, as it happens,
we have that physical model

23:08.951 --> 23:09.471
here.

23:09.470 --> 23:18.330
Here, this is it.

23:18.328 --> 23:22.798
<<Technical
adjustment>>

23:22.799 --> 23:25.659
Okay, and we have some marbles.

23:25.660 --> 23:28.590
So notice what's different
about this one.

23:28.588 --> 23:30.038
I'll hold it up so you can see
it.

23:30.039 --> 23:33.109
There's the surface. Right?

23:33.108 --> 23:35.348
And here's a slice through one.

23:35.353 --> 23:35.863
Right?

23:35.858 --> 23:43.008
That's H_2 with -- this valley
is H_2 with a Br atom.

23:43.009 --> 23:46.639
This valley is HBr,
with an H atom.

23:46.635 --> 23:47.485
Right?

23:47.490 --> 23:51.040
So we can try rolling balls and
see what happens here.

23:51.039 --> 23:56.089
So here I am far away.

23:56.089 --> 23:58.499
The H atom is far away from HBr.

23:58.500 --> 23:59.680
And I do that.

23:59.680 --> 24:03.170
And it's vibrating,
but it doesn't succeed.

24:03.173 --> 24:03.843
Right?

24:03.839 --> 24:04.849
I can do it a little bit more.

24:04.848 --> 24:09.698
And most reactions aren't
successful.

24:09.700 --> 24:16.470
Oh close. Okay?

24:16.470 --> 24:19.550
And as it comes out,
it may be vibrating when it

24:19.553 --> 24:23.493
comes out, or it may not be
vibrating when it comes -- oh.

24:23.490 --> 24:25.190
What's the cross?

24:25.190 --> 24:30.210
The cross is that transition
structure -- right?

24:30.210 --> 24:31.770
-- or the transition state.

24:31.769 --> 24:37.389


24:37.390 --> 24:37.870
Right?

24:37.866 --> 24:41.286
So you could do every possible
trajectory.

24:41.288 --> 24:44.618
You could have different
velocities at which A is

24:44.615 --> 24:47.895
colliding with BC,
and you can have different

24:47.904 --> 24:51.034
amounts of vibration,
and different phases of

24:51.030 --> 24:51.750
vibration.

24:51.750 --> 24:54.830
I could start it going this
way, or I could start it going

24:54.826 --> 24:55.416
this way.

24:55.420 --> 24:59.190
And if I did every possible one
of those, then I could average

24:59.194 --> 25:02.914
over all them and see how many
of them succeeded -- right?

25:02.910 --> 25:04.220
-- in reaction.

25:04.220 --> 25:06.930
And that would allow me to
predict the rate of this

25:06.928 --> 25:07.468
process.

25:07.470 --> 25:09.490
<<Technical
adjustment>>

25:09.490 --> 25:12.410
Okay, so people have done that
kind of thing.

25:12.410 --> 25:17.440
But studying lots of random
trajectories provides too much

25:17.443 --> 25:18.243
detail.

25:18.240 --> 25:22.900
No one really cares about all
those individual trajectories.

25:22.900 --> 25:27.480
What you care about is what
fraction succeed.

25:27.480 --> 25:30.620
And if you could do that in a
simpler way than rolling it a

25:30.623 --> 25:33.613
zillion times and averaging,
then that would be a better

25:33.605 --> 25:34.305
approach.

25:34.308 --> 25:38.748
So it's better to summarize
this thing statistically using

25:38.750 --> 25:42.090
collective terms;
not individual paths but

25:42.088 --> 25:45.808
collective terms,
such as enthalpy and entropy.

25:45.809 --> 25:47.679
And you can do it in this way.

25:47.680 --> 25:53.240
Okay, you have a steepest
descent path from the pass.

25:53.240 --> 25:57.270
Suppose you slice this surface
with a knife perpendicular to

25:57.272 --> 25:59.152
the screen,
along that path,

25:59.148 --> 26:01.388
and then fold it out to make it
flat,

26:01.390 --> 26:04.140
and look at the cross-section
of it.

26:04.140 --> 26:07.180
Okay, and now we'll tip it up
and it looks like that.

26:07.180 --> 26:10.390
Does everybody see how it looks
like that?

26:10.390 --> 26:13.410
Okay, we sliced along the path
that goes up over the transition

26:13.410 --> 26:13.800
state.

26:13.798 --> 26:16.908
Okay, so we have potential
energy as a function of distance

26:16.905 --> 26:18.615
along the reaction coordinate.

26:18.618 --> 26:21.758
But of course we're going to
summarize a whole bunch of

26:21.756 --> 26:22.566
things here.

26:22.568 --> 26:26.118
Nothing rolls exactly along
that path.

26:26.122 --> 26:26.892
Right?

26:26.890 --> 26:30.560
So we're going to lose some of
the specificity of the reaction

26:30.556 --> 26:32.476
coordinate by grouping things.

26:32.480 --> 26:36.140
We're not going to take a
trajectory, but a sequence of

26:36.144 --> 26:37.234
three species.

26:37.230 --> 26:40.260
The first species is the
starting material;

26:40.259 --> 26:43.249
the second species is the
transition state;

26:43.250 --> 26:46.250
and the third species is the
product.

26:46.250 --> 26:49.720
And now instead of having an
explicit meaning for every

26:49.720 --> 26:52.930
geometry along that path,
what we're going to do is

26:52.930 --> 26:55.470
associate each of those starting
materials,

26:55.470 --> 26:59.410
transition state and products,
with a certain enthalpy and a

26:59.407 --> 27:03.217
certain entropy;
that is, a certain free energy.

27:03.220 --> 27:05.840
So we have -- instead we're
going to plot free energy

27:05.843 --> 27:09.263
vertically,
incorporate entropy -- that is,

27:09.258 --> 27:14.658
how loose these things are --
as well as enthalpy there;

27:14.663 --> 27:15.523
energy.

27:15.519 --> 27:17.749
And now we just have three
values of free energy:

27:17.750 --> 27:19.750
the free energy of the starting
material;

27:19.750 --> 27:21.270
the free energy of the
transition state;

27:21.269 --> 27:22.779
the free energy of the product.

27:22.778 --> 27:27.128
And now we can use those -- but
we've lost a lot of specificity

27:27.125 --> 27:29.715
in what the reaction coordinate
is.

27:29.720 --> 27:31.880
It's just a sequence now of
three species.

27:31.880 --> 27:36.130
But we can now use free energy
to determine what can happen.

27:36.130 --> 27:37.480
We already could do that.

27:37.480 --> 27:39.050
But how rapidly?

27:39.048 --> 27:43.508
And you do that with the theory
that Eyring made up when he drew

27:43.512 --> 27:47.412
that surface in 1935,
called Transition State Theory.

27:47.410 --> 27:51.320
You assume that the rate
constant -- and we talked about

27:51.317 --> 27:54.727
this before -- in units per
second is 10^13th.

27:54.730 --> 27:57.480
So things happen
10^13th/second,

27:57.484 --> 28:01.934
times the concentration of the
transition state.

28:01.930 --> 28:06.010
So the idea is that things that
are in the transition state are

28:06.009 --> 28:08.379
moving at the rate
10^13th/second.

28:08.380 --> 28:10.570
So if you know how many are at
the transition state,

28:10.567 --> 28:12.537
then you know how many are
going to product;

28:12.538 --> 28:14.848
10^13th times that,
per second.

28:14.845 --> 28:15.455
Right?

28:15.460 --> 28:17.050
And you know how to do an
equilibrium;

28:17.049 --> 28:18.019
we already do that.

28:18.019 --> 28:20.509
All we do is use that special
double dagger,

28:20.509 --> 28:25.419
to mean the difference in
energy going from the starting

28:25.416 --> 28:28.626
material to the transition
state,

28:28.630 --> 28:30.330
the difference in free energy.

28:30.328 --> 28:32.478
Now we can calculate that
equilibrium constant.

28:32.480 --> 28:34.620
We know how much starting
material there is;

28:34.619 --> 28:35.939
the Law of Mass Action.

28:35.940 --> 28:38.920
We know how much transition
state there is in equilibrium

28:38.920 --> 28:40.410
with that starting material.

28:40.410 --> 28:40.890
Right?

28:40.890 --> 28:44.790
So that e^-ΔG/RT
is the equilibrium constant for

28:44.786 --> 28:47.616
getting the transition state;
multiply it by the

28:47.622 --> 28:49.452
concentration of the starting
material.

28:49.450 --> 28:51.650
You have the concentration of
the transition state.

28:51.650 --> 28:55.550
Multiply it by 10^13th,
and you know how fast it's

28:55.554 --> 28:56.034
going.

28:56.031 --> 28:56.751
Right?

28:56.750 --> 28:59.850
So it assumes that there's a
universal rate constant for

28:59.848 --> 29:02.158
transition states going to the
product;

29:02.160 --> 29:04.110
10^13th/second.

29:04.108 --> 29:05.918
That's about how fast things
vibrate.

29:05.920 --> 29:09.820
So things won't stay on the
potato chip, they'll roll off,

29:09.818 --> 29:13.648
and the rate at which they roll
off is 10^13th/second.

29:13.650 --> 29:16.560
This is, of course,
an approximation.

29:16.561 --> 29:18.101
It isn't correct.

29:18.098 --> 29:20.728
Because there's not true
equilibrium between the

29:20.730 --> 29:23.250
transition state and the
starting material.

29:23.250 --> 29:26.690
For true equilibrium the same
number must be going in and out.

29:26.688 --> 29:27.138
Right?

29:27.140 --> 29:28.800
But when things get to the
transition state,

29:28.797 --> 29:30.567
often they keep going,
they don't come back.

29:30.568 --> 29:33.458
So it's not really a rigorous
theory, but it's a very,

29:33.462 --> 29:36.032
very helpful theory for
approximate purposes.

29:36.029 --> 29:39.949
And that's what I say here.

29:39.949 --> 29:40.819
Okay?

29:40.818 --> 29:43.808
So using energies to predict
equilibria and rates for

29:43.810 --> 29:46.720
one-step reactions;
free radical halogenations.

29:46.720 --> 29:48.820
And let me look,
we do have time to go through

29:48.820 --> 29:50.830
this stuff, I think;
at least most of it.

29:50.828 --> 29:54.518
We've already seen this,
that you break a chlorine

29:54.520 --> 29:56.480
molecule into two atoms.

29:56.480 --> 30:00.150
Then you do single electron
curved arrows;

30:00.150 --> 30:02.450
take the hydrogen away from
methyl --

30:02.450 --> 30:04.360
from methane,
to give methyl,

30:04.358 --> 30:08.228
and then it attacks chlorine --
we've seen this before -- and

30:08.229 --> 30:11.519
the chlorine atom comes back to
constitute a chain reaction.

30:11.522 --> 30:11.972
Okay?

30:11.970 --> 30:15.310
So it's catalytic in radicals.

30:15.308 --> 30:19.538
Okay, now we break and make
bonds in this.

30:19.538 --> 30:23.828
So we've already seen average
bond energies that might tell us

30:23.833 --> 30:26.793
how hard it is to break a bond
-- right?

30:26.788 --> 30:29.368
-- if that's what we have to do
to get to the transition state.

30:29.368 --> 30:31.468
So we may be on the way to
getting rates.

30:31.470 --> 30:34.930
But are these average bond
energies real bond energies,

30:34.930 --> 30:39.110
or are they just a trick for
reckoning the enthalpy,

30:39.108 --> 30:41.568
the total energy,
the heat of formation or

30:41.568 --> 30:43.698
whatever,
of a particular molecule?

30:43.700 --> 30:46.690
And we talked about this before
and saw that mostly it is a

30:46.686 --> 30:48.866
trick;
that individual bond energies

30:48.865 --> 30:49.285
change.

30:49.291 --> 30:49.781
Right?

30:49.779 --> 30:52.429
So average bond energies are
not what you want to use for

30:52.430 --> 30:54.510
this purpose;
although they might be in the

30:54.509 --> 30:57.109
ballpark of the right numbers,
but they're not the right

30:57.109 --> 30:57.629
numbers.

30:57.630 --> 31:01.660
What you really need are bond
dissociation energies;

31:01.660 --> 31:04.940
the actual energy it takes to
break a specific bond.

31:04.940 --> 31:08.200
And we've talked about how you
could get that from

31:08.201 --> 31:09.201
spectroscopy.

31:09.200 --> 31:10.620
Those are real.

31:10.618 --> 31:13.478
The average bond energies are
just a way of calculating

31:13.481 --> 31:14.491
molecular energy.

31:14.490 --> 31:19.150
So Appendix II of the
Streitwieser and Heathcock book

31:19.145 --> 31:24.335
shows various specific bonds
between the groups in column A

31:24.338 --> 31:28.278
and the atoms or groups in row A
there,

31:28.279 --> 31:29.489
in the top row.

31:29.490 --> 31:33.290
And those were the best values
when that book was published;

31:33.288 --> 31:37.358
the best values as of 2003 are
a little bit changed from that,

31:37.355 --> 31:41.285
and were tabulated by Barney
Ellison, whose picture I showed

31:41.287 --> 31:43.217
you the time before last.

31:43.220 --> 31:46.370
So here's a table from Blanksby
and Ellison, that shows a bunch

31:46.365 --> 31:48.645
of these things and how well
they're known.

31:48.650 --> 31:52.770
The H_2 bond dissociation
energy is 104.206,

31:52.766 --> 31:56.496
plus or minus 0.003
kilocalories/mol.

31:56.500 --> 31:57.650
So it's very well-known.

31:57.650 --> 31:59.480
So some of them are very,
very well-known,

31:59.478 --> 32:01.618
and some of them are known only
approximately.

32:01.619 --> 32:03.369
Let's look at a few of them.

32:03.369 --> 32:07.729
So H_2 104.2;
HF 136;

32:07.730 --> 32:10.840
HCl 103;
HBr 87;

32:10.839 --> 32:12.439
HI 71.

32:12.440 --> 32:15.490
So as you go down the halogens,
the bonds get weaker and

32:15.490 --> 32:15.990
weaker.

32:15.990 --> 32:17.590
Why should that be?

32:17.588 --> 32:20.638
Why do larger halogens give
weaker bonds?

32:20.640 --> 32:23.480
It's because they have poorer
overlap with hydrogen,

32:23.484 --> 32:26.614
at normal bond distances,
because their orbitals are very

32:26.609 --> 32:29.059
diffuse;
they don't have high numbers in

32:29.063 --> 32:31.023
the region where the hydrogen
is.

32:31.019 --> 32:36.289
And you have the energy match
also is unfavorable.

32:36.288 --> 32:39.588
So if you have HF,
with good overlap and a very

32:39.590 --> 32:42.750
low F, then you get lots of
stabilization;

32:42.750 --> 32:46.540
the sum or those two red arrows
is big, a strong bond.

32:46.538 --> 32:50.978
And if it's HI,
the overlap isn't so good,

32:50.982 --> 32:54.562
and the energy match is better.

32:54.558 --> 32:58.278
But still the amount by which
the electrons go down is not as

32:58.275 --> 32:59.385
much as with HF.

32:59.390 --> 33:02.360
So we can see qualitatively why
that is.

33:02.358 --> 33:06.428
So less electron stabilization
means a weaker bond.

33:06.430 --> 33:09.500
And we're going to talk about
this more next semester.

33:09.500 --> 33:11.280
This is just to give you a
flavor of it.

33:11.278 --> 33:15.268
And here, in Table II,
we see there's the same trend

33:15.272 --> 33:20.892
in bonding with methyl groups;
that the fluorine-methyl bond

33:20.885 --> 33:25.915
is 115, but the iodine-methyl
bond is only 58.

33:25.920 --> 33:29.800
But if you go across hydrogen
with the different alkyls --

33:29.803 --> 33:32.663
methyl, ethyl,
isopropyl, t-butyl --

33:32.664 --> 33:36.144
they're all very close to 100
kilocalories/mol.

33:36.140 --> 33:38.290
But not the same,
and that will turn out to make

33:38.285 --> 33:41.235
a difference;
as we'll see early next

33:41.241 --> 33:42.231
semester.

33:42.230 --> 33:45.000
And if you look at some of the
other kinds of radicals,

33:44.999 --> 33:46.639
you see there are differences.

33:46.640 --> 33:50.340
There are special cases for
vinyl, allyl -- remember allyl

33:50.337 --> 33:52.347
alcohol -- phenyl and benzyl.

33:52.348 --> 33:56.208
And I'll show you just a little
bit about that.

33:56.210 --> 34:01.320
Are these unusual bond
dissociation energy values due

34:01.317 --> 34:05.147
to unusual bonds or unusual
radicals?

34:05.150 --> 34:08.530
That is, standard we have:
here's a starting material;

34:08.530 --> 34:11.060
here's the bond;
here's the product as the

34:11.059 --> 34:13.999
bond's broken -- for making the
radicals.

34:14.000 --> 34:18.940
So we can get a strong bond,
either by lowering -- by making

34:18.938 --> 34:23.038
the bond strong,
or by making the radicals bad;

34:23.039 --> 34:26.109
either way increases the
barrier.

34:26.112 --> 34:26.882
Right?

34:26.880 --> 34:30.480
Similarly we can make a small
one, either by making the bond

34:30.481 --> 34:32.681
weak or making the radical
stable.

34:32.679 --> 34:35.449
Is this something that it's
meaningful to talk about?

34:35.449 --> 34:37.689
Well let's look at it in the
case of these special cases.

34:37.690 --> 34:41.580
So vinyl, you see,
is 110 kilocalories/mol.

34:41.579 --> 34:44.389
It's the bond to H.

34:44.389 --> 34:46.579
So it's a very strong bond. Why?

34:46.579 --> 34:49.559
Is there something special
about the vinyl radical?

34:49.559 --> 34:51.539
There's no special
stabilization.

34:51.539 --> 34:54.939
There's no overlap between that
singly occupied orbital,

34:54.940 --> 34:56.160
which is a σ
orbital,

34:56.159 --> 34:58.409
and the double bond,
which is a π orbital.

34:58.409 --> 35:00.759
There's nothing especially
stable about the vinyl radical.

35:00.760 --> 35:03.990
But if you look at the bond in
the starting material,

35:03.992 --> 35:05.672
the C-H bond,
it has sp^2

35:05.670 --> 35:07.910
hybridization of the carbon.

35:07.909 --> 35:10.049
So that one's a strong bond.

35:10.050 --> 35:13.180
That one's hard to break,
because the bond is unusually

35:13.177 --> 35:15.677
strong;
not because the radicals are

35:15.684 --> 35:17.034
unusually unstable.

35:17.032 --> 35:17.532
Okay?

35:17.530 --> 35:21.580
Or if you look at phenyl,
it's the same deal.

35:21.579 --> 35:25.189
You have a σ SOMO
and the π bonds,

35:25.190 --> 35:28.880
the low LUMOs that might
stabilize that singly occupied

35:28.884 --> 35:32.274
orbital's electron,
are perpendicular or orthogonal

35:32.273 --> 35:32.703
to it.

35:32.699 --> 35:34.739
So again it's hard to break
that bond.

35:34.739 --> 35:37.659
On the other hand,
the allyl -- and remember allyl

35:37.657 --> 35:41.167
alcohol we were talking about --
here's an allyl radical.

35:41.170 --> 35:45.020
Now there's overlap,
π overlap between the

35:45.018 --> 35:48.638
SOMO and the π* and
the π.

35:48.639 --> 35:51.399
It turns out -- and we'll talk
about this more next time --

35:51.400 --> 35:55.360
that when you mix those two,
the π* on the right

35:55.362 --> 35:58.832
and the SOMO in the middle,
you get stabilization.

35:58.829 --> 36:02.349
You get the same stabilization
by mixing the π with

36:02.351 --> 36:05.341
the SOMO, and if you mix both of
them with the SOMO,

36:05.344 --> 36:06.934
you get that structure.

36:06.929 --> 36:08.229
But this isn't the time to talk
about that.

36:08.230 --> 36:11.470
But at any rate,
the normal, the starting bond,

36:11.465 --> 36:12.305
is normal.

36:12.309 --> 36:15.199
It's an sp^3 C-H bond,
a normal bond.

36:15.199 --> 36:18.249
But in this case the radical is
unusually stable.

36:18.250 --> 36:22.660
So it's easy to break that one;
10 kilocalories easier than for

36:22.655 --> 36:24.025
normal C-H bonds.

36:24.030 --> 36:25.690
And the same for benzyl.

36:25.690 --> 36:31.290
Okay, now possibility of doing
a halogenation.

36:31.289 --> 36:34.129
Let's look first from the point
of view of the equilibrium

36:34.132 --> 36:36.432
constant from this,
at the difference in energy

36:36.425 --> 36:38.515
between starting material and
product.

36:38.518 --> 36:41.608
So we look at what bonds are
broken, and what bonds are

36:41.605 --> 36:42.115
formed.

36:42.119 --> 36:45.429
The red bonds are broken,
the green bonds are formed.

36:45.429 --> 36:48.629
So there'll be a cost for
breaking the red bonds and

36:48.626 --> 36:51.756
there'll be a return for making
the green bonds.

36:51.760 --> 36:53.240
And let's see how big it is.

36:53.239 --> 36:55.779
Okay, we're going to do it for
fluorine, chlorine,

36:55.780 --> 36:56.870
bromine and iodine.

36:56.869 --> 37:00.189
Okay, in every case we're
breaking a C-H bond,

37:00.186 --> 37:03.206
105 kilocalories/mol,
and we're breaking a

37:03.206 --> 37:05.046
halogen-halogen bond.

37:05.050 --> 37:07.180
But those are different,
for the different halogens;

37:07.179 --> 37:09.609
although interestingly not
monotonic.

37:09.610 --> 37:13.320
It's not a smooth progression,
it goes up and then down again.

37:13.320 --> 37:16.520
And the cost is the sum of
those two;

37:16.518 --> 37:18.388
what it's going to cost to
break those bonds.

37:18.389 --> 37:19.449
How about making bonds?

37:19.449 --> 37:23.089
We're going to make the C-X
bond and we're going to make the

37:23.090 --> 37:23.770
H-X bond.

37:23.769 --> 37:26.189
So the returns will be that.

37:26.190 --> 37:29.190
And now we see whether we can
make a living doing this.

37:29.190 --> 37:31.350
What will the profit be? Right?

37:31.349 --> 37:35.329
So in the case of fluorine,
251 is much greater than the

37:35.327 --> 37:36.337
cost of 142.

37:36.340 --> 37:40.010
So it's a big -- it's really
exothermic.

37:40.014 --> 37:40.774
Right?

37:40.769 --> 37:42.649
Chlorine, it's only 19.

37:42.650 --> 37:45.580
Bromine is only 9,
and iodine is

37:45.583 --> 37:47.953
minus 12.

37:47.949 --> 37:49.779
What does that mean?

37:49.780 --> 37:52.920
It means you can't do this
reaction with iodine.

37:52.920 --> 37:54.820
The equilibrium lies is in the
wrong direction.

37:54.820 --> 37:59.870
Okay, so already the
equilibrium constant and how

37:59.871 --> 38:06.291
energy relates to it tells you
that something is impossible to

38:06.293 --> 38:07.033
do.

38:07.030 --> 38:08.610
But the others seem to be
possible.

38:08.610 --> 38:10.960
But will they happen?

38:10.960 --> 38:12.360
How fast will they be?

38:12.360 --> 38:15.240
Do you have to wait until the
end of the universe in order for

38:15.237 --> 38:16.037
this to happen?

38:16.039 --> 38:20.279
Well let's look at how the
rate, which will depend on the

38:20.280 --> 38:21.190
mechanism.

38:21.190 --> 38:23.460
The equilibrium constant
doesn't depend on the path.

38:23.460 --> 38:26.350
It's just how high the starting
material is and how high the

38:26.351 --> 38:26.991
product is.

38:26.989 --> 38:30.419
But how fast you get depends on
the barriers you have to go

38:30.418 --> 38:30.948
across.

38:30.949 --> 38:35.169
So let's suppose -- let's just
try breaking two bonds,

38:35.168 --> 38:38.348
changing partners,
and forming two bonds.

38:38.353 --> 38:39.073
Okay?

38:39.070 --> 38:42.410
Then we have to -- to get to
the barrier, we have to break

38:42.407 --> 38:43.107
two bonds.

38:43.110 --> 38:45.370
So that cost -- we're going to
have to spend,

38:45.367 --> 38:47.057
in order to get to the barrier.

38:47.059 --> 38:48.749
So is this a plausible
mechanism?

38:48.750 --> 38:52.650
How fast would the reaction be,
if we used that mechanism?

38:52.650 --> 38:56.230
Well at room temperature,
say 300 Kelvin,

38:56.228 --> 39:00.968
then it's 10^3/4ths of how high
it is to get there;

39:00.969 --> 39:02.449
then times 10^13th/second.

39:02.449 --> 39:11.039
But notice that 10^13th times
10^-106, which is 3/4ths of 142,

39:11.043 --> 39:13.723
is 10^-93/second.

39:13.719 --> 39:17.369
10^93^( )seconds is a long,
long time.

39:17.369 --> 39:20.069
I don't know how old the
universe is, but I suspect

39:20.068 --> 39:20.818
that's longer.

39:20.824 --> 39:21.314
Right?

39:21.309 --> 39:22.729
So what about this mechanism?

39:22.730 --> 39:23.930
Plausible?

39:23.929 --> 39:24.979
Implausible?

39:24.980 --> 39:26.270
How could you make it happen?

39:26.269 --> 39:28.979
Shai?

39:28.980 --> 39:30.130
Student:  Change the
temperature.

39:30.130 --> 39:30.470
Prof: Pardon me?

39:30.469 --> 39:30.939
Student:  Change the
temperature.

39:30.940 --> 39:31.830
Prof: Change the
temperature;

39:31.829 --> 39:35.239
because we can change that
3/4ths to something else by --

39:35.242 --> 39:38.902
to a much smaller number -- by
increasing the temperature.

39:38.900 --> 39:40.570
So no way to do that one.

39:40.570 --> 39:46.190
But if we go to 3000 Kelvin,
then it's 250 reactions per

39:46.190 --> 39:47.110
second.

39:47.110 --> 39:50.080
So that's quite feasible,
as long as nothing else

39:50.081 --> 39:52.801
happens;
something else might be even

39:52.802 --> 39:53.332
faster.

39:53.329 --> 39:53.929
Right?

39:53.929 --> 39:57.159
But at least this mechanism
could work, if you were in a

39:57.161 --> 39:59.511
flame say, or in Professor
Chupka's oven,

39:59.512 --> 40:01.572
that we talked about last time.

40:01.570 --> 40:06.790
Okay, now let's look at
Eyring's H + H_2 here.

40:06.789 --> 40:08.659
So we want to get from this
valley to the other valley.

40:08.659 --> 40:09.819
How do we do it?

40:09.820 --> 40:14.010
This mechanism would be to
break a bond and then -- so

40:14.012 --> 40:16.862
dissociation and then
association.

40:16.860 --> 40:19.540
But uh, it's very slow to get
up there -- right?

40:19.539 --> 40:21.209
-- to get up to that plateau of
breaking a bond.

40:21.210 --> 40:24.450
There's a much easier way to
get from one valley to the

40:24.449 --> 40:24.809
other.

40:24.809 --> 40:25.649
What is it?

40:25.650 --> 40:29.340
Go through the pass. Right?

40:29.340 --> 40:33.790
So instead of doing that slow
reaction, you can do this much

40:33.786 --> 40:37.246
faster reaction,
making a new bond as you break

40:37.253 --> 40:38.463
the old one.

40:38.460 --> 40:41.540
So you don't have to pay all
the cost of breaking the old

40:41.539 --> 40:44.179
one, and you're getting
something back for it.

40:44.179 --> 40:47.179
So you can have a free radical
chain substitution,

40:47.179 --> 40:51.159
where you have an X atom -- and
we've talked about this before.

40:51.159 --> 40:52.499
Take the H away from R.

40:52.500 --> 40:56.160
Then the R group takes away X
from X_2.

40:56.159 --> 40:58.409
And it can just go round and
round.

40:58.409 --> 41:01.089
There's this machine,
very much like the machine that

41:01.090 --> 41:03.820
Professor Sharpless talked
about, that goes around and

41:03.822 --> 41:04.392
around.

41:04.389 --> 41:06.899
You feed in starting material,
and the products come out.

41:06.900 --> 41:08.370
And you don't -- it's a
catalyst;

41:08.369 --> 41:10.869
you don't have to go to such
high energies as you normally

41:10.867 --> 41:11.697
would have to do.

41:11.699 --> 41:15.589
So the possibility of
halogenation -- here we looked

41:15.588 --> 41:20.008
at it at equilibrium and saw
that forget it with iodine;

41:20.010 --> 41:21.010
the others look okay.

41:21.010 --> 41:24.510
And for a mechanism with a
reasonable rate,

41:24.510 --> 41:27.790
we could change those two
columns, exchange them,

41:27.789 --> 41:33.849
so that we make the H-X,
as we break CH_3-H --

41:33.849 --> 41:37.459
so the X atom helps you do that
-- and that generates then a

41:37.461 --> 41:39.581
CH_3 group,
which helps the reaction on the

41:39.576 --> 41:39.856
right.

41:39.860 --> 41:43.010
So now, step one,
how much energy do you have to

41:43.014 --> 41:43.624
put in?

41:43.619 --> 41:49.419
You're paying 105 but you're
getting back 136.

41:49.420 --> 41:51.070
So that's great. Right?

41:51.070 --> 41:54.650
The first step seems plausible
now;

41:54.650 --> 41:57.160
although you don't know how
high the barrier is that you

41:57.159 --> 41:59.349
have to get from starting
material to product.

41:59.349 --> 42:00.999
But at least it's much easier.

42:01.000 --> 42:03.210
So the top one,
it looks good all around.

42:03.210 --> 42:06.510
The chlorine and bromine will
be a little touchy,

42:06.512 --> 42:09.952
on those first two steps,
because they're uphill in

42:09.952 --> 42:10.712
energy.

42:10.710 --> 42:14.530
But step two is good in all
cases.

42:14.530 --> 42:18.830
Okay, so what we need to do is
be able to predict activation

42:18.833 --> 42:19.493
energy.

42:19.489 --> 42:22.819
But Rome wasn't built in a day,
and that's going to happen next

42:22.824 --> 42:25.954
semester, to get into this and
to talk in more detail about

42:25.945 --> 42:27.555
these catalytic reactions.

42:27.559 --> 42:31.999
Notice that this is exactly the
kind of thing Sharpless was

42:31.996 --> 42:33.216
talking about.

42:33.219 --> 42:36.579
If you could find a way of
lowering one of these barriers,

42:36.579 --> 42:38.819
then the catalytic cycle would
work.

42:38.820 --> 42:40.120
He was saying,
remember, that it was

42:40.117 --> 42:41.577
democratic;
that all the steps,

42:41.577 --> 42:44.307
as you go around the cycle,
have to be at the same -- go at

42:44.309 --> 42:46.679
the same rate,
or else everything stops up,

42:46.681 --> 42:50.331
stops and waits before it tries
to get over some big step.

42:50.329 --> 42:52.729
So you have to have all the
steps be fast;

42:52.730 --> 42:57.780
and that's why he was saying
that that diisopropylethylamine

42:57.775 --> 43:00.935
helped the formation of
omeprazole.

43:00.940 --> 43:05.160
Well so we've been doing
organic chemistry this semester.

43:05.159 --> 43:08.119
Some people might doubt that.

43:08.119 --> 43:10.949
There'll be no doubt next
semester that everyone will

43:10.949 --> 43:13.399
agree that what we do is organic
chemistry.

43:13.400 --> 43:16.600
We're going to talk about the
chemistry of functional groups

43:16.599 --> 43:20.069
and sugars and amino acids and
all carbonyl groups and esters;

43:20.070 --> 43:20.860
all these things.

43:20.860 --> 43:24.170
But there's a reason that it's
been a little different this

43:24.170 --> 43:24.800
semester.

43:24.800 --> 43:27.700
We've talked mostly about
physical-organic chemistry.

43:27.699 --> 43:30.669
And the reason is because of
where I came from;

43:30.670 --> 43:32.010
that I did my Ph.D.

43:32.010 --> 43:34.840
-- and in fact I took a course
as an undergraduate with Paul

43:34.842 --> 43:35.902
Bartlett at Harvard.

43:35.900 --> 43:38.970
And as you've seen from our
common ancestry,

43:38.974 --> 43:41.554
he was a physical-organic
chemist;

43:41.550 --> 43:44.740
more interested in how
reactions work than in what you

43:44.737 --> 43:45.397
can make.

43:45.400 --> 43:50.390
Okay, so there's this book that
came out in 1939,

43:50.389 --> 43:52.249
went through at least three
editions --

43:52.250 --> 43:55.370
I have the Second and Third
Editions here --

43:55.369 --> 43:58.299
which is called The Nature
of the Chemical Bond.

43:58.300 --> 44:01.330
And this was a fabulously
influential book;

44:01.329 --> 44:06.319
even if it is the one that said
it was 126 kilocalories/mol,

44:06.320 --> 44:11.310
to take carbon away from
graphite, when we know it's 171.

44:11.309 --> 44:18.449
So Pauling was arguably the
most influential chemist of the

44:18.454 --> 44:20.924
Twentieth Century.

44:20.920 --> 44:22.410
He got two Nobel Prizes.

44:22.409 --> 44:24.029
>

44:24.030 --> 44:27.120
Recording of Professor Jack
Dunitz:  At the time when I

44:27.123 --> 44:30.073
was reading that book I was
wondering whether chemistry was

44:30.065 --> 44:33.105
really as interesting as I had
hoped it was going to be.

44:33.110 --> 44:39.800
And I think I was almost ready
to give it up and do something

44:39.798 --> 44:40.578
else.

44:40.579 --> 44:46.009
I didn't care very much for
this chemistry which was full of

44:46.007 --> 44:50.327
facts and recipes and very
little thought in it,

44:50.331 --> 44:53.921
very little intellectual
structure.

44:53.920 --> 44:59.650
And Pauling's book gave me a
glimpse of what the future of

44:59.648 --> 45:03.868
chemistry was going to be and
particularly,

45:03.867 --> 45:06.177
perhaps, my future.

45:06.179 --> 45:07.619
Prof: Right, okay.

45:07.619 --> 45:09.929
So that's what we've been doing
the first semester,

45:09.929 --> 45:12.189
is this kind of thing,
thinking about the chemical

45:12.193 --> 45:12.613
bond.

45:12.610 --> 45:15.120
We started with wondering,
with Newton,

45:15.115 --> 45:19.005
whether there was an atomic
force law, and then we looked to

45:19.007 --> 45:21.907
see if we could see bonds,
or feel them.

45:21.909 --> 45:25.749
And then we tried to understand
bonding and reactivity,

45:28.599 --> 45:30.959
which most people believe is
the fundamental way to

45:30.960 --> 45:32.330
understand things properly.

45:32.329 --> 45:37.319
And then we learned how
chemists learned to treasure the

45:37.324 --> 45:38.964
molecular model.

45:38.960 --> 45:42.610
Things like this,
that turned out to be really,

45:42.612 --> 45:45.632
really useful tools --
composition,

45:45.630 --> 45:47.750
constitution,
configuration,

45:47.750 --> 45:53.960
and conformation --
and finally energy. Right?

45:53.960 --> 45:58.260
So I hope that we've this
semester,

45:58.260 --> 46:01.050
if we haven't done as much
organic chemistry as some people

46:01.045 --> 46:03.535
would care for,
that at least we've raised some

46:03.539 --> 46:07.979
big questions;
like how does science know

46:07.976 --> 46:08.956
things?

46:08.958 --> 46:10.078
Right?

46:10.079 --> 46:12.609
Or, compared to what?

46:12.610 --> 46:14.570
Those are the really big
questions.

46:14.570 --> 46:17.980
But even if we're only focusing
on the specific content of the

46:17.981 --> 46:21.231
course, interested in bonds,
here are two questions for you

46:21.226 --> 46:22.286
to think about.

46:22.289 --> 46:28.909
Were chemical bonds discovered
or were they invented?

46:28.909 --> 46:32.819
To what extent are chemical
bonds real?

46:32.820 --> 46:35.690
Or to what extent are they a
figment of a chemist's

46:35.686 --> 46:36.486
imagination?

46:36.489 --> 46:40.659
This is the kind of thing we've
been aiming at all semester.

46:40.659 --> 46:43.159
So you should be in a position
to think about this now.

46:43.159 --> 46:50.039
Or would we even have chemical
bonds, without our own chemical

46:50.043 --> 46:51.513
forbearers?

46:51.510 --> 46:54.160
So we've looked at how the idea
of bonds and these different

46:54.155 --> 46:55.585
properties of bonds developed.

46:55.590 --> 47:00.420
But suppose chemistry was
developing in some other solar

47:00.422 --> 47:01.042
system.

47:01.039 --> 47:01.829
Right?

47:01.829 --> 47:04.069
What would happen there?

47:08.125 --> 47:10.775
before they had the idea of
bonds.

47:10.780 --> 47:13.570
Would bonds have been necessary?

47:13.570 --> 47:17.960
Is chemistry going to evolve,
such that all you need do is

47:17.963 --> 47:21.823
put stuff into a computer,
solve quantum mechanics,

47:21.815 --> 47:23.585
and forget about bonds?

47:23.588 --> 47:24.358
Okay?

47:24.360 --> 47:26.970
The answers to these questions
aren't obvious,

47:26.967 --> 47:29.227
but they're good ones to think
about.

47:29.230 --> 47:34.300
So this is the end,
and good luck on the final.

47:34.300 --> 47:35.950
Are you fired up?

47:35.949 --> 47:37.739
Students:  Yeah.

47:37.739 --> 47:39.189
Prof: Are you ready to
go?

47:39.190 --> 47:41.260
Good.

47:41.260 --> 47:42.790
Thanks.

47:42.789 --> 47:48.999