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I am going to start now by
telling you a little bit more

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about Lewis theory.
Last time we went through

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aspects of the cube theory of
Lewis and showed how that could

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account for single bonds and
double bonds,

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but not triple bonds.
And that when that was

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superseded by the electron pair
theory, the idea being that

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these electron pairs would,
in fact, be oriented at the

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vertices of a tetrahedron.
And I showed you that

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tetrahedron, as described in a
cube last time,

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that you could then account for
triple bonds.

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And, if you looked at the
notes, you also saw that certain

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aspects of the dynamic behavior
of certain bond types,

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rotation around single bonds,
hindered restricted rotation

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around double bonds,
and so forth.

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Those were accounted for by
this electron pair theory in

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which the four pairs of
electrons were oriented at these

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vertices of a tetrahedron.
So, that was another quite

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important triumph of that part
of Lewis's theory.

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And the problem was,
although that electron pair

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theory initially put forward by
Lewis was so successful at

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accounting for the properties of
many different kinds of

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molecules and was a good
description of their electronic

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structure, there was one class
of molecules,

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a very important class of
molecules, namely those known as

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aromatic.

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And the most important member
of the class of aromatic

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compounds is,
in fact, the benzene molecule.

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Benzene has the formula C six H
six.

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And we can easily calculate the
number of valence electrons in

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benzene if we just say 4 for
carbon times 6,

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plus 1 times 6 for the number
of valance electrons from each

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of the six hydrogens.
And that is 30 electrons.

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So, in trying to understand how
these 30 electrons in a valence

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shell of benzene hold this
molecule together,

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it is known to be a planar
molecule, how do those electrons

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not only hold it together,
--

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-- but how do they account for
the structure of benzene,

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and how do they account for its
amazing stability?

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And this picture that I have
drawn here is a representation

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of benzene, I will explain to
you in a moment,

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but it comes from a person by
the name of Ernest C.

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Crocker.

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Ernest C.
Crocker was an MIT Bachelor of

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Science degree holder,
who earned that degree in 1917.

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He was an MIT undergraduate
like you.

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And he published a paper.
Let me write down the reference

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for that paper.

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This is the Journal of the
American Chemical Society,

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1922, Volume 44,
Page 1618.

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That paper was the first paper
in which the Lewis electron pair

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theory was applied to an
understanding of the electronic

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structure of aromatic molecules,
in particular,

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benzene.
And the amazing thing about

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that paper is --
Well, there are many amazing

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things, but one of the amazing
things about that paper is that

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there is only one author on that
paper, Ernest C.

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Crocker.
And Ernest, who was a very

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bright individual,
nonetheless did not go on in

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graduate school to earn a Ph.D.
in chemistry,

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had many various
chemistry-related interests.

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He explained the chemistry of
many different kinds of

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fragrances and odors.
I think he was referred to as

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"the man with the million dollar
nose."

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So, this person had quite a
variety of interests.

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He worked in what was then the
Applied Chemistry Laboratory at

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MIT after his graduation with
his Bachelor of Science degree.

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And one of the things he was
thinking about was how to use

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modern electronic structure
descriptions,

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such as Lewis theory,
to explain molecules like

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benzene.
And so, if you go and read this

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paper, you are going to find a
very lucid discussion of how the

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Lewis electron pair theory could
represent benzene according to

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this formula that I have drawn
here.

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And in this formula,
there is considered to be an

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electron pair between each
carbon and each of the hydrogen

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nuclei.
There is an electron pair along

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each carbon-carbon axis,
as shown here,

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and here, and so on,
all the way around the ring.

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And then, finally,
you have six more electrons to

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come up to the number of 30,
which is the number of

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electrons in benzene.
And so, the question really is

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what to do with this remaining
six electrons.

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And I have shown them around
the outside of the ring,

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here, which is where Ernest
arranged them in his work.

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And I just want to point out
that he put forward the idea

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that these six electrons were
circulating around the plane of

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the ring and involved a net
one-half bond between each pair

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of adjacent carbon atoms in the
benzene ring.

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So, in effect,
when we draw benzene this way,

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with a circle in the middle,
we know that that circle

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represents the circulating six
electrons in what we are going

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to call the pi system.
But Ernest C.

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Crocker was the man who put the
circle into the middle of

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benzene.
And he was an MIT undergrad.

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And this was a sole-authored
paper.

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Aromaticity has a vast history
in chemistry,

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and it is still a very active
and unfolding history because of

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the problems,
to our understanding,

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posed by electrons that seem to
be circulating around a whole

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molecule rather than localized
between pairs of nuclei.

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So, Ernest Crocker,
Bachelor of Science,

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1917, MIT, had a huge hand in
that.

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I thought you might find that
interesting.

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And, having looked at benzene
rings like that,

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I will now draw them perhaps
another way that is also useful,

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which comes from KekulÈ.

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Because I want to continue our
discussion of Lewis acid-base

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theory.
And I am going to draw two

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molecules here that are going to
be pretty similar.

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When I write a molecule,
as I have done here on the

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left, I haven't explicitly
indicated each of the hydrogens

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that are present on the
periphery of this substituted

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benzene ring.
But you should understand from

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a formula like this that this is
the molecule boron C 18 H 15.

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And over here I am drawing

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explicitly, at each of these
peripheral positions on the

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substituted benzene rings,
fluorine atoms in place of the

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hydrogens.
So, this is a different

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molecule with formula B C 18 F

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These are both Lewis acids.

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And based on our discussion,
last time, if you were to add

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ammonia to one of these
molecules, where would the lone

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pair of electrons on the ammonia
bind?

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The boron.
So, yes, you have here a

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trigonal planer boron center.
And, if you were to add an

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ammonia molecule,
the lone pair of electrons

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would come in and stick to the
boron --

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-- because the boron is
electron deficient.

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00:11:07,000 --> 00:11:11,000
Just like the aluminum we
discussed last time,

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it has only six electrons
around it, and it wants eight.

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00:11:17,000 --> 00:11:23,000
But what if we were to add one
ammonia molecule to a flask

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containing both of those Lewis
acids that would then be

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competing for the ammonia
molecule?

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00:11:38,000 --> 00:11:42,000
What I am asking you to do is
something I will ask you to do

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throughout this semester,
and that is to analyze a

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molecule's properties based on
its structure and its

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composition.

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Exactly.
She said that it would

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preferentially stick to the one
with the fluorines because these

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very electronegative fluorines
are drawing electron density

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away from the boron.
This is one of our most

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electronegative elements.

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So you have a whole bunch of
fluorines in that molecule.

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The whole thing,
we call it perfluorinated.

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It is a perfluorinated triaryl
boron reagent.

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These, in fact,
are great Lewis acids,

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really powerful Lewis acids.
And they are modern Lewis acids

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whose implementation in chemical
processes has come about really

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in the last 10,
15 years.

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00:13:07,000 --> 00:13:11,000
And, in fact we were talking a
little bit about Professor

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Schrock last time.
In some of his research,

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he has used that perfluorinated
Lewis acid as an activator in

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catalysis to get catalytic
polymerization reactions to

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work.
And that is a very popular

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approach these days in Lewis
acid chemistry.

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The design of new kinds of
Lewis acids with interesting

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molecular architectures is
something that is very much a

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current topic of interest in
research in chemistry,

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because you can make lots of
chemical processes happen when

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you have something that can tug
on electron pairs.

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And this one tugs a lot harder
than that one because this one

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has very electronegative
fluorines to pull electron

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density away from that boron and
to adjust the distribution of

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00:14:00,000 --> 00:14:04,000
the electron density in the
molecule.

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00:14:04,000 --> 00:14:07,000
And we will be talking more
about electron density and

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distribution in a few minutes in
connection with what I am going

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to show you now.
And that is --

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That has to do with this
molecule, which is the SO two

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molecule.
Anyone know where SO two

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comes from in nature?
Or in the environment,

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I should say?

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Volcanoes, absolutely.
And also coal-burning power

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plants.
Coal is a very dirty fuel,

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and it contains a lot of
sulfur.

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And, when you burn that coal
without controlling the way you

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burn it, you emit SO two
into the atmosphere.

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So, that can be a big problem.
And we will try to understand

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why.
One of the things that SO two

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can do when it gets into
the atmosphere is it can react

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with dioxygen.
And that can give you --

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00:15:23,000 --> 00:15:25,000
-- SO three.

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00:15:30,000 --> 00:15:35,000
And if SO two and SO
three are present in the

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atmosphere and if there is also
water present in the atmosphere,

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acid rain, that is exactly the
type of process that we will be

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talking about here.
SO two and SO three

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are examples of what we
call anhydrides.

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Anhydride is a word that means
without water.

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00:16:03,000 --> 00:16:08,000
And so you should not be
surprised that SO two

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can react with water.
And when it reacts with water,

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it takes up water.
And the product of that

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reaction will look like this.

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I draw it like that.
Okay.

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So, H two O plus SO two going
to H two SO three.

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00:16:48,000 --> 00:16:56,000
The name of this
molecule is

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00:16:56,000 --> 00:17:01,000
sulfurous acid.
And, alternatively,

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00:17:01,000 --> 00:17:05,000
when SO three reacts
with water --

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I have one extra electron pair
that should not have been there.

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00:17:22,000 --> 00:17:25,000
So, both SO two and SO three,

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as they react with water,
are going from a situation in

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which they are electron
deficient to a situation in

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which the sulfur attains an
octet.

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00:17:44,000 --> 00:17:46,000
Okay?
And you should verify that the

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number of electrons that I have
drawn up here actually is

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consistent with the elements
that I am using with the stated

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00:17:53,000 --> 00:17:56,000
charge that I am using.
But when SO three

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reacts with H two O to
give H two SO four,

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00:17:59,000 --> 00:18:02,000
we have now got sulfuric acid.

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00:18:08,000 --> 00:18:11,000
Okay.
And, as I did over there,

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00:18:11,000 --> 00:18:17,000
I have two acids that I want
here now to compare in terms of

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00:18:17,000 --> 00:18:22,000
their relative strengths.
Here I have a Lewis acid SO

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00:18:22,000 --> 00:18:28,000
three and a Lewis acid
SO two engaging in a

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00:18:28,000 --> 00:18:34,000
hydration reaction,
which produces sulfurous acid

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00:18:34,000 --> 00:18:39,000
and sulfuric acid.
And the type of acids that

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00:18:39,000 --> 00:18:42,000
these are on the bottom is
Bronsted acids,

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00:18:42,000 --> 00:18:43,000
--

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00:18:48,000 --> 00:18:53,000
-- distinguished from Lewis
acids in that the way that they

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behave as acids is through
ionization that produces a

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00:18:58,000 --> 00:19:02,000
proton.
They are also Lewis acids

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00:19:02,000 --> 00:19:06,000
because the Lewis definition of
acidity is far more general,

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00:19:06,000 --> 00:19:11,000
in saying that acids are simply
entities that can accept a pair

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00:19:11,000 --> 00:19:15,000
of electrons.
Protons can accept a pair of

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00:19:15,000 --> 00:19:17,000
electrons, so they are Lewis
acids.

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00:19:17,000 --> 00:19:21,000
But if you are talking about
Bronsted acids,

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00:19:21,000 --> 00:19:26,000
you are talking exclusively
about protons that are produced

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00:19:26,000 --> 00:19:31,000
by ionization of some kind of a
Bronsted acid.

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00:19:31,000 --> 00:19:38,000
Which one of these is the
stronger acid?

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00:19:38,000 --> 00:19:44,000
Sulfuric acid.
And why?

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00:19:50,000 --> 00:19:53,000
Yes, down here.
You got the other one right.

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00:20:00,000 --> 00:20:02,000
Exactly.
When this ionizes,

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00:20:02,000 --> 00:20:05,000
you get SO four minus.

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00:20:05,000 --> 00:20:10,000
I will draw is a slightly
different way that is quicker.

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00:20:10,000 --> 00:20:13,000
You get HSO four minus.

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00:20:13,000 --> 00:20:19,000
There is your ionization.
And the idea now is that this O

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00:20:19,000 --> 00:20:23,000
minus that you have,
the negative charge can

239
00:20:23,000 --> 00:20:27,000
actually be shared among a
greater number of

240
00:20:27,000 --> 00:20:31,000
electronegative oxygens here,
namely four,

241
00:20:31,000 --> 00:20:36,000
as compared to here,
where we have only three

242
00:20:36,000 --> 00:20:42,000
electronegative oxygens.
It is a consideration of the

243
00:20:42,000 --> 00:20:47,000
very electronegative elements in
your molecule that will help you

244
00:20:47,000 --> 00:20:51,000
understand the properties that
these molecules will have in

245
00:20:51,000 --> 00:20:55,000
terms of acid-base chemistry.
Now, how many electrons do we

246
00:20:55,000 --> 00:21:00,000
have in the valance shell of SO
three?

247
00:00:24,000 --> 00:21:03,000
And, that being the case,

248
00:21:03,000 --> 00:21:10,000
what molecule from last time
does that remind you of?

249
00:21:20,000 --> 00:21:27,000
Maybe seeing a picture of it
will help refresh your memory.

250
00:21:27,000 --> 00:21:30,000
AlCl three.
Exactly.

251
00:21:30,000 --> 00:21:34,000
I am going to show it to you
anyway.

252
00:21:34,000 --> 00:21:40,000
And this is going to be faster
than the last time,

253
00:21:40,000 --> 00:21:45,000
if I set this up right.
Just to remind you.

254
00:21:45,000 --> 00:21:52,000
And if we could have the lights
down just a little bit for a

255
00:21:52,000 --> 00:21:54,000
moment.

256
00:22:03,000 --> 00:22:06,000
I want to refresh your memory
of the electron density

257
00:22:06,000 --> 00:22:09,000
distribution here in AlCl
three.

258
00:22:09,000 --> 00:22:12,000
This is an electron density
isosurface of AlCl three.

259
00:22:12,000 --> 00:22:14,000
And what you are noticing is

260
00:22:14,000 --> 00:22:18,000
that the electron density drops
to a low value in between the

261
00:22:18,000 --> 00:22:21,000
central aluminum and the
radially disposed chlorides,

262
00:22:21,000 --> 00:22:25,000
the three chlorides that
surround that central aluminum

263
00:22:25,000 --> 00:22:27,000
ion.
And the coloring in this is

264
00:22:27,000 --> 00:22:31,000
such that the blue regions
represent regions in space where

265
00:22:31,000 --> 00:22:36,000
there is a high probability of
finding paired electrons.

266
00:22:36,000 --> 00:22:40,000
So, basically you have three Cl
minus's that are packed tightly

267
00:22:40,000 --> 00:22:42,000
around an Al three plus.

268
00:22:42,000 --> 00:22:46,000
This is a very ionic compound.
See the empty region in space

269
00:22:46,000 --> 00:22:50,000
between aluminum and chloride,
and the polarization of that

270
00:22:50,000 --> 00:22:54,000
otherwise spherical cloud of
electrons around the chloride in

271
00:22:54,000 --> 00:22:57,000
the direction of that positively
charged aluminum?

272
00:22:57,000 --> 00:23:02,000
There is your electron density
distribution for that.

273
00:23:02,000 --> 00:23:06,000
And now I want you to keep that
in mind, and we will compare the

274
00:23:06,000 --> 00:23:10,000
isoelectronic SO three
molecule to it.

275
00:23:21,000 --> 00:23:24,000
SO three.
Here is another case where we

276
00:23:24,000 --> 00:23:27,000
have 3 times 8,
24 valance electrons in a

277
00:23:27,000 --> 00:23:29,000
system.
But the character of this

278
00:23:29,000 --> 00:23:33,000
molecule in terms of electron
density distribution is very

279
00:23:33,000 --> 00:23:37,000
different.
While on the blackboard,

280
00:23:37,000 --> 00:23:41,000
I am not able to really tell
you very much about the

281
00:23:41,000 --> 00:23:45,000
difference between SO three
and AlCl three,

282
00:23:45,000 --> 00:23:50,000
here I think you can
see that indeed they are quite

283
00:23:50,000 --> 00:23:53,000
different.
This is an electron density

284
00:23:53,000 --> 00:23:58,000
isosurface at the same contour
level as what we were looking at

285
00:23:58,000 --> 00:24:03,000
for AlCl three.
Now, to explain this and to

286
00:24:03,000 --> 00:24:08,000
understand just what is going on
here, you need to remember that

287
00:24:08,000 --> 00:24:12,000
the electronegativity difference
between the central sulfur and

288
00:24:12,000 --> 00:24:16,000
the peripheral oxygens is not
very great compared to the

289
00:24:16,000 --> 00:24:19,000
electronegativity difference
between aluminum,

290
00:24:19,000 --> 00:24:23,000
which is a very electropositive
and metallic element,

291
00:24:23,000 --> 00:24:26,000
and chlorine,
which is a very electronegative

292
00:24:26,000 --> 00:24:30,000
halogen.
And so, what that results in,

293
00:24:30,000 --> 00:24:33,000
as shown here,
is a much more equal sharing of

294
00:24:33,000 --> 00:24:36,000
the electrons between that
central sulfur and these

295
00:24:36,000 --> 00:24:40,000
peripheral oxygens.
So, even though these things

296
00:24:40,000 --> 00:24:44,000
are both Lewis acids and they
both have 24 valance electrons,

297
00:24:44,000 --> 00:24:46,000
the electron density
distribution in

298
00:24:46,000 --> 00:24:51,000
three-dimensional space for
these molecules and the covalent

299
00:24:51,000 --> 00:24:55,000
verses ionic character of these
molecules, is really quite

300
00:24:55,000 --> 00:24:57,000
different.

301
00:25:05,000 --> 00:25:09,000
Our section that is going to be
devoted to bonding has not

302
00:25:09,000 --> 00:25:13,000
really kicked into gear yet,
but the nice thing is that

303
00:25:13,000 --> 00:25:16,000
Lewis theory applies both to
acid-base chemistry and to

304
00:25:16,000 --> 00:25:20,000
bonding, so we are able to talk
a little bit about that.

305
00:25:20,000 --> 00:25:24,000
In a few moments,
I will tell you a little more

306
00:25:24,000 --> 00:25:27,000
about an issue that is very
important in chemistry as

307
00:25:27,000 --> 00:25:30,000
regards bonding.

308
00:25:36,000 --> 00:25:42,000
And it has to do with what
happens when acids,

309
00:25:42,000 --> 00:25:46,000
like sulfuric acid,
ionize in water.

310
00:25:46,000 --> 00:25:55,000
When Bronsted acids ionize in
water, we get this ion produced.

311
00:25:55,000 --> 00:26:03,000
H three O plus,
which is the hydronium ion.

312
00:26:10,000 --> 00:26:13,000
That is to say that if you
ionize in water some Bronsted

313
00:26:13,000 --> 00:26:18,000
acid, the protons that are
produced through that ionization

314
00:26:18,000 --> 00:26:22,000
are not floating around freely,
naturally, because they are

315
00:26:22,000 --> 00:26:26,000
positively charged and they are
attracted to negatively charged

316
00:26:26,000 --> 00:26:29,000
electrons.
So, they look around in

317
00:26:29,000 --> 00:26:33,000
solution and find the next
source of an electron that they

318
00:26:33,000 --> 00:26:35,000
can.
And you know that if we draw

319
00:26:35,000 --> 00:26:39,000
out a molecule like water,
according to the Lewis dot

320
00:26:39,000 --> 00:26:42,000
structure, it has two extra
pairs of electrons,

321
00:26:42,000 --> 00:26:46,000
in addition to those two pairs
of electrons it is using in

322
00:26:46,000 --> 00:26:50,000
making bonds to the two
hydrogens that are on the oxygen

323
00:26:50,000 --> 00:26:54,000
of the water molecule.
So, H plus is not just

324
00:26:54,000 --> 00:26:58,000
isolated around by itself in
solution.

325
00:26:58,000 --> 00:27:01,000
It perches on an oxygen lone
pair.

326
00:27:01,000 --> 00:27:07,000
So, H three O plus is
what you get when Bronsted acids

327
00:27:07,000 --> 00:27:10,000
ionize in water.
And furthermore,

328
00:27:10,000 --> 00:27:16,000
when you put these things in
solution you find that you

329
00:27:16,000 --> 00:27:22,000
organize the water molecules
that are close to the hydronium

330
00:27:22,000 --> 00:27:25,000
ion.
Let's draw here a neighboring

331
00:27:25,000 --> 00:27:28,000
water molecule.

332
00:27:33,000 --> 00:27:34,000
And another one.

333
00:27:38,000 --> 00:27:43,000
And I think you can imagine
that throughout a solution,

334
00:27:43,000 --> 00:27:48,000
we might have many of the kinds
of interactions that I have

335
00:27:48,000 --> 00:27:52,000
drawn here as dotted
peach-colored lines.

336
00:27:52,000 --> 00:27:56,000
Those lines represent what we
call hydrogen bonds.

337
00:27:56,000 --> 00:28:01,000
And hydrogen bonds are
enormously important in

338
00:28:01,000 --> 00:28:05,000
chemistry.
Later, when we talk about the

339
00:28:05,000 --> 00:28:08,000
structure of proteins in DNA,
in particular,

340
00:28:08,000 --> 00:28:12,000
you may be aware that the DNA
double helix is held together by

341
00:28:12,000 --> 00:28:16,000
a network of hydrogen bonds
between complimentary base

342
00:28:16,000 --> 00:28:19,000
pairs.
So hydrogen bonds are not only

343
00:28:19,000 --> 00:28:23,000
restricted to the hydronium ion
in aqueous solution.

344
00:28:23,000 --> 00:28:27,000
There are many other types of
molecules that can form what we

345
00:28:27,000 --> 00:28:32,000
call hydrogen bonds.
Another really interesting

346
00:28:32,000 --> 00:28:37,000
thing is that in water,
the hydronium ion can move

347
00:28:37,000 --> 00:28:41,000
around really rapidly,
much more rapidly than

348
00:28:41,000 --> 00:28:46,000
molecules normally diffuse
through aqueous solution.

349
00:28:46,000 --> 00:28:51,000
And the reason for that is if
you look at the arrangement of

350
00:28:51,000 --> 00:28:56,000
electrons and nuclei here,
all I have to do is,

351
00:28:56,000 --> 00:29:01,000
without even moving the nuclei
much at all, reorganize the

352
00:29:01,000 --> 00:29:06,000
hydrogen bonding network as
such.

353
00:29:12,000 --> 00:29:15,000
And now you can see that
through just a slight set of

354
00:29:15,000 --> 00:29:20,000
motions, our hydronium ion has
moved from the left-hand side of

355
00:29:20,000 --> 00:29:24,000
this hydrogen bonded network,
where you can see that it is

356
00:29:24,000 --> 00:29:28,000
indicated with the positive
charge and the three solid lines

357
00:29:28,000 --> 00:29:33,000
drawn to the oxygen,
over to the right-hand side.

358
00:29:33,000 --> 00:29:36,000
But it did that not by coming
off and moving over,

359
00:29:36,000 --> 00:29:40,000
but rather through just
redistribution of the electron

360
00:29:40,000 --> 00:29:45,000
density, so that the positively
charged part ends up down on the

361
00:29:45,000 --> 00:29:48,000
other side.
And so this way of propagating

362
00:29:48,000 --> 00:29:52,000
hydronium ions in aqueous
solution is one of the really

363
00:29:52,000 --> 00:29:56,000
special aspects of Bronsted acid
chemistry that takes place in

364
00:29:56,000 --> 00:30:00,000
water.
And I think I will also show

365
00:30:00,000 --> 00:30:04,000
you what a hydrogen bond looks
like from the standpoint of

366
00:30:04,000 --> 00:30:06,000
electron density.

367
00:30:18,000 --> 00:30:21,000
First, I am just going to show
you the position of the nuclei

368
00:30:21,000 --> 00:30:24,000
in a very simple hydrogen bonded
system.

369
00:30:37,000 --> 00:30:40,000
Here what you can see,
the oxygens are drawn in red as

370
00:30:40,000 --> 00:30:44,000
spheres and the hydrogens are
drawn in white as spheres.

371
00:30:44,000 --> 00:30:48,000
You can see that the geometry
around the oxygen atoms is

372
00:30:48,000 --> 00:30:51,000
slightly pyramidal.
And that is due,

373
00:30:51,000 --> 00:30:55,000
of course, to the presence of
that extra lone pair here,

374
00:30:55,000 --> 00:31:00,000
up above one oxygen and here,
up above the other oxygen.

375
00:31:00,000 --> 00:31:04,000
And what we have now is a
hydrogen serving in a bridging

376
00:31:04,000 --> 00:31:07,000
fashion.
And the number of electrons in

377
00:31:07,000 --> 00:31:11,000
this system is exactly 2 times
8, because we have two water

378
00:31:11,000 --> 00:31:14,000
molecules and we have an
H plus.

379
00:31:14,000 --> 00:31:18,000
So this is a positively charged
ion in which a hydronium ion,

380
00:31:18,000 --> 00:31:23,000
and you can pick either side,
actually, is interacting with

381
00:31:23,000 --> 00:31:28,000
one of the lone pairs of the
other water molecule.

382
00:31:28,000 --> 00:31:31,000
And you could imagine lots of
different types of water

383
00:31:31,000 --> 00:31:34,000
clusters like this that are
singly positively charged.

384
00:31:34,000 --> 00:31:38,000
And people have done a lot of
work to study such clusters in

385
00:31:38,000 --> 00:31:40,000
solution.
What you should remember,

386
00:31:40,000 --> 00:31:44,000
though, is that the size of the
spheres that I have drawn there

387
00:31:44,000 --> 00:31:48,000
to represent those oxygens and
hydrogens is somewhat arbitrary.

388
00:31:48,000 --> 00:31:51,000
But what is not arbitrary is
the way that the electron

389
00:31:51,000 --> 00:31:53,000
density represents a molecule
like this.

390
00:31:53,000 --> 00:31:57,000
So, we will show that to you
next.

391
00:32:13,000 --> 00:32:15,000
Here it is.
And if we could have the lights

392
00:32:15,000 --> 00:32:19,000
down just a little bit,
please, since this one is a

393
00:32:19,000 --> 00:32:22,000
little harder to see.
What you should see here is

394
00:32:22,000 --> 00:32:26,000
that we have the same structure
now surrounding that

395
00:32:26,000 --> 00:32:30,000
representation of the water
molecule hydrogen bonded to the

396
00:32:30,000 --> 00:32:34,000
hydronium ion that I drew a
moment ago.

397
00:32:34,000 --> 00:32:38,000
We now have this sort of mesh,
which is exactly what we have

398
00:32:38,000 --> 00:32:41,000
been looking at with these other
molecules, namely,

399
00:32:41,000 --> 00:32:46,000
an electron density isosurface.
And what you can see is that

400
00:32:46,000 --> 00:32:50,000
the electron density is falling
to a pretty small value in the

401
00:32:50,000 --> 00:32:53,000
middle, here,
where we have the proton that

402
00:32:53,000 --> 00:32:57,000
is the connecting glue binding
together these two water

403
00:32:57,000 --> 00:33:02,000
molecules in this 16 valance
electron system.

404
00:33:02,000 --> 00:33:06,000
And after one more
representation of that,

405
00:33:06,000 --> 00:33:10,000
we will be onto our next topic.

406
00:33:20,000 --> 00:33:24,000
And this one is a solid display
of the electron density

407
00:33:24,000 --> 00:33:30,000
isosurface associated with this
hydrogen bonded cluster.

408
00:33:30,000 --> 00:33:34,000
And it is, once again,
color mapped with this function

409
00:33:34,000 --> 00:33:39,000
that tells us about the
probability of finding electrons

410
00:33:39,000 --> 00:33:43,000
paired up together in space.
There is H three O plus

411
00:33:43,000 --> 00:33:47,000
hydrogen bonded to H
two O.

412
00:33:47,000 --> 00:33:52,000
The blue color represents those
regions in space where you are

413
00:33:52,000 --> 00:33:55,000
most likely to find pairs of
electrons.

414
00:33:55,000 --> 00:34:00,000
And you can see that the two OH
bonds over here are nicely

415
00:34:00,000 --> 00:34:05,000
colored blue.
The lone pair of electrons up

416
00:34:05,000 --> 00:34:09,000
here is nicely colored blue.
And then we have an interesting

417
00:34:09,000 --> 00:34:14,000
situation where there is some
blue in between that bridging H

418
00:34:14,000 --> 00:34:18,000
plus and the two lone
pairs that are pointed at it

419
00:34:18,000 --> 00:34:21,000
that produces,
in fact, our hydrogen bond.

420
00:34:21,000 --> 00:34:25,000
So, there is a picture of
hydrogen bonding in terms of

421
00:34:25,000 --> 00:34:30,000
electron density.
And it is a type of bonding

422
00:34:30,000 --> 00:34:35,000
that compliments the straight,
covalent, and ionic bonding

423
00:34:35,000 --> 00:34:41,000
that I was talking about in
terms of SO three and

424
00:34:41,000 --> 00:34:45,000
AlCl three.
So, we have added this third

425
00:34:45,000 --> 00:34:50,000
type of hydrogen bonding to our
list of bonding interests.

426
00:34:50,000 --> 00:34:55,000
And now, we will talk more
about what we can do when we

427
00:34:55,000 --> 00:35:00,000
consider Bronsted acids
ionizing.

428
00:35:15,000 --> 00:35:20,000
Here is a generic
representation of the formula of

429
00:35:20,000 --> 00:35:22,000
a Bronsted acid,
HA.

430
00:35:22,000 --> 00:35:28,000
A might be, for example,
the HSO four minus

431
00:35:28,000 --> 00:35:34,000
ion that we showed over there.
When we put a Bronsted acid in

432
00:35:34,000 --> 00:35:36,000
aqueous solution,
as I said before,

433
00:35:36,000 --> 00:35:39,000
we can get ionization into H
plus and A minus.

434
00:35:39,000 --> 00:35:41,000
But we know that it is not just

435
00:35:41,000 --> 00:35:44,000
H plus.
It is actually H three O plus

436
00:35:44,000 --> 00:35:46,000
**H3O^+**.
And H three O plus is

437
00:35:46,000 --> 00:35:50,000
further hydrogen bonded in
networks in the water system.

438
00:35:50,000 --> 00:35:53,000
But, for simplicity,
I will just write it as H plus

439
00:35:53,000 --> 00:35:57,000
right here.
Recently, in your crash review

440
00:35:57,000 --> 00:36:00,000
of thermodynamics,
you were talking about

441
00:36:00,000 --> 00:36:03,000
equilibria and equilibrium
constants.

442
00:36:03,000 --> 00:36:09,000
And we are going to make use of
some of that right here because

443
00:36:09,000 --> 00:36:12,000
we are going to talk about the
acidity constant,

444
00:36:12,000 --> 00:36:15,000
Ka.
And that is going to be defined

445
00:36:15,000 --> 00:36:20,000
as equal to the hydrogen or
hydronium ion concentration

446
00:36:20,000 --> 00:36:24,000
times the concentration of the
conjugate base,

447
00:36:24,000 --> 00:36:29,000
A minus --
When a Bronsted acid ionizes it

448
00:36:29,000 --> 00:36:34,000
produces what we call the
conjugate base of the acid.

449
00:36:34,000 --> 00:36:37,000
Here is conjugate base --

450
00:36:45,000 --> 00:36:49,000
-- divided by the concentration
of the acid.

451
00:36:49,000 --> 00:36:53,000
And this is at equilibrium.

452
00:36:59,000 --> 00:37:02,000
And let me just emphasize
something so that you don't

453
00:37:02,000 --> 00:37:05,000
forget.
This is an important piece of

454
00:37:05,000 --> 00:37:08,000
nomenclature.
These square brackets here

455
00:37:08,000 --> 00:37:12,000
refer to concentration,
usually in molarity.

456
00:37:19,000 --> 00:37:21,000
Okay?
So that is what we are talking

457
00:37:21,000 --> 00:37:24,000
about.
And concentration is something

458
00:37:24,000 --> 00:37:28,000
that can be measured.
You may be familiar,

459
00:37:28,000 --> 00:37:31,000
for example,
with the pH meter invented by

460
00:37:31,000 --> 00:37:34,000
Arnold O.
Beckman and its utility in

461
00:37:34,000 --> 00:37:40,000
measuring the concentration of
hydrogen ions in solution.

462
00:37:40,000 --> 00:37:43,000
Well, we can make use of
information like that to talk

463
00:37:43,000 --> 00:37:47,000
about the properties of our
Bronsted acids.

464
00:37:54,000 --> 00:38:00,000
How can we do that?
Well, let's say we are going to

465
00:38:00,000 --> 00:38:08,000
take a particular acid such as
this one, which is acetic acid.

466
00:38:14,000 --> 00:38:19,000
You know the smell of acetic
acid if you have ever been in an

467
00:38:19,000 --> 00:38:24,000
establishment where they were
making barbecued chicken wings.

468
00:38:24,000 --> 00:38:27,000
That is the smell of acetic
acid.

469
00:38:27,000 --> 00:38:32,000
A beautiful smell.
Anyway, what you do here is you

470
00:38:32,000 --> 00:38:35,000
are trying to figure out what is
going on.

471
00:38:35,000 --> 00:38:40,000
You have some concentration of
the acid HA, which is,

472
00:38:40,000 --> 00:38:43,000
we are going to talk about,
acetic acid.

473
00:38:43,000 --> 00:38:48,000
And in solution there may also
be a hydrogen ion or a hydronium

474
00:38:48,000 --> 00:38:51,000
ion.
And then there may also be A

475
00:38:51,000 --> 00:38:55,000
minus, which in the case of
acetic acid would be acetate,

476
00:38:55,000 --> 00:38:57,000
--

477
00:39:02,000 --> 00:39:06,000
-- where we have two
electronegative oxygens,

478
00:39:06,000 --> 00:39:11,000
among which the negative charge
can be shared and the acetate

479
00:39:11,000 --> 00:39:15,000
ion, which is the conjugate base
of acidic acid.

480
00:39:15,000 --> 00:39:20,000
So we make a table.
We need to have some initial

481
00:39:20,000 --> 00:39:24,000
concentration.
That is to say let's consider,

482
00:39:24,000 --> 00:39:27,000
for example,
tenth molar acetic acid.

483
00:39:27,000 --> 00:39:32,000
We are just choosing tenth
molar as a concentration for

484
00:39:32,000 --> 00:39:38,000
acetic acid solution.
What that means is you have

485
00:39:38,000 --> 00:39:42,000
pure acetic acid.
And then you dissolve it in

486
00:39:42,000 --> 00:39:46,000
water and bring it up to a total
volume such that the

487
00:39:46,000 --> 00:39:51,000
concentration was 0.1 molar,
assuming that none of it had

488
00:39:51,000 --> 00:39:54,000
been ionized yet.
And so that means we have an

489
00:39:54,000 --> 00:40:00,000
initial concentration of acetic
acid of 0.1 molar.

490
00:40:00,000 --> 00:40:03,000
And initially,
before the ionization,

491
00:40:03,000 --> 00:40:08,000
we have zero H plus or
hydronium and zero A minus.

492
00:40:08,000 --> 00:40:12,000
And then, the concentration

493
00:40:12,000 --> 00:40:15,000
changes.
And it changes because the HA

494
00:40:15,000 --> 00:40:20,000
ionizes to some particular
extent, depending on the KA

495
00:40:20,000 --> 00:40:26,000
value for the acetic acid.
And what is going to happen is

496
00:40:26,000 --> 00:40:32,000
that some of the HA ionizes.
And the amount of the HA that

497
00:40:32,000 --> 00:40:37,000
is undergoing ionization is x,
so we are going to lose x.

498
00:40:37,000 --> 00:40:42,000
And then, for every HA that
ionizes, we get that same amount

499
00:40:42,000 --> 00:40:46,000
of H plus produced and
that same amount of A minus.

500
00:40:46,000 --> 00:40:48,000
And so then,

501
00:40:48,000 --> 00:40:53,000
after the system reaches
equilibrium, we will finally

502
00:40:53,000 --> 00:40:57,000
have 0.1 minus x as our
concentration of HA

503
00:40:57,000 --> 00:41:01,000
and x and x will be our
concentrations,

504
00:41:01,000 --> 00:41:04,000
respectively,
of H plus and A minus.

505
00:41:04,000 --> 00:41:10,000
And so let me put this board

506
00:41:10,000 --> 00:41:13,000
all the way up.

507
00:41:18,000 --> 00:41:24,000
Therefore, we can write the
following, that Ka is equal to x

508
00:41:24,000 --> 00:41:29,000
squared over 0.1 over x by

509
00:41:29,000 --> 00:41:35,000
substituting into the expression
for the acidity constant.

510
00:41:35,000 --> 00:41:39,000
Ka is our acidity constant.

511
00:41:46,000 --> 00:41:52,000
And we can go to a table and
look up the acidity constant for

512
00:41:52,000 --> 00:41:57,000
acetic acid because it is a
known quantity.

513
00:41:57,000 --> 00:42:03,000
And it turns out that that is
1.8x10^-5.

514
00:42:03,000 --> 00:42:06,000
And now that we have this
equation for the acidity

515
00:42:06,000 --> 00:42:09,000
constant and we know what the
acidity constant is,

516
00:42:09,000 --> 00:42:13,000
we can solve this for x.
Of course, this is a cubic

517
00:42:13,000 --> 00:42:15,000
equation.
We are going to get two roots.

518
00:42:15,000 --> 00:42:19,000
You will see that you get a
positive root and a negative

519
00:42:19,000 --> 00:42:21,000
root.
The negative root is

520
00:42:21,000 --> 00:42:24,000
meaningless because
concentration cannot be

521
00:42:24,000 --> 00:42:28,000
negative, so you pick the
positive root.

522
00:42:28,000 --> 00:42:33,000
And when you have done that,
you can then go ahead and

523
00:42:33,000 --> 00:42:37,000
answer questions,
like, what is the pH of the

524
00:42:37,000 --> 00:42:40,000
solution?
And what is the percent

525
00:42:40,000 --> 00:42:42,000
ionization?

526
00:42:47,000 --> 00:42:49,000
And we can talk about that.
So next time,

527
00:42:49,000 --> 00:42:51,000
at the beginning of class,
we will do that calculation.

528
00:42:51,000 --> 00:42:54,000
We will find what the pH of a
tenth molar solution of acetic

529
00:42:54,000 --> 00:42:57,000
acid would be.
We will also go on and talk

530
00:42:57,000 --> 00:43:00,000
about pH and the pKa scale,
and also a general equation for

531
00:43:00,381 --> 00:43:03,000
discussing titrations and
buffers.