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PROFESSOR: We're pretty
much ready to get started.

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Let's settle down and take a
look at the clicker question.

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So take 10 more seconds.
 

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Very good.
 

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Most people had this right, and
the trick here is just to think

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about the sign of delta g,
whether it's negative and

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positive, and think about the
equation and the influence of

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temperature on that equation.
 

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So whether it's going to make
delta s a bigger factor or a

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smaller factor and how
that will play out.

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So you can look at the equation
and figure out what the signs

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have to be and then the
influence of temperature.

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All right, so let's move to the
first slide that I have today,

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which is welcome to the
middle of the semester.

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So I'm Kathy Drennan and this
is lecture 19 of 36, which

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means that you are halfway
through the course.

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And so what you heard on Monday
before the exam was about

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thermodynamics, and if you
don't have all your delta g's

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and delta h's and if you don't
have entropy full in mind,

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that's OK, we are not really
leaving thermodynamics,

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we're going into chemical
equilibrium, which is all

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about thermodynamics.
 

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So you're going to hear a lot
more about delta g, delta h,

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temperature, and about our
friend, entropy as we go

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along in the second half.
 

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So it's the middle
of the semester.

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That means that you've had two
of the sort of four hour exams

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-- remember the fourth hour
exam is actually combined

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with the final exam.
 

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So the final exam is 200 points
of cumulative material, and 100

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points of new material, so
you've done two now of those

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four sort of hour exams.
 

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Just to remind you of some of
the topics you have seen and

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the topics coming ahead, this
is on the syllabus, and we're

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actually where we're supposed
to be on the syllabus, so if

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you want to take a look at that
ever to see where we're going,

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we're actually on track.
 

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So the first half of the course
are a lot of basic principles,

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and we're moving today into
chemical equilibrium, so a lot

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more delta g's, delta
h's coming on.

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And then we're going to move
into acid base, which is

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acid base equilibrium.
 

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So we're not going to
be leaving equilibrium

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or thermodynamics.
 

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Then we're going to go into
oxidation reduction, which is

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also about equilibrium, and
then transition metals,

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and end with kenetics.
 

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And so, these altogether
represent the fundamentals

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needed for the study of
biochemistry, organic

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chemistry, any kind of
chemistry, biology, the life

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sciences, many things -- so
you're getting all the

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fundamental principles of
chemistry in this class.

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So along those lines, I just
thought I would share something

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that happened to me on
Wednesday when I was riding the

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T, the Silver Line,
in particular.

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So I don't know if any of you
have had this kind of

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experience yet where you're on
public transportation and

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someone next to you says, "So,
are you a student?" Maybe you

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have a notebook out or a
book out or something.

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And you say, "Yes," and they
said, "Oh, what are you

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studying?" And then you say
"Well, you know, chemistry,

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math, physics." And they're
like "Oh." And then they go

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busy themselves doing
something else.

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Or they tell you "I didn't
really like those subjects

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in school." And then they
stop talking to you.

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So how many people have had
that experience so far, that

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you scare the person next
to you by what you study?

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OK, a few people.
 

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If I ask that question four
years from now, I think it'll

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be like half the class, eight
years from now it'll

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be everybody.
 

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So this is kind of common.
 

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But what happened to me on the
Silver Line was actually pretty

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exciting, because I've had that
other experience many times.

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So, I was wearing my keys
around my neck, because women's

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professional clothes, no
pockets, with a little MIT

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cord, and the person next to be
on the Silver Line said "So, do

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you go to the Georgia Tech of
the east?" And I said "Well, I

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am a professor at MIT." And he
said "Well, I'm a mechanical

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engineer and I went to Georgia
Tech." And so he said, "So,

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what do you teach?" I said,
"Chemistry." And he said,

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"Chemistry -- I really wish I
had paid more attention in

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chemistry." I said, "Well, what
do you do now?" And he said

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"Well, I work for the army, and
I'm part of a team that has

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mechanical engineers,
electrical engineers, and

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chemists, and we're trying to
figure out ways to detect

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explosives." So I said, "Oh,
well have you heard of the head

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of the Chemistry Department at
MIT, Tim Swager who works in

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the area, and he said,
"Yes," he knew the name.

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And so he said that one of his
porblems on the team, and in

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talking to the chemist, his
chemistry language is not

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really good enough, and so he
was really struggling, and that

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the best results of this team
effort would be if everyone

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could really talk
to each other.

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So he wished that he had
paid more attention in

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his chemistry class.
 

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And so I, of course, my
connection with chemistry was

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by wanting to understand
biology, but for everyone it

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might be a little
bit different.

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So, as I mentioned in the
beginning of the class, one

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challenge that you have this
semester is figure out

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what your connection
to chemistry is.

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What are you going to
use chemistry for?

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How does this fit into
what you want to do?

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And maybe for some of
you, you're not going

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to know that yet.
 

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Hopefully it won't take till
you have a job doing something

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to realize that you're lacking
something in your education.

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And so, probably if you stay in
science and engineering, need

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chemistry, good to
learn it all now.

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And from exam 2, we see that
you are learning it now

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and that's really great.
 

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So, some day maybe someone in
this room will be involved in

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national security, and if
you're not a chemist, you'll be

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able to talk to the chemists
and make really good

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progress toward that work.
 

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So, chemistry -- it's important
in medicine, national security,

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the economy, energy
initiatives, a lot of the big

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things going on now.
 

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It's a fundamental, and you
will get in this course,

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the fundamentals.
 

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So if you have any good tea or
bus or airplane conversations,

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let me know -- I'll catalog
those for future reference.

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It's always a touch of how
what we do here connects

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with the real world.
 

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All right, so we're not going
far from thermodynamics, we're

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going into chemical
equilibrium.

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And we're going to be talking
a lot about delta g.

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So if delta g is not your
friend yet, don't worry, you

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can still bond with delta g.
 

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All right, so chemical
reactions, chemical reactions

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can go into a state
of equilibrium.

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And it's a dynamic equilibrium,
the reaction is still

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happening, but if a reaction is
an equilibrium, the rate of the

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forward reaction will equal the
rate of the reverse reaction,

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so there'll be no net
change in composition.

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So let's take a look
at an example.

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So let's look at a reaction in
which we have nitrogen gas, and

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we have hydrogen gas, and they
are reacting to form ammonia.

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Suppose we just start with
nitrogen gas and hydrogen

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gas and we don't have
any ammonia left.

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So if we consider
concentrations versus time.

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So say we start with, we have
some nitrogen gas, some

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concentration of nitrogen gas.
 

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As it reacts with hydrogen, the
concentration will decrease

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and then level off.
 

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We'll start with some amount
of hydrogen gas, and its

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concentration will also
decrease and level off.

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And in the beginning we won't
have any of the product, any

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of the ammonia, so its
concentration will increase

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and then level off.
 

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So when these reactions
level off, you're

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reaching equilibrium.
 

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The reaction is still
happening, but the rate of the

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forward reaction is equal to
the rate of the reverse

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reaction, so there's
no net change.

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So the concentrations are
staying the same, but there's

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still -- the reaction
is still going forward.

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So let's think about the case
when we have pure reactants

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when we haven't formed
enough products yet

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to reach equilibrium.
 

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So if we have pure reactants,
the reaction is going to be

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spontaneous in the
forward direction.

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So we'll have a reaction
that is spontaneous in

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the forward direction.
 

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And what will that mean
about our friend delta g?

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Is it going to be greater
or less than zero?

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So it'll be less than zero --
so delta g or the forward

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reaction will be
less than zero.

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So when delta g is negative,
the reaction is spontaneous

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in the forward direction.
 

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So what about when you have
pure products, then the

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reaction should be spontaneous
in the reverse direction.

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So you have spontaneous in the
reverse direction, and what

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does that mean about
the sign of delta g?

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Greater or less than zero?
 

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Greater, so it'll be positive.
 

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So, we can think about
that in terms of a plot.

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We can think about free
energy versus the

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progress of the reaction.
 

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So, the progress of the
reaction is going this

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direction as you go along.
 

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So in the beginning if you have
pure reactants, delta g is

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going to be less than zero.
 

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And you're going to proceed
along in the forward

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direction spontaneously.
 

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If, on the other hand you have
pure products, delta g will be

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positive, so you'll be
spontaneous in the reverse

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direction, and the reaction
will go in the reverse

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direction until what happens?
 

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Till you reach equilibrium.
 

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And what would delta
g be at equilibrium?

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Zero.
 

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So you see, there is a great
relationship between delta g

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and equilibrium, so we have
not left delta g behind.

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So, delta g is going to
change as the components

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of the reaction change.
 

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As you have more products or
more reactants, you're going

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to have a different delta g.
 

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So let's look at
some equations.

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So delta g is the change in
free energy, the difference in

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free energy, at some point
in the reaction at any time

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with amount of composition.
 

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We also have delta g nought,
which talks about delta g under

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particular conditions, so it's
sort of the standard

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free energy.
 

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We have a term called q, which
is the reaction quotient,

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which tells you about
products and reactants.

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We have our friend r, which is
the gas constant, and this

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depends on temperature.
 

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So temperature is a
term involved here.

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So the delta g at any point in
the reaction is going to depend

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on the delta g nought for that
reaction, and the reaction

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quotient, products and
reactants, and we'll define

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this in a minute, and then
the temperature as well.

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So we need to know more
about what q is, what this

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reaction quotient is.
 

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So this slide looks a little
bit scary, but it's going to be

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fine, because a lot of the
terms are going to cancel out.

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So we're going to talk about q,
this reaction quotient, and

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we're going to have different
types of problems -- some where

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we're talking about gases, and
others we're talking

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about solutions.
 

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So you can see two different
kinds of q's, one that depends

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on partial pressure of the gas,
and another that depends

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on concentration.
 

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So here is our equation again
that we just saw -- delta g

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equals delta g nought plus r t
natural log of q, and here

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we've expanded the term for q.
 

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So p to the sub x is the
partial pressure of a

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particular gas, and so in this
equation, we have a plus b

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going to c plus d, the top of
the line or the products.

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So we have the partial pressure
of gas c, and this is over a

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reference, partial pressure,
raised to the power c, the

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coefficient, and then also we
have d, the partial pressure of

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gas d, over a reference raised
to the small letter d.

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On the bottom of the terms for
the reactants, partial pressure

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00:15:36 --> 00:15:39
of gas a over a reference
raised to the coefficient a,

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partial pressure of gas b
over the reference raised

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to the coefficient b.
 

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Now what's great is that the
partial pressure is one bar,

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and so that basically cancels
out as far as we're concerned.

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And so the term for q
is much simplified.

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You won't see problems that
have the reference in them, so

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you can just think about q in
terms of products

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over reactants.
 

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And you just have to remember
that the coefficients in

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the reactions do matter.
 

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If you're talking about
solutions, the only difference

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is that we'll be talking about
molar, so we have one molar,

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so the reference term
here also cancels out.

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When you see something in
brackets, like c in brackets,

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here that telling you it's
a concentration term.

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So here, q is the
concentration of c raised

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to its coefficiency.
 

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00:16:34 --> 00:16:39
The concentration of d
raised to its coefficient

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00:16:39 --> 00:16:40
d over reactants.
 

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Concentration of a to a,
concentration of b raised to b.

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So the thing in x indicates
it's a concentration term.

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00:16:51 --> 00:16:55
So q is just products over
reactants, considering the

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stoichiometry of the
particular reaction.

270
00:17:01 --> 00:17:05
So what about the
equilibrium constant k?

271
00:17:05 --> 00:17:10
So at equilibrium you told me
that delta g equals zero, and

272
00:17:10 --> 00:17:15
at equilibrium q, the reaction
quotient equals k, the

273
00:17:15 --> 00:17:17
equilibrium constant.
 

274
00:17:17 --> 00:17:22
So we can consider that in
terms of this expression, if

275
00:17:22 --> 00:17:25
we're talking about this
expression at equilibrium,

276
00:17:25 --> 00:17:29
delta g is going to equal zero.
 

277
00:17:29 --> 00:17:33
And so, we just set this
whole term equal to zero.

278
00:17:33 --> 00:17:36
We can rearrange the equation
bringing delta g nought

279
00:17:36 --> 00:17:39
to the other side.
 

280
00:17:39 --> 00:17:43
And so we have delta g at
nought equals minus r t

281
00:17:43 --> 00:17:49
natural log of K, because at
equilibrium, k is equal to q.

282
00:17:49 --> 00:17:54
So now we have another term to
solve for delta g, and an

283
00:17:54 --> 00:17:58
equation that relates delta g
nought to be equilibrium

284
00:17:58 --> 00:18:04
constant k.
 

285
00:18:04 --> 00:18:09
So k, the equilibrium's
constant has the same form as

286
00:18:09 --> 00:18:13
q, but we're only talking
about the concentrations or

287
00:18:13 --> 00:18:16
the partial pressures of
things at equilibrium.

288
00:18:16 --> 00:18:20
So it's the same, it's product
over reactants, same

289
00:18:20 --> 00:18:25
expressions as q, but in the
corner you say at equilibrium.

290
00:18:25 --> 00:18:28
So you're only talking about
the concentrations of

291
00:18:28 --> 00:18:32
things at equilibrium if
you're solving for k.

292
00:18:32 --> 00:18:35
If you're solving for q, it's
the concentration or the

293
00:18:35 --> 00:18:41
partial pressure at any time
in that particular reaction.

294
00:18:41 --> 00:18:46
Important thing, products
over reactants.

295
00:18:46 --> 00:18:51
All right, so, we can rewrite
the equation one more way.

296
00:18:51 --> 00:18:55
So I just told you that delta
g nought is equal to minus

297
00:18:55 --> 00:18:58
r t natural log of K.
 

298
00:18:58 --> 00:19:03
So we can substitute into the
expression minus r t natural

299
00:19:03 --> 00:19:09
log of k, and now we can
rearrange this equation.

300
00:19:09 --> 00:19:12
And so, if we rearrange it, we
have delta g, the delta g at

301
00:19:12 --> 00:19:16
any particular point in
the reaction equals r t

302
00:19:16 --> 00:19:19
natural log of q over k.
 

303
00:19:19 --> 00:19:22
And this equation is helpful
for people if they're thinking

304
00:19:22 --> 00:19:27
about what is the equilibrium
constant, what concentrations

305
00:19:27 --> 00:19:30
do I have now -- we're not
at equilibrium, what

306
00:19:30 --> 00:19:34
concentrations do I have now,
what is q now in the reaction,

307
00:19:34 --> 00:19:36
how does that compare to k?
 

308
00:19:36 --> 00:19:39
And when you know what those
values are, you'll know

309
00:19:39 --> 00:19:41
something about the direction
of the reaction because

310
00:19:41 --> 00:19:43
you'll know if delta g
is positive or negative.

311
00:19:43 --> 00:19:46
It'll to be spontaneous in
the forward direction or

312
00:19:46 --> 00:19:47
in the reverse direction.
 

313
00:19:47 --> 00:19:50
So this is a handy equation
for thinking about the

314
00:19:50 --> 00:19:55
relationship q k delta g.
 

315
00:19:55 --> 00:19:57
So let's think about that
relationship for a minute.

316
00:19:57 --> 00:20:08
If q is less than k, what
is the sign of delta g?

317
00:20:08 --> 00:20:13
So it would be negative, which
means the forward direction

318
00:20:13 --> 00:20:16
of the reaction will occur.
 

319
00:20:16 --> 00:20:20
So if you think about it, you
can think about in terms

320
00:20:20 --> 00:20:22
of products and reactants.
 

321
00:20:22 --> 00:20:28
So at equilibrium then, if q is
less than k at equilibrium,

322
00:20:28 --> 00:20:30
there are more products than
there are right now, so you

323
00:20:30 --> 00:20:32
need to make more products.
 

324
00:20:32 --> 00:20:35
So you would have delta g would
be negative, you'll see that

325
00:20:35 --> 00:20:38
mathematically, and you can
think about it in terms of

326
00:20:38 --> 00:20:41
whether you're going to make
more products or less products.

327
00:20:41 --> 00:20:45
If q is greater than
k, what is delta g?

328
00:20:45 --> 00:20:52
So it would be positive and the
reverse direction would occur.

329
00:20:52 --> 00:20:55
So you think that at q, if it's
larger than k, it has more

330
00:20:55 --> 00:20:58
products in its terms, and at
equilibrium there are less

331
00:20:58 --> 00:21:02
products, so you need to go in
a direction that will get rid

332
00:21:02 --> 00:21:06
of some of those products so
you'll reach equilibrium again.

333
00:21:06 --> 00:21:09
So this equation is very
helpful in thinking about the

334
00:21:09 --> 00:21:12
direction of the reaction --
which direction will

335
00:21:12 --> 00:21:15
it be spontaneous.
 

336
00:21:15 --> 00:21:18
So let's look at an example.
 

337
00:21:18 --> 00:21:22
K is given in this example,
and then we have a bunch

338
00:21:22 --> 00:21:24
of partial pressures.
 

339
00:21:24 --> 00:21:27
And we're asked which direction
the reaction will go.

340
00:21:27 --> 00:21:31
So what do I need to do to
answer this question, what

341
00:21:31 --> 00:21:32
do I need to calculate?
 

342
00:21:32 --> 00:21:40
So if I'm given k, and a bunch
of partial pressures, what do

343
00:21:40 --> 00:21:43
I first need to calculate?
 

344
00:21:43 --> 00:21:45
Q, right.
 

345
00:21:45 --> 00:21:49
So let's calculate q.
 

346
00:21:49 --> 00:21:53
So q, we're going to talk about
products over reactants, so

347
00:21:53 --> 00:21:58
we're going to talk about be
partial pressure of the

348
00:21:58 --> 00:22:04
ammonia, and there are two
of them being formed.

349
00:22:04 --> 00:22:07
Our reactants, we want to talk
about the partial pressure of

350
00:22:07 --> 00:22:13
the nitrogen, and the partial
pressure of the hydrogen gas,

351
00:22:13 --> 00:22:19
and again include the
stoichiometry, so we

352
00:22:19 --> 00:22:21
have three there.
 

353
00:22:21 --> 00:22:26
So now I can plug in my values,
so I'm told I have 1 .

354
00:22:26 --> 00:22:32
1 bar, and down here I have 5 .
 

355
00:22:32 --> 00:22:35
5 and 2 .
 

356
00:22:35 --> 00:22:41
2 to the 3, again, considering
the stoichiometry.

357
00:22:41 --> 00:22:44
And if you do the
math, you get 2 .

358
00:22:44 --> 00:22:48
1 times 10 to the minus 2.
 

359
00:22:48 --> 00:22:49
That's your q value.
 

360
00:22:49 --> 00:22:54
Now given your k value, which
the problem states, and this q

361
00:22:54 --> 00:22:57
value, let's do a clicker
question, tell me which

362
00:22:57 --> 00:23:17
direction the reaction will go.
 

363
00:23:17 --> 00:23:40
All right, 10 seconds.
 

364
00:23:40 --> 00:23:43
So, 77%, pretty good.
 

365
00:23:43 --> 00:23:48
So, q is greater than k here.
 

366
00:23:48 --> 00:23:52
And if q is greater
than k, what will be

367
00:23:52 --> 00:23:54
true about delta g?
 

368
00:23:54 --> 00:24:09
I have another clicker
question for that --

369
00:24:09 --> 00:24:14
yell out the answer.
 

370
00:24:14 --> 00:24:16
What is it?
 

371
00:24:16 --> 00:24:17
Positive, right.
 

372
00:24:17 --> 00:24:21
So you're going to shift
towards reactants, so

373
00:24:21 --> 00:24:23
you're going to go in
the reverse direction.

374
00:24:23 --> 00:24:27
So you think about whether
there are more products or less

375
00:24:27 --> 00:24:34
products at equilibrium, and so
there are more products, so we

376
00:24:34 --> 00:24:38
have to think about which
direction it'll go, and here,

377
00:24:38 --> 00:25:08
ammonium will dissociate until
equilibrium is reached again.

378
00:25:08 --> 00:25:10
OK.
 

379
00:25:10 --> 00:25:17
So let's think more about
what k is going to tell us.

380
00:25:17 --> 00:25:21
So k tells us about the mixture
of products and reactants at

381
00:25:21 --> 00:25:25
equilibrium, whether we can
expect low or high

382
00:25:25 --> 00:25:32
concentration of reactants
at equilibrium.

383
00:25:32 --> 00:25:42
So let's look at
another example.

384
00:25:42 --> 00:25:50
So when you have k that's
greater than one, so more

385
00:25:50 --> 00:25:54
products than reactants at
equilibrium, you can think

386
00:25:54 --> 00:26:02
about this in terms of higher
products at equilibrium.

387
00:26:02 --> 00:26:13
When you have k less than
one, we're going to

388
00:26:13 --> 00:26:17
have lower products.
 

389
00:26:17 --> 00:26:24
So again, think about k in
terms of products over

390
00:26:24 --> 00:26:35
reactants at equilibrium.
 

391
00:26:35 --> 00:26:38
So if k is greater than one,
there are more products

392
00:26:38 --> 00:26:39
than reactants.
 

393
00:26:39 --> 00:26:41
If it's less than one, there
will be less reactants

394
00:26:41 --> 00:27:05
than products.
 

395
00:27:05 --> 00:27:07
So let's look at an
example of that.

396
00:27:07 --> 00:27:13
Let's look at when k
is greater than one.

397
00:27:13 --> 00:27:16
And I have the equation
up there and I'll

398
00:27:16 --> 00:27:17
write it here as well.
 

399
00:27:17 --> 00:27:28
So we have 2 n o 2, and two
double arrows, and n 2 o 4.

400
00:27:28 --> 00:27:34
So we have a k
value here of 6 .

401
00:27:34 --> 00:27:40
84, so that's greater
than one value.

402
00:27:40 --> 00:27:44
So let's think about
this reaction.

403
00:27:44 --> 00:27:47
So over here instead of
concentration, we're going to

404
00:27:47 --> 00:27:51
talk about partial pressure
because we're talking about

405
00:27:51 --> 00:27:56
gas, and we have time.
 

406
00:27:56 --> 00:28:01
So initially we
have a reactant.

407
00:28:01 --> 00:28:08
And the reactant starts at some
concentration and decreases and

408
00:28:08 --> 00:28:13
then reaches a straight line,
so reaches equilibrium.

409
00:28:13 --> 00:28:19
So we have our reactant here.
 

410
00:28:19 --> 00:28:24
Originally we have no product,
and so product is going to go

411
00:28:24 --> 00:28:28
up and be formed and then
it's going to level off

412
00:28:28 --> 00:28:35
as you reach equilibrium.
 

413
00:28:35 --> 00:28:42
So initially, what is
true about q and k?

414
00:28:42 --> 00:28:57
So with no products, what
is true about q and k?

415
00:28:57 --> 00:29:00
Q is less than k.
 

416
00:29:00 --> 00:29:03
And so what's true
about delta g?

417
00:29:03 --> 00:29:06
Less than zero, it'll be
negative, so it'll be

418
00:29:06 --> 00:29:08
spontaneous in the
forward direction.

419
00:29:08 --> 00:29:10
So you're going to be
spontaneous in the forward

420
00:29:10 --> 00:29:15
direction and you're going
to make your product.

421
00:29:15 --> 00:29:21
So now let's calculate what
the concentrations are

422
00:29:21 --> 00:29:25
going to be at equilibrium.
 

423
00:29:25 --> 00:29:37
So initially, so you have your
initial pressure for the

424
00:29:37 --> 00:29:48
reaction, 2 n o 2 going to
n 2 o 2, and our initial

425
00:29:48 --> 00:29:59
concentrations are given as one
bar, and we have no product.

426
00:29:59 --> 00:30:07
Now we talk about the change as
we go toward equilibrium, how

427
00:30:07 --> 00:30:12
much does the reactant change?
 

428
00:30:12 --> 00:30:13
What do I write here?
 

429
00:30:13 --> 00:30:16
What change?
 

430
00:30:16 --> 00:30:20
Minus x minus something x?
 

431
00:30:20 --> 00:30:21
Minus 2 x.
 

432
00:30:21 --> 00:30:24
So again, we're considering
the stoichiometry,

433
00:30:24 --> 00:30:27
and what's over here?
 

434
00:30:27 --> 00:30:37
So just plus x, and then at
equilibrium we now have

435
00:30:37 --> 00:30:46
1 minus 2 x and x.
 

436
00:30:46 --> 00:30:49
So we're talking about
equilibrium concentrations,

437
00:30:49 --> 00:30:54
so we're talking about
k, so k equals 6 .

438
00:30:54 --> 00:30:59
84, which is going to be equal
to the partial pressure of the

439
00:30:59 --> 00:31:03
product over the partial
pressure of the

440
00:31:03 --> 00:31:07
reactant squared.
 

441
00:31:07 --> 00:31:18
So it's going to be equal to
x over 1 minus 2 x squared.

442
00:31:18 --> 00:31:27
So x, if you calculate it out,
should equal point 381 bar.

443
00:31:27 --> 00:31:37
And then if we do 1 minus 2
times 0.381 bar, we get 0 .

444
00:31:37 --> 00:31:43
238 bar.
 

445
00:31:43 --> 00:31:50
So if we go back over here, our
products at equilibrium -- oh,

446
00:31:50 --> 00:31:57
I guess I should write what --
so x is our product and

447
00:31:57 --> 00:32:02
this is our reactant.
 

448
00:32:02 --> 00:32:07
So the product we have 0 .
 

449
00:32:07 --> 00:32:12
381, and our reactant at
equilibrium is going

450
00:32:12 --> 00:32:18
to be 0.238 bar.
 

451
00:32:18 --> 00:32:23
So we have more product than
reactant at equilibrium, which

452
00:32:23 --> 00:32:29
is consistent with the value
of k being greater than one.

453
00:32:29 --> 00:32:32
So, when you know something
about the equilibrium constant,

454
00:32:32 --> 00:32:35
you know something about the
reaction and whether you would

455
00:32:35 --> 00:32:44
expect more products or
reactants at equilibrium.

456
00:32:44 --> 00:32:50
So again, you can think about
this in terms of q and k.

457
00:32:50 --> 00:32:53
All right, so now we are
going to go toward our

458
00:32:53 --> 00:32:56
next clicker question.
 

459
00:32:56 --> 00:33:01
So if we can rewrite the
expression for delta g equals

460
00:33:01 --> 00:33:07
minus r t natural log of k, and
express it in terms of k, and

461
00:33:07 --> 00:33:10
now we can think about then
what is that relationship.

462
00:33:10 --> 00:33:15
If you have a large value for
k, what do you expect to be

463
00:33:15 --> 00:33:36
true about delta g nought?
 

464
00:33:36 --> 00:33:53
All right, let's give
that 10 seconds.

465
00:33:53 --> 00:33:56
OK, why don't you discuss for
a minute with your friends

466
00:33:56 --> 00:34:17
whether you agree with
that 78% or not.

467
00:34:17 --> 00:34:47
All right, now we're going to
re-poll, so click in again.

468
00:34:47 --> 00:34:53
Now give the right answer.
 

469
00:34:53 --> 00:34:57
Interesting.
 

470
00:34:57 --> 00:35:00
It actually usually goes the
other direction, that after

471
00:35:00 --> 00:35:03
there's a discussion, more
people come to the

472
00:35:03 --> 00:35:04
same conclusion.
 

473
00:35:04 --> 00:35:07
So I guess it's a matter of if
the professor asks that, you

474
00:35:07 --> 00:35:10
assume that that must have
been the wrong answer.

475
00:35:10 --> 00:35:16
Was that people's logic?
 

476
00:35:16 --> 00:35:19
So what are the points of doing
this, and we're going to

477
00:35:19 --> 00:35:22
actually do this kind of thing
a few more times in class, is

478
00:35:22 --> 00:35:27
that collectively, and I was
actually just at an education

479
00:35:27 --> 00:35:31
meeting about science down at
the Howard Hughes Medical

480
00:35:31 --> 00:35:36
Institute, that statistics show
that if you have a group where

481
00:35:36 --> 00:35:38
everyone in the group has the
wrong answer and they're

482
00:35:38 --> 00:35:41
allowed to discuss it, there's
a good chance they'll come

483
00:35:41 --> 00:35:43
up with the right answer.
 

484
00:35:43 --> 00:35:46
So that it's not just about one
person in the group having the

485
00:35:46 --> 00:35:48
right answer, convincing
everyone else that they're

486
00:35:48 --> 00:35:51
right, that the act of
discussing often leads

487
00:35:51 --> 00:35:53
to new answers.
 

488
00:35:53 --> 00:35:58
So now that you know that it's
not a trick on my part to tell

489
00:35:58 --> 00:36:01
you you got it wrong, we'll see
next time whether this, in

490
00:36:01 --> 00:36:05
fact, holds, that the act of
discussing helps give

491
00:36:05 --> 00:36:07
the right answer.
 

492
00:36:07 --> 00:36:13
Anyway, so if k is large, it is
true that delta g nought would

493
00:36:13 --> 00:36:17
tend to be negative and more --
it would be negative and

494
00:36:17 --> 00:36:19
more on the large side.
 

495
00:36:19 --> 00:36:23
So one can think about if
there's more products over

496
00:36:23 --> 00:36:26
reactants, that's going to
indicate something about the

497
00:36:26 --> 00:36:30
delta g nought for the
reaction, and the k -- the k,

498
00:36:30 --> 00:36:32
if it's greater than 1, if it's
a big number, then there are

499
00:36:32 --> 00:36:36
more products than reactants,
and delta g nought would be

500
00:36:36 --> 00:36:39
negative and would tend
to be a large number.

501
00:36:39 --> 00:36:45
All right, so this is more
actually kind of simple

502
00:36:45 --> 00:36:51
bookkeeping involved that if
you know steps in the reactions

503
00:36:51 --> 00:36:55
and you know equilibrium
constants, you can calculate an

504
00:36:55 --> 00:36:59
overall equilibrium constant
for that reaction.

505
00:36:59 --> 00:37:02
So you can write a
reaction as the sum of

506
00:37:02 --> 00:37:05
different components.
 

507
00:37:05 --> 00:37:10
And so up here, we are going
to try to add these first

508
00:37:10 --> 00:37:13
two equations to get
this net equation.

509
00:37:13 --> 00:37:22
So we have 2 gas p 3 c l 2
going to 2 p l c 3, and

510
00:37:22 --> 00:37:23
that's equilibrium 1.
 

511
00:37:23 --> 00:37:27
And so then in the next
reaction, some of that is being

512
00:37:27 --> 00:37:33
consumed reacting with another
c l 2, giving you p c l 5, and

513
00:37:33 --> 00:37:38
the net reaction we're
interested in has 2 p 5 c l

514
00:37:38 --> 00:37:41
2's going to 2 p c l 5.
 

515
00:37:41 --> 00:37:46
All right, what do I have to do
before I can add these together

516
00:37:46 --> 00:37:52
effectively and have
things cancel out?

517
00:37:52 --> 00:37:55
I need to multiply what?
 

518
00:37:55 --> 00:37:59
Second equation by 2, yeah.
 

519
00:37:59 --> 00:38:06
So to get that to work I would
need to have 2's there, then

520
00:38:06 --> 00:38:11
this is going to cancel out and
these will add up, so we have

521
00:38:11 --> 00:38:15
5 and then we have two
of the main products.

522
00:38:15 --> 00:38:21
So if I do that, and I have the
equilibrium constant for one

523
00:38:21 --> 00:38:24
and for two, how am I
going to get equilibrium

524
00:38:24 --> 00:38:28
constant for three?
 

525
00:38:28 --> 00:38:36
I'm going to multiply
k 1 by k 2 and k 2.

526
00:38:36 --> 00:38:40
So I'm going to have to
multiply k 2 in there twice,

527
00:38:40 --> 00:38:44
because there's two of those
-- we'd multiply that up.

528
00:38:44 --> 00:38:48
So if you have different parts
of reactions and you can sum

529
00:38:48 --> 00:38:53
them together, then you can
multiply out the individual k's

530
00:38:53 --> 00:38:55
to get the new value of k.
 

531
00:38:55 --> 00:38:59
So that's something that's just
useful that you'll run into in

532
00:38:59 --> 00:39:05
doing these types of problems.
 

533
00:39:05 --> 00:39:07
All right.
 

534
00:39:07 --> 00:39:12
Now we're going to think
about how equilibriums

535
00:39:12 --> 00:39:16
respond to stress.
 

536
00:39:16 --> 00:39:19
And I always feel like
I need to pause.

537
00:39:19 --> 00:39:25
MIT students, you guys are some
of the smartest, most talented

538
00:39:25 --> 00:39:27
scientists in the world.
 

539
00:39:27 --> 00:39:30
I don't know if you
fully appreciate how

540
00:39:30 --> 00:39:32
smart you all are.
 

541
00:39:32 --> 00:39:39
But this concept is
tough for MIT students.

542
00:39:39 --> 00:39:43
So Le Chatelier's principle
says that a system in

543
00:39:43 --> 00:39:48
equilibrium that is subjected
to with stress tends to

544
00:39:48 --> 00:39:57
react in such a way to
minimize that stress.

545
00:39:57 --> 00:40:00
I have advisees coming to my
office saying, "I'm

546
00:40:00 --> 00:40:03
double-majoring in this and
that and I'm taking five

547
00:40:03 --> 00:40:08
classes and I have UROP and I
have this lab exercise -- I

548
00:40:08 --> 00:40:11
don't know what's going on, so
I've been thinking a lot about

549
00:40:11 --> 00:40:17
it and I think I should add
a third major." Le

550
00:40:17 --> 00:40:20
Chatelier would be very
unhappy with that.

551
00:40:20 --> 00:40:26
Le Chatelier would say that the
appropriate response is to drop

552
00:40:26 --> 00:40:33
one of the majors, to
minimize the stress.

553
00:40:33 --> 00:40:37
So in doing these problems,
what I want to encourage you

554
00:40:37 --> 00:40:42
to do is think the opposite
of what you would do.

555
00:40:42 --> 00:40:45
Minimize the stress.
 

556
00:40:45 --> 00:40:48
If you think about that
you'll be all set.

557
00:40:48 --> 00:40:50
All right.
 

558
00:40:50 --> 00:40:55
So Le Chatelier's principle
actually is very useful.

559
00:40:55 --> 00:40:59
If you think about minimizing
the stress, you'll be able to

560
00:40:59 --> 00:41:04
predict the direction that
the reaction will shift.

561
00:41:04 --> 00:41:06
So the reaction's going to
shift in a way to minimize the

562
00:41:06 --> 00:41:09
stress, so you can predict it.
 

563
00:41:09 --> 00:41:12
If you're thinking along these
lines, you say, oh, that system

564
00:41:12 --> 00:41:16
was stressed, and then you can
think about how that reaction

565
00:41:16 --> 00:41:19
or that system is
going to respond.

566
00:41:19 --> 00:41:24
So let's give some examples.
 

567
00:41:24 --> 00:41:29
So, we have a system in
equilibrium -- we started out,

568
00:41:29 --> 00:41:33
we had our nitrogen and our
hydrogen and we had no product.

569
00:41:33 --> 00:41:36
We reacted the hydrogen and the
nitrogen, their forming

570
00:41:36 --> 00:41:39
products, and eventually they
reach equilibrium, their delta

571
00:41:39 --> 00:41:43
g equals zero there's still the
reaction going on, but

572
00:41:43 --> 00:41:45
there's no net change.
 

573
00:41:45 --> 00:41:49
All right, now the system
is going to be stressed.

574
00:41:49 --> 00:41:54
So we're going to add
more of a reactant.

575
00:41:54 --> 00:41:59
How will the system react
to minimize that stress?

576
00:41:59 --> 00:42:00
What is it going to do?
 

577
00:42:00 --> 00:42:05
It now has too much of
one of the reactants.

578
00:42:05 --> 00:42:09
You'll form more products, and
that's going to use up some of

579
00:42:09 --> 00:42:12
your other reactant, which will
go down, and you're going

580
00:42:12 --> 00:42:16
to form more product until
equilibrium is reached again.

581
00:42:16 --> 00:42:20
And one thing that I'll
mention that the ratio

582
00:42:20 --> 00:42:21
has to be the same.
 

583
00:42:21 --> 00:42:25
The equilibrium constant is
a constant given the same

584
00:42:25 --> 00:42:27
temperature, but you're not
necessarily always going to

585
00:42:27 --> 00:42:30
have the same concentrations,
but you should have the same

586
00:42:30 --> 00:42:32
ratios, the same value of k.
 

587
00:42:32 --> 00:42:36
All right, so what about
if you add more product,

588
00:42:36 --> 00:42:40
what's going to happen?
 

589
00:42:40 --> 00:42:43
What direction will
the reaction shift?

590
00:42:43 --> 00:42:47
Right, it's going to shift
toward the reactants, so you're

591
00:42:47 --> 00:42:51
going to make more of each of
the two reactants until

592
00:42:51 --> 00:42:54
again, you find your
equilibrium again.

593
00:42:54 --> 00:42:57
And then the reaction's
still going but there's

594
00:42:57 --> 00:42:59
no net change anymore.
 

595
00:42:59 --> 00:43:03
All right, so let's think about
this -- let's think about this

596
00:43:03 --> 00:43:05
in terms of the math as well.
 

597
00:43:05 --> 00:43:09
If you want to stick with the
math, that's OK, you can think

598
00:43:09 --> 00:43:12
about calculating
delta g's here.

599
00:43:12 --> 00:43:14
So if you're a system in
equilibrium and you add more

600
00:43:14 --> 00:43:18
hydrogen, the system will
respond to minimize

601
00:43:18 --> 00:43:19
that increase.
 

602
00:43:19 --> 00:43:23
So it's going to make more
product that will minimize

603
00:43:23 --> 00:43:26
the increase, it
shifts to the right.

604
00:43:26 --> 00:43:31
And this can be explained
in terms of q and k.

605
00:43:31 --> 00:43:35
So, you can think about, again,
do you have more products now

606
00:43:35 --> 00:43:39
or did you have more products
at equilibrium, and if you're

607
00:43:39 --> 00:43:43
adding more reactants,
momentarily q will

608
00:43:43 --> 00:43:47
become less than k.
 

609
00:43:47 --> 00:43:52
And so, you would get a
negative delta g, which would

610
00:43:52 --> 00:43:56
make it spontaneous in
the forward direction.

611
00:43:56 --> 00:43:59
So some people like to think
about this in terms of delta

612
00:43:59 --> 00:44:03
g equals r t natural
log of q over k.

613
00:44:03 --> 00:44:08
So you think about if q is less
than k, what sign you have for

614
00:44:08 --> 00:44:10
delta g, and that's tells you
whether the reaction is

615
00:44:10 --> 00:44:14
spontaneous in the forward
or the reverse direction.

616
00:44:14 --> 00:44:17
And let me just give you
one hint for taking

617
00:44:17 --> 00:44:19
exams in this unit.
 

618
00:44:19 --> 00:44:23
That use of the arrow is really
good, or saying "toward

619
00:44:23 --> 00:44:26
product" or "reactant." I can't
tell you how many people write

620
00:44:26 --> 00:44:30
-- know what the answer is and
write left when mean right, or

621
00:44:30 --> 00:44:32
write right when
they mean left.

622
00:44:32 --> 00:44:36
But if you draw an arrow you
never really get it wrong, and

623
00:44:36 --> 00:44:39
when you say products or
reactants it's a lot harder

624
00:44:39 --> 00:44:41
to make that mistake.
 

625
00:44:41 --> 00:44:44
So if you're not good with
right or left, which let me

626
00:44:44 --> 00:44:48
tell you a large fraction of
people are not, hedge your

627
00:44:48 --> 00:44:50
bets, you can write everything,
more products, arrows, and then

628
00:44:50 --> 00:44:53
write if you want, then
you're pretty sure that

629
00:44:53 --> 00:44:55
you have it all in there.
 

630
00:44:55 --> 00:44:56
OK.
 

631
00:44:56 --> 00:45:03
So again, we can explain
this in terms of q or k.

632
00:45:03 --> 00:45:04
All right.
 

633
00:45:04 --> 00:45:08
So let's just quickly talk
about adding more products.

634
00:45:08 --> 00:45:10
We did this already.
 

635
00:45:10 --> 00:45:13
If more products are added.
then q is going to be greater

636
00:45:13 --> 00:45:17
than k momentarily, and you
would shift toward reactants,

637
00:45:17 --> 00:45:25
shift toward the left, and
again, we saw that down there.

638
00:45:25 --> 00:45:29
So tell me a final clicker
question and then we're done.

639
00:45:29 --> 00:45:53
What happens if you
remove products and why?

640
00:45:53 --> 00:46:02
OK, 10 seconds.
 

641
00:46:02 --> 00:46:07
See if we can get in the 90's.
 

642
00:46:07 --> 00:46:10
No, no 90's today, we'll
have to do it next time,

643
00:46:10 --> 00:46:12
but we got 73 right.
 

644
00:46:12 --> 00:46:16
So we're going to make
more products as well.

645
00:46:16 --> 00:46:16