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

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00:00:24,560 --> 00:00:43,190
Let's settle down and take a
look at the clicker question.

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00:00:43,190 --> 00:00:59,070
So take 10 more seconds.

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00:00:59,070 --> 00:01:00,740
Very good.

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00:01:00,740 --> 00:01:04,170
Most people had this right, and
the trick here is just to

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00:01:04,170 --> 00:01:07,750
think about the sign of delta
g, whether it's negative and

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00:01:07,750 --> 00:01:11,840
positive, and think about the
equation and the influence of

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00:01:11,840 --> 00:01:15,340
temperature on that equation.

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00:01:15,340 --> 00:01:19,050
So whether it's going to make
delta s a bigger factor or a

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00:01:19,050 --> 00:01:21,710
smaller factor and how
that will play out.

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00:01:21,710 --> 00:01:24,310
So you can look at the equation
and figure out what

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00:01:24,310 --> 00:01:29,430
the signs have to be and then
the influence of temperature.

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00:01:29,430 --> 00:01:35,550
All right, so let's move to the
first slide that I have

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00:01:35,550 --> 00:01:40,190
today, which is welcome to the
middle of the semester.

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00:01:40,190 --> 00:01:45,760
So I'm Kathy Drennan and this
is lecture 19 of 36, which

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00:01:45,760 --> 00:01:49,170
means that you are halfway
through the course.

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00:01:49,170 --> 00:01:53,240
And so what you heard on Monday
before the exam was

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00:01:53,240 --> 00:01:56,620
about thermodynamics, and if you
don't have all your delta

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00:01:56,620 --> 00:02:01,270
g's and delta h's and if you
don't have entropy full in

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00:02:01,270 --> 00:02:05,330
mind, that's OK, we are not
really leaving thermodynamics,

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00:02:05,330 --> 00:02:08,220
we're going into chemical
equilibrium, which is all

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00:02:08,220 --> 00:02:09,380
about thermodynamics.

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00:02:09,380 --> 00:02:13,100
So you're going to hear a lot
more about delta g, delta h,

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00:02:13,100 --> 00:02:17,660
temperature, and about our
friend, entropy as we go along

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00:02:17,660 --> 00:02:19,550
in the second half.

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00:02:19,550 --> 00:02:22,480
So it's the middle
of the semester.

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00:02:22,480 --> 00:02:26,500
That means that you've had two
of the sort of four hour exams

35
00:02:26,500 --> 00:02:29,450
-- remember the fourth hour exam
is actually combined with

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00:02:29,450 --> 00:02:30,880
the final exam.

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00:02:30,880 --> 00:02:33,900
So the final exam is 200 points
of cumulative material,

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00:02:33,900 --> 00:02:37,440
and 100 points of new material,
so you've done two

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00:02:37,440 --> 00:02:41,620
now of those four sort
of hour exams.

40
00:02:41,620 --> 00:02:44,610
Just to remind you of some of
the topics you have seen and

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00:02:44,610 --> 00:02:47,200
the topics coming ahead, this is
on the syllabus, and we're

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00:02:47,200 --> 00:02:50,730
actually where we're supposed
to be on the syllabus, so if

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00:02:50,730 --> 00:02:53,390
you want to take a look at that
ever to see where we're

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00:02:53,390 --> 00:02:55,990
going, we're actually
on track.

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00:02:55,990 --> 00:02:58,330
So the first half of the course
are a lot of basic

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00:02:58,330 --> 00:03:01,910
principles, and we're moving
today into chemical

47
00:03:01,910 --> 00:03:04,800
equilibrium, so a lot
more delta g's,

48
00:03:04,800 --> 00:03:07,340
delta h's coming on.

49
00:03:07,340 --> 00:03:10,150
And then we're going to move
into acid base, which is acid

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00:03:10,150 --> 00:03:11,650
base equilibrium.

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00:03:11,650 --> 00:03:13,530
So we're not going to be
leaving equilibrium or

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00:03:13,530 --> 00:03:14,760
thermodynamics.

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00:03:14,760 --> 00:03:17,320
Then we're going to go into
oxidation reduction, which is

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00:03:17,320 --> 00:03:21,030
also about equilibrium, and then
transition metals, and

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00:03:21,030 --> 00:03:22,940
end with kenetics.

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00:03:22,940 --> 00:03:27,020
And so, these altogether
represent the fundamentals

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00:03:27,020 --> 00:03:29,940
needed for the study of
biochemistry, organic

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00:03:29,940 --> 00:03:32,850
chemistry, any kind of
chemistry, biology, the life

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00:03:32,850 --> 00:03:35,180
sciences, many things -- so
you're getting all the

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fundamental principles of
chemistry in this class.

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00:03:38,770 --> 00:03:43,030
So along those lines, I just
thought I would share

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something that happened to me on
Wednesday when I was riding

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00:03:46,280 --> 00:03:48,710
the 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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00:04:01,880 --> 00:04:04,030
And you say, "Yes," and they
said, "Oh, what are you

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00:04:04,030 --> 00:04:06,630
studying?" And then you say
"Well, you know, chemistry,

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00:04:06,630 --> 00:04:12,270
math, physics." And they're like
"Oh." And then they go

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busy themselves doing
something else.

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00:04:14,120 --> 00:04:18,450
Or they tell you "I didn't
really like those subjects in

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00:04:18,450 --> 00:04:21,040
school." And then they
stop talking to you.

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00:04:21,040 --> 00:04:23,890
So how many people have had that
experience so far, that

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00:04:23,890 --> 00:04:26,560
you scare the person next to
you by what you study?

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00:04:26,560 --> 00:04:29,530
OK, a few people.

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00:04:29,530 --> 00:04:31,700
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

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now it'll be everybody.

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00:04:34,840 --> 00:04:36,750
So this is kind of common.

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00:04:36,750 --> 00:04:39,450
But what happened to me on the
Silver Line was actually

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pretty exciting, because
I've had that other

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experience many times.

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So, I was wearing my keys
around my neck, because

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00:04:47,170 --> 00:04:50,140
women's professional clothes, no
pockets, with a little MIT

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00:04:50,140 --> 00:04:55,600
cord, and the person next to
be on the Silver Line said

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00:04:55,600 --> 00:05:04,220
"So, do you go to the Georgia
Tech of the east?" And I said

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00:05:04,220 --> 00:05:09,790
"Well, I am a professor at MIT."
And he said "Well, I'm a

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mechanical engineer and I went
to Georgia Tech." And so he

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00:05:15,130 --> 00:05:17,490
said, "So, what do you teach?"
I said, "Chemistry." And he

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00:05:17,490 --> 00:05:19,170
said, "Chemistry --

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00:05:19,170 --> 00:05:24,890
I really wish I had paid more
attention in chemistry." I

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00:05:24,890 --> 00:05:26,570
said, "Well, what do you do
now?" And he said "Well, I

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00:05:26,570 --> 00:05:29,840
work for the army, and I'm
part of a team that has

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00:05:29,840 --> 00:05:32,230
mechanical engineers, electrical
engineers, and

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00:05:32,230 --> 00:05:35,250
chemists, and we're trying to
figure out ways to detect

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00:05:35,250 --> 00:05:38,200
explosives." So I said, "Oh,
well have you heard of the

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00:05:38,200 --> 00:05:40,560
head of the Chemistry Department
at MIT, Tim Swager

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00:05:40,560 --> 00:05:43,890
who works in the area, and he
said, "Yes," he knew the name.

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00:05:43,890 --> 00:05:47,840
And so he said that one of his
porblems on the team, and in

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00:05:47,840 --> 00:05:51,560
talking to the chemist, his
chemistry language is not

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00:05:51,560 --> 00:05:54,610
really good enough, and so he
was really struggling, and

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00:05:54,610 --> 00:05:57,650
that the best results of this
team effort would be if

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00:05:57,650 --> 00:05:59,530
everyone could really
talk to each other.

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00:05:59,530 --> 00:06:03,720
So he wished that he had paid
more attention in his

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00:06:03,720 --> 00:06:05,070
chemistry class.

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00:06:05,070 --> 00:06:09,980
And so I, of course, my
connection with chemistry was

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00:06:09,980 --> 00:06:13,260
by wanting to understand
biology, but for everyone it

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00:06:13,260 --> 00:06:14,790
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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00:06:16,970 --> 00:06:19,260
challenge that you have this
semester is figure out what

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00:06:19,260 --> 00:06:20,970
your connection to
chemistry is.

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00:06:20,970 --> 00:06:22,910
What are you going to
use chemistry for?

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00:06:22,910 --> 00:06:25,260
How does this fit into
what you want to do?

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00:06:25,260 --> 00:06:26,910
And maybe for some of you,
you're not going

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00:06:26,910 --> 00:06:27,940
to know that yet.

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00:06:27,940 --> 00:06:31,120
Hopefully it won't take till you
have a job doing something

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00:06:31,120 --> 00:06:35,030
to realize that you're lacking
something in your education.

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00:06:35,030 --> 00:06:40,540
And so, probably if you stay
in science and engineering,

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00:06:40,540 --> 00:06:43,410
need chemistry, good to
learn it all now.

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00:06:43,410 --> 00:06:47,480
And from exam 2, we see that
you are learning it now and

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00:06:47,480 --> 00:06:48,550
that's really great.

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00:06:48,550 --> 00:06:51,660
So, some day maybe someone in
this room will be involved in

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00:06:51,660 --> 00:06:54,370
national security, and if you're
not a chemist, you'll

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00:06:54,370 --> 00:06:56,870
be able to talk to the chemists
and make really good

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00:06:56,870 --> 00:06:59,140
progress toward that work.

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00:06:59,140 --> 00:07:01,130
So, chemistry -- it's important
in medicine,

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00:07:01,130 --> 00:07:05,140
national security, the economy,
energy initiatives, a

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00:07:05,140 --> 00:07:07,130
lot of the big things
going on now.

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00:07:07,130 --> 00:07:10,150
It's a fundamental, and you will
get in this course, the

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00:07:10,150 --> 00:07:11,520
fundamentals.

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00:07:11,520 --> 00:07:16,500
So if you have any good tea or
bus or airplane conversations,

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00:07:16,500 --> 00:07:17,430
let me know --

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00:07:17,430 --> 00:07:20,220
I'll catalog those for
future reference.

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00:07:20,220 --> 00:07:23,270
It's always a touch of how what
we do here connects with

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00:07:23,270 --> 00:07:25,790
the real world.

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00:07:25,790 --> 00:07:29,700
All right, so we're not going
far from thermodynamics, we're

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00:07:29,700 --> 00:07:31,910
going into chemical
equilibrium.

139
00:07:31,910 --> 00:07:34,710
And we're going to be talking
a lot about delta g.

140
00:07:34,710 --> 00:07:40,370
So if delta g is not your friend
yet, don't worry, you

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00:07:40,370 --> 00:07:45,510
can still bond with delta g.

142
00:07:45,510 --> 00:07:53,030
All right, so chemical
reactions, chemical reactions

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00:07:53,030 --> 00:07:56,910
can go into a state
of equilibrium.

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00:07:56,910 --> 00:07:59,700
And it's a dynamic equilibrium,
the reaction is

145
00:07:59,700 --> 00:08:03,490
still happening, but if a
reaction is an equilibrium,

146
00:08:03,490 --> 00:08:07,480
the rate of the forward reaction
will equal the rate

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00:08:07,480 --> 00:08:11,570
of the reverse reaction, so
there'll be no net change in

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00:08:11,570 --> 00:08:14,290
composition.

149
00:08:14,290 --> 00:08:19,310
So let's take a look
at an example.

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00:08:19,310 --> 00:08:27,220
So let's look at a reaction in
which we have nitrogen gas,

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00:08:27,220 --> 00:08:33,640
and we have hydrogen
gas, and they are

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00:08:33,640 --> 00:08:41,450
reacting to form ammonia.

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00:08:41,450 --> 00:08:46,650
Suppose we just start with
nitrogen gas and hydrogen gas

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00:08:46,650 --> 00:08:49,490
and we don't have any
ammonia left.

155
00:08:49,490 --> 00:08:56,210
So if we consider concentrations
versus time.

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00:08:56,210 --> 00:08:59,290
So say we start with, we have
some nitrogen gas, some

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00:08:59,290 --> 00:09:01,580
concentration of nitrogen gas.

158
00:09:01,580 --> 00:09:06,170
As it reacts with hydrogen,
the concentration will

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00:09:06,170 --> 00:09:11,970
decrease and then level off.

160
00:09:11,970 --> 00:09:15,830
We'll start with some amount
of hydrogen gas, and its

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00:09:15,830 --> 00:09:22,730
concentration will also decrease
and level off.

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00:09:22,730 --> 00:09:25,830
And in the beginning we won't
have any of the product, any

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00:09:25,830 --> 00:09:30,510
of the ammonia, so its
concentration will increase

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00:09:30,510 --> 00:09:36,230
and then level off.

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00:09:36,230 --> 00:09:39,370
So when these reactions level
off, you're reaching

166
00:09:39,370 --> 00:09:40,070
equilibrium.

167
00:09:40,070 --> 00:09:42,520
The reaction is still happening,
but the rate of the

168
00:09:42,520 --> 00:09:45,370
forward reaction is equal to
the rate of the reverse

169
00:09:45,370 --> 00:09:47,680
reaction, so there's
no net change.

170
00:09:47,680 --> 00:09:51,230
So the concentrations are
staying the same, but there's

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00:09:51,230 --> 00:09:56,390
still -- the reaction is
still going forward.

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00:09:56,390 --> 00:10:01,290
So let's think about the case
when we have pure reactants

173
00:10:01,290 --> 00:10:04,470
when we haven't formed enough
products yet to reach

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00:10:04,470 --> 00:10:07,050
equilibrium.

175
00:10:07,050 --> 00:10:15,690
So if we have pure reactants,
the reaction is going to be

176
00:10:15,690 --> 00:10:19,490
spontaneous in the forward
direction.

177
00:10:19,490 --> 00:10:25,340
So we'll have a reaction
that is spontaneous

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00:10:25,340 --> 00:10:31,010
in the forward direction.

179
00:10:31,010 --> 00:10:36,590
And what will that mean about
our friend delta g?

180
00:10:36,590 --> 00:10:42,380
Is it going to be greater
or less than zero?

181
00:10:42,380 --> 00:10:45,540
So it'll be less than zero --
so delta g or the forward

182
00:10:45,540 --> 00:10:47,370
reaction will be
less than zero.

183
00:10:47,370 --> 00:10:50,720
So when delta g is negative, the
reaction is spontaneous in

184
00:10:50,720 --> 00:10:53,020
the forward direction.

185
00:10:53,020 --> 00:10:58,670
So what about when you have
pure products, then the

186
00:10:58,670 --> 00:11:03,870
reaction should be spontaneous
in the reverse direction.

187
00:11:03,870 --> 00:11:13,690
So you have spontaneous in the
reverse direction, and what

188
00:11:13,690 --> 00:11:19,750
does that mean about the
sign of delta g?

189
00:11:19,750 --> 00:11:22,270
Greater or less than zero?

190
00:11:22,270 --> 00:11:27,060
Greater, so it'll be positive.

191
00:11:27,060 --> 00:11:31,950
So, we can think about that
in terms of a plot.

192
00:11:31,950 --> 00:11:39,790
We can think about free
energy versus the

193
00:11:39,790 --> 00:11:41,840
progress of the reaction.

194
00:11:41,840 --> 00:11:50,145
So, the progress of the
reaction is going this

195
00:11:50,145 --> 00:11:53,170
direction as you go along.

196
00:11:53,170 --> 00:12:02,810
So in the beginning if you have
pure reactants, delta g

197
00:12:02,810 --> 00:12:07,200
is going to be less than zero.

198
00:12:07,200 --> 00:12:11,950
And you're going to proceed
along in the forward direction

199
00:12:11,950 --> 00:12:14,550
spontaneously.

200
00:12:14,550 --> 00:12:20,690
If, on the other hand you have
pure products, delta g will be

201
00:12:20,690 --> 00:12:26,880
positive, so you'll be
spontaneous in the reverse

202
00:12:26,880 --> 00:12:31,880
direction, and the reaction
will go in the reverse

203
00:12:31,880 --> 00:12:38,180
direction until what happens?

204
00:12:38,180 --> 00:12:41,170
Till you reach equilibrium.

205
00:12:41,170 --> 00:12:44,810
And what would delta g
be at equilibrium?

206
00:12:44,810 --> 00:12:49,440
Zero.

207
00:12:49,440 --> 00:12:54,530
So you see, there is a great
relationship between delta g

208
00:12:54,530 --> 00:13:03,830
and equilibrium, so we have
not left delta g behind.

209
00:13:03,830 --> 00:13:08,230
So, delta g is going to change
as the components of the

210
00:13:08,230 --> 00:13:09,730
reaction change.

211
00:13:09,730 --> 00:13:13,500
As you have more products or
more reactants, you're going

212
00:13:13,500 --> 00:13:19,250
to have a different delta g.

213
00:13:19,250 --> 00:13:22,600
So let's look at
some equations.

214
00:13:22,600 --> 00:13:28,330
So delta g is the change in free
energy, the difference in

215
00:13:28,330 --> 00:13:32,460
free energy, at some point in
the reaction at any time with

216
00:13:32,460 --> 00:13:34,100
amount of composition.

217
00:13:34,100 --> 00:13:37,930
We also have delta g nought,
which talks about delta g

218
00:13:37,930 --> 00:13:41,360
under particular conditions, so
it's sort of the standard

219
00:13:41,360 --> 00:13:43,330
free energy.

220
00:13:43,330 --> 00:13:46,940
We have a term called q, which
is the reaction quotient,

221
00:13:46,940 --> 00:13:50,420
which tells you about products
and reactants.

222
00:13:50,420 --> 00:13:54,700
We have our friend r, which is
the gas constant, and this

223
00:13:54,700 --> 00:13:56,750
depends on temperature.

224
00:13:56,750 --> 00:14:00,040
So temperature is a term
involved here.

225
00:14:00,040 --> 00:14:04,350
So the delta g at any point in
the reaction is going to

226
00:14:04,350 --> 00:14:10,240
depend on the delta g nought
for that reaction, and the

227
00:14:10,240 --> 00:14:12,980
reaction quotient, products
and reactants, and we'll

228
00:14:12,980 --> 00:14:18,390
define this in a minute, and
then the temperature as well.

229
00:14:18,390 --> 00:14:22,790
So we need to know more about
what q is, what this reaction

230
00:14:22,790 --> 00:14:25,540
quotient is.

231
00:14:25,540 --> 00:14:29,760
So this slide looks a little bit
scary, but it's going to

232
00:14:29,760 --> 00:14:33,760
be fine, because a lot of the
terms are going to cancel out.

233
00:14:33,760 --> 00:14:38,140
So we're going to talk about q,
this reaction quotient, and

234
00:14:38,140 --> 00:14:40,650
we're going to have different
types of problems -- some

235
00:14:40,650 --> 00:14:42,840
where we're talking about
gases, and others we're

236
00:14:42,840 --> 00:14:45,510
talking about solutions.

237
00:14:45,510 --> 00:14:48,780
So you can see two different
kinds of q's, one that depends

238
00:14:48,780 --> 00:14:51,300
on partial pressure of the gas,
and another that depends

239
00:14:51,300 --> 00:14:52,870
on concentration.

240
00:14:52,870 --> 00:14:56,520
So here is our equation again
that we just saw -- delta g

241
00:14:56,520 --> 00:15:00,730
equals delta g nought plus r t
natural log of q, and here

242
00:15:00,730 --> 00:15:03,590
we've expanded the term for q.

243
00:15:03,590 --> 00:15:08,070
So p to the sub x is the
partial pressure of a

244
00:15:08,070 --> 00:15:11,930
particular gas, and so in this
equation, we have a plus b

245
00:15:11,930 --> 00:15:16,740
going to c plus d, the top of
the line or the products.

246
00:15:16,740 --> 00:15:19,660
So we have the partial pressure
of gas c, and this is

247
00:15:19,660 --> 00:15:23,660
over a reference, partial
pressure, raised to the power

248
00:15:23,660 --> 00:15:28,240
c, the coefficient, and then
also we have d, the partial

249
00:15:28,240 --> 00:15:31,030
pressure of gas d, over a
reference raised to the

250
00:15:31,030 --> 00:15:32,750
small letter d.

251
00:15:32,750 --> 00:15:35,890
On the bottom of the terms for
the reactants, partial

252
00:15:35,890 --> 00:15:38,842
pressure of gas a over a
reference raised to the

253
00:15:38,842 --> 00:15:42,150
coefficient a, partial pressure
of gas b over the

254
00:15:42,150 --> 00:15:46,020
reference raised to
the coefficient b.

255
00:15:46,020 --> 00:15:50,120
Now what's great is that the
partial pressure is one bar,

256
00:15:50,120 --> 00:15:54,100
and so that basically cancels
out as far as we're concerned.

257
00:15:54,100 --> 00:15:58,260
And so the term for q
is much simplified.

258
00:15:58,260 --> 00:16:01,980
You won't see problems that have
the reference in them, so

259
00:16:01,980 --> 00:16:04,200
you can just think about
q in terms of

260
00:16:04,200 --> 00:16:06,200
products over reactants.

261
00:16:06,200 --> 00:16:08,810
And you just have to remember
that the coefficients in the

262
00:16:08,810 --> 00:16:12,280
reactions do matter.

263
00:16:12,280 --> 00:16:15,110
If you're talking about
solutions, the only difference

264
00:16:15,110 --> 00:16:19,550
is that we'll be talking about
molar, so we have one molar,

265
00:16:19,550 --> 00:16:22,850
so the reference term here
also cancels out.

266
00:16:22,850 --> 00:16:26,720
When you see something in
brackets, like c in brackets,

267
00:16:26,720 --> 00:16:29,820
here that telling you it's
a concentration term.

268
00:16:29,820 --> 00:16:33,990
So here, q is the concentration
of c raised to

269
00:16:33,990 --> 00:16:34,530
its coefficiency.

270
00:16:34,530 --> 00:16:38,350
The concentration of
d raised to its

271
00:16:38,350 --> 00:16:40,080
coefficient d over reactants.

272
00:16:40,080 --> 00:16:43,395
Concentration of a to
a, concentration

273
00:16:43,395 --> 00:16:45,210
of b raised to b.

274
00:16:45,210 --> 00:16:51,510
So the thing in x indicates
it's a concentration term.

275
00:16:51,510 --> 00:16:55,860
So q is just products over
reactants, considering the

276
00:16:55,860 --> 00:17:01,310
stoichiometry of the particular
reaction.

277
00:17:01,310 --> 00:17:05,720
So what about the equilibrium
constant k?

278
00:17:05,720 --> 00:17:10,580
So at equilibrium you told me
that delta g equals zero, and

279
00:17:10,580 --> 00:17:15,100
at equilibrium q, the reaction
quotient equals k, the

280
00:17:15,100 --> 00:17:17,730
equilibrium constant.

281
00:17:17,730 --> 00:17:22,360
So we can consider that in terms
of this expression, if

282
00:17:22,360 --> 00:17:25,340
we're talking about this
expression at equilibrium,

283
00:17:25,340 --> 00:17:29,230
delta g is going
to equal zero.

284
00:17:29,230 --> 00:17:33,040
And so, we just set this whole
term equal to zero.

285
00:17:33,040 --> 00:17:36,600
We can rearrange the equation
bringing delta g nought to the

286
00:17:36,600 --> 00:17:39,570
other side.

287
00:17:39,570 --> 00:17:43,080
And so we have delta g at
nought equals minus r t

288
00:17:43,080 --> 00:17:49,660
natural log of K, because at
equilibrium, k is equal to q.

289
00:17:49,660 --> 00:17:54,160
So now we have another term to
solve for delta g, and an

290
00:17:54,160 --> 00:17:58,220
equation that relates delta
g nought to be equilibrium

291
00:17:58,220 --> 00:18:04,560
constant k.

292
00:18:04,560 --> 00:18:09,220
So k, the equilibrium's constant
has the same form as

293
00:18:09,220 --> 00:18:13,420
q, but we're only talking about
the concentrations or

294
00:18:13,420 --> 00:18:16,500
the partial pressures of
things at equilibrium.

295
00:18:16,500 --> 00:18:20,580
So it's the same, it's product
over reactants, same

296
00:18:20,580 --> 00:18:25,360
expressions as q, but in the
corner you say at equilibrium.

297
00:18:25,360 --> 00:18:28,570
So you're only talking about the
concentrations of things

298
00:18:28,570 --> 00:18:32,380
at equilibrium if you're
solving for k.

299
00:18:32,380 --> 00:18:35,490
If you're solving for q, it's
the concentration or the

300
00:18:35,490 --> 00:18:41,420
partial pressure at any time in
that particular reaction.

301
00:18:41,420 --> 00:18:46,780
Important thing, products
over reactants.

302
00:18:46,780 --> 00:18:51,630
All right, so, we can rewrite
the equation one more way.

303
00:18:51,630 --> 00:18:56,200
So I just told you that delta g
nought is equal to minus r t

304
00:18:56,200 --> 00:19:01,460
natural log of K. So we can
substitute into the expression

305
00:19:01,460 --> 00:19:05,950
minus r t natural log
of k, and now we can

306
00:19:05,950 --> 00:19:09,470
rearrange this equation.

307
00:19:09,470 --> 00:19:12,290
And so, if we rearrange it, we
have delta g, the delta g at

308
00:19:12,290 --> 00:19:16,400
any particular point in the
reaction equals r t natural

309
00:19:16,400 --> 00:19:19,140
log of q over k.

310
00:19:19,140 --> 00:19:22,630
And this equation is helpful for
people if they're thinking

311
00:19:22,630 --> 00:19:27,910
about what is the equilibrium
constant, what concentrations

312
00:19:27,910 --> 00:19:30,870
do I have now -- we're not
at equilibrium, what

313
00:19:30,870 --> 00:19:34,610
concentrations do I have now,
what is q now in the reaction,

314
00:19:34,610 --> 00:19:36,560
how does that compare to k?

315
00:19:36,560 --> 00:19:39,590
And when you know what those
values are, you'll know

316
00:19:39,590 --> 00:19:41,740
something about the direction of
the reaction because you'll

317
00:19:41,740 --> 00:19:43,690
know if delta g is positive
or negative.

318
00:19:43,690 --> 00:19:46,690
It'll to be spontaneous in the
forward direction or in the

319
00:19:46,690 --> 00:19:47,930
reverse direction.

320
00:19:47,930 --> 00:19:50,400
So this is a handy equation
for thinking about the

321
00:19:50,400 --> 00:19:55,320
relationship q k delta g.

322
00:19:55,320 --> 00:19:57,930
So let's think about that
relationship for a minute.

323
00:19:57,930 --> 00:20:08,980
If q is less than k, what
is the sign of delta g?

324
00:20:08,980 --> 00:20:13,950
So it would be negative, which
means the forward direction of

325
00:20:13,950 --> 00:20:16,360
the reaction will occur.

326
00:20:16,360 --> 00:20:20,200
So if you think about it, you
can think about in terms of

327
00:20:20,200 --> 00:20:22,580
products and reactants.

328
00:20:22,580 --> 00:20:28,140
So at equilibrium then, if q is
less than k at equilibrium,

329
00:20:28,140 --> 00:20:30,850
there are more products than
there are right now, so you

330
00:20:30,850 --> 00:20:32,650
need to make more products.

331
00:20:32,650 --> 00:20:35,110
So you would have delta g would
be negative, you'll see

332
00:20:35,110 --> 00:20:38,280
that mathematically, and you can
think about it in terms of

333
00:20:38,280 --> 00:20:39,510
whether you're going
to make more

334
00:20:39,510 --> 00:20:41,550
products or less products.

335
00:20:41,550 --> 00:20:45,280
If q is greater than
k, what is delta g?

336
00:20:45,280 --> 00:20:49,780
So it would be positive
and the reverse

337
00:20:49,780 --> 00:20:52,040
direction would occur.

338
00:20:52,040 --> 00:20:55,230
So you think that at q, if it's
larger than k, it has

339
00:20:55,230 --> 00:20:58,520
more products in its terms, and
at equilibrium there are

340
00:20:58,520 --> 00:21:01,930
less products, so you need to
go in a direction that will

341
00:21:01,930 --> 00:21:04,110
get rid of some of those
products so you'll reach

342
00:21:04,110 --> 00:21:06,740
equilibrium again.

343
00:21:06,740 --> 00:21:09,630
So this equation is very helpful
in thinking about the

344
00:21:09,630 --> 00:21:12,920
direction of the reaction --
which direction will it be

345
00:21:12,920 --> 00:21:15,840
spontaneous.

346
00:21:15,840 --> 00:21:18,560
So let's look at an example.

347
00:21:18,560 --> 00:21:22,730
K is given in this example, and
then we have a bunch of

348
00:21:22,730 --> 00:21:24,070
partial pressures.

349
00:21:24,070 --> 00:21:25,890
And we're asked which
direction the

350
00:21:25,890 --> 00:21:27,710
reaction will go.

351
00:21:27,710 --> 00:21:31,090
So what do I need to do to
answer this question, what do

352
00:21:31,090 --> 00:21:32,250
I need to calculate?

353
00:21:32,250 --> 00:21:40,950
So if I'm given k, and a bunch
of partial pressures, what do

354
00:21:40,950 --> 00:21:43,810
I first need to calculate?

355
00:21:43,810 --> 00:21:45,010
Q, right.

356
00:21:45,010 --> 00:21:49,120
So let's calculate q.

357
00:21:49,120 --> 00:21:53,110
So q, we're going to talk about
products over reactants,

358
00:21:53,110 --> 00:21:58,990
so we're going to talk about
be partial pressure of the

359
00:21:58,990 --> 00:22:04,150
ammonia, and there are two
of them being formed.

360
00:22:04,150 --> 00:22:07,960
Our reactants, we want to talk
about the partial pressure of

361
00:22:07,960 --> 00:22:13,690
the nitrogen, and the partial
pressure of the hydrogen gas,

362
00:22:13,690 --> 00:22:19,360
and again include the
stoichiometry, so we have

363
00:22:19,360 --> 00:22:21,460
three there.

364
00:22:21,460 --> 00:22:26,740
So now I can plug in my values,
so I'm told I have 1 .

365
00:22:26,740 --> 00:22:32,280
1 bar, and down here I have 5 .

366
00:22:32,280 --> 00:22:35,170
5 and 2 .

367
00:22:35,170 --> 00:22:41,590
2 to the 3, again, considering
the stoichiometry.

368
00:22:41,590 --> 00:22:44,290
And if you do the math,
you get 2 .

369
00:22:44,290 --> 00:22:48,140
1 times 10 to the minus 2.

370
00:22:48,140 --> 00:22:49,550
That's your q value.

371
00:22:49,550 --> 00:22:54,480
Now given your k value, which
the problem states, and this q

372
00:22:54,480 --> 00:22:57,860
value, let's do a clicker
question, tell me which

373
00:22:57,860 --> 00:23:17,020
direction the reaction
will go.

374
00:23:17,020 --> 00:23:40,470
All right, 10 seconds.

375
00:23:40,470 --> 00:23:43,330
So, 77%, pretty good.

376
00:23:43,330 --> 00:23:48,640
So, q is greater than k here.

377
00:23:48,640 --> 00:23:52,910
And if q is greater than
k, what will be

378
00:23:52,910 --> 00:23:54,580
true about delta g?

379
00:23:54,580 --> 00:24:09,540
I have another clicker question
for that -- yell out

380
00:24:09,540 --> 00:24:14,950
the answer.

381
00:24:14,950 --> 00:24:16,310
What is it?

382
00:24:16,310 --> 00:24:17,370
Positive, right.

383
00:24:17,370 --> 00:24:21,370
So you're going to shift towards
reactants, so you're

384
00:24:21,370 --> 00:24:23,540
going to go in the reverse
direction.

385
00:24:23,540 --> 00:24:27,570
So you think about whether there
are more products or

386
00:24:27,570 --> 00:24:32,340
less products at equilibrium,
and so there are more

387
00:24:32,340 --> 00:24:36,790
products, so we have to think
about which direction it'll

388
00:24:36,790 --> 00:24:52,290
go, and here, ammonium will
dissociate until equilibrium

389
00:24:52,290 --> 00:25:08,410
is reached again.

390
00:25:08,410 --> 00:25:10,280
OK.

391
00:25:10,280 --> 00:25:17,480
So let's think more about what
k is going to tell us.

392
00:25:17,480 --> 00:25:20,860
So k tells us about the mixture
of products and

393
00:25:20,860 --> 00:25:25,240
reactants at equilibrium,
whether we can expect low or

394
00:25:25,240 --> 00:25:32,570
high concentration of reactants
at equilibrium.

395
00:25:32,570 --> 00:25:42,800
So let's look at another
example.

396
00:25:42,800 --> 00:25:50,890
So when you have k that's
greater than one, so more

397
00:25:50,890 --> 00:25:54,400
products than reactants at
equilibrium, you can think

398
00:25:54,400 --> 00:26:02,560
about this in terms of higher
products at equilibrium.

399
00:26:02,560 --> 00:26:13,765
When you have k less than
one, we're going

400
00:26:13,765 --> 00:26:17,770
to have lower products.

401
00:26:17,770 --> 00:26:24,440
So again, think about k in
terms of products over

402
00:26:24,440 --> 00:26:35,070
reactants at equilibrium.

403
00:26:35,070 --> 00:26:37,440
So if k is greater than
one, there are more

404
00:26:37,440 --> 00:26:39,060
products than reactants.

405
00:26:39,060 --> 00:26:41,320
If it's less than one,
there will be less

406
00:26:41,320 --> 00:27:05,000
reactants than products.

407
00:27:05,000 --> 00:27:07,060
So let's look at an
example of that.

408
00:27:07,060 --> 00:27:13,850
Let's look at when k is
greater than one.

409
00:27:13,850 --> 00:27:16,025
And I have the equation
up there and I'll

410
00:27:16,025 --> 00:27:17,910
write it here as well.

411
00:27:17,910 --> 00:27:28,420
So we have 2 n o 2, and two
double arrows, and n 2 o 4.

412
00:27:28,420 --> 00:27:34,690
So we have a k value
here of 6 .

413
00:27:34,690 --> 00:27:40,720
84, so that's greater
than one value.

414
00:27:40,720 --> 00:27:44,640
So let's think about
this reaction.

415
00:27:44,640 --> 00:27:47,920
So over here instead of
concentration, we're going to

416
00:27:47,920 --> 00:27:51,000
talk about partial pressure
because we're talking about

417
00:27:51,000 --> 00:27:56,400
gas, and we have time.

418
00:27:56,400 --> 00:28:01,250
So initially we have
a reactant.

419
00:28:01,250 --> 00:28:04,540
And the reactant starts at
some concentration and

420
00:28:04,540 --> 00:28:12,160
decreases and then reaches a
straight line, so reaches

421
00:28:12,160 --> 00:28:13,730
equilibrium.

422
00:28:13,730 --> 00:28:19,250
So we have our reactant here.

423
00:28:19,250 --> 00:28:24,250
Originally we have no product,
and so product is going to go

424
00:28:24,250 --> 00:28:28,940
up and be formed and then it's
going to level off as you

425
00:28:28,940 --> 00:28:35,350
reach equilibrium.

426
00:28:35,350 --> 00:28:42,380
So initially, what is
true about q and k?

427
00:28:42,380 --> 00:28:57,260
So with no products, what
is true about q and k?

428
00:28:57,260 --> 00:29:00,090
Q is less than k.

429
00:29:00,090 --> 00:29:03,760
And so what's true
about delta g?

430
00:29:03,760 --> 00:29:06,060
Less than zero, it'll be
negative, so it'll be

431
00:29:06,060 --> 00:29:08,540
spontaneous in the forward
direction.

432
00:29:08,540 --> 00:29:10,510
So you're going to be
spontaneous in the forward

433
00:29:10,510 --> 00:29:15,190
direction and you're going
to make your product.

434
00:29:15,190 --> 00:29:21,630
So now let's calculate what the
concentrations are going

435
00:29:21,630 --> 00:29:25,700
to be at equilibrium.

436
00:29:25,700 --> 00:29:37,680
So initially, so you have your
initial pressure for the

437
00:29:37,680 --> 00:29:48,510
reaction, 2 n o 2 going to
n 2 o 2, and our initial

438
00:29:48,510 --> 00:29:54,470
concentrations are
given as one bar,

439
00:29:54,470 --> 00:29:59,910
and we have no product.

440
00:29:59,910 --> 00:30:07,290
Now we talk about the change as
we go toward equilibrium,

441
00:30:07,290 --> 00:30:12,380
how much does the
reactant change?

442
00:30:12,380 --> 00:30:13,400
What do I write here?

443
00:30:13,400 --> 00:30:16,670
What change?

444
00:30:16,670 --> 00:30:20,660
Minus x minus something x?

445
00:30:20,660 --> 00:30:21,890
Minus 2 x.

446
00:30:21,890 --> 00:30:24,150
So again, we're considering
the stoichiometry,

447
00:30:24,150 --> 00:30:27,680
and what's over here?

448
00:30:27,680 --> 00:30:38,380
So just plus x, and then at
equilibrium we now have 1

449
00:30:38,380 --> 00:30:46,980
minus 2 x and x.

450
00:30:46,980 --> 00:30:50,000
So we're talking about
equilibrium concentrations, so

451
00:30:50,000 --> 00:30:54,690
we're talking about
k, so k equals 6 .

452
00:30:54,690 --> 00:30:59,600
84, which is going to be equal
to the partial pressure of the

453
00:30:59,600 --> 00:31:03,430
product over the partial
pressure of

454
00:31:03,430 --> 00:31:07,980
the reactant squared.

455
00:31:07,980 --> 00:31:18,400
So it's going to be equal to
x over 1 minus 2 x squared.

456
00:31:18,400 --> 00:31:27,030
So x, if you calculate it out,
should equal point 381 bar.

457
00:31:27,030 --> 00:31:37,910
And then if we do 1 minus 2
times 0.381 bar, we get 0 .

458
00:31:37,910 --> 00:31:43,450
238 bar.

459
00:31:43,450 --> 00:31:50,170
So if we go back over here, our
products at equilibrium --

460
00:31:50,170 --> 00:31:57,440
oh, I guess I should write what
-- so x is our product

461
00:31:57,440 --> 00:32:02,510
and this is our reactant.

462
00:32:02,510 --> 00:32:07,360
So the product we have 0 .

463
00:32:07,360 --> 00:32:12,140
381, and our reactant
at equilibrium is

464
00:32:12,140 --> 00:32:18,020
going to be 0.238 bar.

465
00:32:18,020 --> 00:32:23,760
So we have more product than
reactant at equilibrium, which

466
00:32:23,760 --> 00:32:29,500
is consistent with the value of
k being greater than one.

467
00:32:29,500 --> 00:32:31,910
So, when you know something
about the equilibrium

468
00:32:31,910 --> 00:32:35,620
constant, you know something
about the reaction and whether

469
00:32:35,620 --> 00:32:44,690
you would expect more products
or reactants at equilibrium.

470
00:32:44,690 --> 00:32:50,900
So again, you can think about
this in terms of q and k.

471
00:32:50,900 --> 00:32:53,500
All right, so now we are
going to go toward our

472
00:32:53,500 --> 00:32:56,410
next clicker question.

473
00:32:56,410 --> 00:33:01,460
So if we can rewrite the
expression for delta g equals

474
00:33:01,460 --> 00:33:06,940
minus r t natural log of k, and
express it in terms of k,

475
00:33:06,940 --> 00:33:09,960
and now we can think about
then what is that

476
00:33:09,960 --> 00:33:10,940
relationship.

477
00:33:10,940 --> 00:33:15,110
If you have a large value for
k, what do you expect to be

478
00:33:15,110 --> 00:33:36,870
true about delta g nought?

479
00:33:36,870 --> 00:33:53,880
All right, let's give
that 10 seconds.

480
00:33:53,880 --> 00:33:56,770
OK, why don't you discuss for
a minute with your friends

481
00:33:56,770 --> 00:34:17,740
whether you agree with
that 78% or not.

482
00:34:17,740 --> 00:34:47,250
All right, now we're going to
re-poll, so click in again.

483
00:34:47,250 --> 00:34:53,850
Now give the right answer.

484
00:34:53,850 --> 00:34:57,400
Interesting.

485
00:34:57,400 --> 00:35:00,280
It actually usually goes the
other direction, that after

486
00:35:00,280 --> 00:35:03,400
there's a discussion, more
people come to the same

487
00:35:03,400 --> 00:35:04,560
conclusion.

488
00:35:04,560 --> 00:35:07,860
So I guess it's a matter of if
the professor asks that, you

489
00:35:07,860 --> 00:35:10,510
assume that that must have
been the wrong answer.

490
00:35:10,510 --> 00:35:16,500
Was that people's logic?

491
00:35:16,500 --> 00:35:19,230
So what are the points of doing
this, and we're going to

492
00:35:19,230 --> 00:35:22,870
actually do this kind of thing
a few more times in class, is

493
00:35:22,870 --> 00:35:27,670
that collectively, and I was
actually just at an education

494
00:35:27,670 --> 00:35:31,510
meeting about science down at
the Howard Hughes Medical

495
00:35:31,510 --> 00:35:35,870
Institute, that statistics show
that if you have a group

496
00:35:35,870 --> 00:35:38,660
where everyone in the group
has the wrong answer and

497
00:35:38,660 --> 00:35:41,360
they're allowed to discuss it,
there's a good chance they'll

498
00:35:41,360 --> 00:35:43,000
come up with the right answer.

499
00:35:43,000 --> 00:35:46,520
So that it's not just about one
person in the group having

500
00:35:46,520 --> 00:35:48,690
the right answer, convincing
everyone else that they're

501
00:35:48,690 --> 00:35:51,300
right, that the act of
discussing often

502
00:35:51,300 --> 00:35:53,300
leads to new answers.

503
00:35:53,300 --> 00:35:58,010
So now that you know that it's
not a trick on my part to tell

504
00:35:58,010 --> 00:36:01,950
you you got it wrong, we'll see
next time whether this, in

505
00:36:01,950 --> 00:36:06,430
fact, holds, that the act of
discussing helps give the

506
00:36:06,430 --> 00:36:07,780
right answer.

507
00:36:07,780 --> 00:36:13,290
Anyway, so if k is large, it
is true that delta g nought

508
00:36:13,290 --> 00:36:16,810
would tend to be negative and
more -- it would be negative

509
00:36:16,810 --> 00:36:19,800
and more on the large side.

510
00:36:19,800 --> 00:36:23,080
So one can think about if
there's more products over

511
00:36:23,080 --> 00:36:26,180
reactants, that's going to
indicate something about the

512
00:36:26,180 --> 00:36:30,150
delta g nought for the reaction,
and the k -- the k,

513
00:36:30,150 --> 00:36:32,935
if it's greater than 1, if it's
a big number, then there

514
00:36:32,935 --> 00:36:36,100
are more products than
reactants, and delta g nought

515
00:36:36,100 --> 00:36:39,290
would be negative and would
tend to be a large number.

516
00:36:39,290 --> 00:36:45,430
All right, so this is more
actually kind of simple

517
00:36:45,430 --> 00:36:50,840
bookkeeping involved that
if you know steps in the

518
00:36:50,840 --> 00:36:54,780
reactions and you know
equilibrium constants, you can

519
00:36:54,780 --> 00:36:57,350
calculate an overall
equilibrium

520
00:36:57,350 --> 00:36:59,660
constant for that reaction.

521
00:36:59,660 --> 00:37:02,650
So you can write a reaction
as the sum of different

522
00:37:02,650 --> 00:37:05,060
components.

523
00:37:05,060 --> 00:37:11,080
And so up here, we are going to
try to add these first two

524
00:37:11,080 --> 00:37:13,990
equations to get this
net equation.

525
00:37:13,990 --> 00:37:22,610
So we have 2 gas p 3 c l 2 going
to 2 p l c 3, and that's

526
00:37:22,610 --> 00:37:23,960
equilibrium 1.

527
00:37:23,960 --> 00:37:27,010
And so then in the next
reaction, some of that is

528
00:37:27,010 --> 00:37:31,670
being consumed reacting with
another c l 2, giving you p c

529
00:37:31,670 --> 00:37:38,000
l 5, and the net reaction we're
interested in has 2 p 5

530
00:37:38,000 --> 00:37:41,720
c l 2's going to 2 p c l 5.

531
00:37:41,720 --> 00:37:45,720
All right, what do I have to
do before I can add these

532
00:37:45,720 --> 00:37:52,460
together effectively and
have things cancel out?

533
00:37:52,460 --> 00:37:55,450
I need to multiply what?

534
00:37:55,450 --> 00:37:59,150
Second equation by 2, yeah.

535
00:37:59,150 --> 00:38:06,870
So to get that to work I would
need to have 2's there, then

536
00:38:06,870 --> 00:38:11,080
this is going to cancel out and
these will add up, so we

537
00:38:11,080 --> 00:38:15,630
have 5 and then we have two
of the main products.

538
00:38:15,630 --> 00:38:20,680
So if I do that, and I have the
equilibrium constant for

539
00:38:20,680 --> 00:38:24,120
one and for two, how am I
going to get equilibrium

540
00:38:24,120 --> 00:38:28,970
constant for three?

541
00:38:28,970 --> 00:38:36,710
I'm going to multiply
k 1 by k 2 and k 2.

542
00:38:36,710 --> 00:38:40,160
So I'm going to have to multiply
k 2 in there twice,

543
00:38:40,160 --> 00:38:44,050
because there's two of those
-- we'd multiply that up.

544
00:38:44,050 --> 00:38:48,460
So if you have different parts
of reactions and you can sum

545
00:38:48,460 --> 00:38:52,390
them together, then you can
multiply out the individual

546
00:38:52,390 --> 00:38:55,870
k's to get the new value of k.

547
00:38:55,870 --> 00:38:59,410
So that's something that's just
useful that you'll run

548
00:38:59,410 --> 00:39:05,690
into in doing these
types of problems.

549
00:39:05,690 --> 00:39:07,510
All right.

550
00:39:07,510 --> 00:39:10,950
Now we're going to
think about how

551
00:39:10,950 --> 00:39:16,510
equilibriums respond to stress.

552
00:39:16,510 --> 00:39:19,150
And I always feel like
I need to pause.

553
00:39:19,150 --> 00:39:24,500
MIT students, you guys are some
of the smartest, most

554
00:39:24,500 --> 00:39:27,160
talented scientists
in the world.

555
00:39:27,160 --> 00:39:30,090
I don't know if you fully
appreciate how

556
00:39:30,090 --> 00:39:32,140
smart you all are.

557
00:39:32,140 --> 00:39:39,300
But this concept is tough
for MIT students.

558
00:39:39,300 --> 00:39:43,340
So Le Chatelier's principle
says that a system in

559
00:39:43,340 --> 00:39:49,260
equilibrium that is subjected to
with stress tends to react

560
00:39:49,260 --> 00:39:57,570
in such a way to minimize
that stress.

561
00:39:57,570 --> 00:40:00,550
I have advisees coming to
my office saying, "I'm

562
00:40:00,550 --> 00:40:03,620
double-majoring in this and
that and I'm taking five

563
00:40:03,620 --> 00:40:07,880
classes and I have UROP and I
have this lab exercise --

564
00:40:07,880 --> 00:40:10,730
I don't know what's going on,
so I've been thinking a lot

565
00:40:10,730 --> 00:40:17,160
about it and I think I should
add a third major." Le

566
00:40:17,160 --> 00:40:20,610
Chatelier would be very
unhappy with that.

567
00:40:20,610 --> 00:40:25,930
Le Chatelier would say that the
appropriate response is to

568
00:40:25,930 --> 00:40:33,510
drop one of the majors, to
minimize the stress.

569
00:40:33,510 --> 00:40:37,160
So in doing these problems, what
I want to encourage you

570
00:40:37,160 --> 00:40:42,480
to do is think the opposite
of what you would do.

571
00:40:42,480 --> 00:40:45,900
Minimize the stress.

572
00:40:45,900 --> 00:40:48,200
If you think about that
you'll be all set.

573
00:40:48,200 --> 00:40:50,040
All right.

574
00:40:50,040 --> 00:40:55,440
So Le Chatelier's principle
actually is very useful.

575
00:40:55,440 --> 00:40:59,480
If you think about minimizing
the stress, you'll be able to

576
00:40:59,480 --> 00:41:04,030
predict the direction that
the reaction will shift.

577
00:41:04,030 --> 00:41:06,910
So the reaction's going to shift
in a way to minimize the

578
00:41:06,910 --> 00:41:09,390
stress, so you can predict it.

579
00:41:09,390 --> 00:41:12,250
If you're thinking along these
lines, you say, oh, that

580
00:41:12,250 --> 00:41:16,060
system was stressed, and then
you can think about how that

581
00:41:16,060 --> 00:41:19,370
reaction or that system
is going to respond.

582
00:41:19,370 --> 00:41:24,380
So let's give some examples.

583
00:41:24,380 --> 00:41:29,230
So, we have a system in
equilibrium -- we started out,

584
00:41:29,230 --> 00:41:31,600
we had our nitrogen
and our hydrogen

585
00:41:31,600 --> 00:41:33,110
and we had no product.

586
00:41:33,110 --> 00:41:36,080
We reacted the hydrogen and the
nitrogen, their forming

587
00:41:36,080 --> 00:41:39,800
products, and eventually they
reach equilibrium, their delta

588
00:41:39,800 --> 00:41:43,510
g equals zero there's still
the reaction going on, but

589
00:41:43,510 --> 00:41:45,530
there's no net change.

590
00:41:45,530 --> 00:41:49,990
All right, now the system
is going to be stressed.

591
00:41:49,990 --> 00:41:54,670
So we're going to add
more of a reactant.

592
00:41:54,670 --> 00:41:59,720
How will the system react
to minimize that stress?

593
00:41:59,720 --> 00:42:00,410
What is it going to do?

594
00:42:00,410 --> 00:42:05,930
It now has too much of
one of the reactants.

595
00:42:05,930 --> 00:42:09,530
You'll form more products, and
that's going to use up some of

596
00:42:09,530 --> 00:42:12,505
your other reactant, which will
go down, and you're going

597
00:42:12,505 --> 00:42:16,940
to form more product until
equilibrium is reached again.

598
00:42:16,940 --> 00:42:21,050
And one thing that I'll mention
that the ratio has to

599
00:42:21,050 --> 00:42:21,660
be the same.

600
00:42:21,660 --> 00:42:25,000
The equilibrium constant is
a constant given the same

601
00:42:25,000 --> 00:42:27,610
temperature, but you're not
necessarily always going to

602
00:42:27,610 --> 00:42:30,060
have the same concentrations,
but you should have the same

603
00:42:30,060 --> 00:42:32,710
ratios, the same value of k.

604
00:42:32,710 --> 00:42:37,200
All right, so what about if you
add more product, what's

605
00:42:37,200 --> 00:42:40,120
going to happen?

606
00:42:40,120 --> 00:42:43,940
What direction will the
reaction shift?

607
00:42:43,940 --> 00:42:47,160
Right, it's going to shift
toward the reactants, so

608
00:42:47,160 --> 00:42:51,150
you're going to make more of
each of the two reactants

609
00:42:51,150 --> 00:42:54,920
until again, you find your
equilibrium again.

610
00:42:54,920 --> 00:42:57,830
And then the reaction's still
going but there's no net

611
00:42:57,830 --> 00:42:59,490
change anymore.

612
00:42:59,490 --> 00:43:02,800
All right, so let's think about
this -- let's think

613
00:43:02,800 --> 00:43:05,440
about this in terms of
the math as well.

614
00:43:05,440 --> 00:43:09,060
If you want to stick with the
math, that's OK, you can think

615
00:43:09,060 --> 00:43:12,350
about calculating
delta g's here.

616
00:43:12,350 --> 00:43:14,840
So if you're a system in
equilibrium and you add more

617
00:43:14,840 --> 00:43:17,490
hydrogen, the system
will respond to

618
00:43:17,490 --> 00:43:19,390
minimize that increase.

619
00:43:19,390 --> 00:43:23,490
So it's going to make more
product that will minimize the

620
00:43:23,490 --> 00:43:26,930
increase, it shifts
to the right.

621
00:43:26,930 --> 00:43:31,390
And this can be explained
in terms of q and k.

622
00:43:31,390 --> 00:43:34,150
So, you can think about,
again, do you have more

623
00:43:34,150 --> 00:43:39,130
products now or did you have
more products at equilibrium,

624
00:43:39,130 --> 00:43:43,990
and if you're adding more
reactants, momentarily q will

625
00:43:43,990 --> 00:43:47,740
become less than k.

626
00:43:47,740 --> 00:43:52,260
And so, you would get a negative
delta g, which would

627
00:43:52,260 --> 00:43:56,640
make it spontaneous in the
forward direction.

628
00:43:56,640 --> 00:44:00,210
So some people like to think
about this in terms of delta g

629
00:44:00,210 --> 00:44:03,100
equals r t natural
log of q over k.

630
00:44:03,100 --> 00:44:08,040
So you think about if q is less
than k, what sign you

631
00:44:08,040 --> 00:44:10,780
have for delta g, and that's
tells you whether the reaction

632
00:44:10,780 --> 00:44:14,310
is spontaneous in the forward
or the reverse direction.

633
00:44:14,310 --> 00:44:17,030
And let me just give you
one hint for taking

634
00:44:17,030 --> 00:44:19,380
exams in this unit.

635
00:44:19,380 --> 00:44:23,340
That use of the arrow is really
good, or saying "toward

636
00:44:23,340 --> 00:44:26,440
product" or "reactant." I can't
tell you how many people

637
00:44:26,440 --> 00:44:29,500
write -- know what the answer
is and write left when mean

638
00:44:29,500 --> 00:44:32,350
right, or write right
when they mean left.

639
00:44:32,350 --> 00:44:36,350
But if you draw an arrow you
never really get it wrong, and

640
00:44:36,350 --> 00:44:39,640
when you say products or
reactants it's a lot harder to

641
00:44:39,640 --> 00:44:41,610
make that mistake.

642
00:44:41,610 --> 00:44:44,610
So if you're not good with right
or left, which let me

643
00:44:44,610 --> 00:44:48,040
tell you a large fraction of
people are not, hedge your

644
00:44:48,040 --> 00:44:49,950
bets, you can write everything,
more products,

645
00:44:49,950 --> 00:44:53,100
arrows, and then write if you
want, then you're pretty sure

646
00:44:53,100 --> 00:44:55,930
that you have it all in there.

647
00:44:55,930 --> 00:44:56,810
OK.

648
00:44:56,810 --> 00:45:03,050
So again, we can explain this
in terms of q or k.

649
00:45:03,050 --> 00:45:04,990
All right.

650
00:45:04,990 --> 00:45:08,880
So let's just quickly talk about
adding more products.

651
00:45:08,880 --> 00:45:10,040
We did this already.

652
00:45:10,040 --> 00:45:13,260
If more products are added. then
q is going to be greater

653
00:45:13,260 --> 00:45:17,730
than k momentarily, and you
would shift toward reactants,

654
00:45:17,730 --> 00:45:25,480
shift toward the left, and
again, we saw that down there.

655
00:45:25,480 --> 00:45:29,250
So tell me a final clicker
question and then we're done.

656
00:45:29,250 --> 00:45:53,610
What happens if you remove
products and why?

657
00:45:53,610 --> 00:46:02,930
OK, 10 seconds.

658
00:46:02,930 --> 00:46:07,540
See if we can get in the 90's.

659
00:46:07,540 --> 00:46:10,080
No, no 90's today, we'll have
to do it next time,

660
00:46:10,080 --> 00:46:12,430
but we got 73 right.

661
00:46:12,430 --> 00:46:16,380
So we're going to make more
products as well.