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CATHERINE DRENNAN:
So radioactive decay

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is kind of a classic example
of a first-order process.

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So we are doing one
little tiny section

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of the chapter on
nuclear chemistry,

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and we're doing that all today.

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And so all we're really
covering is problems associated

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with first-order processes.

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So this is just a small
introduction to this idea.

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So radioactive decay has
a lot of applications.

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There are medical applications,
including imaging organs

00:00:56.910 --> 00:00:59.000
and bones, including the heart.

00:00:59.000 --> 00:01:02.160
And so there is a compound
that you already saw

00:01:02.160 --> 00:01:03.740
called Cardiolite.

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And so we talked about
this in transition metals

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because you have a
transition metal.

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And what is the geometry
of this compound?

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Octahedral, and we have
cyanide ligands, which

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what kind of field strength?

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Strong.

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Yeah.

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So this compound
was designed in part

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by an MIT professor,
Alan Davison.

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You could go talk to him about
this incredible discovery

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and invention.

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It's used about seven
million times a year

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or to image various organs and
has been for a very long time.

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It's off patent now.

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But this patent made Allen
Davison, MIT, and MIT Chemistry

00:01:45.970 --> 00:01:48.020
Department an enormous
amount of money.

00:01:48.020 --> 00:01:49.740
And so you could go
talk to him about it,

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except he's happily retired
living in one of his homes.

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[LAUGHTER]

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So you can't really do that.

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But anyway, so this uses
an isotope of technetium,

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which is metastable isotope.

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And so it's 99.

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It's an isotope of the
normal 98 atomic mass.

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And so the next
challenge, you're

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always looking for
the next great thing,

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the next great imaging agent.

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So this is still a very
active area of research,

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and there's actually a talk just
this week on campus about work

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in this area.

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So this is transition metals
combined with radioactivity.

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So it's two topics
here in the class.

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So another, of
course, important use

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is the potential
of nuclear energy

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and the current use
of nuclear energy.

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This has many
challenges, and I don't

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want to go on record of what
I think about nuclear energy.

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I think it's a
complicated problem.

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There are a lot of challenges.

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But one I'd like to
bring up, because I think

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it's particularly
interesting to me,

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is what to do with the waste.

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And so one story that I
heard about actually there

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was a documentary
made about this.

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Finland had this idea to create
this three-mile long tunnel,

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and they wanted to store 12,000
metric tons of nuclear waste.

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And they wanted the containers
to store it for 100,000 years.

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And this documentary asked
a number of questions

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about this idea, such as, what
kind of container do you use,

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and how do you know the material
you design your container is

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going to last 100,000 years?

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As experimental
scientists, we like

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to test how long things last.

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But you can't really
do this experiment.

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Also, it kind of
brought up the idea,

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do you guard this facility
for 100,000 years?

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Because you can make bombs out
of a lot of this radioactive

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waste.

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So you kind of
need to protect it.

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But maybe you
should just bury it

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and then no one knows
it's there so you

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don't have to guard it so
they can't find it and use it.

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But then what if
someone stumbles upon it

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and releases all of
this radioactivity?

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So that would be bad.

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So do you put warning
signs for people

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who will be around 100,000 years
from now, saying, hey, don't

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go in here.

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It looks like a pretty tunnel.

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But, hey, the half-life
of the thing stored here

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are 100,000 years.

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So this is pretty
radioactive still.

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Don't go inside.

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And if you write this sign,
what language do you put it in?

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So the documentary pointed
out that Neanderthals

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existed like 40,000 years ago.

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So 100,000 years from now,
what's going to be going on?

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How do you write a sign to
people that long in the future?

00:04:36.070 --> 00:04:39.130
Anyway, I just think that these
are sort of interesting ideas

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and brings up the point that
as scientists and engineers,

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we need to think not
only about the science

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and engineering of
what we're doing,

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but the ramifications to
society and the sociology

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as well as politics involved
in some of this science.

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So this is an interesting
area for that intersection

00:04:57.970 --> 00:05:00.950
of the social sciences
and the natural sciences

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and engineering.

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So radioactive
decay-- definitely

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a useful thing, dangerous and
useful all at the same time.

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Oh, look at that.

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You know the clicker
question's coming up

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at the bottom of the page.

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We're not there yet.

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It's OK.

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We're not there yet.

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I just added that at
the end and apparently

00:05:20.970 --> 00:05:23.130
didn't animate it well.

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So the decay of a nucleus is
independent of how many nuclei

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are around it.

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That's what makes it
a first-order process.

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So because it's a
first-order process,

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we can apply those first-order
integrated rate laws

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that we just derived.

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So we had our rate log of the
concentration of something

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A equals its original
concentration

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to the e to minus k, which is
our rate constant times time

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and also our half-life
equation that we just used.

00:05:53.240 --> 00:05:55.945
So instead of
concentration of A,

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though, we're going to
have a different thing

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to express what we're
interested in here, which

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is N, the number of nuclei.

00:06:05.020 --> 00:06:08.990
So we can just write that
same expression down.

00:06:08.990 --> 00:06:10.640
But instead of
concentration of A,

00:06:10.640 --> 00:06:12.750
we're just going to
use capital N. So

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N, the number of nuclei
at some particular time,

00:06:15.570 --> 00:06:19.680
equals how many nuclei were
present originally times e

00:06:19.680 --> 00:06:21.010
to the minus k.

00:06:21.010 --> 00:06:23.080
And here it is a
rate constant still,

00:06:23.080 --> 00:06:26.480
but it's a decay constant in
that the rate you're measuring

00:06:26.480 --> 00:06:28.290
is radioactive decay.

00:06:28.290 --> 00:06:29.760
So it kind of has
a special name.

00:06:29.760 --> 00:06:31.593
Although, if you use
rate constant for that,

00:06:31.593 --> 00:06:34.480
that is what it
is, so that's OK.

00:06:34.480 --> 00:06:35.820
t is still time.

00:06:35.820 --> 00:06:40.870
And yes, N to the o is the
original number of nuclei.

00:06:40.870 --> 00:06:43.240
So we're just going to
do a clicker question

00:06:43.240 --> 00:06:45.530
about how one goes
about calculating

00:06:45.530 --> 00:06:46.940
the number of nuclei.

00:06:58.670 --> 00:06:59.363
10 more seconds.

00:07:16.080 --> 00:07:21.790
So someone want to tell me
for one of the Green Lantern

00:07:21.790 --> 00:07:29.450
T-shirts, what is wrong
with the other answers?

00:07:29.450 --> 00:07:31.279
I think I saw your
hand up first.

00:07:31.279 --> 00:07:31.820
Sorry, folks.

00:07:37.237 --> 00:07:38.070
AUDIENCE: Let's see.

00:07:38.070 --> 00:07:40.320
So answers one
and two, they have

00:07:40.320 --> 00:07:44.840
the wrong-- what was it--
the molar mass of technetium.

00:07:44.840 --> 00:07:45.700
Is that technetium?

00:07:45.700 --> 00:07:50.352
Yeah And answer four does not
multiply by Avogadro's number.

00:07:50.352 --> 00:07:52.310
So that's going to give
you the number of moles

00:07:52.310 --> 00:07:53.370
of the particle.

00:07:53.370 --> 00:07:54.411
CATHERINE DRENNAN: Right.

00:07:54.411 --> 00:07:56.400
Great job.

00:07:56.400 --> 00:07:57.190
It's Thanksgiving.

00:07:57.190 --> 00:08:00.650
I thought we needed
a good prize today.

00:08:00.650 --> 00:08:02.060
So right.

00:08:02.060 --> 00:08:05.110
So one thing you
also want to remember

00:08:05.110 --> 00:08:07.740
make sure that your
units are good.

00:08:07.740 --> 00:08:09.770
And it's really
important in doing

00:08:09.770 --> 00:08:12.890
this-- you can take
this back-- to remember

00:08:12.890 --> 00:08:18.990
to use the number that is here,
this atomic mass number, not

00:08:18.990 --> 00:08:23.786
the one from the periodic table
in calculating the problem.

00:08:23.786 --> 00:08:25.910
Actually, the periodic
table disappeared from that.

00:08:25.910 --> 00:08:26.910
Oh, well.

00:08:26.910 --> 00:08:30.940
So if you use the periodic
table, it's a close answer

00:08:30.940 --> 00:08:32.340
but sometimes.

00:08:32.340 --> 00:08:34.080
Sometimes it won't be so close.

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But remember, when it tells
you about the isotope,

00:08:37.590 --> 00:08:40.880
it always has the
atomic mass that you

00:08:40.880 --> 00:08:43.780
should be using in the problem
as part of the questions.

00:08:43.780 --> 00:08:45.610
So keep that in mind.

00:08:45.610 --> 00:08:48.370
And yeah, you definitely want
to remember Avogadro's number.

00:08:48.370 --> 00:08:49.930
And the answers
are such that it's

00:08:49.930 --> 00:08:51.679
hard to tell that you messed up.

00:08:51.679 --> 00:08:53.220
With the wavelength,
it's really easy

00:08:53.220 --> 00:08:55.410
to tell you messed up if you
didn't use Avogadro's number

00:08:55.410 --> 00:08:56.826
because it doesn't
make any sense.

00:08:56.826 --> 00:08:58.920
With these, it's
a little harder.

00:08:58.920 --> 00:09:02.180
So remember to use the
isotope's atomic mass

00:09:02.180 --> 00:09:04.180
and also remember to
use Avogadro's number

00:09:04.180 --> 00:09:05.190
when doing this.

00:09:05.190 --> 00:09:08.610
And then you should be fine.

00:09:08.610 --> 00:09:10.140
So this is really similar.

00:09:10.140 --> 00:09:12.140
It's really similar,
depending on whether you're

00:09:12.140 --> 00:09:16.160
talking about chemical
kinetics or nuclear kinetics

00:09:16.160 --> 00:09:20.020
in doing these problems
in terms of the equations.

00:09:20.020 --> 00:09:25.650
But in chemical kinetics, you're
measuring the concentration.

00:09:25.650 --> 00:09:30.080
Whereas with nuclear kinetics,
you're measuring decay events.

00:09:30.080 --> 00:09:33.080
And so usually how do
you measure decay events?

00:09:33.080 --> 00:09:38.020
And the most common way is
here, our Geiger counter.

00:09:38.020 --> 00:09:40.530
So I just want to-- it's
always important every once

00:09:40.530 --> 00:09:42.410
in a while at MIT
to double check

00:09:42.410 --> 00:09:45.030
that the rooms that
you're teaching in

00:09:45.030 --> 00:09:48.440
have not been contaminated by
some wonderful experiments.

00:09:48.440 --> 00:09:49.810
So, so far, we're good.

00:09:49.810 --> 00:09:52.220
So here, this is working.

00:09:52.220 --> 00:09:54.000
You can hear the chips, I think.

00:09:54.000 --> 00:09:55.211
This is pretty good.

00:09:55.211 --> 00:09:56.960
You don't have to be
concerned about this.

00:09:56.960 --> 00:09:58.501
There's always some
background level.

00:09:58.501 --> 00:09:59.240
It's fine.

00:09:59.240 --> 00:10:05.240
So there are gases in
here that will get ionized

00:10:05.240 --> 00:10:06.920
by radiation, which gives off.

00:10:06.920 --> 00:10:09.120
Then that's translated
into that clicking noise.

00:10:09.120 --> 00:10:10.450
So that's what is happening.

00:10:10.450 --> 00:10:13.090
So it's measuring,
with our thing,

00:10:13.090 --> 00:10:16.890
whether there are any
radioactive events going on.

00:10:16.890 --> 00:10:18.800
And this is called
a Geiger counter.

00:10:18.800 --> 00:10:21.040
And we use X-rays in my lab.

00:10:21.040 --> 00:10:24.850
So I went and stole this
from our X-ray facility

00:10:24.850 --> 00:10:25.730
before I came here.

00:10:25.730 --> 00:10:27.146
Luckily, it's
almost Thanksgiving,

00:10:27.146 --> 00:10:29.040
so no one was
collecting any data.

00:10:29.040 --> 00:10:32.850
So no one will get in trouble
for taking this right now.

00:10:32.850 --> 00:10:35.720
And Hans Geiger is
the person who came up

00:10:35.720 --> 00:10:37.940
with this idea and this device.

00:10:37.940 --> 00:10:40.480
Does anyone remember where
we heard that name before?

00:10:40.480 --> 00:10:44.000
Think back class two.

00:10:44.000 --> 00:10:48.600
So he did that amazing
gold foil experiment.

00:10:48.600 --> 00:10:51.810
And so our ping pong balls
that we were throwing

00:10:51.810 --> 00:10:53.740
were duplicating the
experiment that he

00:10:53.740 --> 00:10:55.310
did as a graduate student.

00:10:55.310 --> 00:10:57.160
And luckily, I think
he was smart enough

00:10:57.160 --> 00:10:59.430
to realize that when you're
working with things--

00:10:59.430 --> 00:11:02.110
he was working with a lot of
radioactivity at that point--

00:11:02.110 --> 00:11:04.570
that once you know exactly
how much radioactivity you're

00:11:04.570 --> 00:11:08.710
working with-- and so these
were very early day experiments.

00:11:08.710 --> 00:11:11.550
And he came up with
this device that helped

00:11:11.550 --> 00:11:12.850
him know how safe he was.

00:11:12.850 --> 00:11:16.490
And this is still sort
of the standard thing

00:11:16.490 --> 00:11:20.030
to have these around and
double check that there

00:11:20.030 --> 00:11:22.530
is no radiation leaks
in places like that.

00:11:22.530 --> 00:11:25.140
So the Geiger
counter-- all right.

00:11:25.140 --> 00:11:30.160
So also a couple of
more terminology things.

00:11:30.160 --> 00:11:33.970
Decay rate is also called
activity or specific activity.

00:11:33.970 --> 00:11:37.600
So you're talking about how
active your substance is.

00:11:37.600 --> 00:11:41.470
That's really how
radioactive is it.

00:11:41.470 --> 00:11:44.370
And activity also
has the letter A.

00:11:44.370 --> 00:11:46.480
So we were talking about
the concentration of A.

00:11:46.480 --> 00:11:47.480
Now we have A again.

00:11:47.480 --> 00:11:49.550
There's a lot of
A's in this unit.

00:11:49.550 --> 00:11:54.810
So that's the change now in
the number of nuclei over time-

00:11:54.810 --> 00:11:58.310
that's the rate expression,
or the rate law-- k,

00:11:58.310 --> 00:12:01.490
the decay constant, times
the number of nuclei.

00:12:01.490 --> 00:12:04.900
And because activity is
proportional to the number

00:12:04.900 --> 00:12:08.230
of nuclei, we can also
take this expression

00:12:08.230 --> 00:12:11.600
that we had before
that had the N's in it

00:12:11.600 --> 00:12:12.740
and rewrite it with A.

00:12:12.740 --> 00:12:15.990
So now it's really just like
that first-order expression

00:12:15.990 --> 00:12:19.210
we had but without the
concentration term.

00:12:19.210 --> 00:12:22.830
So we have the activity
at some time equals

00:12:22.830 --> 00:12:26.180
the original activity
of the material times

00:12:26.180 --> 00:12:27.930
e to the minus kt.

00:12:27.930 --> 00:12:29.880
And all of these
equations are going

00:12:29.880 --> 00:12:32.400
to be on your equation sheet.

00:12:32.400 --> 00:12:35.080
But if you mess up and use
the wrong equation for this,

00:12:35.080 --> 00:12:36.580
it doesn't matter,
as long as you're

00:12:36.580 --> 00:12:39.010
using the first-order equation.

00:12:39.010 --> 00:12:41.680
Whether it's
concentration or activity,

00:12:41.680 --> 00:12:44.820
it's the same idea
that you can determine,

00:12:44.820 --> 00:12:47.710
if you know the rate constant
or the decay constant,

00:12:47.710 --> 00:12:51.210
how much material is left,
how much activity is left,

00:12:51.210 --> 00:12:56.320
how many nuclei are left
after a given amount of time.

00:12:56.320 --> 00:12:58.000
So I know what you're
all thinking now.

00:12:58.000 --> 00:13:00.000
You're thinking,
this is fantastic,

00:13:00.000 --> 00:13:02.540
but what about the units?

00:13:02.540 --> 00:13:05.370
We musts here about the units.

00:13:05.370 --> 00:13:11.890
So the SI units for activity
are the becquerel, BQ.

00:13:11.890 --> 00:13:16.230
And one becquerel is one
radioactive disintegration

00:13:16.230 --> 00:13:18.140
per second.

00:13:18.140 --> 00:13:20.560
And this is the newer unit.

00:13:20.560 --> 00:13:23.480
The older unit was
called a curie,

00:13:23.480 --> 00:13:26.930
and sometimes you will still
see this in the literature.

00:13:26.930 --> 00:13:31.120
And a curie, one
curie, was 3.7 times 10

00:13:31.120 --> 00:13:34.110
to the 10th
disintegrations per second.

00:13:34.110 --> 00:13:39.020
So it was a much larger number
than the current SI unit.

00:13:39.020 --> 00:13:44.100
So this was what one gram of a
radium specific activity was.

00:13:44.100 --> 00:13:45.760
So they used this big number.

00:13:45.760 --> 00:13:48.230
But it was not really
practical because you

00:13:48.230 --> 00:13:51.030
want to tell people like how
much radiation would be safe

00:13:51.030 --> 00:13:53.350
for them to have in a year
or something like that.

00:13:53.350 --> 00:13:56.900
And you didn't want to use
this giant number for that.

00:13:56.900 --> 00:13:58.830
So we've moved to here.

00:13:58.830 --> 00:14:04.920
So does anyone know or want to
guess who the older unit was

00:14:04.920 --> 00:14:08.950
named for of radioactivity?

00:14:08.950 --> 00:14:11.000
One might think Marie Curie.

00:14:11.000 --> 00:14:13.160
But a lot of the
evidence suggests

00:14:13.160 --> 00:14:16.720
it was actually her
husband, Pierre Curie,

00:14:16.720 --> 00:14:17.820
who it was named after.

00:14:17.820 --> 00:14:19.800
It's a bit controversial.

00:14:19.800 --> 00:14:21.600
But they both worked
together, and they

00:14:21.600 --> 00:14:24.250
worked with Henri Becquerel.

00:14:24.250 --> 00:14:26.850
And they all won
the 1983 Nobel Prize

00:14:26.850 --> 00:14:28.970
for discovering radioactivity.

00:14:28.970 --> 00:14:34.390
Three years later, Pierre Curie
was killed crossing the street.

00:14:34.390 --> 00:14:39.100
He slipped when it was raining,
and a horse and wagon, I guess,

00:14:39.100 --> 00:14:41.650
ran over him and killed him.

00:14:41.650 --> 00:14:46.400
So this is, I think, an example
of someone who's so brilliant,

00:14:46.400 --> 00:14:47.970
but you say, they're
so brilliant,

00:14:47.970 --> 00:14:50.810
but do they look both ways
before they cross the street?

00:14:50.810 --> 00:14:52.430
So you are all very brilliant.

00:14:52.430 --> 00:14:54.600
And I encourage
you look both ways

00:14:54.600 --> 00:14:56.410
before you cross the street.

00:14:56.410 --> 00:14:58.610
Anyway, so he died.

00:14:58.610 --> 00:15:02.290
And some of the stories are that
they named the unit after him

00:15:02.290 --> 00:15:03.480
as a tribute.

00:15:03.480 --> 00:15:05.780
Others say, well, it's
really for both of them.

00:15:05.780 --> 00:15:08.545
But in any case, now it's
named after the third person,

00:15:08.545 --> 00:15:09.341
Henri Becquerel.

00:15:13.620 --> 00:15:16.810
So radioactivity,
I'm going to tell you

00:15:16.810 --> 00:15:19.350
a little bit about
radioactivity.

00:15:19.350 --> 00:15:21.170
This chart is not
in your handout

00:15:21.170 --> 00:15:23.280
because you're not
responsible for knowing

00:15:23.280 --> 00:15:27.500
all this information, so I
just didn't put it in there.

00:15:27.500 --> 00:15:29.299
But you can look this up.

00:15:29.299 --> 00:15:30.840
There's a couple of
points I did make

00:15:30.840 --> 00:15:33.160
in your handout,
which is there are

00:15:33.160 --> 00:15:39.330
different types of
nuclear radiation.

00:15:39.330 --> 00:15:43.650
We have alpha particles, alpha
decay, beta decay, gamma decay.

00:15:43.650 --> 00:15:45.940
Some of those involve
a mass change.

00:15:45.940 --> 00:15:49.850
So like an alpha particle is
the same as a helium-4 nucleus--

00:15:49.850 --> 00:15:52.880
two protons, two neutrons.

00:15:52.880 --> 00:15:55.580
Beta decay involves an electron.

00:15:55.580 --> 00:15:58.220
Gamma is a photon.

00:15:58.220 --> 00:16:00.180
So there are definitely
different types.

00:16:00.180 --> 00:16:03.310
Some mass change, some not.

00:16:03.310 --> 00:16:07.900
There are also really dramatic
differences in half-life.

00:16:07.900 --> 00:16:10.500
So again, half-life depends
on the material in question.

00:16:10.500 --> 00:16:14.020
It depends on that decay
constant, that rate constant.

00:16:14.020 --> 00:16:16.500
And if we look at this
table, we can see things

00:16:16.500 --> 00:16:18.490
from milli seconds.

00:16:18.490 --> 00:16:22.395
And if we look at some
of these, d is for a day.

00:16:22.395 --> 00:16:24.190
a is for year.

00:16:24.190 --> 00:16:25.570
y is also for year.

00:16:25.570 --> 00:16:27.710
So sometimes you'll
see y for year.

00:16:27.710 --> 00:16:29.025
Sometimes you'll see a.

00:16:29.025 --> 00:16:32.280
I think most people guess
that y is for a year.

00:16:32.280 --> 00:16:34.680
That a is for year,
I don't really know.

00:16:34.680 --> 00:16:36.720
But anyway, in
this table it's a.

00:16:36.720 --> 00:16:38.840
So if you see that,
don't be confused.

00:16:38.840 --> 00:16:44.860
And Ga, that's giga
years, so 10 to the ninth.

00:16:44.860 --> 00:16:48.740
That's where the
Finland 100,000 years

00:16:48.740 --> 00:16:52.940
comes from, that we need to
keep the stuff safe for a very,

00:16:52.940 --> 00:16:56.650
very, very, very, very,
very long amount of time

00:16:56.650 --> 00:16:59.640
for giga years.

00:16:59.640 --> 00:17:05.569
So in some decay processes,
such as uranium-238,

00:17:05.569 --> 00:17:10.770
you have more than one type
of nuclear radiation going on.

00:17:10.770 --> 00:17:15.510
And it can involve a very
long and complicated series

00:17:15.510 --> 00:17:17.569
of different events.

00:17:17.569 --> 00:17:20.819
So here at MIT, we spend
most of our time talking

00:17:20.819 --> 00:17:22.540
about science and engineering.

00:17:22.540 --> 00:17:24.099
But I feel like
every once in a while

00:17:24.099 --> 00:17:28.540
we should throw in some poetry
into our science classes.

00:17:28.540 --> 00:17:33.570
So once a year I like
to read a chemistry poem

00:17:33.570 --> 00:17:35.590
to enrich our lives.

00:17:35.590 --> 00:17:40.549
And today is that day in 2014.

00:17:40.549 --> 00:17:42.090
And the poem I'm
going to read to you

00:17:42.090 --> 00:17:46.330
is called "The Days
of Our Half-Lives,"

00:17:46.330 --> 00:17:49.870
and it is by Professor
Mala Radhakrishnan.

00:17:49.870 --> 00:17:54.430
She got her PhD here at MIT
in the Chemistry department.

00:17:54.430 --> 00:17:57.950
And she wrote this book, which
she wanted me to point out

00:17:57.950 --> 00:18:01.260
is available on Amazon if you're
looking for a Christmas present

00:18:01.260 --> 00:18:05.250
for a very, very
geeky friend of yours.

00:18:05.250 --> 00:18:08.230
And it's illustrated by
another MIT chemistry

00:18:08.230 --> 00:18:11.560
PhD, Mary O'Reilly, who
actually did the illustrations

00:18:11.560 --> 00:18:13.870
for the videos that I've
been showing you in class.

00:18:13.870 --> 00:18:19.760
So MIT chemists, just really
multi-talented individuals.

00:18:19.760 --> 00:18:22.520
So I will read
you this poem now.

00:18:22.520 --> 00:18:26.240
And as I read it to
you, I will point out

00:18:26.240 --> 00:18:29.730
what is happening in
this decay process

00:18:29.730 --> 00:18:35.200
because all of Mala's poetry
is scientifically correct.

00:18:39.620 --> 00:18:44.480
So "Days of Our Half-lives."

00:18:44.480 --> 00:18:47.510
"My dearest love, I am
writing you to tell you

00:18:47.510 --> 00:18:49.470
all that I've been through.

00:18:49.470 --> 00:18:52.370
I've changed my whole identity.

00:18:52.370 --> 00:18:55.690
But loved, I can't
pretend to be.

00:18:55.690 --> 00:19:00.620
When I was uranium-238,
you were on my case

00:19:00.620 --> 00:19:03.020
to start losing weight.

00:19:03.020 --> 00:19:06.340
For 5 billion years I'd
hoped and I'd prayed,

00:19:06.340 --> 00:19:10.620
and finally I had
an alpha decay.

00:19:10.620 --> 00:19:15.380
Two protons and two neutrons
went right out the door.

00:19:15.380 --> 00:19:19.250
And now I was thorium-234.

00:19:19.250 --> 00:19:22.580
But my nucleus was still
unfit for your eyes,

00:19:22.580 --> 00:19:26.210
not positive enough
for its large size.

00:19:26.210 --> 00:19:29.240
But this time my half-life
was not very long,

00:19:29.240 --> 00:19:32.330
because my will to change
was really quite strong.

00:19:32.330 --> 00:19:36.790
It took just a month, not even
a millennium, to beta decay

00:19:36.790 --> 00:19:39.540
into protactinium.

00:19:39.540 --> 00:19:44.310
But still, rejected me right off
the bat-- protactinium, who's

00:19:44.310 --> 00:19:45.790
heard of that?

00:19:45.790 --> 00:19:53.270
So beta decay I did once
more to become uranium-234.

00:19:53.270 --> 00:19:57.480
Myself again but a new isotope,
you still weren't satisfied.

00:19:57.480 --> 00:19:59.480
But I still had hope.

00:19:59.480 --> 00:20:02.340
Three alpha decays
'twas hard, but I

00:20:02.340 --> 00:20:11.020
stayed on through thorium
then radium and then radon.

00:20:11.020 --> 00:20:14.060
I thought that I would
finally please you.

00:20:14.060 --> 00:20:17.840
My mass was a healthy 222.

00:20:17.840 --> 00:20:22.580
But you said, although
I like your mass,

00:20:22.580 --> 00:20:25.223
I don't want to be
with a noble gas.

00:20:28.990 --> 00:20:30.016
They dress so well.

00:20:33.120 --> 00:20:35.150
You had a point though.

00:20:35.150 --> 00:20:37.100
I wasn't reactive.

00:20:37.100 --> 00:20:40.420
So in order to please
you, I stayed proactive.

00:20:40.420 --> 00:20:43.900
A few days later, I found
you and said, two more alpha

00:20:43.900 --> 00:20:47.470
decays, and now I am lead.

00:20:49.980 --> 00:20:52.260
But you shook your head.

00:20:52.260 --> 00:20:56.850
You were not too keen on
my mass number of 214.

00:20:56.850 --> 00:20:59.910
I had a bad experience
with that mass before,

00:20:59.910 --> 00:21:04.388
and an unstable astatine
walked right out the door.

00:21:04.388 --> 00:21:06.840
So in order to
change, I went away.

00:21:06.840 --> 00:21:09.730
But all I could do
was just beta decay.

00:21:09.730 --> 00:21:12.250
My hopes and my dreams
started to go under,

00:21:12.250 --> 00:21:16.870
because beta decay does
not change a mass number.

00:21:16.870 --> 00:21:22.850
To bismuth and polonium,
I hoped and I beckoned.

00:21:22.850 --> 00:21:26.520
My half-life was 1
6 4 microseconds.

00:21:26.520 --> 00:21:28.600
And then finally,
I alpha decayed.

00:21:28.600 --> 00:21:36.100
And then I was lead with a
prize worthy mass of 210.

00:21:36.100 --> 00:21:39.120
Got to admit, I was
getting quite tired,

00:21:39.120 --> 00:21:42.940
and my patience with
you had nearly expired.

00:21:42.940 --> 00:21:45.610
You were more demanding
than any I'd dated.

00:21:45.610 --> 00:21:49.790
And much of my energy
had been liberated.

00:21:49.790 --> 00:21:52.700
But you still weren't
happy, but you had a fix.

00:21:52.700 --> 00:21:56.020
I really like the number 206.

00:21:56.020 --> 00:21:57.960
So I waited for
years until the day

00:21:57.960 --> 00:22:03.800
which began with another
beta decay and then one more.

00:22:03.800 --> 00:22:06.950
And finally, in
the end, I alpha-ed

00:22:06.950 --> 00:22:09.970
to lead 206, my friend.

00:22:09.970 --> 00:22:11.200
To change any further.

00:22:11.200 --> 00:22:15.750
I wouldn't be able-- not longer
active, but happily stable.

00:22:15.750 --> 00:22:17.380
It took me a
million years to do,

00:22:17.380 --> 00:22:21.360
but look how I've changed,
and all just for you.

00:22:21.360 --> 00:22:23.240
Wait, what did you say?

00:22:23.240 --> 00:22:26.120
I've gotten so old
that you'd rather

00:22:26.120 --> 00:22:29.400
be with a young lass of gold?

00:22:29.400 --> 00:22:30.430
Well, I give up.

00:22:30.430 --> 00:22:32.020
We're through, my pumpkin.

00:22:32.020 --> 00:22:35.380
Shouldn't all my effort
be counting for something?

00:22:35.380 --> 00:22:38.310
Well, you won't be able
to rule me anymore,

00:22:38.310 --> 00:22:44.840
because I'm leaving you
not for one atom, but four.

00:22:44.840 --> 00:22:47.070
That's right.

00:22:47.070 --> 00:22:51.380
While you were away
diffusing, I found

00:22:51.380 --> 00:22:54.625
some chlorines that I
found quite amusing.

00:22:57.170 --> 00:23:02.070
And we're going
to form lead, Cl4,

00:23:02.070 --> 00:23:04.800
and you won't be
hearing from me anymore.

00:23:04.800 --> 00:23:06.800
See, over the years,
I've grown quite wise.

00:23:06.800 --> 00:23:09.430
I've learned that
love's about compromise.

00:23:09.430 --> 00:23:11.450
You still have half
of your half-lives

00:23:11.450 --> 00:23:13.880
to live, so go out there.

00:23:13.880 --> 00:23:18.050
It's your turn to give."

00:23:18.050 --> 00:23:19.810
Thank you.

00:23:19.810 --> 00:23:23.680
[APPLAUSE]

00:23:25.690 --> 00:23:27.941
There's a whole book
of them on Amazon.

00:23:32.050 --> 00:23:35.920
So that is first order.

00:23:35.920 --> 00:23:38.600
First order is pretty exciting
because it has nuclear decay.

00:23:38.600 --> 00:23:40.540
Second order-- not
quite as exciting.

00:23:40.540 --> 00:23:43.750
But we should talk
about it anyway.

00:23:43.750 --> 00:23:47.399
So second order
integrated rate loss--

00:23:47.399 --> 00:23:49.190
we're not going to go
through a derivation.

00:23:49.190 --> 00:23:50.850
It's in your book.

00:23:50.850 --> 00:23:54.380
But here is the equation,
if you do the derivation.

00:23:54.380 --> 00:23:59.060
So now we have 1 over the
concentration of A at time t

00:23:59.060 --> 00:24:03.210
equals rate constant
k times t plus 1

00:24:03.210 --> 00:24:09.610
over the original
concentration of A.

00:24:09.610 --> 00:24:14.590
And we could plot this one over
concentration of t versus time.

00:24:14.590 --> 00:24:17.242
And if we did that, you
would have the opportunity

00:24:17.242 --> 00:24:18.450
for another clicker question.

00:24:30.260 --> 00:24:31.071
10 more seconds.

00:24:44.470 --> 00:24:46.570
90s, yeah-- it's kind
of hard to come up

00:24:46.570 --> 00:24:48.870
with clicker questions
in this unit, so.

00:24:48.870 --> 00:24:53.460
But it's fun, for Thanksgiving,
we'll have lots of 90s.

00:24:53.460 --> 00:24:56.730
So we can just look, and this
is actually an expression

00:24:56.730 --> 00:24:58.360
for a straight line again.

00:24:58.360 --> 00:25:03.310
So we're plotting on the y-axis
one over a concentration of A

00:25:03.310 --> 00:25:07.500
at all the various different
times versus time over here.

00:25:07.500 --> 00:25:09.540
And so our intercept
is going to be

00:25:09.540 --> 00:25:12.120
1 over the initial
concentration of A.

00:25:12.120 --> 00:25:15.670
And our slope is
going to be what?

00:25:15.670 --> 00:25:17.600
k, right.

00:25:17.600 --> 00:25:21.120
So again, you can measure
your concentration

00:25:21.120 --> 00:25:24.710
as it changes with time, how
the concentration changes,

00:25:24.710 --> 00:25:28.070
plot it, and just determine
your rate constant

00:25:28.070 --> 00:25:31.710
for that particular material.

00:25:31.710 --> 00:25:37.850
So second order half-life--
we can do another derivation.

00:25:37.850 --> 00:25:42.160
But in this case, I will
just give you the equation.

00:25:42.160 --> 00:25:46.440
So half-life equals
1 over k times

00:25:46.440 --> 00:25:49.370
your original
concentration of A.

00:25:49.370 --> 00:25:52.720
And so this is different
from first order.

00:25:52.720 --> 00:25:56.050
There is a concentration
term in the equation.

00:25:56.050 --> 00:25:58.780
So for second
order half-life, it

00:25:58.780 --> 00:26:01.440
does depend on the
starting concentration.

00:26:01.440 --> 00:26:02.940
So that's really
the big difference.

00:26:02.940 --> 00:26:04.536
In first order,
it doesn't depend

00:26:04.536 --> 00:26:05.785
on the starting concentration.

00:26:05.785 --> 00:26:08.510
It just depends on the rate
constant or the decay constant,

00:26:08.510 --> 00:26:10.430
which depends on the
material in question.

00:26:10.430 --> 00:26:12.440
With second order,
you do need to know

00:26:12.440 --> 00:26:14.890
how much you had originally.

00:26:14.890 --> 00:26:17.430
So again, how do you know if
it's a first or a second order

00:26:17.430 --> 00:26:18.760
process?

00:26:18.760 --> 00:26:22.630
And here, you really have to
determine it experimentally.

00:26:22.630 --> 00:26:24.530
So one thing you
could do is measure

00:26:24.530 --> 00:26:28.550
how A changes over time and
then plot your data using

00:26:28.550 --> 00:26:30.530
the equation for first order.

00:26:30.530 --> 00:26:33.680
And you may see that,
yeah, that does not

00:26:33.680 --> 00:26:35.990
form a straight line
when you're plotting

00:26:35.990 --> 00:26:38.210
with natural log of
a concentration of A.

00:26:38.210 --> 00:26:42.100
But then if you try plotting it
1 over the concentration of A,

00:26:42.100 --> 00:26:44.760
you get a beautiful straight
line with your data.

00:26:44.760 --> 00:26:47.190
And so you'd say, that's
a second-order process.

00:26:47.190 --> 00:26:50.750
So again, you're determining
these things experimentally,

00:26:50.750 --> 00:26:53.390
collecting data,
plotting the data,

00:26:53.390 --> 00:26:55.880
determining rate
constants, determining

00:26:55.880 --> 00:26:57.165
the order of the reaction.

00:27:00.370 --> 00:27:04.260
Now, this is very exciting.

00:27:04.260 --> 00:27:08.270
What we're going to talk
about is the relationship

00:27:08.270 --> 00:27:12.830
between the rate constants
and equilibrium constants.

00:27:12.830 --> 00:27:13.590
So I love this.

00:27:13.590 --> 00:27:14.970
I love when we
come back to stuff

00:27:14.970 --> 00:27:17.100
that we've talked
about before and see it

00:27:17.100 --> 00:27:19.540
in a slightly different way.

00:27:19.540 --> 00:27:21.640
So at equilibrium,
we talked about how

00:27:21.640 --> 00:27:23.855
it's a dynamic process.

00:27:23.855 --> 00:27:25.730
And you have the rate
of the forward reaction

00:27:25.730 --> 00:27:27.370
equal the rate of
the reverse reaction.

00:27:27.370 --> 00:27:28.710
Reactions are still going.

00:27:28.710 --> 00:27:30.360
They haven't stopped.

00:27:30.360 --> 00:27:34.710
But the rates are equal
in both directions.

00:27:34.710 --> 00:27:38.380
So we've talked about how
to write an equilibrium

00:27:38.380 --> 00:27:40.550
constant for reaction.

00:27:40.550 --> 00:27:44.400
So if we have a reaction of
A plus B going to C plus D,

00:27:44.400 --> 00:27:48.960
we can write our equilibrium
constant k and its products

00:27:48.960 --> 00:27:50.780
over reactants.

00:27:50.780 --> 00:27:52.880
Unless one of our
products or reactants

00:27:52.880 --> 00:27:56.300
is a solid or a very
dilute solution.

00:27:56.300 --> 00:27:57.780
It's the solvent.

00:27:57.780 --> 00:28:01.030
And I heard from your TAs
that in the last problem set,

00:28:01.030 --> 00:28:05.690
some people had forgotten what
goes into q or k expressions.

00:28:05.690 --> 00:28:08.400
So it's good to review that for
this next unit and exam four

00:28:08.400 --> 00:28:12.810
and the final-- so
products over reactants.

00:28:12.810 --> 00:28:17.180
Now suppose we
tell you that it's

00:28:17.180 --> 00:28:21.500
a second-order process and the
rate of the forward reaction

00:28:21.500 --> 00:28:24.610
here, A plus B, we
can write the rate

00:28:24.610 --> 00:28:26.650
law for that forward
reaction being

00:28:26.650 --> 00:28:30.920
second order, first order
in A and first order in B.

00:28:30.920 --> 00:28:32.980
So the rate constant for
the forward direction

00:28:32.980 --> 00:28:37.130
is k 1 and then times the
concentration of A times

00:28:37.130 --> 00:28:39.430
the concentration of B.

00:28:39.430 --> 00:28:45.280
For the reverse reaction, the
rate constant is k minus 1.

00:28:45.280 --> 00:28:47.330
And this is generally
true in all the problems.

00:28:47.330 --> 00:28:52.710
If it's a first step, you have
plus 1 k1 on the top, k minus 1

00:28:52.710 --> 00:28:53.650
on the bottom.

00:28:53.650 --> 00:28:57.170
So we have k minus 1 times
the concentration of C and D

00:28:57.170 --> 00:29:00.970
So that's the
backward direction.

00:29:00.970 --> 00:29:06.360
So at equilibrium,
these rates are equal.

00:29:06.360 --> 00:29:07.460
We just talked about that.

00:29:07.460 --> 00:29:08.418
We've seen that before.

00:29:08.418 --> 00:29:10.580
The rate of the forward
reactions, so k1 times

00:29:10.580 --> 00:29:16.460
A times B is equal to k
minus 1 times C times D

00:29:16.460 --> 00:29:18.980
when you're at equilibrium.

00:29:18.980 --> 00:29:21.770
So we can rearrange
this equation now

00:29:21.770 --> 00:29:25.690
and say C and D over
here over divide

00:29:25.690 --> 00:29:31.560
by A and B. It's going to be
equal to k1 over k minus 1.

00:29:31.560 --> 00:29:35.490
And we also just saw that
C times D over A times B

00:29:35.490 --> 00:29:39.160
was equal to k.

00:29:39.160 --> 00:29:45.460
So therefore, our equilibrium
constant k equals k 1,

00:29:45.460 --> 00:29:49.630
the rate constant for
direction, over k minus 1,

00:29:49.630 --> 00:29:52.540
the rate constant for
the reversed direction.

00:29:52.540 --> 00:29:56.090
So here we're relating
equilibrium constants and rate

00:29:56.090 --> 00:29:58.160
constants.

00:29:58.160 --> 00:30:00.220
So we thought a lot
about what's true

00:30:00.220 --> 00:30:02.910
if you have a big
equilibrium constant.

00:30:02.910 --> 00:30:06.220
If you have a big
equilibrium constant,

00:30:06.220 --> 00:30:10.270
if you have an equilibrium
constant much greater than 1,

00:30:10.270 --> 00:30:13.530
what's the ratio of products
and reactants at equilibrium?

00:30:13.530 --> 00:30:17.390
Is there more or less products
at equilibrium and reactants?

00:30:17.390 --> 00:30:18.560
More.

00:30:18.560 --> 00:30:20.070
So we thought about
that, and now we

00:30:20.070 --> 00:30:23.380
can think about the relationship
of the rate constants.

00:30:23.380 --> 00:30:28.030
So if k is greater than 1,
is k 1 greater or less than k

00:30:28.030 --> 00:30:29.480
minus 1?

00:30:29.480 --> 00:30:31.270
Greater.

00:30:31.270 --> 00:30:34.030
And so that would
then be the case

00:30:34.030 --> 00:30:37.400
where you have more products
than reactants at equilibrium.

00:30:37.400 --> 00:30:39.530
If k is less than
1, a case where

00:30:39.530 --> 00:30:42.380
there's more reactants than
products at equilibrium,

00:30:42.380 --> 00:30:46.666
then you have k 1 is
less than k minus 1.

00:30:46.666 --> 00:30:48.040
So again, we can
think about this

00:30:48.040 --> 00:30:49.260
in terms of thermodynamics.

00:30:49.260 --> 00:30:53.620
We can also now think
about it in terms of rates.

00:30:53.620 --> 00:30:57.570
So one more thing that we need
to cover before we end today,

00:30:57.570 --> 00:31:02.300
and that is about elementary
steps and molecularity,

00:31:02.300 --> 00:31:04.910
which I just love
saying that word.

00:31:04.910 --> 00:31:06.400
So on Monday,
we're going to talk

00:31:06.400 --> 00:31:08.110
about mechanism of reactions.

00:31:08.110 --> 00:31:10.587
Most reactions do not
occur in one step,

00:31:10.587 --> 00:31:12.170
and we need to think
about mechanisms.

00:31:12.170 --> 00:31:12.730
I said it was Wednesday.

00:31:12.730 --> 00:31:13.820
But it's actually Monday.

00:31:13.820 --> 00:31:14.690
So it's coming up.

00:31:14.690 --> 00:31:15.884
It's very exciting.

00:31:15.884 --> 00:31:18.050
And we're going to talk a
lot about elementary steps

00:31:18.050 --> 00:31:19.960
when we talk about mechanisms.

00:31:19.960 --> 00:31:26.530
So an elementary step is one
of the steps in the reaction.

00:31:26.530 --> 00:31:28.520
So reactions usually
don't occur in one step.

00:31:28.520 --> 00:31:30.800
They have many
steps, and each step

00:31:30.800 --> 00:31:33.970
is called an
elementary reaction.

00:31:33.970 --> 00:31:38.870
So we talked about last time
that for the overall order

00:31:38.870 --> 00:31:41.340
of the reaction, you can't
just look at the stoichiometry

00:31:41.340 --> 00:31:43.610
and say what the order
of the reaction is.

00:31:43.610 --> 00:31:46.100
So you can't predict
it from stoichiometry

00:31:46.100 --> 00:31:48.020
for an overall reaction.

00:31:48.020 --> 00:31:52.720
But if it's an elementary
reaction, if it's a step,

00:31:52.720 --> 00:31:57.970
that elementary reaction is
written exactly as it occurs.

00:31:57.970 --> 00:32:02.760
So in that case, the order and
the rate law can be predicted.

00:32:02.760 --> 00:32:04.200
So this is you're
breaking it down

00:32:04.200 --> 00:32:07.120
into sort of the smallest
unit, the smallest

00:32:07.120 --> 00:32:10.550
step, this elementary
reaction, so you can just

00:32:10.550 --> 00:32:13.530
look at the stoichiometry
for a single step,

00:32:13.530 --> 00:32:16.180
for an elementary
reaction, and project

00:32:16.180 --> 00:32:19.190
to the order and the rate law.

00:32:19.190 --> 00:32:22.699
So elementary reactions
occur exactly as written.

00:32:22.699 --> 00:32:24.490
So that's what we're
going to do on Monday.

00:32:24.490 --> 00:32:27.080
We're going to break
down our mechanisms

00:32:27.080 --> 00:32:29.800
into elementary steps,
write out the rate laws,

00:32:29.800 --> 00:32:34.610
and then figure out what kind
of mechanism we might have.

00:32:34.610 --> 00:32:39.750
So finally, molecularity--
so molecularity

00:32:39.750 --> 00:32:43.240
is just the number of
things that come together

00:32:43.240 --> 00:32:45.960
to form a product.

00:32:45.960 --> 00:32:53.310
And here we have three names--
unimolecular, bimolecular,

00:32:53.310 --> 00:32:54.990
and termolecular.

00:32:54.990 --> 00:32:57.040
Unimolecular process,
what do you guess?

00:32:57.040 --> 00:33:00.150
How many reactants are coming
together to form product?

00:33:00.150 --> 00:33:02.380
One.

00:33:02.380 --> 00:33:04.580
Bimolecular, what do you guess?

00:33:04.580 --> 00:33:05.740
Two.

00:33:05.740 --> 00:33:09.390
Termolecular is a little harder,
but just give it a whirl.

00:33:09.390 --> 00:33:10.910
Three, yes.

00:33:10.910 --> 00:33:13.700
So bimolecular is very common.

00:33:17.490 --> 00:33:19.740
And termolecular is not.

00:33:19.740 --> 00:33:23.220
So I have three molecules
to come together.

00:33:23.220 --> 00:33:24.690
And if you try to
think about how

00:33:24.690 --> 00:33:27.980
you get three things to come
together all at the same time,

00:33:27.980 --> 00:33:28.910
that's kind of rare.

00:33:28.910 --> 00:33:30.990
Usually, when there are
three things reacting,

00:33:30.990 --> 00:33:32.470
there are multiple
steps involved.

00:33:32.470 --> 00:33:33.870
But two is good.

00:33:33.870 --> 00:33:37.840
Now finally, we'll end
with a clicker question.

00:33:37.840 --> 00:33:40.080
Think about which of
these would be examples

00:33:40.080 --> 00:33:41.671
of unimolecular processes.

00:33:52.820 --> 00:33:53.476
10 seconds.

00:34:08.719 --> 00:34:11.120
So it actually is one and two.

00:34:11.120 --> 00:34:14.100
So most people got the two.

00:34:14.100 --> 00:34:16.290
Yes, that's radioactive decay.

00:34:16.290 --> 00:34:18.909
But the other, you can
have a decomposition.

00:34:18.909 --> 00:34:21.960
So here we have decomposition
into its elements

00:34:21.960 --> 00:34:26.060
is also a first-order process.

00:34:26.060 --> 00:34:27.500
Happy Thanksgiving, everybody.

00:34:27.500 --> 00:34:29.859
See you next Monday.