The van der Waals equation

WEBVTT
Kind: captions
Language: en

00:00:00.150 --> 00:00:02.020
- [Instructor] We have
so far spent many videos

00:00:02.020 --> 00:00:04.270
talking about the ideal gas law,

00:00:04.270 --> 00:00:06.150
that pressure times volume is equal

00:00:06.150 --> 00:00:08.670
to the number of moles
times the ideal gas constant

00:00:08.670 --> 00:00:11.760
times temperature measured in kelvin.

00:00:11.760 --> 00:00:13.030
What we're going to do in this video

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is attempt to modify the ideal gas law

00:00:16.300 --> 00:00:18.170
to try to take into account

00:00:18.170 --> 00:00:19.940
when we're dealing with real gases,

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gases where the volume
of the actual particles

00:00:23.570 --> 00:00:25.670
are worth considering,
that we don't just say

00:00:25.670 --> 00:00:28.160
they're negligible compared to
the volume of the container.

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And intermolecular forces are something

00:00:30.010 --> 00:00:32.400
that we would like to
take into consideration.

00:00:32.400 --> 00:00:34.310
So let's think about how
we could modify this.

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And to help us a little bit,

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I'm just gonna solve for P.

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So I'm gonna divide both sides by volume,

00:00:38.960 --> 00:00:41.580
so we can say pressure is
equal to number of moles

00:00:41.580 --> 00:00:42.860
times ideal gas constant

00:00:42.860 --> 00:00:46.940
times temperature measured
in kelvin divided by volume.

00:00:46.940 --> 00:00:49.090
So first, how would we adjust this

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if we want to take into
account the actual volume

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in which the molecules can move around?

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Well, if we wanted to do that,

00:00:56.970 --> 00:00:59.870
we would replace this
volume right over here

00:00:59.870 --> 00:01:04.870
with this volume minus the
volume of the actual particles.

00:01:04.950 --> 00:01:07.930
So what's the volume of the
actual particles going to be?

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Well, it's going to be
the number of particles

00:01:11.280 --> 00:01:12.830
times some constant,

00:01:12.830 --> 00:01:15.390
based on how large each
of those particles are,

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maybe on average.

00:01:16.500 --> 00:01:18.723
And let's just call that b.

00:01:20.240 --> 00:01:25.000
So we could view this as a
modified ideal gas law equation,

00:01:25.000 --> 00:01:27.330
we're now all of a sudden,
we are taking into account

00:01:27.330 --> 00:01:30.330
the fact that these particles
have some real volume to them,

00:01:31.780 --> 00:01:32.710
but of course we also
know it's not just about

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the volume of the particles,
we also need to adjust

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for the intermolecular
forces between the particles.

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And we know that in many cases
those intermolecular forces

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are attractive forces,

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and so they would take
away from the pressure.

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And so we need some term
that accounts for that,

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a term that accounts for
taking away the pressure

00:01:49.640 --> 00:01:51.490
due to intermolecular forces.

00:01:51.490 --> 00:01:56.127
So term for intermolecular forces.

00:02:01.720 --> 00:02:03.427
Now I know what some
of y'all are thinking.

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"Do we always subtract?

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Might not there be some situations

00:02:06.970 --> 00:02:10.200
in which we actually have
repulsive forces between particles

00:02:10.200 --> 00:02:12.000
and it would actually
add to the pressure?"

00:02:12.000 --> 00:02:13.700
And there could be scenarios like that.

00:02:13.700 --> 00:02:16.850
You could imagine if they all
have a strong negative charge,

00:02:16.850 --> 00:02:19.130
they wanna get away from each
other as far as they can.

00:02:19.130 --> 00:02:22.030
And that could actually
add to the pressure,

00:02:22.030 --> 00:02:24.810
but in that situation, we
could subtract a negative

00:02:24.810 --> 00:02:27.140
and then that would be additive.

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Now, how could we take
this into consideration?

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So we know from Coulomb's
law that the force

00:02:32.660 --> 00:02:35.180
between two particles,
two charged particles

00:02:35.180 --> 00:02:36.210
is going to be proportional

00:02:36.210 --> 00:02:39.670
to the charge on one
particle times the charge

00:02:39.670 --> 00:02:43.350
on the other particle divided
by the distance squared.

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Now, obviously if we're
dealing with a lot of particles

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in a container, we're not
gonna be able to think

00:02:47.780 --> 00:02:51.040
about the forces for
between any two particles.

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But one way to think about it is

00:02:52.470 --> 00:02:55.420
in terms of how concentrated
are the particles generally.

00:02:55.420 --> 00:02:56.840
So when we're trying to think of a term

00:02:56.840 --> 00:02:59.350
that takes into account
the intermolecular forces

00:02:59.350 --> 00:03:00.840
or how much we're reducing the pressure

00:03:00.840 --> 00:03:03.110
because of those intermolecular forces,

00:03:03.110 --> 00:03:06.984
maybe that can be proportional
to not just the concentration

00:03:06.984 --> 00:03:10.030
of the particles, and that'd
be the number of particles

00:03:10.030 --> 00:03:13.764
divided by the volume,
but that times itself,

00:03:13.764 --> 00:03:15.840
because we're talking
about the interaction

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between two particles at a time,

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very similar to what we
see in Coulomb's law,

00:03:19.060 --> 00:03:19.893
because the end of the day

00:03:19.893 --> 00:03:21.760
these really are just Coulomb forces.

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So this thing right over
here is gonna be proportional

00:03:23.990 --> 00:03:26.560
to the concentration times itself.

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Or we could maybe call this some constant,

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for the proportionality,
times n over v squared,

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where a would depend on
the attractive forces

00:03:37.700 --> 00:03:39.240
between gas particles.

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And what we have just constructed,

00:03:40.810 --> 00:03:43.950
and let me rewrite it again,
this ideal gas equation,

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and actually let me put this orange term

00:03:46.410 --> 00:03:47.630
back on the left hand side.

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So if I write it this
way, that pressure plus a

00:03:53.530 --> 00:03:58.530
times n over v squared is equal to n R T

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over the volume of our container

00:04:04.730 --> 00:04:07.820
minus the number of molecules we have

00:04:07.820 --> 00:04:11.660
times some constant b, based
on how large on average

00:04:11.660 --> 00:04:14.190
those molecules or those particles are.

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This right over here is a
pretty good competence equation

00:04:18.480 --> 00:04:20.780
for when we're dealing
with more real gases,

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ones that have intermolecular forces,

00:04:22.600 --> 00:04:25.670
and one where the actual
particles have volume.

00:04:25.670 --> 00:04:28.140
And this actually does a pretty good job,

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and there's a name for it,

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it's called the Van der Waals equation.

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And there's many different
ways you might see it,

00:04:35.020 --> 00:04:36.440
you could see it written like this,

00:04:36.440 --> 00:04:38.260
or we could try to take this blue part

00:04:38.260 --> 00:04:39.550
and get it on the left hand side

00:04:39.550 --> 00:04:41.820
so it really looks like
what we saw at the top.

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Where there it would be
written as, and I'll write it,

00:04:44.320 --> 00:04:45.180
actually write it this way.

00:04:45.180 --> 00:04:50.180
Pressure plus some constant
times the density squared,

00:04:52.180 --> 00:04:54.070
let me close that parentheses,

00:04:54.070 --> 00:04:58.920
times the volume minus
the number of molecules

00:04:58.920 --> 00:05:03.480
times some constant is
going to be equal n R T,

00:05:03.480 --> 00:05:06.390
is going to be equal to n R T.

00:05:06.390 --> 00:05:08.350
And all of this looks really complicated,

00:05:08.350 --> 00:05:11.000
but the end of the day it
is just our ideal gas law

00:05:11.000 --> 00:05:13.730
modified for intermolecular forces

00:05:13.730 --> 00:05:16.513
and the actual volume of the particles.


Electronic transitions and energy

WEBVTT
Kind: captions
Language: en

00:00:00.930 --> 00:00:02.150
- [Lecturer] In this video,

00:00:02.150 --> 00:00:06.310
we're going to be talking
about exciting electrons.

00:00:06.310 --> 00:00:07.810
We can interpret that both ways

00:00:07.810 --> 00:00:09.560
that electrons can be exciting

00:00:09.560 --> 00:00:11.050
and that we're going to excite them

00:00:11.050 --> 00:00:12.990
into higher energy levels.

00:00:12.990 --> 00:00:14.470
Or we're going to think about what happens

00:00:14.470 --> 00:00:16.000
when they get unexcited,

00:00:16.000 --> 00:00:18.560
when they go back into
lower energy levels.

00:00:18.560 --> 00:00:20.040
And to help us understand this,

00:00:20.040 --> 00:00:21.800
I'll start with a simple atom.

00:00:21.800 --> 00:00:23.700
Hydrogen is the simplest I know,

00:00:23.700 --> 00:00:26.060
and we're gonna think about
the version of a hydrogen

00:00:26.060 --> 00:00:27.430
that we typically see the isotope

00:00:27.430 --> 00:00:30.190
that only has one proton in its nucleus.

00:00:30.190 --> 00:00:34.590
And it typically has one
or will have one electron

00:00:34.590 --> 00:00:36.380
if it's a neutral hydrogen atom

00:00:36.380 --> 00:00:38.600
and it would normally
be in its ground state,

00:00:38.600 --> 00:00:39.810
if it isn't excited yet.

00:00:39.810 --> 00:00:41.360
So it's going to be in that first shell

00:00:41.360 --> 00:00:42.970
but it can be excited to other shells.

00:00:42.970 --> 00:00:45.560
It could be excited to the second shell

00:00:45.560 --> 00:00:49.080
or the third shell

00:00:49.080 --> 00:00:50.450
or the fourth shell.

00:00:50.450 --> 00:00:51.990
And this is obviously hand drawn

00:00:51.990 --> 00:00:53.350
and not hand drawn that well,

00:00:53.350 --> 00:00:55.470
and this is really just to help us

00:00:55.470 --> 00:00:56.780
for visualization purposes.

00:00:56.780 --> 00:00:59.320
We know that electrons don't orbit nuclei

00:00:59.320 --> 00:01:01.200
the way planets orbit stars.

00:01:01.200 --> 00:01:04.300
They have both particle
and wave like properties,

00:01:04.300 --> 00:01:06.300
and they're more of a
probability density function

00:01:06.300 --> 00:01:07.680
of where you might find them.

00:01:07.680 --> 00:01:10.050
And these energy levels are associated

00:01:10.050 --> 00:01:13.990
with different probability
densities of various energies.

00:01:13.990 --> 00:01:16.420
But this is what an electron
will typically look like.

00:01:16.420 --> 00:01:19.210
If we're thinking about just
a neutral hydrogen atom,

00:01:19.210 --> 00:01:21.260
where the electrons in its ground state.

00:01:21.260 --> 00:01:23.424
Now let's say we're dealing
with a hydrogen atom

00:01:23.424 --> 00:01:25.860
where the electron has already
been excited a little bit.

00:01:25.860 --> 00:01:27.810
So instead of it being in the first shell,

00:01:27.810 --> 00:01:31.970
it's already in the second
shell right over here.

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And what we're going to
do is we're gonna hit it

00:01:34.820 --> 00:01:38.470
with a photon that excites it even more.

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And the photon.

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And we know that light has both particle

00:01:41.760 --> 00:01:42.990
and wave like properties.

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When we think of it as a particle,

00:01:44.180 --> 00:01:45.760
we think of it as a photon,

00:01:45.760 --> 00:01:47.860
but I will depict it like this.

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So this light has a
wavelength of 486 nanometers.

00:01:55.630 --> 00:01:59.520
And we know that that photon that hits it

00:01:59.520 --> 00:02:01.900
with a wavelength of 486 nanometers

00:02:01.900 --> 00:02:06.680
has sufficient energy to excite
this electron in this case,

00:02:06.680 --> 00:02:11.220
actually from N equals
two from the second shell

00:02:11.220 --> 00:02:12.590
to the fourth shell.

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So it'll go all the way over there.

00:02:17.900 --> 00:02:20.252
So it will absorb that photon.

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And then after some time
it can come back down

00:02:23.760 --> 00:02:26.030
and when it comes back down,
I could do it over here.

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So after some time it can,
that electron right over here,

00:02:30.530 --> 00:02:34.370
that excited electron, it can
go back from the fourth shell

00:02:34.370 --> 00:02:35.920
to the second shell.

00:02:35.920 --> 00:02:36.930
And when it does it,

00:02:36.930 --> 00:02:41.530
it will emit a photon
of that same wavelength.

00:02:41.530 --> 00:02:43.060
So why is that does that

00:02:43.060 --> 00:02:48.060
it will emit a photon of 486 nanometers.

00:02:50.070 --> 00:02:50.903
So just like that,

00:02:50.903 --> 00:02:52.820
we already are starting to understand

00:02:52.820 --> 00:02:54.610
that photons of the right energy

00:02:54.610 --> 00:02:59.380
can excite an electron by a
shell or more than one shell.

00:02:59.380 --> 00:03:00.500
When we talk about quantum mechanics,

00:03:00.500 --> 00:03:03.380
is this notion that photons
need a certain amount of energy

00:03:03.380 --> 00:03:05.350
in order to be able to excite the electron

00:03:05.350 --> 00:03:08.470
to the next energy level or
the energy level after that.

00:03:08.470 --> 00:03:10.360
Things in between don't work.

00:03:10.360 --> 00:03:13.220
And the same thing is true when
you're emitting the energy,

00:03:13.220 --> 00:03:16.460
the electrons is not gonna go
from the fourth energy level

00:03:16.460 --> 00:03:19.310
to someplace in between
the fourth and the third.

00:03:19.310 --> 00:03:20.380
It can't do that.

00:03:20.380 --> 00:03:22.480
It has these quantum states.

00:03:22.480 --> 00:03:24.200
It's going to be there in
the fourth or the third

00:03:24.200 --> 00:03:26.230
or the second or the first,

00:03:26.230 --> 00:03:28.910
there's no such thing as
a three and a half shell.

00:03:28.910 --> 00:03:31.660
And we can actually answer based on this,

00:03:31.660 --> 00:03:34.090
we can think about what
is the energy difference

00:03:34.090 --> 00:03:36.340
between these shells.

00:03:36.340 --> 00:03:38.710
And the energy difference
between the shells

00:03:38.710 --> 00:03:42.100
is essentially the energy
of the photon that we emit

00:03:42.100 --> 00:03:44.570
when we go from the fourth energy shell

00:03:44.570 --> 00:03:47.000
from the fourth shell to the second shell.

00:03:47.000 --> 00:03:48.990
To figure out the energy of that photon,

00:03:48.990 --> 00:03:51.820
we just have to think
about some useful formulas

00:03:51.820 --> 00:03:53.520
in quantum mechanics.

00:03:53.520 --> 00:03:56.200
The first and I'm gonna just
look at it right over here

00:03:56.200 --> 00:03:58.830
is that the energy is
equal to Planck's constant

00:03:58.830 --> 00:04:00.430
times the frequency.

00:04:00.430 --> 00:04:01.950
So this thing that looks like a V

00:04:01.950 --> 00:04:03.292
this is actually the Greek letter,

00:04:03.292 --> 00:04:06.050
the lowercase Greek letter Nu,

00:04:06.050 --> 00:04:08.480
and this is what we
typically use for frequency,

00:04:08.480 --> 00:04:10.340
especially when we're
talking about frequencies

00:04:10.340 --> 00:04:11.470
of things like light.

00:04:11.470 --> 00:04:14.900
And we also know how to go
between frequency and wavelength,

00:04:14.900 --> 00:04:16.470
because we see that the speed of light

00:04:16.470 --> 00:04:20.120
is equal to whatever the
wavelength of that light is

00:04:20.120 --> 00:04:22.530
times the frequency of that light.

00:04:22.530 --> 00:04:25.590
So how would we figure out
the energy of one photon,

00:04:25.590 --> 00:04:28.290
of 486 nanometer light?

00:04:28.290 --> 00:04:30.130
Well, we could think about it this way.

00:04:30.130 --> 00:04:32.670
We can first figure out its frequency

00:04:32.670 --> 00:04:35.680
using C is equal to Lambda times new.

00:04:35.680 --> 00:04:37.100
Let me write this down.

00:04:37.100 --> 00:04:39.390
So we know that see the speed of light

00:04:39.390 --> 00:04:41.810
is equal to the wavelength of the light

00:04:41.810 --> 00:04:46.040
times the frequency of that light.

00:04:46.040 --> 00:04:48.160
And so if we know the wavelength,

00:04:48.160 --> 00:04:50.380
we can figure out the frequency

00:04:50.380 --> 00:04:53.260
by dividing both sides by Lambda.

00:04:53.260 --> 00:04:54.810
So let's do that.

00:04:54.810 --> 00:04:56.800
So if we divide both sides by Lambda,

00:04:56.800 --> 00:05:00.030
we get that the frequency of the light

00:05:00.030 --> 00:05:02.060
is going to be equal to the speed of light

00:05:02.060 --> 00:05:04.290
divided by the wavelength of the light.

00:05:04.290 --> 00:05:06.550
Remember, they've given us the
wavelength of the light here,

00:05:06.550 --> 00:05:09.940
486 nanometers, or at least
I have given it to you.

00:05:09.940 --> 00:05:12.420
And then you could take
this and plug it back

00:05:12.420 --> 00:05:14.790
into Planck's equation up here,

00:05:14.790 --> 00:05:16.540
that energy is equal to Planck's constant

00:05:16.540 --> 00:05:19.390
times the frequency to
figure out the energy.

00:05:19.390 --> 00:05:20.770
So let me write that down.

00:05:20.770 --> 00:05:24.720
So the energy is going to be
equal to Planck's constant

00:05:24.720 --> 00:05:26.040
times the frequency,

00:05:26.040 --> 00:05:27.720
well we know the
frequency right over here.

00:05:27.720 --> 00:05:31.190
So it's going to be equal
to Planck's constant times,

00:05:31.190 --> 00:05:36.190
the speed of light divided by
the wavelength of our light,

00:05:36.810 --> 00:05:40.370
which we know is 486 nanometers,

00:05:40.370 --> 00:05:44.500
486 nanometers.

00:05:44.500 --> 00:05:47.170
So we could say, just
scroll down a little bit,

00:05:47.170 --> 00:05:49.930
that the energy is going to
be equal to Planck's constant

00:05:49.930 --> 00:05:54.930
times the speed of light divided by

00:05:55.480 --> 00:05:58.360
instead of writing the wave
length is 486 nanometers,

00:05:58.360 --> 00:06:03.360
I can write it as 486 times 10
to the negative ninth meters

00:06:06.530 --> 00:06:10.260
a nanometer is just one
billionth of a meter,

00:06:10.260 --> 00:06:12.060
and then we can just
get our calculator out

00:06:12.060 --> 00:06:14.010
and we know what Planck's constant is.

00:06:14.010 --> 00:06:14.950
They give it right over here.

00:06:14.950 --> 00:06:17.120
We know what the speed of
light is right over here.

00:06:17.120 --> 00:06:19.140
And we know that we have a maximum,

00:06:19.140 --> 00:06:21.350
over here they're giving
us four significant figures

00:06:21.350 --> 00:06:22.280
in each of these.

00:06:22.280 --> 00:06:24.270
And then we have three
significant figures here.

00:06:24.270 --> 00:06:25.210
So our answer's going to be

00:06:25.210 --> 00:06:27.134
in terms of three significant figures.

00:06:27.134 --> 00:06:32.134
I'm going to get Planck's
constant, which is 6.626

00:06:34.550 --> 00:06:38.170
times 10 to the negative
34th joule seconds.

00:06:38.170 --> 00:06:39.960
So let me write that down.

00:06:39.960 --> 00:06:44.960
So times 10 to the negative 34th,

00:06:45.370 --> 00:06:48.460
and I'm gonna multiply that
times the speed of light.

00:06:48.460 --> 00:06:50.713
So times 2.998

00:06:54.140 --> 00:06:59.130
times 10 to the eighth meters per second

00:06:59.130 --> 00:07:01.070
gets me this business.

00:07:01.070 --> 00:07:03.413
And then I'm gonna divide that by 486

00:07:07.200 --> 00:07:11.670
times 10 to the negative ninth gives me,

00:07:11.670 --> 00:07:14.530
I think we deserve a
little bit of a drum roll,

00:07:14.530 --> 00:07:16.170
gives me this.

00:07:16.170 --> 00:07:19.950
And if we were to look at
three significant figures,

00:07:19.950 --> 00:07:24.950
this would be 4.09 times
10 to the negative 19th.

00:07:26.190 --> 00:07:28.870
And Planck's constant here
has given in terms of jewels,

00:07:28.870 --> 00:07:33.870
4.09 times 10 to the negative 19 joules.

00:07:35.950 --> 00:07:37.710
So what that tells us
is that the difference

00:07:37.710 --> 00:07:40.820
in these energy levels is this many joules

00:07:40.820 --> 00:07:42.580
or the energy of that photon

00:07:42.580 --> 00:07:45.640
that has a wavelength of 486 nanometers.

00:07:45.640 --> 00:07:50.640
That energy is 4.09 times 10
to the negative 19 joules.


Spectrophotometry and the Beer–Lambert Law

WEBVTT
Kind: captions
Language: en

00:00:00.700 --> 00:00:02.959
- [Instructor] What I want
to do in this video is

00:00:02.959 --> 00:00:05.020
to talk a little bit
about spectrophotometry.

00:00:05.020 --> 00:00:09.330
Spectrophotometry, photometry,

00:00:09.330 --> 00:00:12.120
which sounds fairly sophisticated,

00:00:12.120 --> 00:00:15.480
but it's really based on
a fairly simple principle.

00:00:15.480 --> 00:00:19.356
So if I have, let's say
we have two solutions

00:00:19.356 --> 00:00:21.620
that contain some type of solute.

00:00:21.620 --> 00:00:25.240
So that is solution one, and
then this is solution two.

00:00:25.240 --> 00:00:28.620
And let's just assume that our
beakers have the same width.

00:00:28.620 --> 00:00:30.390
Now let's say solution,
let me put it right here.

00:00:30.390 --> 00:00:33.540
Number one, and number two.

00:00:33.540 --> 00:00:34.840
Now let's say that solution one

00:00:34.840 --> 00:00:37.870
has less of the solute in it.

00:00:37.870 --> 00:00:39.900
So let me, let me make...

00:00:39.900 --> 00:00:42.270
So that's the water line right there.

00:00:42.270 --> 00:00:44.520
So this guy has less of it,
and let's say it's yellow,

00:00:44.520 --> 00:00:46.330
or to our eyes, it looks yellow.

00:00:46.330 --> 00:00:48.160
So this has less of it.

00:00:48.160 --> 00:00:50.410
So this hasm actuallym
let me do it this way.

00:00:50.410 --> 00:00:51.550
Let me shade it in like this.

00:00:51.550 --> 00:00:54.400
So it has less of it.

00:00:54.400 --> 00:00:57.720
And let's say solution number
two has more of the solute,

00:00:57.720 --> 00:00:59.160
so it's more.

00:00:59.160 --> 00:01:01.550
So I'll just kind of represent that

00:01:01.550 --> 00:01:03.820
as more closely packed lines.

00:01:03.820 --> 00:01:06.410
So the concentration of
the solute is higher here.

00:01:06.410 --> 00:01:09.080
So let me write higher concentration.

00:01:09.080 --> 00:01:11.063
Higher concentration.

00:01:12.150 --> 00:01:14.800
Concentration, and let's say,

00:01:14.800 --> 00:01:19.650
and this is a lower, lower concentration.

00:01:19.650 --> 00:01:21.480
Now let's think about what will happen

00:01:21.480 --> 00:01:25.920
if we shine some light
through each of these beakers,

00:01:25.920 --> 00:01:29.510
and let's just assume that we
are shining at a wavelength

00:01:29.510 --> 00:01:32.687
of light that is specific to the...

00:01:32.687 --> 00:01:35.120
That that is specifically
sensitive to the solute

00:01:35.120 --> 00:01:37.080
that we have dissolved in here.

00:01:37.080 --> 00:01:39.980
But I'll just leave that
pretty general right now.

00:01:39.980 --> 00:01:43.530
So let's say I have some
light here of some intensity.

00:01:43.530 --> 00:01:45.350
So let's just call that...

00:01:45.350 --> 00:01:48.610
Let's call that the incident intensity.

00:01:48.610 --> 00:01:51.930
I'll just say that it's
I0, so it's some intensity.

00:01:51.930 --> 00:01:54.730
What's going to happen as the light exits

00:01:54.730 --> 00:01:57.450
the other side of this beaker right here?

00:01:57.450 --> 00:02:00.470
Well, some of it is going to be absorbed

00:02:00.470 --> 00:02:03.148
by our little molecules inside the beaker,

00:02:03.148 --> 00:02:05.320
so you're going to have less light

00:02:05.320 --> 00:02:06.450
come out to the other side.

00:02:06.450 --> 00:02:07.533
I'll call this I1.

00:02:09.530 --> 00:02:13.700
Now, in this situation, if
we shined the same amount

00:02:13.700 --> 00:02:17.118
of light into this beaker, so
it's the same number that is,

00:02:17.118 --> 00:02:18.380
that is the same, the
same intensity of light,

00:02:18.380 --> 00:02:19.530
what's going to happen?

00:02:20.369 --> 00:02:22.540
Well, more is going to
be absorbed as the light

00:02:22.540 --> 00:02:23.830
travels through this beaker.

00:02:23.830 --> 00:02:27.180
It's just going to bump
into more molecules,

00:02:27.180 --> 00:02:29.180
'cause it's a higher concentration here.

00:02:29.180 --> 00:02:31.510
So the light that comes out when you have

00:02:31.510 --> 00:02:34.890
a higher concentration, I'll
call that the intensity,

00:02:34.890 --> 00:02:37.946
I'll call that I2, this is going to have

00:02:37.946 --> 00:02:41.720
a lower intensity of light
that's being transmitted

00:02:41.720 --> 00:02:42.710
than this one over here.

00:02:42.710 --> 00:02:47.020
In this case, I2 is going
to have a lower intensity,

00:02:47.020 --> 00:02:49.680
is going to be less than I1.

00:02:49.680 --> 00:02:54.520
If you have another beaker
that is maybe twice as wide,

00:02:54.520 --> 00:02:57.210
it's twice as wide, and
let's say it has the same

00:02:57.210 --> 00:02:59.670
concentration as number
two, we'll call this one

00:02:59.670 --> 00:03:03.000
number three, it has the same
concentration as number two.

00:03:03.000 --> 00:03:05.420
So I'll try to make it
look fairly similar,

00:03:05.420 --> 00:03:08.270
and you were to shine some light in here.

00:03:08.270 --> 00:03:10.670
Let's say you shine
the same light in here,

00:03:10.670 --> 00:03:13.840
and you have some light that
makes it through, that exits,

00:03:13.840 --> 00:03:16.600
and then this is actually
what your eyes would see.

00:03:16.600 --> 00:03:19.300
So this is I3 right there.

00:03:19.300 --> 00:03:20.700
What do you think's going to happen?

00:03:20.700 --> 00:03:23.240
Well, it's the same
concentration, but this light

00:03:23.240 --> 00:03:26.110
has to travel a further
distance of that concentration.

00:03:26.110 --> 00:03:29.130
So once again, it's going
to bump into more molecules

00:03:29.130 --> 00:03:32.130
and more of it will be absorbed,

00:03:32.130 --> 00:03:34.520
and so less light will be transmitted.

00:03:34.520 --> 00:03:36.023
So I2 is less than I1, and I3,

00:03:37.890 --> 00:03:40.040
I3 is actually going to be the least.

00:03:40.040 --> 00:03:42.890
And if you were looking at
these, this has the least light,

00:03:42.890 --> 00:03:44.580
this has a little bit more
light being transmitted,

00:03:44.580 --> 00:03:46.940
this has the most light being transmitted.

00:03:46.940 --> 00:03:47.960
So if you were to look at this,

00:03:47.960 --> 00:03:50.280
if you placed your eyeball right here,

00:03:50.280 --> 00:03:52.960
this one right here would
have the lightest color.

00:03:52.960 --> 00:03:55.140
You're getting the most
light into your eye.

00:03:55.140 --> 00:03:56.910
This would be a slightly darker color,

00:03:56.910 --> 00:03:58.750
and this would be the darkest color.

00:03:58.750 --> 00:04:00.030
That makes complete sense.

00:04:00.030 --> 00:04:02.520
If you dissolve something,
if you dissolve a little bit

00:04:02.520 --> 00:04:04.490
of something in water, it will
still be pretty transparent.

00:04:04.490 --> 00:04:06.740
If you dissolve a lot
of something in water,

00:04:06.740 --> 00:04:08.090
it'll be more opaque.

00:04:08.090 --> 00:04:09.990
And if the cup that you're dissolving in,

00:04:09.990 --> 00:04:12.370
or the beaker that you're
in, gets even longer,

00:04:12.370 --> 00:04:14.200
it'll get even more opaque.

00:04:14.200 --> 00:04:16.441
So hopefully, that gives you the intuition

00:04:16.441 --> 00:04:18.660
behind spectrophotometry.

00:04:18.660 --> 00:04:20.598
And so the next question is, well,

00:04:20.598 --> 00:04:21.977
what is it even good for?

00:04:21.977 --> 00:04:22.810
Why would I even care?

00:04:22.810 --> 00:04:24.720
Well, you could actually
use this information.

00:04:24.720 --> 00:04:27.150
You could see how much
light is transmitted

00:04:27.150 --> 00:04:29.740
versus how much you put
in to actually figure out

00:04:29.740 --> 00:04:31.210
the concentration of a solution.

00:04:31.210 --> 00:04:32.880
That's why we're even talking about it

00:04:32.880 --> 00:04:35.010
in a chemistry context.

00:04:35.010 --> 00:04:36.060
So before we do that,

00:04:37.587 --> 00:04:39.839
and I'll show you an example
of that in the next video,

00:04:39.839 --> 00:04:42.640
let me just define some,
really, some terms of ways

00:04:42.640 --> 00:04:44.560
of measuring how concentrated this is,

00:04:44.560 --> 00:04:47.330
or ways of measuring how
much light is transmitted

00:04:47.330 --> 00:04:49.121
versus how much was put in.

00:04:49.121 --> 00:04:53.403
So the first thing I will
define is transmittance.

00:04:56.730 --> 00:04:59.080
And so when the people
who defined it said, well,

00:04:59.080 --> 00:05:01.100
you know, what we care about
is how much is transmitted

00:05:01.100 --> 00:05:04.520
versus how much went in, so
let's just define transmittance

00:05:04.520 --> 00:05:05.770
as that ratio.

00:05:05.770 --> 00:05:08.420
So in this example, the
transmittance of number one

00:05:08.420 --> 00:05:11.306
would be the amount that got through

00:05:11.306 --> 00:05:14.570
over the amount that you put in.

00:05:14.570 --> 00:05:18.470
Over here, the transmittance
would be the amount

00:05:18.470 --> 00:05:21.430
that you got out over the
amount that you put in.

00:05:21.430 --> 00:05:25.290
And as we see, this one right
here will be a lower number.

00:05:25.290 --> 00:05:27.580
I2 is lower than I1,

00:05:27.580 --> 00:05:31.020
so this will have a lower
transmittance then number one.

00:05:31.020 --> 00:05:32.900
So let's call this transmittance two.

00:05:32.900 --> 00:05:34.420
This is transmittance one.

00:05:34.420 --> 00:05:39.260
And transmittance three is
the light that comes out,

00:05:39.260 --> 00:05:42.610
that gets through, over
the light that goes in,

00:05:42.610 --> 00:05:44.760
and this is the smallest
number, followed by that,

00:05:44.760 --> 00:05:45.630
followed by that.

00:05:45.630 --> 00:05:47.540
So this will have the least transmittance,

00:05:47.540 --> 00:05:50.540
it's the most opaque, followed
by that, followed by that.

00:05:50.540 --> 00:05:53.300
Now another definition,
which is really kind of

00:05:53.300 --> 00:05:55.240
a derivative of the transmittance,

00:05:55.240 --> 00:05:56.450
and not in the calculus sense,

00:05:56.450 --> 00:05:58.970
it's just derived from
transmittance, and we'll see,

00:05:58.970 --> 00:06:02.260
it has pretty neat properties,
is the notion of absorbance.

00:06:02.260 --> 00:06:03.800
And so here, we're trying to measure,

00:06:03.800 --> 00:06:05.090
how good is it at absorbing?

00:06:05.090 --> 00:06:06.920
This is measuring, how good
are you at transmitting?

00:06:06.920 --> 00:06:08.900
A higher number says
you're transmitting a lot,

00:06:08.900 --> 00:06:11.270
but absorbance is how
good you're absorbing,

00:06:11.270 --> 00:06:12.380
so it's kind of the opposite.

00:06:12.380 --> 00:06:13.380
If you're good at transmitting,

00:06:13.380 --> 00:06:14.720
that means you're bad at absorbing,

00:06:14.720 --> 00:06:16.130
You don't have a lot to absorb.

00:06:16.130 --> 00:06:17.540
If you're good at absorbing,

00:06:17.540 --> 00:06:19.430
that means you're not transmitting much.

00:06:19.430 --> 00:06:20.710
So absorbance.

00:06:21.820 --> 00:06:26.020
Absorbance, right here,
and absorbance is defined

00:06:26.020 --> 00:06:31.020
as the negative log of transmittance.

00:06:31.040 --> 00:06:34.010
And this logarithm is base 10,

00:06:34.010 --> 00:06:36.610
or you could view that if the
transmittance, we've already

00:06:36.610 --> 00:06:41.150
defined as the negative, the
negative log of the light

00:06:41.150 --> 00:06:46.080
that is transmitted over
the light that is input,

00:06:46.080 --> 00:06:47.750
but the easiest way is the negative log

00:06:47.750 --> 00:06:49.344
of the transmittance.

00:06:49.344 --> 00:06:50.350
And so, if transmittance
is a large number,

00:06:50.350 --> 00:06:52.900
absorbance is a small
number, which makes sense.

00:06:52.900 --> 00:06:54.700
Now, what's also cool about this.

00:06:54.700 --> 00:06:56.810
is there something called
the Beer-Lambert law,

00:06:56.810 --> 00:06:59.500
which you could verify, and this is...

00:06:59.500 --> 00:07:01.790
We'll actually use this in the next video,

00:07:01.790 --> 00:07:04.610
Beer-Lambert law.

00:07:04.610 --> 00:07:07.180
I actually don't know the
history of where it came from,

00:07:07.180 --> 00:07:09.160
and I'm sure it's based
on somebody named Beer,

00:07:09.160 --> 00:07:11.540
but I always imagined it's
based on someone transmitting

00:07:11.540 --> 00:07:14.707
light through beer, the Beer-Lambert law.

00:07:16.688 --> 00:07:20.380
And this tells us, this
tells us that the absorbance

00:07:20.380 --> 00:07:24.360
is proportional to the path length.

00:07:24.360 --> 00:07:27.030
So this would be, how far
does the light have to go

00:07:27.030 --> 00:07:28.230
through the solution?

00:07:28.230 --> 00:07:31.230
So it's proportional to the path length

00:07:31.230 --> 00:07:34.920
times the concentration,
times the concentration.

00:07:34.920 --> 00:07:38.550
Usually we use molarity
for the concentration.

00:07:38.550 --> 00:07:41.970
Or another way to say it
is that the absorbance

00:07:41.970 --> 00:07:43.910
is equal to some constant.

00:07:43.910 --> 00:07:46.600
It's usually a lowercase
Epsilon like that.

00:07:46.600 --> 00:07:50.400
Some constant, and this is
dependent on the solution,

00:07:50.400 --> 00:07:53.210
or the solute in question,
what we actually have in here

00:07:53.210 --> 00:07:56.113
and the temperature and the
pressure and all of that.

00:07:56.113 --> 00:08:00.330
It's equal to constant times
the length it has to travel,

00:08:00.330 --> 00:08:02.150
times the concentration.

00:08:02.150 --> 00:08:03.360
Let me make it clear right here.

00:08:03.360 --> 00:08:04.840
This thing right here,

00:08:04.840 --> 00:08:07.253
this thing right here is concentration.

00:08:08.480 --> 00:08:10.100
Concentration.

00:08:10.100 --> 00:08:12.830
The reason why this is super
useful, as you can imagine,

00:08:12.830 --> 00:08:15.863
so let's say we have an axis right here.

00:08:16.890 --> 00:08:20.620
That's axis, and over here,
I'm measuring concentration.

00:08:20.620 --> 00:08:22.820
This is our concentration axis,

00:08:22.820 --> 00:08:24.809
and we're measuring it as molarity.

00:08:24.809 --> 00:08:26.730
And let's say the molarity starts at zero.

00:08:26.730 --> 00:08:31.297
It goes, you know, I
don't know, .1, .2, .3,

00:08:32.390 --> 00:08:33.570
so on and so forth.

00:08:33.570 --> 00:08:36.400
And over here, you are
measuring absorbance.

00:08:36.400 --> 00:08:39.040
In the vertical axis
you measure absorbance.

00:08:39.040 --> 00:08:42.100
Now, let's say you have some solution,

00:08:42.100 --> 00:08:43.390
and you know the concentration,

00:08:43.390 --> 00:08:46.620
you know it is a .1 molar concentration.

00:08:46.620 --> 00:08:49.090
So let me write down M for molar.

00:08:49.090 --> 00:08:50.237
And you measure its absorbance

00:08:50.237 --> 00:08:51.770
and you just get some number here.

00:08:51.770 --> 00:08:54.840
So you measure its absorbance
and you get its absorbance,

00:08:54.840 --> 00:08:57.660
so this is a low concentration,
didn't absorb that much.

00:08:57.660 --> 00:08:59.660
You get, I don't know some number here,

00:08:59.660 --> 00:09:00.760
so let's say it's .25.

00:09:04.940 --> 00:09:08.490
And then let's say that
you then take another known

00:09:08.490 --> 00:09:11.460
concentration, let's say .2 molar,

00:09:11.460 --> 00:09:14.130
and you say that, oh
look, it has an absorbance

00:09:14.130 --> 00:09:18.060
right here at .5, and I should
put a zero in front of these.

00:09:18.060 --> 00:09:20.300
0.5 and 0.25.

00:09:20.300 --> 00:09:22.980
What this tells you, this
is a linear relationship.

00:09:22.980 --> 00:09:24.807
For any concentration,

00:09:24.807 --> 00:09:27.170
the absorbance is going to be on a line.

00:09:27.170 --> 00:09:29.560
And if you want a little
review of algebra,

00:09:29.560 --> 00:09:31.390
Epsilon times the length
will be the slope.

00:09:31.390 --> 00:09:33.660
But the important thing to realize

00:09:33.660 --> 00:09:35.780
is that you have a line here.

00:09:35.780 --> 00:09:37.860
You have a line here, and why?

00:09:37.860 --> 00:09:39.660
And the reason that's useful
is you could use a little bit

00:09:39.660 --> 00:09:41.330
of algebra, figure out
the equation of a line,

00:09:41.330 --> 00:09:43.770
or you could just look at it
graphically and say, okay,

00:09:43.770 --> 00:09:45.750
I had two known concentrations,

00:09:45.750 --> 00:09:47.930
and I was able to figure
out the absorbance.

00:09:47.930 --> 00:09:50.310
You can then go the other way around.

00:09:50.310 --> 00:09:53.770
You could then measure for
some unknown concentration.

00:09:53.770 --> 00:09:55.110
You could figure out its absorbance.

00:09:55.110 --> 00:09:56.727
So let's say there's some
unknown concentration,

00:09:56.727 --> 00:10:00.670
and you figure out its
absorbance is right over here.

00:10:00.670 --> 00:10:02.060
Let's say it's .4.

00:10:02.060 --> 00:10:04.200
Then you can just go on this
line right here, and you say,

00:10:04.200 --> 00:10:06.500
okay, well then that must be,

00:10:06.500 --> 00:10:08.840
that must be a
concentration of this, well,

00:10:08.840 --> 00:10:10.040
whatever number this is.

00:10:10.040 --> 00:10:11.860
And you could measure it,

00:10:11.860 --> 00:10:13.587
or you could actually
figure it out algebraically.

00:10:13.587 --> 00:10:16.920
And so this will be
pretty close to .2 molar,

00:10:16.920 --> 00:10:18.710
a little bit less than 0.2 molar.

00:10:18.710 --> 00:10:20.620
And we're gonna actually
do an example of that

00:10:20.620 --> 00:10:21.953
in the next video.


Worked example: Calculating concentration using the Beer–Lambert law

WEBVTT
Kind: captions
Language: en

00:00:00.173 --> 00:00:01.290
- [Instructor] So I have a question here

00:00:01.290 --> 00:00:03.740
from the Kotz, Treichel,
and Townsend Chemistry

00:00:03.740 --> 00:00:05.320
and Chemical Reactivity book,

00:00:05.320 --> 00:00:07.220
and I got their permission to do this.

00:00:07.220 --> 00:00:11.130
And it says a solution
of potassium permanganate

00:00:11.130 --> 00:00:15.143
has an absorbance of 0.539

00:00:16.840 --> 00:00:20.420
when measured at 540 nanometers

00:00:20.420 --> 00:00:23.291
in a one centimeter cell.

00:00:23.291 --> 00:00:28.291
What is the concentration of
the potassium permanganate?

00:00:28.900 --> 00:00:33.060
Prior to determining the
absorbance for the unknown solution

00:00:33.060 --> 00:00:35.720
the following calibration
data were collected

00:00:35.720 --> 00:00:38.660
for the spectrophotometer.

00:00:38.660 --> 00:00:40.830
So the way that we would tackle this

00:00:40.830 --> 00:00:43.900
is we know that there
is a linear relationship

00:00:43.900 --> 00:00:47.110
between absorbance and concentration.

00:00:47.110 --> 00:00:48.690
We could describe it something like this,

00:00:48.690 --> 00:00:50.930
that absorbance is going to be equal

00:00:50.930 --> 00:00:55.930
to sum slope times are concentration.

00:00:56.470 --> 00:00:58.440
And you could say sum y-intercept,

00:00:58.440 --> 00:01:00.040
if we're a purist about it,

00:01:00.040 --> 00:01:01.870
then the y intercept should be zero

00:01:01.870 --> 00:01:03.690
because at a zero concentration,

00:01:03.690 --> 00:01:06.090
you should have a zero absorbance.

00:01:06.090 --> 00:01:08.330
But the way that chemists
would typically do it,

00:01:08.330 --> 00:01:12.120
is that they would put
these points into a computer

00:01:12.120 --> 00:01:14.590
and then a computer do
a linear aggression.

00:01:14.590 --> 00:01:15.990
You could also do that by hand

00:01:15.990 --> 00:01:18.990
but that's a little bit out
of the scope of this video.

00:01:18.990 --> 00:01:21.050
And I did that, I went to Desmos

00:01:21.050 --> 00:01:24.560
and I typed in the numbers that they gave.

00:01:24.560 --> 00:01:26.960
And this is what I got,

00:01:26.960 --> 00:01:28.410
so I just typed in these numbers

00:01:28.410 --> 00:01:31.290
and then it fit a linear
regression line to it

00:01:31.290 --> 00:01:34.240
and it got these parameters,
m is equal to this

00:01:34.240 --> 00:01:36.240
and b is equal to this.

00:01:36.240 --> 00:01:37.970
Now we could say significant figures

00:01:37.970 --> 00:01:39.870
it seems like the small
significant figures here

00:01:39.870 --> 00:01:41.360
we have have our three,

00:01:41.360 --> 00:01:43.390
but we could just view the m and the b

00:01:43.390 --> 00:01:45.750
as intermediate numbers
in our calculations.

00:01:45.750 --> 00:01:48.570
What I'm going to do is
I'm gonna use m and b,

00:01:48.570 --> 00:01:50.380
and then my final I'll answer

00:01:50.380 --> 00:01:53.170
I'm going to round to
three significant figures.

00:01:53.170 --> 00:01:54.180
So what this tells us,

00:01:54.180 --> 00:01:57.333
is that absorbance is going to be 5.65333

00:02:01.070 --> 00:02:04.153
times our concentration minus 0.0086.

00:02:08.870 --> 00:02:11.710
And now they've given us what A is.

00:02:11.710 --> 00:02:14.530
Let me get rid of all of this stuff here.

00:02:14.530 --> 00:02:18.570
They told us that our absorbance is 0.539,

00:02:18.570 --> 00:02:23.570
so we know that 0.539 is equal
to 5.65333C minus 0.0086.

00:02:32.680 --> 00:02:34.300
And then if you wanna solve for C,

00:02:34.300 --> 00:02:36.360
let's see, we could add
this to both sides first.

00:02:36.360 --> 00:02:41.360
So you get 0.539 plus
0.0086 is equal to 5.65333C,

00:02:48.500 --> 00:02:50.360
and then divide both sides by this,

00:02:50.360 --> 00:02:52.200
and you would get C is equal to,

00:02:52.200 --> 00:02:54.920
is going to be approximately
equal to, be a little careful

00:02:54.920 --> 00:02:58.060
all of these would really be approximate.

00:02:58.060 --> 00:03:03.060
C is gonna be equal to 0.539
plus 0.0086 divided by 5.65333.

00:03:12.370 --> 00:03:15.540
And of course we want to round
to three significant figures.

00:03:15.540 --> 00:03:20.540
All right, 0.539 plus
0.0086 is equal to that,

00:03:23.870 --> 00:03:27.940
divided by 5.65333 is equal to this,

00:03:31.170 --> 00:03:33.660
so if we go three significant figures

00:03:33.660 --> 00:03:35.750
this is going to be 0.0969.

00:03:40.050 --> 00:03:41.780
So I would write the concentration

00:03:41.780 --> 00:03:44.213
is approximately 0.0969 Molar.


Introduction to spectroscopy

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:03.250
- In this video, we're gonna
talk about spectroscopy,

00:00:03.250 --> 00:00:05.120
which is all about the interactions

00:00:05.120 --> 00:00:06.900
between light and matter.

00:00:06.900 --> 00:00:08.740
And when we're talking about light,

00:00:08.740 --> 00:00:10.750
we're not just talking
about visible light,

00:00:10.750 --> 00:00:14.910
We're talking about electromagnetic
radiation in general.

00:00:14.910 --> 00:00:17.210
And so what I'm going to do
to give us an intuition here

00:00:17.210 --> 00:00:20.480
is use the PhET simulator by
the University of Colorado.

00:00:20.480 --> 00:00:22.700
I encourage you to go to this URL

00:00:22.700 --> 00:00:24.610
and try it out for yourself.

00:00:24.610 --> 00:00:27.170
But you can see what the simulator does is

00:00:27.170 --> 00:00:31.120
it allows us to essentially
see how different wavelengths

00:00:31.120 --> 00:00:36.090
of electromagnetic radiation
can interact with matter,

00:00:36.090 --> 00:00:38.100
in this case various molecules.

00:00:38.100 --> 00:00:39.270
And just to get our bearings,

00:00:39.270 --> 00:00:41.760
we can click on this
light spectrum diagram,

00:00:41.760 --> 00:00:44.160
and we can see that on this diagram

00:00:44.160 --> 00:00:46.620
what people would normally
consider radio waves.

00:00:46.620 --> 00:00:49.030
These are some of the lowest frequencies

00:00:49.030 --> 00:00:51.680
and longest wavelengths of light.

00:00:51.680 --> 00:00:53.290
And then when you get
to higher frequencies,

00:00:53.290 --> 00:00:55.440
you get to microwave, and
the higher the frequency,

00:00:55.440 --> 00:00:57.640
there's also the higher
the energy per photon.

00:00:57.640 --> 00:00:59.660
And then you get higher
frequencies in that

00:00:59.660 --> 00:01:01.600
and higher energy, that's infrared,

00:01:01.600 --> 00:01:03.430
and then higher frequency and energy,

00:01:03.430 --> 00:01:04.290
that's visible light.

00:01:04.290 --> 00:01:06.080
That's what our eyes can sense.

00:01:06.080 --> 00:01:08.870
And then you get even higher
frequency, and more energy.

00:01:08.870 --> 00:01:12.610
You get to ultraviolet. Then
X-ray and then gamma rays.

00:01:12.610 --> 00:01:14.440
And this isn't a linear scale.

00:01:14.440 --> 00:01:16.610
You can see that this is
a logarithmic scale here.

00:01:16.610 --> 00:01:18.770
This is in powers of 10.

00:01:18.770 --> 00:01:22.190
So we see some pretty dramatic
increases in frequency

00:01:22.190 --> 00:01:25.130
and energy as we go from
the left to the right.

00:01:25.130 --> 00:01:28.250
But in this video, we're
gonna focus in particular,

00:01:28.250 --> 00:01:33.250
on microwave, infrared, visible
and ultraviolet wavelengths

00:01:33.660 --> 00:01:37.170
of electromagnetic light,
or electromagnetic waves,

00:01:37.170 --> 00:01:40.563
and think about how they
interact with molecules.

00:01:42.180 --> 00:01:44.690
So if we start with microwave radiation,

00:01:44.690 --> 00:01:46.370
and here we have a water molecule,

00:01:46.370 --> 00:01:47.940
I've picked that right over there

00:01:47.940 --> 00:01:50.520
and I can get my simulation going.

00:01:50.520 --> 00:01:54.760
You can see what it's doing
is, when it gets absorbed,

00:01:54.760 --> 00:01:58.700
it causes a rotational
transition in the water molecule.

00:01:58.700 --> 00:02:02.010
It makes the water molecule
rotate in a different way

00:02:02.010 --> 00:02:03.250
than it was before.

00:02:03.250 --> 00:02:06.230
And then the water molecule
can also emit the radiation

00:02:06.230 --> 00:02:08.100
and then rotate differently.

00:02:08.100 --> 00:02:10.050
And so you can see it
doesn't always do that.

00:02:10.050 --> 00:02:12.300
There's a little bit of
a probability involved,

00:02:12.300 --> 00:02:14.820
but this is actually the
basis of how microwaves work,

00:02:14.820 --> 00:02:16.090
your microwave oven,

00:02:16.090 --> 00:02:18.710
is it causes the water molecules

00:02:18.710 --> 00:02:21.570
to get agitated in a rotational way,

00:02:21.570 --> 00:02:24.770
which increases the heat in that system.

00:02:24.770 --> 00:02:27.390
Now we could also look at infrared light,

00:02:27.390 --> 00:02:29.000
which is once again, we have to remember,

00:02:29.000 --> 00:02:30.940
gets us into higher frequencies,

00:02:30.940 --> 00:02:33.113
and see what that does to molecules.

00:02:34.350 --> 00:02:36.060
So based on this simulation,

00:02:36.060 --> 00:02:40.080
it looks like the infrared
light is when it gets absorbed,

00:02:40.080 --> 00:02:43.240
it causes this water
molecule to start to vibrate.

00:02:43.240 --> 00:02:46.210
So microwave radiation caused it to rotate

00:02:46.210 --> 00:02:48.700
or to have a change in
state of its rotation,

00:02:48.700 --> 00:02:51.210
while infrared makes it vibrate.

00:02:51.210 --> 00:02:53.770
And we could see that with
other molecules as well.

00:02:53.770 --> 00:02:55.393
Let's try carbon monoxide.

00:02:56.370 --> 00:02:58.510
Once again, it's not rotating it,

00:02:58.510 --> 00:03:01.510
it's causing it to vibrate.

00:03:01.510 --> 00:03:03.560
Now what about visible light?

00:03:03.560 --> 00:03:05.860
Well, visible light will
have different interactions

00:03:05.860 --> 00:03:08.120
with different types of molecules,

00:03:08.120 --> 00:03:11.133
but let's try it out
with nitrogen dioxide.

00:03:12.340 --> 00:03:15.700
So there's certain situations
where nitrogen dioxide

00:03:15.700 --> 00:03:18.570
will absorb, that's
when you saw it glowing

00:03:18.570 --> 00:03:19.670
and what you see when it's glowing,

00:03:19.670 --> 00:03:21.880
what it's really doing
is it's putting electrons

00:03:21.880 --> 00:03:25.400
into a higher energy state,
or into a higher orbital

00:03:25.400 --> 00:03:27.240
and then when it stops glowing,

00:03:27.240 --> 00:03:29.480
it means that those
electrons are going back

00:03:29.480 --> 00:03:30.850
to a lower energy state.

00:03:30.850 --> 00:03:33.560
They are re-emitting radiation.

00:03:33.560 --> 00:03:34.393
So there, you can see it.

00:03:34.393 --> 00:03:38.330
You can see that just now,
it's remitting visible light,

00:03:38.330 --> 00:03:40.010
in this case a different direction.

00:03:40.010 --> 00:03:43.370
And when it did that, the
electron that was excited,

00:03:43.370 --> 00:03:46.290
went to a lower energy state.

00:03:46.290 --> 00:03:50.350
Now what about, let's think
about ultraviolet light,

00:03:50.350 --> 00:03:53.180
which has even higher
energy than visible light.

00:03:53.180 --> 00:03:54.030
What can that do?

00:03:55.860 --> 00:03:58.970
Well, here, we can see that
it takes, in certain cases,

00:03:58.970 --> 00:04:01.620
electrons, and it's able
to excite them so much

00:04:01.620 --> 00:04:04.050
that it's able to break that bond itself.

00:04:04.050 --> 00:04:06.140
And so let me keep resetting it.

00:04:06.140 --> 00:04:07.730
So you can actually break bonds.

00:04:07.730 --> 00:04:09.460
Let's see what it can do to some ozone?

00:04:09.460 --> 00:04:11.610
Same thing, it excites it so much

00:04:11.610 --> 00:04:13.710
that it can actually break the bond.

00:04:13.710 --> 00:04:17.020
It's exciting electrons so
much. I can keep resetting it.

00:04:17.020 --> 00:04:19.540
So the big picture here, the big takeaway.

00:04:19.540 --> 00:04:21.370
You could have microwave radiation,

00:04:21.370 --> 00:04:24.640
which tends to change the
rotational motion of a molecule.

00:04:24.640 --> 00:04:27.730
We saw that with the water molecules.

00:04:27.730 --> 00:04:29.800
You have infrared radiation,

00:04:29.800 --> 00:04:32.440
which is higher energy
and higher frequency,

00:04:32.440 --> 00:04:36.420
which tends to lead to a
change in vibrational motion.

00:04:36.420 --> 00:04:40.210
And then you have visible light,
which can excite electrons,

00:04:40.210 --> 00:04:41.700
take them to a higher energy state,

00:04:41.700 --> 00:04:44.530
and then be readmitted
when the electron goes back

00:04:44.530 --> 00:04:45.700
to its base state.

00:04:45.700 --> 00:04:47.780
And then you can have ultraviolet light,

00:04:47.780 --> 00:04:49.930
that's so powerful, it
can excite electrons

00:04:49.930 --> 00:04:53.153
so that in some cases it can
even break covalent bonds.


Real gases: Deviations from ideal behavior

WEBVTT
Kind: captions
Language: en

00:00:00.760 --> 00:00:02.070
- [Instructor] We've
already spent some time

00:00:02.070 --> 00:00:05.710
looking at the ideal gas
law, and also thinking about

00:00:05.710 --> 00:00:08.420
scenarios where things might diverge

00:00:08.420 --> 00:00:11.130
from what at least the
ideal gas law might predict.

00:00:11.130 --> 00:00:12.610
And what we're going to do in this video

00:00:12.610 --> 00:00:14.670
is dig a little bit deeper into scenarios

00:00:14.670 --> 00:00:16.390
where we might diverge a little bit

00:00:16.390 --> 00:00:19.510
from the ideal gas law, or
maybe I guess, a lot of it

00:00:19.510 --> 00:00:21.540
in certain situations.

00:00:21.540 --> 00:00:23.620
So I have three scenarios here.

00:00:23.620 --> 00:00:25.960
This first scenario right over here,

00:00:25.960 --> 00:00:29.700
I have a high temperature,
high temperature,

00:00:29.700 --> 00:00:33.420
and I have a large volume.

00:00:33.420 --> 00:00:35.460
And both of these are really important

00:00:35.460 --> 00:00:37.810
because when we think
about when we get close

00:00:37.810 --> 00:00:41.670
to being ideal, that
situation's where the volume

00:00:41.670 --> 00:00:45.340
of the particles themselves
are negligible to the volume

00:00:45.340 --> 00:00:46.410
of the container.

00:00:46.410 --> 00:00:48.980
And at least here, looks
like that might be the case

00:00:48.980 --> 00:00:51.220
'cause we're dealing
with a very large volume.

00:00:51.220 --> 00:00:52.980
Even this isn't drawn to scale.

00:00:52.980 --> 00:00:54.480
I just drew the particles this size

00:00:54.480 --> 00:00:55.990
just so that you could see them.

00:00:55.990 --> 00:00:59.260
And high temperature,
that helps us realize

00:00:59.260 --> 00:01:02.760
that well maybe the
intermolecular interactions

00:01:02.760 --> 00:01:04.630
or attractions between the particles

00:01:04.630 --> 00:01:06.810
aren't going to be that significant.

00:01:06.810 --> 00:01:10.390
And so in a high temperature,
large volume scenario,

00:01:10.390 --> 00:01:14.290
this might be pretty close to ideal.

00:01:14.290 --> 00:01:15.830
Now it's not gonna be perfectly ideal

00:01:15.830 --> 00:01:18.440
because real gases have some volume,

00:01:18.440 --> 00:01:21.960
and they do have some
intermolecular interactions.

00:01:21.960 --> 00:01:24.290
But now let's change
things up a little bit.

00:01:24.290 --> 00:01:26.520
Let's now move to the same volume.

00:01:26.520 --> 00:01:28.703
So we're still dealing
with a large volume.

00:01:29.550 --> 00:01:31.870
But let's lower the temperature.

00:01:31.870 --> 00:01:34.050
So low temperature.

00:01:34.050 --> 00:01:36.190
And we can see because
temperature is proportional

00:01:36.190 --> 00:01:38.480
to average kinetic
energy of the particles,

00:01:38.480 --> 00:01:41.310
that here, these arrows on
average are a little bit smaller.

00:01:41.310 --> 00:01:42.930
And let's say we lower the temperature

00:01:42.930 --> 00:01:45.110
close to the condensation point.

00:01:45.110 --> 00:01:47.830
Remember, the condensation point of a gas,

00:01:47.830 --> 00:01:51.620
that's a situation where
the molecules are attracting

00:01:51.620 --> 00:01:53.810
each other, and even starting
to clump up together.

00:01:53.810 --> 00:01:55.930
They're starting to, if
we're thinking about say,

00:01:55.930 --> 00:01:59.360
water vapors, they're starting
to get into little droplets

00:01:59.360 --> 00:02:02.200
of liquid water, because
they're getting so attracted

00:02:02.200 --> 00:02:03.330
to each other.

00:02:03.330 --> 00:02:04.450
So in this situation,

00:02:04.450 --> 00:02:07.140
where we have just
lowered the temperature,

00:02:07.140 --> 00:02:10.520
the ideal gas law would already
predict that if you keep

00:02:10.520 --> 00:02:12.950
everything else constant, that
the pressure would go down.

00:02:12.950 --> 00:02:14.370
If we solve for pressure,

00:02:14.370 --> 00:02:18.620
we would have P is equal to nRT over V.

00:02:18.620 --> 00:02:20.570
So if you just lowered temperature,

00:02:20.570 --> 00:02:22.590
the ideal gas law would already predict

00:02:22.590 --> 00:02:24.680
that your pressure would be lower.

00:02:24.680 --> 00:02:27.520
But in this situation with a real gas,

00:02:27.520 --> 00:02:29.430
because we're close to
that condensation point,

00:02:29.430 --> 00:02:32.650
these gases, these particles
are more and more attracted

00:02:32.650 --> 00:02:33.483
to each other.

00:02:33.483 --> 00:02:35.790
So they're less likely
to bump into the sides

00:02:35.790 --> 00:02:36.960
of the container, or if they do,

00:02:36.960 --> 00:02:38.960
they're going to do it with less vigor.

00:02:38.960 --> 00:02:41.290
So in this situation for a real gas,

00:02:41.290 --> 00:02:44.290
because of the intermolecular attraction

00:02:44.290 --> 00:02:46.570
between the particles,
you would actually have

00:02:46.570 --> 00:02:50.440
a lower pressure than even the
ideal gas law would predict.

00:02:50.440 --> 00:02:52.040
Ideal gas law would already predict

00:02:52.040 --> 00:02:54.430
that if you lower the temperature,
pressure would go down.

00:02:54.430 --> 00:02:57.190
But you would see that a
real gas in this scenario,

00:02:57.190 --> 00:03:02.190
P, even lower, even lower for a real gas.

00:03:02.390 --> 00:03:04.110
Now let's go to another scenario.

00:03:04.110 --> 00:03:08.440
Let's go to a scenario where
we keep the high temperature

00:03:08.440 --> 00:03:10.910
that we had in the original scenario,

00:03:10.910 --> 00:03:15.910
but now we have a small
volume, small volume.

00:03:16.100 --> 00:03:19.210
Maybe this top of the
container is a piston,

00:03:19.210 --> 00:03:21.990
and we push it down like this.

00:03:21.990 --> 00:03:25.120
Well the ideal gas law, if
we just solve for P again,

00:03:25.120 --> 00:03:27.850
P is equal to nRT over V.

00:03:27.850 --> 00:03:29.040
It would already predict

00:03:29.040 --> 00:03:31.640
that if you decrease the denominator here,

00:03:31.640 --> 00:03:34.390
that's going to increase the
value of the entire expression.

00:03:34.390 --> 00:03:37.120
So it would already
predict that you would have

00:03:37.120 --> 00:03:40.460
a higher pressure, that
the particles will bounce

00:03:40.460 --> 00:03:42.870
into the sides of the
container more frequently,

00:03:42.870 --> 00:03:45.180
and with more vigor.

00:03:45.180 --> 00:03:47.660
But if we have a really small
volume of the container,

00:03:47.660 --> 00:03:49.630
we no longer can assume that the volume

00:03:49.630 --> 00:03:52.280
of the particles themselves
are going to be negligible

00:03:52.280 --> 00:03:54.120
compared to the volume of the container.

00:03:54.120 --> 00:03:57.310
And so the effective
volume, to move around in

00:03:57.310 --> 00:04:00.460
is even lower than we're
seeing in this equation.

00:04:00.460 --> 00:04:03.010
So these particles have even
less space to bounce around in

00:04:03.010 --> 00:04:05.240
because they take up some of the space.

00:04:05.240 --> 00:04:07.270
So they're going to bounce
off the sides of the container

00:04:07.270 --> 00:04:10.330
more frequently and even more vigor.

00:04:10.330 --> 00:04:15.330
So here, pressure even
higher for a real gas

00:04:15.630 --> 00:04:17.887
than what is predicted
by the ideal gas law.