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Current time:0:00Total duration:13:06

What I want to do in this video
is to talk a little bit about spectrophotometry. Spectrophotometry sounds fairly
sophisticated, but it's really based on a fairly
simple principle. So let's say we have two
solutions that contain some type of solute. So that is solution one, and
then this is solution two. And let's just assume that our
beakers have the same width. Now let's say solution 1-- let
me put it right here, number 1, and number 2. Now let's say that solution 1
has less of the solute in it. So that's the water
line right there. So this guy has less of it. And let's say it's yellow or to
our eyes it looks yellow. So this has less of it. Actually, let me
do it this way. Let me shade it in like this. So it has less of it. And let's say solution number
2 has more of the solute. So it's more. So I'll just kind of represent
that as more closely packed lines. So the concentration of the
solute is higher here. So let me write higher
concentration. And let's say this is a
lower concentration. Now let's think about what will
happen if we shine some light through each
of these beakers. And let's just assume that we
are shining at a wavelength of light that is specifically
sensitive to the solute that we have dissolved in here. I'll just leave that pretty
general right now. So let's say I have some light
here of some intensity. So let's just call that the
incident intensity. I'll say that's I0. So it's some intensity. What's going to happen as the
light exits the other side of this beaker right here? Well, some of it is going
to be at absorbed. Some of this light, at certain
frequencies, is going to be absorbed by our little molecules
inside the beaker. And so you're actually going to
have less light coming out from the other side. Especially less of those
specific frequencies that these molecules in here
like to absorb. So your're going to have less
light come out the other side. I'll call this I1. Now in this situation, if we
shine the same amount of light-- so I0-- that's supposed
to be an arrow there, but my arrow is kind
of degrading. If we shined the same amount of
light into this beaker-- so it's the same number, that and
that is the same-- the same intensity of light, what's
going to happen? Well more of those specific
frequencies of light are going to be absorbed as the light
travels through this beaker. It's just going to bump into
more molecules because it's a higher concentration here. So the light that comes out
when you have a higher concentration-- I'll call the
intensity I2-- this is going to have a lower intensity of
light that's being transmitted than this one over here. In this case, I2 is going to
have a lower intensity, is going to be less than I1. And hopefully, that makes
intuitive sense. These light, if you imagine,
photons are just going to bump into more molecules. They're going to be absorbed
by more molecules. So there'll be fewer that make
it through than these right here, because here it is
less concentrated. It's also the case if the
beaker was thicker. Let me draw another beaker. If you have another beaker that
is maybe twice as wide, and let's say it has the same
concentration as number 1. We'll call this one number 3. It has the same concentration
as number 2, so I'll try to make it look fairly
similar to this. And you were to shine
some light in here. Generally you want to focus on
the frequencies that this is the best at absorbing. But let's say you shine the
same light in here. And you have some light that
makes it through, that exits. And this is actually what
your eyes would see. So this is I3 right
there, what do you think is going to happen? Well it's the same
concentration, but this light has to travel a further
distance to that concentration. So once again, it's going to
bump into more molecules and more of it will be absorbed. And so less light will
be transmitted. So I2 is less than I1, and I3
is actually going to be the least. And if you were looking at
these, this has the least light, this has a little bit
more light being transmitted, this has the most light
being transmitted. So if you were to look at
this, if you placed your eyeball right here-- those are
eyelashes-- this one right here would have the
lightest color. You're getting the most
light into your eye. This would be a slightly darker
color, and this would be the darkest color. That makes complete sense. If you dissolve something, if
you dissolve a little bit of something in water, it will
still be pretty transparent. If you dissolve a lot of
something in water, it'll be more opaque. And if the cup that you're
dissolving in, or the beaker that you're in gets
even longer, it'll get even more opaque. So hopefully that gives you
the intuition behind spectrophotometry. And so the next question is,
well what is it even good for? Why would I even care? Well you could actually
use this information. You could see how much light is
transmitted versus how much you put in to actually
figure out the concentration of a solution. That's why we're even
talking about it in a chemistry context. So before we do that-- and I'll
show you an example of that in the next video-- let me
just define some terms of ways of measuring how
concentrated this is. Or ways of measuring how much
light is transmitted versus how much was put in. So the first thing I will
define is transmittance. And so when the people who
defined it said, well you know, what we care about is how
much is transmitted versus how much went in. So let's just define
transmittance as that ratio, the amount that gets through. So in this example, the
transmittance of number 1 would be the amount that got
through over the amount that you put in. Over here, the transmittance
would be the amount that you got out over the amount
that you put in. And as we see, this one right
here will be a lower number. I2 is lower than I1. So this will have a lower
transmittance than number 1. So let's call this
transmittance 2. This is transmittance 1. And transmittance 3 is the light
that comes out, that gets through, over the
light that goes in. And this is the smallest number,
followed by that, followed by that. So this will have the least
transmittance-- it's the most opaque-- followed by that,
followed by that. Now another definition-- which
was really kind of a derivative of the-- not in the
calculus sense, this is just derived from transmittance and
we'll see it has pretty neat properties-- is the notion
of absorbance. And so here, we're trying
to measure how good is it at absorbing? This is measuring how good
are you at transmitting? A higher number says your
transmitting a lot. But absorbance is how good
you're absorbing. So it's kind of the opposite. If you're good at transmitting,
that means you're bad at absorbing, you
don't have a lot to absorb. If you're good at absorbing,
that means you're not transmitting much. So absorbance right here. And that is defined as the
negative log of transmittance. And this logarithm is base 10. Or you could view that, the
transmittance we've already defined, as the negative log
of the light that is transmitted over the light
that is input. But the easiest way is the
negative log of the transmittance. So if transmittance is a large
number, absorbance is a small number, which makes sense. If you're transmitting a lot
of light, the absorbance number's going to be very small,
which means you're not absorbing that much. If transmittance is a low
number, that means you're absorbing a lot. And so this will actually
be a large number. And that's what the negative
log gives us. Now what's also cool about this
is, there's something called the Beer-Lambert law,
which you could verify. We'll actually use this
in the next video, the Beer-Lambert law. I actually don't know the
history of where it came from. And I'm sure it's based on
somebody named Beer, but I always imagined it's based on
someone transmitting light through beer. The Beer-Lambert law tells
us that the absorbance is proportional-- I should write it
like this-- the absorbance is proportional to the path
length-- so this would be how far does the light have to
go through the solution. So it's proportional to the
path length times the concentration. And usually, we use molarity
for the concentration. Or another way to say it is that
the absorbance is equal to some constant-- it's usually
a lowercase epsilon like that-- and this is
dependent on the solution, or the solute in question, what we
actually have in here, and the temperature, and the
pressure, and all of that. Well it's equal to some
constant, times the length it has to travel, times
the concentration. Let me make it clear
right here. This thing right here
is concentration. And the reason why this is
super useful is, you can imagine, if you have something
of a known concentration-- let me draw right here. So let's say we have an axis
right here, that's axis. And over here I'm measuring
concentration. This is our concentration
axis. And we're measuring
it as molarity. And let's say the molarity
starts at 0. It goes, I don't know, 0.1, 0.2,
0.3, so on and so forth. And over here you're measuring
absorbance, in the vertical axis you measure absorbance. You measure absorbance
just like that. Now let's say you have some
solution and you know the concentration, you know it is
a 0.1 molar concentration. So let me write down
M for molar. And you measure its absorbance,
and you just get some number here. So you measure its absorbance
and you get its absorbance. So this is a low concentration,
it didn't absorb that much. You get, I don't know,
some number here, so let's say it's 0.25. And then, let's say that you
then take another known concentration, let's
say 0.2 molar. And you say that, oh look, it
has an absorbance of 0.5. So let me do that in
a different color. It has an absorbance,
right here, at 0.5. And I should put a 0 in front
of these, 0.5 and 0.25. What this tells you, this is
a linear relationship. That for any concentration,
the absorbance is going to be on a line. And if you want a little
review of algebra, this epsilon is actually going to
be the slope of that line. Well actually, the
epsilon times the length will be the slope. I don't want to confuse
you too much. But the important thing
to realize is that you have a line here. And the reason that's useful
is-- you could use a little bit of algebra to figure out
the equation of the line. Or you could just look at it
graphically and say, OK, I had two known concentrations and I
was able to figure out the absorbance because I know that
it's a linear relationship, the Beer-Lambert law. And if you just kept taking
measurements, it would all show up along this line. You can then go the
other way around. You could then measure for some
unknown concentration. You could figure out
its absorbance. So let's say there's some
unknown concentration, and you figure out its absorbance
is right over here. Let's say it's 0.4, it has
an absorbance of 0.4. Then you can just go on this
line right here, and you say OK, well then that must be a
concentration of whatever number this is. Then you could measure it, or
you can actually figure it out algebraically. And so this will be pretty
close to 0.2 molar, or a little bit less than
0.2 molar. And we're going to actually
do an example of that in the next video.