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What I want to do in this video is to talk a little bit

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about spectrophotometry.

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Spectrophotometry sounds fairly sophisticated, but it's

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really based on a fairly simple principle.

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So let's say we have two solutions that contain some

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type of solute.

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So that is solution one, and then this is solution two.

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And let's just assume that our beakers have the same width.

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Now let's say solution 1-- let me put it right here, number

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1, and number 2.

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Now let's say that solution 1 has less of the solute in it.

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So that's the water line right there.

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So this guy has less of it.

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And let's say it's yellow or to our eyes it looks yellow.

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So this has less of it.

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Actually, let me do it this way.

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Let me shade it in like this.

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So it has less of it.

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And let's say solution number 2 has more of the solute.

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So it's more.

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So I'll just kind of represent that as more

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closely packed lines.

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So the concentration of the solute is higher here.

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So let me write higher concentration.

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And let's say this is a lower concentration.

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Now let's think about what will happen if we shine some

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light through each of these beakers.

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And let's just assume that we are shining at a wavelength of

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light that is specifically sensitive to the solute that

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we have dissolved in here.

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I'll just leave that pretty general right now.

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So let's say I have some light here of some intensity.

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So let's just call that the incident intensity.

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I'll say that's I0.

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So it's some intensity.

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What's going to happen as the light exits the other side of

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this beaker right here?

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Well, some of it is going to be at absorbed.

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Some of this light, at certain frequencies, is going to be

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absorbed by our little molecules inside the beaker.

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And so you're actually going to have less light coming out

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from the other side.

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Especially less of those specific frequencies that

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these molecules in here like to absorb.

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So your're going to have less light come out the other side.

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I'll call this I1.

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Now in this situation, if we shine the same amount of

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light-- so I0-- that's supposed to be an arrow there,

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but my arrow is kind of degrading.

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If we shined the same amount of light into this beaker-- so

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it's the same number, that and that is the same-- the same

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intensity of light, what's going to happen?

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Well more of those specific frequencies of light are going

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to be absorbed as the light travels through this beaker.

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It's just going to bump into more molecules because it's a

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higher concentration here.

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So the light that comes out when you have a higher

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concentration-- I'll call the intensity I2-- this is going

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to have a lower intensity of light that's being transmitted

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than this one over here.

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In this case, I2 is going to have a lower intensity, is

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going to be less than I1.

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And hopefully, that makes intuitive sense.

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These light, if you imagine, photons are just going to bump

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into more molecules.

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They're going to be absorbed by more molecules.

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So there'll be fewer that make it through than these right

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here, because here it is less concentrated.

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It's also the case if the beaker was thicker.

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Let me draw another beaker.

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If you have another beaker that is maybe twice as wide,

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and let's say it has the same concentration as number 1.

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We'll call this one number 3.

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It has the same concentration as number 2, so I'll try to

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make it look fairly similar to this.

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And you were to shine some light in here.

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Generally you want to focus on the frequencies that this is

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the best at absorbing.

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But let's say you shine the same light in here.

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And you have some light that makes it through, that exits.

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And this is actually what your eyes would see.

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So this is I3 right there, what do you

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think is going to happen?

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Well it's the same concentration, but this light

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has to travel a further distance to that

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concentration.

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So once again, it's going to bump into more molecules and

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more of it will be absorbed.

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And so less light will be transmitted.

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So I2 is less than I1, and I3 is actually going to be the

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least.

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And if you were looking at these, this has the least

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light, this has a little bit more light being transmitted,

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this has the most light being transmitted.

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So if you were to look at this, if you placed your

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eyeball right here-- those are eyelashes-- this one right

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here would have the lightest color.

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You're getting the most light into your eye.

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This would be a slightly darker color, and this would

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be the darkest color.

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That makes complete sense.

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If you dissolve something, if you dissolve a little bit of

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something in water, it will still be pretty transparent.

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If you dissolve a lot of something in water, it'll be

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more opaque.

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And if the cup that you're dissolving in, or the beaker

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that you're in gets even longer, it'll

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get even more opaque.

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So hopefully that gives you the intuition behind

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spectrophotometry.

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And so the next question is, well what is it even good for?

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Why would I even care?

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Well you could actually use this information.

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You could see how much light is transmitted versus how much

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you put in to actually figure out the

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concentration of a solution.

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That's why we're even talking about it

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in a chemistry context.

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So before we do that-- and I'll show you an example of

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that in the next video-- let me just define some terms of

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ways of measuring how concentrated this is.

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Or ways of measuring how much light is transmitted versus

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how much was put in.

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So the first thing I will define is transmittance.

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And so when the people who defined it said, well you

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know, what we care about is how much is transmitted versus

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how much went in.

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So let's just define transmittance as that ratio,

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the amount that gets through.

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So in this example, the transmittance of number 1

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would be the amount that got through over the amount that

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you put in.

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Over here, the transmittance would be the amount that you

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got out over the amount that you put in.

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And as we see, this one right here will be a lower number.

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I2 is lower than I1.

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So this will have a lower transmittance than number 1.

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So let's call this transmittance 2.

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This is transmittance 1.

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And transmittance 3 is the light that comes out, that

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gets through, over the light that goes in.

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And this is the smallest number, followed by that,

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followed by that.

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So this will have the least transmittance-- it's the most

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opaque-- followed by that, followed by that.

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Now another definition-- which was really kind of a

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derivative of the-- not in the calculus sense, this is just

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derived from transmittance and we'll see it has pretty neat

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properties-- is the notion of absorbance.

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And so here, we're trying to measure how

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good is it at absorbing?

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This is measuring how good are you at transmitting?

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A higher number says your transmitting a lot.

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But absorbance is how good you're absorbing.

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So it's kind of the opposite.

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If you're good at transmitting, that means

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you're bad at absorbing, you don't have a lot to absorb.

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If you're good at absorbing, that means you're not

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transmitting much.

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So absorbance right here.

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And that is defined as the negative log of transmittance.

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And this logarithm is base 10.

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Or you could view that, the transmittance we've already

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defined, as the negative log of the light that is

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transmitted over the light that is input.

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But the easiest way is the negative log of the

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transmittance.

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So if transmittance is a large number, absorbance is a small

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number, which makes sense.

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If you're transmitting a lot of light, the absorbance

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number's going to be very small, which means you're not

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absorbing that much.

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If transmittance is a low number, that means you're

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absorbing a lot.

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And so this will actually be a large number.

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And that's what the negative log gives us.

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Now what's also cool about this is, there's something

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called the Beer-Lambert law, which you could verify.

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We'll actually use this in the next video, the

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Beer-Lambert law.

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I actually don't know the history of where it came from.

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And I'm sure it's based on somebody named Beer, but I

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always imagined it's based on someone transmitting light

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through beer.

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The Beer-Lambert law tells us that the absorbance is

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proportional-- I should write it like this-- the absorbance

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is proportional to the path length-- so this would be how

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far does the light have to go through the solution.

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So it's proportional to the path length times the

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concentration.

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And usually, we use molarity for the concentration.

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Or another way to say it is that the absorbance is equal

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to some constant-- it's usually a lowercase epsilon

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like that-- and this is dependent on the solution, or

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the solute in question, what we actually have in here, and

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the temperature, and the pressure, and all of that.

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Well it's equal to some constant, times the length it

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has to travel, times the concentration.

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Let me make it clear right here.

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This thing right here is concentration.

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And the reason why this is super useful is, you can

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imagine, if you have something of a known concentration-- let

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me draw right here.

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So let's say we have an axis right here, that's axis.

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And over here I'm measuring concentration.

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This is our concentration axis.

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And we're measuring it as molarity.

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And let's say the molarity starts at 0.

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It goes, I don't know, 0.1, 0.2, 0.3, so on and so forth.

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And over here you're measuring absorbance, in the vertical

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axis you measure absorbance.

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You measure absorbance just like that.

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Now let's say you have some solution and you know the

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concentration, you know it is a 0.1 molar concentration.

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So let me write down M for molar.

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And you measure its absorbance, and you just get

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some number here.

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So you measure its absorbance and you get its absorbance.

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So this is a low concentration, it didn't

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absorb that much.

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You get, I don't know, some number here, so

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let's say it's 0.25.

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And then, let's say that you then take another known

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concentration, let's say 0.2 molar.

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And you say that, oh look, it has an absorbance of 0.5.

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So let me do that in a different color.

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It has an absorbance, right here, at 0.5.

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And I should put a 0 in front of these, 0.5 and 0.25.

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What this tells you, this is a linear relationship.

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That for any concentration, the absorbance is

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going to be on a line.

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And if you want a little review of algebra, this

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epsilon is actually going to be the slope of that line.

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Well actually, the epsilon times the

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length will be the slope.

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I don't want to confuse you too much.

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But the important thing to realize is that

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you have a line here.

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And the reason that's useful is-- you could use a little

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bit of algebra to figure out the equation of the line.

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Or you could just look at it graphically and say, OK, I had

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two known concentrations and I was able to figure out the

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absorbance because I know that it's a linear relationship,

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the Beer-Lambert law.

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And if you just kept taking measurements, it would all

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show up along this line.

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You can then go the other way around.

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You could then measure for some unknown concentration.

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You could figure out its absorbance.

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So let's say there's some unknown concentration, and you

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figure out its absorbance is right over here.

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Let's say it's 0.4, it has an absorbance of 0.4.

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Then you can just go on this line right here, and you say

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OK, well then that must be a concentration of whatever

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number this is.

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Then you could measure it, or you can actually figure it out

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algebraically.

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And so this will be pretty close to 0.2 molar, or a

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little bit less than 0.2 molar.

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And we're going to actually do an example of

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that in the next video.

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