Introduction à la spectrophotométrie

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.