Beer's Law - Theoretical Principles
There are also several variations of the spectrophotometry such as Depending on the range of wavelength of light source, it can be classified into two different types: a linear relationship between the absorbance and the concentration Since absorption, \(\epsilon\), and path length are known, we can. log10I0/IT. Relationship between %Transmittance and light path length and concentration For the mathematically minded: Transmittance = IT/I0*; Absorbance = log10(I0/IT) If you are unclear how to do this practise beforehand . Colored compounds are colored because of the absorption of visible radiation. The color is a result of Mathematically, this relationship is expressed by equation 1: Transmittance (T = I/I0) of Light by a Sample. Absorbance.
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?
- Spectrophotometry introduction
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 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.
Spectrophotometry - Chemistry LibreTexts
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. And over here you're measuring absorbance, in the vertical axis you measure absorbance. You measure absorbance just like that.ClinChem: absorbance and concentration in spectrophotometry
Now let's say you have some solution and you know the concentration, you know it is a 0. 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. And then, let's say that you then take another known concentration, let's say 0. On the other hand, if all visible wavelengths are transmitted i. Visible spectrophotometers, in practice, use a prism to narrow down a certain range of wavelength to filter out other wavelengths so that the particular beam of light is passed through a solution sample.
Devices and mechanism Figure 1 illustrates the basic structure of spectrophotometers. Detailed mechanism is described below. First a collimator lens transmits a straight beam of light photons that passes through a monochromator prism to split it into several component wavelengths spectrum.
A single wavelenth spectrophotometer You need a spectrometer to produce a variety of wavelengths because different compounds absorb best at different wavelengths. For example, p-nitrophenol acid form has the maximum absorbance at approximately nm and p-nitrophenolate basic form absorb best at nm, as shown in Figure 3.
An isosbestic point is the wavelength in which the absorbance of two or more species are the same. The appearance of an isosbestic point in a reaction demonstrates that an intermediate is NOT required to form a product from a reactant.
How to relate the transmittance to the absorbance, concentration, and molar absorptivity?
An example of isosbestic point Referring back to Figure 1 and Figure 5the amount of photons that goes through the cuvette and into the detector is dependent on the length of the cuvette and the concentration of the sample. Once you know the intensity of light after it passes through the cuvette, you can relate it to transmittance T. Transmittance is the fraction of light that passes through the sample.
This can be calculated using the equation: Transmittance is related to absorption by the expression: With the amount of absorbance known from the above equation, you can determine the unknown concentration of the sample by using Beer-Lambert Law. Transmittance illustrated by Heesung Shim Beer-Lambert Law Beer-Lambert Law also known as Beer's Law states that there is a linear relationship between the absorbance and the concentration of a sample.