# Path length and absorbance relationship tips

### Beer's Law - Theoretical Principles

These useful tips and tricks will help you get the best out of any circular dichroism measurement. Since CD is an absorption technique based on Beer's Law, the sample If a sample is too concentrated or the cell pathlength is too long, the sample will The following relationship exists between the signal-to-noise and the. Relationship between %Transmittance and light path length and concentration Absorbance increases linearly with concentration as predicted by the Beer- Lambert Law . Quick tips. You can use the extinction coefficient obtained in the first. An explanation of the Beer-Lambert Law, and the terms absorbance and molar the Beer-Lambert Law (below), the relationship between A (the absorbance) and the two Both concentration and solution length are allowed for in the Beer- Lambert Law. Exactly how you plot the vertical scale doesn't affect this in any way.

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.

**Beers Law**

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?

### Spectrophotometry introduction (video) | Khan Academy

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. 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.

## Spectrophotometry introduction

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. 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. And you say that, oh look, it has an absorbance of 0. So let me do that in a different color. It has an absorbance, right here, at 0.

### Chem - Experiment II

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

You can choose any wavelength to create a calibration plot, the only differerence will be the slope of the line. When you actually choose your wavelength to create your calibration graph, you would generally like to choose a wavelength where there is room for the concentration to decrease.

Look at the spectrum above. Do you think nm would be a good wavelength to use for a calibration graph? You would not choose that wavelength because when you lower the concentration, you would not be able to see much of a difference in the absorbance, and the calculations would be inaccurate. You would most likely want to choose wavelengths like nm or nm where there is a lot of room for absorbance change.

Now for the fun part! Using the calibration plot that YOU made from the data two pages ago. We are going to determing the concentration of an unknown solution. Make sure you have your plot ready, because here we go! Here's a typical problem. You take 3mL of your unknown sample and 7mL water and mix them together. The dilluted sample gives an absorbance of 0.