In this lesson, we'll learn about Beer's Law and how to use spectrophotometry to determine either molar absorbance or concentration in the Beer's Law equation.
Do you know how much caffeine you drink when you have a cup of coffee? Tea? Soda? You can probably find the answer on the internet, but how was that measured? There are many different methods, but one possible method is using spectrophotometry and Beer's Law.
A spectrophotometer is an instrument that can be used to indirectly determine the amount of a compound present. It works by shining a light onto the sample, then the spectrophotometer measures the amount of light that was absorbed. You first set the spectrophotometer to a specific wave length. For most machines, this is fairly simple using the number pad: you simply type in the desired wavelength. The sample is put into a cuvette. A cuvette is simply a clear, square shaped container. Then the cuvette is put into the spectrophotometer and, after a few seconds, it spits out the results. The results are called absorbance and have no units.
This chosen wave length corresponds to a specific color of light: ultraviolet and infrared lights can also be used, depending on the type of spectrophotometer being used. Each compound will absorb, transmit, and reflect a certain wavelength. If we know what wavelength is absorbed by a certain compound, then we can determine how much of that compound is present by seeing how much of the light was absorbed.
So we put the sample into a cuvette and get a number called absorbance. What good does that do? How do we use that information to determine the concentration of the compound of interest in the sample? In order to do this, we use Beer's Law. Beer's Law is that the absorbance, through a known length, is directly proportional to the concentration of the solution. In other words, as long as we know how far the light traveled through the sample, then we can determine the concentration of the solution based on the absorbance. Since we know how long the cuvette is (typically 1 cm), we can determine the concentration.
The equation for Beer's Law is that absorbance equals the molar absorptivity shown as epsilon (in this equation) times the length times the concentration:
So there is still one more term we need to define, molar absorptivity. Molar absorptivity is unique for each substance and each wavelength; it refers to how much of a particular wavelength of light will be absorbed by a substance. The units for molar absorptivity is per Molar*cm. In order to determine the molar absorptivity, we run a series of tests with increasing concentrations of the substance, then we graph the results in order to determine epsilon.
Once molar absorptivity has been determined, Beer's Law can be rearranged to solve for concentration once you've determined absorbance, which is, as you can see:
Determining Molar Absorptivity
So, let's look at an example of determining the molar absorptivity. Let's say you want to compare how much caffeine is in coffee and tea. First, you'll get a pure sample of caffeine and make increasing dilutions by mixing increasing amounts of caffeine with water. Let's use 5 μM, 10 μM, 50 μM, and 100 μM. You set the spectrophotometer to 270 nm and you get the following results:
Then we chart the results and determine the equation of the chart, as you can see here:
It should be a perfectly straight line where it crosses the y-axis at (0, 0). But looking at this graph, you can see that it will actually cross the y-axis at (0, 0.0004). This is due to the fact that the machines are not perfect and you will get a slight variation, but this is within an acceptable range so we may proceed with epsilon being 8777.6. So caffeine absorbs 270 nm of light at a rate of 8777.6/M*cm.
Now that we know the molar absorptivity of caffeine at 270 nm, we can run coffee and tea through. Now typically a cup of coffee will have somewhere around 3.5 μM of caffeine, and a cup of tea will be around 0.82 μM of caffeine. This would result in a very high absorbance. Since most spectrophotometers are only accurate below an absorbance of 1.5, we should dilute the samples first and then simply multiply the result we get by the dilution factor. If you're using a sample that you have no idea the concentration may be, simply run a spectrum of dilution until you find one within a good range.
Since our dilutions that we used to determine epsilon were between 5 - 100 μM we need to dilute the samples. So, we need to do about a 1:100 dilution. We put each of these diluted samples in the cuvette and read the absorbance. So for the coffee, we get an absorbance of 0.2546, and for the tea we get an absorbance of 0.1053.
So for coffee the equation looks like this, and as you can see, says:
And for tea the equation looks like this and says:
So we get 0.000029 M for the coffee and 0.000012 M for the tea. First, we multiply this by the dilution factor of 100, and we see that there is 0.0029 M (2.9 μM) of caffeine in the coffee and 0.0012 M (1.2 μM) of caffeine in the tea.
Let's take a couple moments to review the important information that we've learned. Beer's Law states that the absorbance, through a known length, is directly proportional to the concentration of the solution. It means that absorption is equal to molar absorptivity times length times concentration. Molar absorptivity is determined by measuring the absorbance of a series of known dilutions for a compound. We can then put an unknown sample in a cuvette, which is a clear, square-shaped container, and measure the absorbance in a spectrophotometer, which is an instrument that can be used to indirectly determine the amount of a compound present. We then divide the absorption obtained by the molar absorptivity and determine the concentration of the sample.