Spectrophotometry and Beer's Law

It’s Professor Dave, let’s talk spectrophotometry. As we have learned in a previous tutorial, kinetics is the study of reaction rates. Sometimes we will want to know how quickly or slowly a chemical reaction will happen.

Therefore, any kinetic study will require monitoring the concentrations of a particular reactant or product over time, to see how quickly they are being used up, or formed. Of course we can’t see molecules and count them, they are just too small and too many, so to do this, we have to be clever. We can measure the mass of a precipitate as it is forming, or we can measure the volume, or even the pressure, of a gas that is produced over time.

But what if a reaction does not produce a product in a different phase than the solution? Luckily, one of the most reliable methods involves using spectroscopy, which is the study of how light interacts with matter, so let’s learn about this technique now. All molecules absorb and emit light differently based on what kinds of covalent bonds are in the molecule.

If the products and reactants interact with light differently enough that there is a color change as the reaction occurs, we can monitor this process with an instrument called a spectrophotometer, in order to measure changing concentrations. This will give us data in the form of an absorption spectrum, which displays how much light, through a band of frequencies, is able to pass through a sample to reach the detector. Where there are peaks, it means that not as much of the light of that wavelength is getting to the detector, which means that it is being absorbed by the sample.

If we collect data like this continuously over the duration of a chemical reaction, we can gather information about how rapidly the absorbance changes, and thus how the concentration of a particular substance is changing over time. In order to do this, we will use an equation that relates the amount of material in a sample to the absorption of light passing through it, and this is called Beer’s law. Here, A is for absorbance.

This symbol represents something called the molar absorptivity, a measure of how well a chemical species absorbs a given wavelength of light. B represents the path length, or the distance light has to travel through the sample, which is relevant because the more of a substance the light travels through, the more of it that will be absorbed. And C is the concentration of the sample, which again is relevant because the more concentrated, the more absorbance that will occur.

Absorbance is measured by comparing the intensity of the beam of light as it enters the sample, and the intensity as it leaves the sample and strikes the detector, which are I zero and I respectively, and A will be equal to the the log of I zero over I, or equivalently, the negative log of I over I zero. If we plug the latter version into the original equation, substituting for A, and then solve for I, we can get this version of the law, which displays the exponential relationship between variables that are easily measurable. The primary advantage of this technique is that we can just let a reaction occur normally and measure the rate indirectly by analyzing the light that interacts with the components in solution, rather than stopping the reaction and measuring concentrations directly.

Let’s try one calculation to put this into context. Say that a substance has a molar absorptivity of 0. 35 inverse centimeters inverse molarity.

Light passes through a two-centimeter sample, and hits the detector with an intensity of 0. 12 compared with the incident beam. What is the concentration of the sample?

If we want to use the more basic version of Beer’s law, then first we need to calculate the absorption. We can use this simple equation from before, plugging in one for the initial intensity, and 0. 12 for the other intensity.

That gives us 0. 9208 for A. Then we will use Beer’s law.

We can rearrange to solve for C, our unknown, plug in the absorption we calculated plus the two given values, and we should get around 1. 3 molar for the concentration of the analyte. Gathering this kind of information regarding concentration and plotting it in real time using computer software will allow us to easily infer all kinds of things about the rate law and hence the reaction mechanism for the reaction that is happening in solution, which is incredibly useful data.

To get just a bit more practice, let’s check comprehension.