Absorption Measurements & their Application to Quantitative Analysis
A study of the interaction of light (or other electromagnetic radiation) with matter is an important and versatile tool for the chemist. Indeed, much of our knowledge of chemical substances comes from their specific absorption or emission of light. In this experiment, we are interested in analytical procedures based on the amount of light absorbed (or transmitted) as it passes through a sample. Suppose you look at two solutions of the same substance, one a deeper color than the other. Your common sense tells you that the darker colored one is the more concentrated. In other words, as the color of the solution deepens,you infer that its concentration also increases. This is an underlying principle of spectrophotometry: the intensity of color is a measure of the amount of a material in solution. A second principle of spectrophotometry is that every substance absorbs or transmits certain wavelengths of radiant energy but not other wavelengths. For example, chlorophyll always absorbs red and violet light, while it transmits yellow, green, and blue wavelengths. The transmitted and reflected wavelengths appear green—the color your eye “sees.†The light energy absorbed or transmitted must match exactly the energy required to cause an electronic transition (a movement of an electron from one quantum level to another) in the substance under consideration. Only certain wavelength photons satisfy this energy condition. Thus, the absorption or transmission of specific wavelengths is characteristic for a substance, and a spectral analysis serves as a “fingerprint†of the compound. In recent years spectrophotometric methods have become the most frequently used and important methods of quantitative analysis. They are applicable to many industrial and clinical problems involving the quantitative determination of compounds that are colored or that react to form a colored product.
LIGHT AND THE PERCEPTION OF COLOR Light is a form of electromagnetic radiation. When it falls on a substance, three things can happen:
- the light can be reflected by the substance
- it can be absorbed by the substance
- certain wavelengths can be absorbed and the remainder transmitted or reflected Since reflection of light is of minimal interest in spectrophotometry,we will ignore it and turn to the absorbance and transmittance of light.
The color we see in a sample of solution is due to the selective absorption of certain wavelengths of visible light and transmittance of the remaining wavelengths. If a sample absorbs all wavelengths in the visible region of the spectrum, it will appear black; if it absorbs none of them, it will appear white or colorless. We see the various colors when particular wavelengths of radiant energy strike our eyes. For example, the wavelength we perceive as green is 0.0000195 inches or, expressed more scientifically, 495 nanometers. Suppose we shine a beam of white light at a substance that absorbs blue light. Since the blue component of the white light gets absorbed by the substance, the light that is transmitted is mostly yellow, the complementary color of blue. This yellow light reaches our eyes, and we “see†the substance as a yellow colored substance. The table below gives pairs of complementary colors and the corresponding wavelength ranges.
Wavelength (nm)                           Color Absorbed                               Color Observed
400                                                        violet                                                    yellow-green
435                                                        blue                                                      yellow
495                                                        green                                                   purple
You should remember, of course, that the visible range is only a very small part of the electromagnetic spectrum. Ultraviolet and infrared spectrophotometric methods are suitable for many colorless substances that absorb strongly in the UV or IR spectral regions.
TRANSMITTANCE, ABSORBANCE, AND THE BEER-LAMBERT LAW
We define transmittance as the ratio of the amount of light transmitted to the amount of light that initially fell on the surface.
Absorbance is defined as the negative logarithm of the transmittance, and you will note that absorbance and transmittance bear an inverse relationship.
Absorbance = – log T = – log P/Po
 Going back to our example of chlorophyll, if you have two colored solutions, you may deduce that the darker colored green solution appears darker because it absorbs more of the light falling on it. Because the darker solution is also the more concentrated one, you can also say that the more concentrated one absorbs more of the light. That is, the absorbance increases as concentration increases. Next, suppose that there are two test tubes, both containing the same solution at the same concentration. The only difference is that one of the test tubes is thicker than the other.
We shine light of the same intensity (Po) on both containers. In the first case the light has to travel through only a short distance, whereas in the second case it has to pass through a much longer length of the sample. We might deduce that in the second case more of the light will be absorbed or cut off, since the path length is longer. In other words, absorbance increases as pathlength increases. The two observations described above (those dealing with the relationship between absorbance and concentration and absorbance and path length) constitute the BEER-LAMBERT LAW.
Beer-Lambert Law
Absorbance ∠path length (l)• concentration
A = ε • l • c
where
- A is a dimensionless number.
- ε the proportionality constant, is called the molar extinction coefficient or molar absorptivity. It is a constant for a given substance, provided the temperature and wavelength are constant. It has units of liter/mol • cm.
- l and c have the usual units of length (cm) and concentration (mol/liter).
Plotting Calibration Graphs
Once we have chosen the correct wavelength, the next step is to construct a calibration curve or calibration plot. This consists of a plot of absorbance versus concentration for a series of standard solutions whose concentrations are accurately known. Because calibration curves are used in reading off the unknown concentrations, their accuracy is of absolute importance. Therefore, make the standard solutions as accurately as possible and measure their absorbances carefully. Each standard solution should be prepared in identically the same fashion, the only difference between them being their concentrations. When drawing the calibration graphs, take care not to lose any of the accuracy of the experimental data by choosing axes that are too small. Choose axes to represent the accuracy possible in reading the instrument. For example, if it is possible to read absorbance correct to the second decimal place, say 0.47, then construct the absorbance axis so that 0.47 can be located accurately on it.
Slope of the best straight line through the data points in the calibration plot is 1.65. Plot intercept is 0.008.
Slope = (absorbance)/ (concentration) = 1.65
 Equation of straight line:
 Absorbance = 1.65 (Concentration) + 0.008
To find an unknown concentration for a sample, subtract the intercept from the absorbance reading and divide the result by the slope. Here the equation would be
Concentration = Absorbance – 0.008 /1.65
The Beer-Lambert Law (A = εlc) implies that when concentration is equal to zero (c = 0), absorbance must also be zero (A = 0). In other words, the calibration line must pass through the origin. A major source of error in spectrophotometric analysis is applying the Beer-Lambert Law at inappropriate concentrations. The Beer-Lambert Law is strictly applicable only for dilute solutions. It becomes less and less accurate as the concentration of the solution increases. Once you have the calibration curve set up, you can measure the absorbance of any unknown solution at the same wavelength and read off its concentration from the graph or calculate from the slope.
