## Important Factors

The most important idea in colorimetry is that color intensity is proportional to the concentration. However, this is not always true, especially at high concentrations and color intensities. Also, there are several other important factors to keep in mind when working with colorimetry.

 What colors are absorbed and how intensely they are absorbed depends on the chemical being used and how the electrons and energy levels within it are arranged. The color we see is complementary to the color absorbed by the chemical. The mechanism is that as light passes through a solution, light of a certain wavelength is absorbed by the colored chemical specie. Instruments report both A (absorbance) and %T (transmittance). Be sure to use A. The assumption is that the amount of light absorbed is directly proportional to the concentration of the chemical specie that the light passes through. Also, the amount of light absorbed is directly proportional to the thickness (or path length) of the solution. These factors and assumptions can be summarized as Beer's Law and written as the equation, A = abc. In this equation A is absorbance, a is a proportionality factor called the molar absorptivity, b is the path length, and c is the molar concentration.

### Complementary Color

Regarding the color we see being complementary to the color absorbed, let me show you what I mean.

 To do that let's quickly review the operation of a spectroscope. Here is a spectroscope. The eyepiece is at the near right end. A slit for light and a clamp to hold test tubes is at the far left end. Inside, light will pass through the slit at the far end and then through a diffraction grating before leaving through the eyepiece at the near end. The diffraction grating bends the light in different directions. Each color bends to its own new direction. As we look through the eyepiece, each color appears to be coming from a different place, giving us a spectrum of all the colors. If a solution absorbs any of the colors, that part of the spectrum will not be as bright. In fact, it might be quite dark.

### Concentration

 Take a look at what happens as the solution is made more concentrated. Start with the full spectrum shown here. The true colors of the spectrum will be seen in the lab. With a dilute solution a small portion of the red light is absorbed, making the right end of this spectrum darker. When the solution is made more concentrated, more of the red light is absorbed. Although the true colors of the spectrum don't show up in these pictures, you should be able to see that the red end of the spectrum has been darkened (shortened).

 This can also be represented graphically. Here is one way. This graph shows how much light is getting through. %T stands for the percentage of light that is transmitted through the sample. With white light, all of every color gets through. That is represented by the line across the top, 100% for all wavelengths. With a small concentration of the colored chemical, a small amount of the complementary color is absorbed and less than 100% gets through in the 700nm to 800nm range. As the concentration increases the line representing %T drops lower and lower.

### Transmittance and Absorbance

 Here is another way of graphing the spectrum of a solution. Instead of showing how much light of each colors gets through the solution (top graph), it shows how much light of each color is absorbed by the solution (bottom graph). With a colorless solution, none of the light is absorbed (straight line across the bottom of the graph). With a small concentration of the colored chemical, a small amount of the complementary color is absorbed (slight rise in the line in the 700nm to 800nm range). As the concentration increases, the amount of light that is absorbed (in the 700nm to 800nm range) increases.

Ideally, the absorbance is directly proportional to the concentration of the colored chemical.

### Path Length

 Another factor is the thickness of the solution through which the light must pass. Here we have two samples of the same solution. From the side they have the same color intensity because both test tubes have the same thickness. But looking down through the tube, the tube with the greater sample height absorbs more of the complementary light and has a more intense color. Ideally, the absorbance is directly proportional to the thickness or path length.

 Here is another angle on that. If we start with identical solutions and dilue one, the increased path length makes up for the decreased concentration.

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