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Basic course of UV-Visible/NIR Spectrophotometer
3. Colorimetric Analysis |
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Neglecting cleaning increases absorbance (Bouger-Beer's law). |
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Are you a tropical fish-lover? Caring for an aquarium is somewhat troublesome, although the fish are lovely. |
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Here are Ms. A and Mr. B who keep tropical fish. Ms. A likes keeping things clean, and the aquarium in which the tropical fish are kept is always clear and beautiful. On the other hand, Mr. B is lazy, and the aquarium tends to become muddy. |
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The aquariums of these two persons are placed by the window. Since the water of Ms. A's aquarium is clear, the light that comes in from a window can mostly be seen even through the aquarium. However, since the water of Mr. B's aquarium becomes muddy, light hardly comes in through the aquarium. |
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Of the light that comes in from the window, the percent of light that comes in through the aquarium is called "transmittance (T)." |
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Generally, transmittance is more commonly expressed as a percentage "transmittance (%T)". The part of the light that comes in from the window and is absorbed into the water of the aquarium is calls "absorbance (Abs)." |
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The water of the aquarium that is not cleaned becomes muddy and absorbs light preventing its transmittance, resulting in an increase in absorbance and a decrease in transmittance. In contrast, since the water of the aquarium that is always clean clear lets the light pass through well, the transmittance is close to 100%, and the absorbance is close to zero. |
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Let's make this theory into a mathematical formula. When the light that comes in from the window is defined Io, and the light that comes out from the aquarium is defined as I, the transmittance is I/Io. Furthermore, when the width of the aquarium is defined as ℓ (optical path length), the degree of muddiness of the water (concentration) as c, and a constant (called "molar absorption coefficient") unique to the substance (in this case, the substance that causes muddiness) as ε, the transmittance will become 10-εcℓ (Formula 1).
Absorbance can be obtained with the formula 3, since it is a logarithm of the inverse of the transmittance, suggesting that the absorbance is proportional to the molar absorption coefficient, concentration, and optical path length. This formula 3 is called Bouger-Beer's law. |
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Bouger-Beer's law
The absorbance (Abs) of a solute (coloring substance) is proportional to the concentration of a solution (c) and the thickness of a solution layer (ℓ). |
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| Notes 1) |
Bouger-Beer's law had been called "Lambert-Beer's law". |
| Notes 2) |
Molar absorption coefficient is a constant unique to a substance (solute), and is needed to quantify each substance by spectrometry. |
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