In analytical chemistry, measuring how light interacts with a substance is a fundamental technique. Absorbance quantifies the fraction of light at a specific wavelength that is taken up by a sample as the light passes through it. This optical property allows scientists to identify solution components and, most commonly, determine the exact amount of a chemical present. By shining light through a liquid sample, chemists can indirectly measure the concentration of the dissolved material, making absorbance a powerful tool for quantitative analysis.
Understanding the Dimensionless Measurement
Absorbance (\(A\)) is a logarithmic ratio, not a measurement of light intensity itself. It mathematically compares the incident light intensity (\(I_0\)) to the transmitted light intensity (\(I\)). Specifically, it is the base-ten logarithm of this ratio. If a sample absorbs no light, the transmitted intensity equals the incident intensity, resulting in an absorbance of zero.
Because absorbance is a ratio, it is a dimensionless quantity and does not carry a true physical unit. The units for light intensity cancel out in the division, resulting in a pure number. For practical reporting, absorbance values are frequently cited with the label “Absorbance Units” (AU), which is a conventional label, not a physical unit. Every unit increase in absorbance represents a significant decrease in transmitted light, as the transmitted intensity has decreased by a factor of ten.
The Mathematical Relationship of the Beer-Lambert Law
The theoretical foundation connecting a measured absorbance value to the chemical properties of a solution is described by the Beer-Lambert Law. This law states that the absorbance (\(A\)) of a solution is directly proportional to three factors: concentration, path length, and the material’s inherent ability to absorb light. The mathematical expression of this relationship is \(A = \epsilon b c\), where each variable plays a distinct role in the measurement.
The term \(c\) represents the concentration of the light-absorbing substance, typically expressed in moles per liter (\(mol/L\)). The symbol \(b\) stands for the path length, which is the distance the light beam travels through the sample, usually measured in centimeters (\(cm\)). The proportionality constant, \(\epsilon\) (epsilon), is called the molar absorptivity. This value is unique to a specific chemical at a specific wavelength and indicates how strongly that substance absorbs light.
The units of molar absorptivity are commonly expressed as \(L \cdot mol^{-1} \cdot cm^{-1}\), which ensures the final calculated absorbance value remains unitless. The linear relationship established by the Beer-Lambert Law is why absorbance is such a powerful tool in chemistry. By keeping the path length and wavelength constant, a direct proportionality exists between the measured absorbance and the unknown concentration. This makes it possible to determine an unknown concentration by simply measuring its absorbance.
Instrumentation and Practical Concentration Determination
Absorbance measurements are obtained using a spectrophotometer, an instrument designed to precisely measure the intensity of light transmitted through a solution. The spectrophotometer passes a beam of light at a selected wavelength through the sample, which is contained in a transparent vessel called a cuvette. The instrument then measures the amount of light that hits a detector on the opposite side.
Before measurement, the instrument is calibrated using a “blank” solution. The blank contains all components of the sample except the substance being analyzed. This process sets the baseline, or zero absorbance, by excluding light absorption caused by the solvent or the cuvette itself. After calibration, the instrument measures the sample’s absorbance at the pre-determined wavelength where the substance absorbs light most strongly.
To practically determine the concentration of an unknown sample, a standard curve, or calibration curve, is used. First, a series of standard solutions are prepared, each having a precisely known concentration of the substance. The absorbance of these standard solutions is measured and then plotted on a graph with absorbance on the vertical axis and concentration on the horizontal axis.
The resulting plot should form a straight line, representing the direct proportionality predicted by the Beer-Lambert Law. Once the line is established, the absorbance of the unknown sample is measured under the exact same conditions. By locating the unknown’s absorbance value on the y-axis and tracing it over to the standard curve, the corresponding concentration can be read directly from the x-axis. This simple graphical method provides a highly accurate determination of the unknown concentration.