Absorbance is a measurement used extensively in chemistry and biology to quantify how much light a sample takes in. This technique is applied through a method called spectrophotometry, where a beam of light at a specific wavelength is passed through a liquid sample. The primary purpose of measuring absorbance is to determine the concentration of a light-absorbing substance, or solute, within a solution.
Defining Absorbance
Absorbance, denoted by the symbol $A$, is a measure of the quantity of light that is absorbed by a sample as the light beam passes through it. It describes the optical property of a material to impede the transmission of radiant energy. The measurement is an inverse relationship to transmittance, which is the fraction of the original light intensity that successfully passes through the sample.
Transmittance ($T$) is mathematically defined as the intensity of the light emerging from the sample ($I$) divided by the intensity of the light entering the sample ($I_0$). Absorbance is then calculated by taking the negative logarithm of the transmittance, expressed as $A = -\log_{10}(T)$. This logarithmic relationship means that a small change in transmittance at low values corresponds to a much larger change in absorbance.
The Dimensionless Nature of Absorbance
Absorbance is a quantity that does not have a true physical unit because of its definition as a ratio’s logarithm. It is calculated from the ratio of the incident light intensity ($I_0$) to the transmitted light intensity ($I$), which are both measured in the same units. Since the units of $I_0$ and $I$ cancel out in the division, the resulting ratio is unitless. The logarithm of a unitless ratio, by mathematical definition, also results in a dimensionless number.
Despite this fundamental lack of a physical unit, results are sometimes informally reported using the term “Absorbance Units” (AU) or “Optical Density” (OD) in laboratory reports and scientific literature. These terms are not recognized by international standards as true physical units, but rather serve as convenient placeholders to denote that the value is an absorbance measurement. The International Union of Pure and Applied Chemistry (IUPAC) advises against using the term “Optical Density” when referring to absorbance.
Calculating Absorbance (The Beer-Lambert Law)
The mathematical relationship used to calculate absorbance in practical applications is known as the Beer-Lambert Law, which is expressed as $A = \epsilon cl$. This law establishes a linear relationship between the measured absorbance and three specific properties of the sample and the light path.
The variables on the right side of the equation represent the physical parameters that determine the absorbance value. The variable $c$ is the concentration of the light-absorbing substance, typically measured in moles per liter ($M$ or $mol \cdot L^{-1}$). The variable $l$ is the path length, which is the distance the light travels through the sample, usually determined by the width of the cuvette and typically measured in centimeters ($cm$).
The final component, $\epsilon$, is the molar absorptivity coefficient, also often called the molar extinction coefficient. This coefficient is unique to each substance at a specific wavelength and temperature, representing how strongly the substance absorbs light. Because the final value $A$ must be unitless, the units of $\epsilon$ must precisely cancel out the product of concentration ($c$) and path length ($l$). This means the molar absorptivity coefficient is generally expressed in the compound unit of liters per mole per centimeter ($L \cdot mol^{-1} \cdot cm^{-1}$). Multiplying $L \cdot mol^{-1} \cdot cm^{-1}$ by $mol \cdot L^{-1}$ and $cm$ results in a completely unitless product, validating the dimensionless nature of the calculated absorbance.