# The Beer-Lambert Law and Its Limitation Essay Objective : 1. To determine the linear relationship between absorbance and concentration of an absorbing species. 2. To study the effects of molecular dissociation complex formation on the applicability of the Beer-Lambert Law. 3. To investigate the derivation and limitation of Beer-Lambert Law. Introduction: In optics, the Beer–Lambert law, also known as Beer’s law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the absorption of light to the properties of the material through which the light is traveling. The general Beer-Lambert law is usually written as: A = a() * b * c where A is the measured absorbance, a() is a wavelength-dependent absorptivity coefficient, b is the path length, and c is the analyte concentration. When working in concentration units of molarity, the Beer-Lambert law is written as: A = * b * c where is the wavelength-dependent molar absorptivity coefficient with units of M-1 cm-1. The law states that there is a logarithmic dependence between the transmission (or transmissivity), T, of light through a substance and the product of the absorption coefficient of the substance, ?, and the distance the light travels through the material (i.e., the path length), ?. The absorption coefficient can, in turn, be written as a product of either a molar absorptivity (extinction coefficient) of the absorber, ?, and the molar concentration c of absorbing species in the material, or an absorption cross section, ?, and the (number) density N’ of absorbers. Experimental measurements are usually made in terms of transmittance (T), which is defined as: T = I / Io Modern absorption instruments can usually display the data as either transmittance, %-transmittance, or absorbance. An unknown concentration of an analyte can be determined by measuring the amount of light that a sample absorbs and applying Beer’s law. If the absorptivity coefficient is not known, the unknown concentration can be determined using a working curve of absorbance versus concentration derived from standards. The Beer-Lambert law can be derived from an approximation for the absorption coefficient for a molecule by approximating the molecule by an opaque disk whose cross-sectional area, , represents the effective area seen by a photon of frequency w. If the frequency of the light is far from resonance, the area is approximately 0, and if w is close to resonance the area is a maximum. The linearity of the Beer-Lambert law is limited by chemical and instrumental factors. Causes of non-linearity include: deviations in absorptivity coefficients at high concentrations (> 0. 01M) as a result of electrostatic communications between elements in close proximity spreading of light due to particulates in the sample Beer’s law could be applied to the analysis of any mixture by spectrophotometry, without the need for intensive pre-processing in the sample. An illustration is the willpower of bilirubin in blood vessels plasma trials. The range of pure bilirubin is famous, so the large molar absorption agent is known. Measurements are made in one wavelength that is nearly unique to get bilirubin and at a second wavelength in order to appropriate for feasible interferences. The concentration has by c = Acorrected /?.