mize errors in setting the instrument at the chosen wavelength. This also minimizes apparent deviations
from Beer's law for incident radiation of wide bandwidth (vide infra). The concentrations of unknowns
can then be read directly from the graph or calculated using a factor, i.e. the absorbance reading is
divided by the slope εl. The composition of mixtures of two or more absorbing materials can be
established by measuring standards and samples at two or more wavelengths, preferably corresponding
to the absorbance maximum of each component. The concentrations of the components can be
calculated from a set of simultaneous equations once the respective molar absorptivities at each
wavelength are known, e.g. for two components
The values of , etc., are calculated from calibration graphs for the separate components.
Deviations from the Beer-Lambert Law
There are no known exceptions to the Lambert law for homogeneous samples. Beer's law is a limiting
case applicable only to dilute solutions and monochromatic radiation. Deviations may be observed in
practice, but these are all 'apparent' in the sense that the limiting conditions have been 'contravened'
either chemically or instrumentally. Such deviations show as a curvature of the calibration graph, but
this does not necessarily preclude the use of a particular method unless the deviation is non-
reproducible. Apparent deviations may be summarized as follows:
(1) At concentrations greater than about 0.01 M, refractive index changes and the perturbing effect of
solute molecules or ions on the charge distribution of their neighbours both affect the value of ε.
Positive or negative deviations may result.
(2) Solutes involved in chemical equilibria, i.e. dissociation, association or complex formation, or in
interaction with solvent molecules, may show marked spectral changes with concentration, e.g.
(a) The position of the OH stretching band in the infrared spectrum of benzyl alcohol run in carbon
tetrachloride is concentration sensitive because of polymerization:Absorbance measurements at 3700 cm–^1 show negative deviations at high concentrations, while
those made at 3400 cm–^1 show positive deviations.