Beer's law deals in a similar way with the concentration C of an absorbing species and leads to the
relation
Combining the two gives the Beer-Lambert law which may be expressed in the form
where log 10 (I 0 /I) is defined as the absorbance A and ε is a constant known as the molar absorptivity.*
The value of ε (the absorbance of a 1 M solution in a 1 cm cell) depends upon the nature of the
absorbing species and on the wavelength of the incident radiation. Absorbance is thus seen to be
directly proportional both to the concentration of the absorbing species and to the thickness of the
absorbing medium. It is related to transmittance T defined as I/I 0 (the fraction of radiation transmitted)
by the equation
Instruments used for quantitative measurements may incorporate a transmittance, a percentage
transmittance or an absorbance scale. If the molecular weight of the substance is unknown, ,
representing the absorbance of a 1% solution in a 1 cm cell, may be used in place of ε. Absorbance is an
additive property so that at a particular wavelength, the total absorbance of a solution containing a
number of absorbing components is given by
assuming there is no interaction between the individual solutes. Measured absorbances are increased by
scattering of the radiation at solution-cell and cell-air interfaces and by large molecules or particulate
matter in the solution, but these effects can be cancelled out by measuring the absorbance of all
solutions relative to a blank and using closely matched cells.
Use of the Beer-Lambert Law
Although applicable to measurements in all regions of the electromagnetic spectrum, only in visible,
ultraviolet and infrared spectrometry are quantitative measurements based on the Beer-Lambert law
used extensively. The usual procedure is to prepare a calibration graph, or Beer's law plot, by plotting
absorbance against concentration for a series of standards. This should give a straight line passing
through the origin and a slope equal to the product εl. Measurements are generally made at a maximum
in the absorbance curve to maximize sensitivity and to mini-
* Strictly the molar absorption coefficient.