General considerations and theoretical background
Laws of absorption spectrophotometry
The extent of absorption of radiation by an absorbing system at a given monochromatic wavelength is described by the two classic laws of absorptiometry, which relate the intensity of radiation incident on the absorbing system (I0) to the transmitted intensity (I) (Fig. 1). Lambert’s (or Bouguer’s) law concerns instrumental factors, and states that at a given concentration (c) of a homogeneous absorbing system, the transmitted intensity (I) decreases exponentially with increase in absorption pathlength (l).
Figure 1 Attenuation of a beam of radiation by an absorbing solution.
The complementary Beer’s law deals with concentration and states that for a layer of defined pathlength (l), the transmitted intensity (I) decreases exponentially with the increase in concentration (c) of a homogeneous absorbing system. Combination of these observations gives the familiar Beer–Lambert law:
where e is the molar absorption coefficient of the system. The logarithmic term is linearly related to concentration and pathlength, and is referred to as absorbance (A). The older terms extinction (E) and optical density (OD) are not recommended, although they are often found in the literature.
Transmittance [%T=I/I0) and percentage trans mittance [%T=100(I/I0)] are not linear functions of concentration and pathlength but can be related readily to absorbance:
The molar absorption coefficient (e) is defined as ‘the absorbance of a 1-molar solution in a cell of 1 cm pathlength’ with units of M–1 cm–1 (L mol–1 cm–1).
The term specific absorbance is also used, denoted by A1% 1 cm or A (1%, 1 cm) or A11. This is defined as ‘the absorbance of a 1% w/v solution in a cell of 1 cm pathlength’ (g (100 mL)–1 or g/100 mL). It was formerly known as the ‘specific extinction coefficient’, symbol E1% 1cm or E (1%, 1 cm).
where Mr is the relative molecular mass.
Absorbance is often expressed in logarithmic form in cases where spectra are to be compared. The logarithmic form of the Beer–Lambert law expresses the effects of molar absorption coefficient (ɛ), concentration (c) and pathlength (l) as additive terms
log A=log ɛ+ log c+ log l (15.5)
