Instant Notes: Analytical Chemistry

log ( Io/ It) =A =ec l

where A =the absorbance and e=the molar absorptivity.

The value of e(sometimes incorrectly referred to as the ‘extinction coeffi-

cient’), is most usually quoted for a concentration of 1 M and a path length of

1 cm. However, if the concentration is expressed in mol m-^3 (= 1000 ¥ M) and

l is expressed in meters (=cm/100) then the units of eare m^2 mol-^1 , suggesting

that the absorptivity depends on the effective capture area of the species. This

indicates that ecombines the transition probability and the nature of the

absorbing species. (Note thatein m^2 mol-^1 =ein (cm M)-^1 /10.

Very high values of e, for example over 10 000 for the UV, p– p* absorption of

conjugated polyenes, indicate a favoured transition. Lower values, for example,

eis less than 100 for the n -p* absorption of ketones, show that the transition is

less favoured or ‘forbidden’.

The Beer-Lambert law applies equally to infrared absorption spectra. Spectra

are plotted either as absorbance, A, oras the transmittance, T, against wave-

length, frequency or wavenumber, where

T =(It/I 0 )

or sometimes as percentage transmittance = 100 T.

If the relative molecular mass is unknown, comparison may be made using

E1cm1%representing the absorbance of a 1% solution in a 1 cm cell. It is worth

noting the range of values which each of these parameters may take. A can have

any value from 0 to infinity. T must be between 0 and 1, and eusually has

values from about 1 to 10^6.

If several species in a solution absorb at the same wavelength without chemi-

cally interacting with each other, then the total absorbance is the sum of the

individual absorbances for each species:

A total =e 1 c 1 l +e 2 c 2 l +e 3 c 3 l ...

Calibration graphs of A against c may be plotted to verify that the Beer-Lambert

law applies over the range of concentrations that is to be studied.

It must be appreciated that the absorbance, and hence the transmittance and

absorptivity, vary with wavelength, with the highest absorbance giving a peak

in the absorption spectrum, as shown in Figure 4.Measurements made at the

wavelength of maximum absorbance, lmax, give the highest sensitivity, but care

must be taken over the wavelength chosen and over the wavelength range

around a selected wavelength transmitted through the optics of the

spectrometer, that is the bandpass of the system.

There are no known exceptions to the Beer-Lambert law, but apparent devia-

tions may arise as follows.

198 Section E – Spectrometric techniques

Incident

intensity, Io

Transmitted

c intensity, It

l

Fig. 3. The absorption of radiation by a sample.