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Absorption Coefficient
The amount of radiation absorbed as it passes through a sample is expressed by the absorption coefficient.
When electromagnetic radiation is passed through a sample, some of the radiation, often radiation at a particular frequency or within a frequency range, is absorbed. We begin by seeing the experimental procedures, and the terminology, used in studies of absorption spectroscopy that depend on this phenomenon.
The decrease in the intensity of the radiation as it passes through an absorbing layer of material is proportional to the concentration is a solution, the decrease in intensity is often proportional to the concentration of the absorbing component per litre of solution, the concentration in the SI units of moles per cubic meter is 1000M. On the basis of these ideas, write the differential equation.
dI =
(1000M)I dx (1)
Integration, with the relation dI/I = d(In I) and the limits gives
In I0/I =
(1000M)I or I = I0e-
(1000M)I (2)
The coefficient
is called the absorption coefficient. Since l has the units of meters and 1000M has units of moles per cubic meter, shows that
has the units of m2 mol-1.
Equation (2) is known as Beer’s law, or as the Beer-Lambert law. The concentration dependence that it implies is to be looked on as ideal relation that is not exactly followed by components of real solutions under all circumstances.
Common units: in practical analytical uses of absorption measurements, the relation is recast to base 10 logarithms, the concentration in moles per liter is used, and the length is usually expressed in centimeters. Then, with ε for the proportionality constant, we have
logI0/I = εMl and I = I0-10 εMl
The experimentally determined quantity log(I0/I) is called the absorbence, and the coefficient. All our theoretical work and the absorption coefficient
.
Example: in the infrared absorption spectra of ketones, aldehydes, carboxylic acids, and esters, the “carbonyl” absorption, due to the C
O group, is a prominent feature. For 2-butanone, or methyl ethyl ketone, dissolved in carbon tetrachloride this absorption cell of thickness or length, 0.100 mm gives the absorption band. Calculate the value of the coefficient at the band maximum.
Solution: at the absorption maximum of the band, I0/I = 98/49.5 = 1.98 and In (I0/I) = 0.68. The concentration M is 0.089 mol L-1, and the cell length is 0.100 mm = 1.00 × 10-4 m. the relation gives
In (I0/I)/1000Ml = 0.68/ (89 mol m-3) (1.00 × 10-4 m)
= 76.4 m2 mol-1
Absorption of radiation that is due to a particular molecular level phenomenon often occurs over a range of frequencies, as the absorption band illustrates. The molecular basis of the absorption is then related to the integral of the absorption band. If the absorption band is displayed in terms of frequencies, we deal with
Integrated absorption coefficient = ∫
(v) dv
The integrated absorption coefficient can be estimated by multiplying the maximum value of the absorption coefficient by the width of the band where the coefficient has half the maximum value, the “width at half height.” Estimate the value of the integrated absorption coefficient of the carbonyl band of 2-butanone from the spectrum and the results of example 1.
Solution: the width at half height is about 15 cm-1, and this corresponds to a frequency range of (15 cm-1)(3 × 1010 cm s-1) = 4.5 × 1011 s-1)(76.4 m2 mol-1)
= 3.4 × 1013 m2 mol-1 s-1
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When electromagnetic radiation is passed through a sample, some of the radiation, often radiation at a particular frequency or within a frequency range, is absorbed. We begin by seeing the experimental procedures, and the terminology, used in studies of absorption spectroscopy that depend on this phenomenon.
The decrease in the intensity of the radiation as it passes through an absorbing layer of material is proportional to the concentration is a solution, the decrease in intensity is often proportional to the concentration of the absorbing component per litre of solution, the concentration in the SI units of moles per cubic meter is 1000M. On the basis of these ideas, write the differential equation.
dI =
Integration, with the relation dI/I = d(In I) and the limits gives
In I0/I =
The coefficient
Equation (2) is known as Beer’s law, or as the Beer-Lambert law. The concentration dependence that it implies is to be looked on as ideal relation that is not exactly followed by components of real solutions under all circumstances.
Common units: in practical analytical uses of absorption measurements, the relation is recast to base 10 logarithms, the concentration in moles per liter is used, and the length is usually expressed in centimeters. Then, with ε for the proportionality constant, we have
logI0/I = εMl and I = I0-10 εMl
The experimentally determined quantity log(I0/I) is called the absorbence, and the coefficient. All our theoretical work and the absorption coefficient
Example: in the infrared absorption spectra of ketones, aldehydes, carboxylic acids, and esters, the “carbonyl” absorption, due to the C
Solution: at the absorption maximum of the band, I0/I = 98/49.5 = 1.98 and In (I0/I) = 0.68. The concentration M is 0.089 mol L-1, and the cell length is 0.100 mm = 1.00 × 10-4 m. the relation gives
In (I0/I)/1000Ml = 0.68/ (89 mol m-3) (1.00 × 10-4 m)
= 76.4 m2 mol-1
Absorption of radiation that is due to a particular molecular level phenomenon often occurs over a range of frequencies, as the absorption band illustrates. The molecular basis of the absorption is then related to the integral of the absorption band. If the absorption band is displayed in terms of frequencies, we deal with
Integrated absorption coefficient = ∫
The integrated absorption coefficient can be estimated by multiplying the maximum value of the absorption coefficient by the width of the band where the coefficient has half the maximum value, the “width at half height.” Estimate the value of the integrated absorption coefficient of the carbonyl band of 2-butanone from the spectrum and the results of example 1.
Solution: the width at half height is about 15 cm-1, and this corresponds to a frequency range of (15 cm-1)(3 × 1010 cm s-1) = 4.5 × 1011 s-1)(76.4 m2 mol-1)
= 3.4 × 1013 m2 mol-1 s-1
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