A large number of analytical methods are based on interaction of electromagnetic radiation with matter. Spectrophotometry and colorimetry are analytical methods based on absorption of radiation. These methods are used for quantitative analysis and serve as useful auxiliary for structure elucidation.
Fundamental laws of absorption
When monochromatic (heterogeneous) light is incident upon a homogeneous medium, a part of the incident light is reflected (Ir), a part is absorbed (Ia) by the medium and the remainder is transmitted (It).
Thus, the intensity of incident light is given by
Io=Ir+Ia+It -----------(1)
If comparison cell is used,Ir is very small (about 4%) and can be neglected, thus
Io=Ia+It -----------(2)
Hence, when a beam of light passes through an absorbing medium, for example a solution,a part of the light is absorbed and rest is transmitted. The amount of the light absorbed depends on concentration of the solution and thickness of medium. The quantitative relationship between the amount of light absorbed, concentration and the length of the absorbing medium is governed by two laws.
Lambert's law
Lambert's law states that, "when a beam of monochromatic light is allowed to pass through a transparent homogeneous medium, the rate of decrease of intensity with the thickness of absorbing medium is directly proportional to the intensity of incident radiation".
"The intensity of a transmitted light, through a homogeneous medium, decreases geometrically as the thickness of the medium increases arithmetically".
Mathematically, this law can be expressed as-
– dI α I [-ve sign indicates, as thickness of media
dt increases intensity of light decreases]
or – dI =KI.c --------------(1)
dt
Where, K=Proportionality constant.
I=Intensity of incident light
t=Thickness of the medium (path length).
Rearrange equation (1) as,
– dI =K.dt --------------(2)
I
Let 'Io' be the intensity of incident light and 'It' be intensity of transmitted light through thickness t, then on integrating equation (2) between the limit 'Io' to 'It' and t=0 to t we get,
It t
∫ dI/I= −K∫dt
Io 0
ln(It/Io)=–K.t
–K.t
or It =e --------------(3)
Io
–K.t
or It =Io e ---------------(4)
Beer's law (Beer Lambert's law)
A similar relationship holds between transmittance and concentration of solution was observed by Beer in 1852. Beer's law states that, "When a beam of monochromatic light is passed through a homogeneous transparent medium, the decrease in intensity of the light with thickness of the medium is directly proportional to intensity of incident radiation and concentration of the medium."
Mathematical Expression:
– dI α Ic or – dI =KIc -----------------(5)
dt dt
Where, K=Proportionality constant
c=Concentration of absorbing substance.
Rewrite equation (6),
– dI =Ktdc --------------(6)
I
Let Io be the intensity of incident light at c=0. Integrating equation (7) between the limits Io to It and 0 to c, we get,
It c
∫ dI/I= −K∫dc
Io 0
ln(It/Io)=–K.tc
–K.tc
It =e ---------------(7)
Io
–K.tc
It =Io e ---------------(8)
Definitions
Transmittance (T):
The fraction of incident light that gets transmitted through a medium is called as transmittance of the medium.
T= It.
Io
Absorbance (A) or optical density:
The logarithmic ratio of the intensity of incident light (Io) to that of the transmitted light is called as absorbance. It is also called as optical density or extinction.
A=log₁₀ It.
Io
But,It/Io=T. A=-log T
Absorptivity (a):
Absorbance of a solution having concentration of 1gm/dm³ placed in a cell of 1cm thickness is called absorptivity or extinction coefficient.
Molar absorptivity/molar extinction coefficient(ε):
Molar absorptivity (ε) is defined as the absorbance of a medium having concentration 1mol / dm³ and thickness 1 cm.
From equation (7), we have,
-ε t c
It. =10 or -log₁₀ It. =ε t c ∴log₁₀ It. =εtc
Io Io Io
A=ε t c ε= A.
c t
If c=1 mol / dm³ and 1cm, ε=A
λmax : The wavelength at which a solution shows maximum absorbance is called as λmax.
Deviation from Beer's law
If Beer's law is obeyed, a plot of absorbance verses concentration is linear with a slope ' εt ' and the plot passes through origin (i.e. a=0 when c=0). This plot should be valid for entire range of concentration.
If Beer's law is not obeyed, the measured absorbance can be either greater or smaller than the predicted value. If observed absorbance is greater than the predicted value, the solution exhibits a positive deviation. If it is smaller than the predicted value, the solution exhibits a negative deviation.
Concentration- based deviations
Beer's law is a limiting law and should be expected to apply online only at low concentration (< 0.1M). At higher concentration the average distance between the species responsible for absorption is diminished to the point where each affects the charge distribution of it's neighbours. This interaction is capable of altering their ability to absorb a given wavelength of radiation. A degree of such interaction depends upon the concentration. Occurrence of this phenomenon causes negative deviations the linear relationship between absorbance and concentration.
Value of ε depends upon the value of refractive index of medium and if the refractive index changes with concentration, the law also shows marked deviations.
Instrument- based deviations
If monochromatic radiation is employed, strict adherence to the law is expected. But it is seldom possible, practically to obtain a strict monochromatic radiation and therefore deviations can be accounted for the use of polychromatic radiation.
Chemical- based deviations
If the degree of dissociation, ionisation, association, hydration and complex formation of the absorbing solute alters on diluting or concentrating the solution, apparent deviations from Beer's law are frequently observed.
For example,
Benzylalcohol in chloroform exists in a polymeric equilibrium.
4C₆H₅CH₂OH ⇌ (C₆H₅CH₂OH)4
Dissociation of polymer increases with dilution and hence shows deviations.
Change in the colour of dichromate (CrO) ions in aqueous solution on dilution. The dichromate ion is converted to chromate ions gradually on dilution resulting in deviations from Beer's law.
Cr₂O₇²- + 3H₂O ⇌ 2CrO₄²- + 2H₃O+
(Orange) (Yellow)
explaination is very good
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