## Friday, April 1, 2011

### BT2258 VERIFICATION OF BEER-LAMBERT’S LAW

Aim: To verify Beer-Lambert’s law and to find out the molar extinction and its co-efficient or molar absorptivity.
Principle:
The Beer – Lambert’s law is a linear relationship between absorbance and concentration of an absorbing species.
Beer’s law states that “the intensity of a beam of monochromatic light decreases exponentially with increase in the concentration of absorbing species arithmetically”.
I =Intensity of incident light
C= concentration
k= Proportionality constant
-ln I = kc + b ………….. Equation   1
(On integration, b is constant of integration)
When concentration = 0, there is no absorbance. Hence I = I0
Substituting in equation 1,
-ln I0 = kX0 +b
-ln I0 = b
Substituting the value of b, in equation 1,
-ln I = kc - ln I0
ln I0-ln I = kc
ln = kc (since log A- log B = log )

ekc
e-kc
I = I0e-kc (Beer’s law)……….equation 2
Lambert’s law states that the rate of decrease of intensity (monochromatic light) with the thickness of the medium is directly proportional to the intensity of incident light.

This equation can be simplified, similar to equation 2 to get the following equation ( by replacing ‘c’ with ‘t’)
I = I0e-kt ………….equation 3
Equation 2 and 3 can be combined to get
I = I0e-kct                             (converting natural logarithm to base 10& K =kx0.4343)
10-Kct     (rearranging term)
10Kct   (inverse on the both sides)
logKct (taking log on both sides) ………….equation 4
it can be learnt that Transmittance (T) =  and Absorbance (A) =
Hence A = log
A = log  …………………equation 5
Using equation 4 &5, since A = log  and log = Kct we can infer that
A = Kct                (instead of K, we can use ε)
A= εct    (Mathematical equation for Beer – Lambert’s Law)
Where A = Absorbance or optical density or extinction co-efficient
ε = Molecular extinction coefficient
c = concentration of sample (mmol/lit)
t = path length (normality10 mm or 1 cm)
Absorbance is plotted against concentration of potassium permanganate linear relationship between absorbance and concentration of analyte is verified determining γ (gamma) value. Which indicates the extent of a given set of data and it may be obtained from the following equations.
γ =
Where N = number of pair of data x and y
x = concentration of KMnO4
y = Absorbance
Where value of γ is 1 there would be a perfect linearity lesser the value of   γ  from 1, lesser is the linear character of data. The variation of absorbance Vs concentration is linear and gives a straight lines
A=εct
i.e... A is proportional to c or A=εc   the above equation is y=mx for m=ε
Chemicals Required:
1.      Potassium permanganate
2.      Distilled water
Apparatus required:
1.      Spectrophotometer/ colorimeter
2.      glass cuvettes
Procedure:
1.      A series of test tubes were labeled 1-10 (1, 2, 3…..10) respectively.
2.      The stock KMnO4 solution (10 mM of KMnO4 is prepared by adding 0.158g of KMnO4 and is made up to 1000 ml) diluted into 10%, 20%, 30%, 40%............100% i.e.. KMnO4 was pipetted out into (1, 2, 3, 4….10) ml in respective tubes which was made up to 10ml by distilled water.
3.      The 20%, 40% of the solution was used for the detection of  λmax (i.e.) 20% and 30% o KMnO4 solution absorbance was recorded at different wavelengths ( 400nm – 800nm) using water as a blank.
4.      The above selected wavelength was used for the detection of absorbance of all samples. From the correction co-efficient of KMnO4 (i.e.) γ and molar absorptivity or extinction co-efficient of KMnO4 was calculated.
Result:
The correct co-efficient (γ) of KMnO4 was equal =
The molar absorptivity or extinction co-efficient (ε) of KMnO4 was =

Wavelength selection for 20% KMnO4 solution from their maximum optical density value
 S.No Wavelength Optical density 1 400 2 430 3 470 4 490 5 520 6 550 7 580 8 610 9 700 10 760
Wavelength selection for 40% KMnO4 solution from their maximum optical density value
 S.No Wavelength Optical density 1 400 2 430 3 470 4 490 5 520 6 550 7 580 8 610 9 700 10 760
Absorbance of diluted KMnO4 sample at selected wavelength
 S.No Concentration in %mM Absorbance at 520nM 1 10 2 20 3 30 4 40 5 50 6 60 7 70 8 80 9 90 10 100

Detection of linearity (γ) absorbance Vs concentration of KMnO4
 S. No x Y xy X2 Y2 1 0.1 2 0.2 3 0.3 4 0.4 5 0.5 6 0.6 7 0.7 8 0.8 9 0.9 10 1.0 = = = = Y2=