Lambert- Beer’s Law and its Derivation.pptx

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1. Lambert- Beer’s Law and its Derivation Presented By: Aman Rajput Roll No.: 2458000003 M.Pharm (Pharmaceutical Chemistry) Department of Pharmaceutical Chemistry, Uttaranchal Institute of Pharmaceutical Sciences, Uttaranchal University, Dehradun, India.

2. Introduction: Lambert-Beer’s Law is a fundamental principle in spectrophotometry , which relates the absorption of light to the properties of the material through which the light is passing. It is widely used in pharmaceutical analysis for determining the concentration of a solute in a solution. Lambert law(1760): Johann Heinrich Lambert discovered that the absorbance of light is directly proportional to the path length of the absorbing medium. Beer’s Law(1852): August Beer further extended Lambert’s Law by stating that absorbance is also directly proportional to the concentration of the absorbing substance.

3. Introduction: By combining these two principles, we get Lambert-Beer’s Law : A= ɛc l Where; A: absorbance(unitless) ɛ: Molar absorptivity c: Concentration of the absorbing species l : path length

4. Derivation of Lambert-Beer’s Law: Step 1: Lambert’s law- Consider a beam of monochromatic light of intensity I ​ incident on an absorbing medium of thickness dx . As the light travels through the medium, a fraction of it is absorbed, reducing the intensity to I. The rate of decrease in intensity dI is proportional to the intensity I and the thickness dx : dI /dx = - kI where k is the proportionality constant (absorption coefficient).

5. Rearranging and integrating from x= 0 to x= 1; ∫ I o dI /I= -k ∫ dx ln I- ln Io= -k l In (I/Io)= - kl I= I e - kl This shows that intensity decreases exponentially with path length , proving Lambert’s Law .

6. Step 2: Beer’s law- Beer’s Law states that the absorption coefficient k is directly proportional to the concentration of the absorbing species in the solution: K= ɛc Where; ɛ is the molar absorptivity, c is the concentration of absorbing species. Now, substitute k= ɛc into the lambert’s law equation: I= I e - ɛc l Taking logarithm(base 10) on both sides;

7. log I= log Io- ɛc l Rearranging: log (Io/I)= ɛc l /2.303 By definition, absorbance(A) is, A= log(Io/I) Thus, A= ɛc l This is the Lambert-Beer’s law.

8. Thank you