Unit 3: Topic 13 - Beer-Lambert Law

Question 1

Give a derivation of the Beer-Lambert Law.

Answer 1

For light passing through a spectrometer, intensity for reference is measured. Based on how much light is absorbed, the absorbance of the sample can be captured. Assumptions are that the absorbance is directly related to the concentration of the solution of the sample and the length of the light path. Therefore, letting A be the absorbance, c the concentration, and b the path length, we can include a proportionality constant E so that A = Ebc.

Question 2

An experiment has been constructed to test the Beer-Lambert Law against KMnO4. The experiment is constructed so that the product Eb is held constant throughout. If the Absorbance is calculated to be .2 at .002M of KMnO4 and at .4 for .004M of KMnO4, what should the concentration of potassium permanganate be to measure an absorbance of 1.2?

Answer 2

This is a straightforward calculation using A ~ c. Since the absorbance is .2 at .002M, we should expect the concentration to sextuple if the absorbance does, so the concentration should be 0.012M. (Note: although it was not mentioned here, extrapolating may not be safe because the Beer-Lambert law holds more rigorously for dilute concentrations, around 0.1 < A < 1.0)