Question

Derive an expression for the Beer-Lambert law​

Answer 1

Beer's law stated that absorbance is proportional to the concentrations of the attenuating species in the material sample. The modern derivation of theBeer–Lambert law combines the twolaws and correlates the absorbance to both the concentrations of the attenuating species and the thickness of the material sample.

Answer 2

Explanation:

According to Beer's law,

The concentration is directly proportional to the absorbance. Thus,

A ∝ C

According to Lambert's law,

The path length is directly proportional to the absorbance. Thus,

The expression for the law is:

A ∝ l

Thus, combing the two statements we get:

A ∝ C × l

Removing the sign of proportionality by the constant, ε. The expression for the Beer-Lambert law​ is:

A = ε × l × C

Where,

A is the absorbance

ε is molar absorptivity coefficient

l is the path length

C is the concentration.