In: Chemistry
A solution of a specific vitamin has λmax = 287 nm and a concentration of 8.76 × 10-7 M. The absorbance of the solution at 287 nm is A = 0.190. What is the molar absorptivity of the vitamin at 287 nm? (sample pathlength = 1.00 cm)
Solution :
Beer-Lambert Law
The absorbance of an electronic transition depends on two external factors.
1. The absorbance is directly proportional to the concentration (c) of the solution of the the sample used in the experiment.
A ∝ c
2. The absorbance is directly proportional to the length of the light path (l), which is equal to the width of the cuvette.
A ∝ l
Combining the two relationships,
A ∝ cl
This proportionality can be converted into an equation by including a constant.
A = εcl
This formula is known as the Beer-Lambert Law, and the constant ε is called molar absorptivity or molar extinction coefficient and is a measure of the probability of the electronic transition. The larger the molar absorptivity, the more probable the electronic transition. In uv spectroscopy, the concentration of the sample solution is measured in molL-1 and the length of the light path in cm. Thus, given that absorbance is unitless, the units of molar absorptivity are Lmol-1cm-1.
A = ε * c* ℓ
where
ε is the molar attenuation coefficient of that material
c is the amount concentration of those species;
ℓ is the pathlength.
λmax = 287 , C = 8.76 × 10-7 M , A = 0.190
ε = A/C*l = 0.190/ 8.76 × 10-7 *1 = 2.168 *10-2 *107
= 2.168 *105 Lmol-1cm-1