Q 14-14-61 E - Organic Chemistry (Mcmurry)

Question

Ergosterol, a precursor of vitamin D, has ${\mathrm{\lambda }}_{\max }$=282nm and molar absorptivity $\mathrm{\epsilon }$= 11900. What is the concentration of ergosterol in a solution whose absorbance A=0.065 with a sample pathlength l=1.0cm?

Step-by-Step Solution

Answer

The concentration of ergosterol in a solution is  $5.5\times {10}^{-6}\mathrm{M}$

Introduction

For biochemical applications, as well as medical diagnosis, determination of the concentration of analyte in solution is a crucial step in analysis. In general spectro-photometric methods are used which are base upon the principle that molecules in solution absorb light and the emitted light is then measured with the help of a detector. In UV-Vis visible and ultraviolet light in the wavelength range of 200-900nm are used.

Lambert-Beer’s Law

To determine the concentration of analyte, wavelength usually taken are those, at which molecule display the highest absorbance (peak wavelength). The law which govern the calculation of concentration of substance from photometric measurements is Lambert-Beer’s law.

  Absorbance (A) $=\mathrm{\epsilon }\times \mathrm{c}\times \mathrm{I}$

where, A = absorbance

$\mathrm{\epsilon }$= specific extinction co-efficient

c= concentration

I = pathlength.

The Lambert-Beer law describes the dependence of the absorbance on concentration c, optical path length on a sample specific extinction coefficient $\mathrm{\epsilon }$.

Calculation

Given,

 A= 0.065

 $\mathrm{\epsilon }$=11900L/mol.cm

I= 1.0cm

Using the formula, A $=\mathrm{\epsilon }\times \mathrm{c}\times \mathrm{I}$ , you can find out the concentration of ergosterol,

 $$\begin{gathered} c=\frac{A}{\epsilon \mathrm{I}} \\ =\frac{0.065}{11900\mathrm{L}/\mathrm{mol}.\mathrm{cm}\times 1\mathrm{cm}} \\ =\frac{6.5\times {10}^{-2}}{1.19\times {10}^4\mathrm{L}/\mathrm{mol}}=5.5\times {10}^{-6}\mathrm{M} \end{gathered}$$