Answer : The molar absorptivity coefficient is, [tex]1.505\times 10^{2}M^{-1}cm^{-1}[/tex]
Explanation :
Using Beer-Lambert's law :
Formula used :
[tex]A=\epsilon \times C\times l[/tex]
[tex]A=\log \frac{I_o}{I}[/tex]
[tex]\log \frac{I_o}{I}=\epsilon \times C\times l[/tex]
where,
A = absorbance of solution
C = concentration of solution = [tex]2.00\times 10^{-3}M[/tex]
l = path length = 1.00 cm
[tex]I_o[/tex] = incident light
[tex]I[/tex] = transmitted light
[tex]\epsilon[/tex] = molar absorptivity coefficient = ?
A compound absorb 50 % of the light that means,
Incident light = [tex]I_o[/tex]
Transmitted light = [tex]0.5\times I_o[/tex]
Now put all the given values in the above formula, we get the molar absorptivity coefficient.
[tex]\frac{I_o}{0.5\times I_o}=\epsilon \times (2.00\times 10^{-3}M)\times (1.00cm)[/tex]
[tex]\epsilon=1.505\times 10^{2}M^{-1}cm^{-1}[/tex]
Therefore, the molar absorptivity coefficient is, [tex]1.505\times 10^{2}M^{-1}cm^{-1}[/tex]
