# A substance in an aqueous solution at a concentration of 0.01M shows an optical transmittance of 28% with a path length of 2mm calculate the molar absorption coefficient of the solute? What would be the transmittance in a cell of 1cm thick?

Jun 12, 2018

(a) $\epsilon = \text{280 L·mol"^"-1""cm"^"-1}$; (b) $T = 0.017$.

#### Explanation:

Many compounds absorb ultraviolet (UV) or visible (VIS) light as it passes through a solution.

If a beam of radiation of power ${P}_{0}$ passes through a solution, absorption takes place. The radiation leaving the sample has power $P$.

We can express the amount of radiation absorbed as transmittance $T$.

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} T = \frac{P}{P} _ 0 \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can express the amount of radiation absorbed as absorbance $A$

$A = \log \left({P}_{0} / P\right) = \log \left(\frac{1}{T}\right)$

color(blue)(bar(ul(|color(white)(a/a)A = "-log"Tcolor(white)(a/a)|)))" "

The Beer-Lambert Law

The Beer-Lambert Law states that the absorbance $A$ of a solution is directly proportional to the molar concentration $\text{c}$ of the solute and the path length $l$ (usually expressed in centimetres).

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} A = \epsilon c l \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

$\epsilon$ is a proportionality constant called the molar absorption coefficient.

Now, we can write

$\log T = - \epsilon c l$

or

$\epsilon = - \log \frac{T}{c l}$

Part (a). Calculate the molar absorption coefficient

epsilon = -logT/(cl) = -log0.28/("0.01 mol·L"^"-1" × "0.2 cm") = "280 L·mol"^"-1""cm"^"-1"

Part (b). Calculate the transmittance

$\log T = - \epsilon c l = \text{-280" color(red)(cancel(color(black)("L·mol"^"-1""cm"^"-1")))× 0.01 color(red)(cancel(color(black)("mol·L"^"-1"))) × 1 color(red)(cancel(color(black)("cm"))) = "-2.8}$

$T = {10}^{\text{-2.8}} = 0.0017$