Ishwar S. answered • 09/06/18

University Professor - General and Organic Chemistry

Hello Nelson

We have to use the Beer's Law equation to solve this question.

A = ε l c

Since we have an initial and final amount for absorbance, we can set up a ratio of 2 Beer's Law equation as follows:

A

_{1}ε_{1}l_{1}c_{1}---- = ---------------

A

_{2}ε_{2}l_{2}c_{2}We have to rearrange the above equation to solve for c

_{2}. In order to do so, we have to assume we are using the same cell, which is 1 cm in length. Therefore, l_{1}and l_{2}are the same and will cancel out in the above equation. In addition, the molar extinction coefficient will remain constant since we are assuming the samples were measured in identical conditions. The above equation will then simplify to:A

_{1}c

_{1}

---- = -------

A

_{2}c

_{2}

Rearrange to solve for c

_{2}, you getc

_{2}= A_{2}c_{1}/ A_{1}Now how do we solve for A

_{1}and A_{2}? The intensity of light measured by a solution can be measured in units of Absorbance or %-Transmittance. In your question, T_{1}= 10% and T_{2}= 90%. To convert %-T to absorbance, use the equation,A = 2 - log(%-T)

A

_{1}= 2 - log(10%) = 2 - 1 = 1A

_{2}= 2 - log(90%) = 2 - 1.95 = 0.05Now plug in the numbers, and solve for c

_{2}c

_{2}= A_{2}c_{1}/ A_{1}= (0.05 x 0.001) / 1 = 0.00005 M