Chemistry lab

Question

A 0.001 M solution absorbs 10% of light passed through a cell 1 cm thick. What concentration must be used to absorb 90% of the same radiation? Answer:

Answer 1

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:

 

 A₁          ε₁ l₁ c₁

----  =  ---------------

 A₂          ε₂ l₂ c₂

 

 

We have to rearrange the above equation to solve for c₂.  In order to do so, we have to assume we are using the same cell, which is 1 cm in length.  Therefore, l₁ and l₂ 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:

 

A₁        c₁
---- = -------
A₂        c₂

 

Rearrange to solve for c₂, you get

 

c₂ = A₂ c₁ / A₁

 

Now how do we solve for A₁ and A₂?  The intensity of light measured by a solution can be measured in units of Absorbance or %-Transmittance.  In your question, T₁ = 10% and T₂ = 90%.  To convert %-T to absorbance, use the equation,

 

A = 2 - log(%-T)

 

A₁ = 2 - log(10%) = 2 - 1 = 1

 

A₂ = 2 - log(90%) = 2 - 1.95 = 0.05

 

Now plug in the numbers, and solve for c₂

 

c₂ = A₂c₁ / A₁ = (0.05 x 0.001) / 1 = 0.00005 M