Concetration of the Unknown?

Question

John Bier determines that the slope of the line representing the absorbance of a solution of Red 3 at its analytical wavelength as a function of concentration(in mg/L) is .066 L/mg.

He measures the absorbance at the same wavelength of a solution of Red 3 of unknown concentration in the same cuvette and finds the absorbance 0.27.

What is the concentration of Red 3 in the unknown solution?

I got an answer, but i am not sure.
May someone get a better way to solve the question...i used Beer's Law : A= εbc

Pls,not only answers,clearly explanation...thanx

Answer 1

A=εbC

ε is the molar extriction coefficient
b the width of the cuvette
C the concentration in mole/L

However, by multiplying with certain factors you can change the C into whichever unit you want. E.g. in this case mole/L= 1000 mg/(MW*L) So

A=(εb1000/MW)*C' where C'=mg/L

They give you the slope =(εb1000/MW) =0.066 L/mg (A has no units so the slope should have the inverse units of the concentration)

So your equation is A=0.066C'. Therefore you don't need any more info than just the A to find C'
0.27=0.066C' => C'=0.27/0.066 = 4.09 mg/L

Answer 2

Really need some more info, I think. You're saying the slope of the line is .066 L/mg? Shouldn't the slope be absorbance/concentration? Clarify, please. Also, you would need width of the cuvette for beer's law. That's what b is.

Answer 3

no ******* clue.