[DutchGirl13]

 have final problem on my homework that I began but could not finish because I felt that I ran out of information. It goes as follows:
A 1.00 x10^-4 M solution of substance B has absorbances of 0.840 and 0.360 at 320 nm and 278 nm, respectively, whereas a 1.00 c 10^-4 M solution of substance C has absorbances of 0.480 and 0.432 at these wavelengths, respectively. An unknown solution has A320= 0.386 and A 278= 0.347. All these measurements were carried out under the same conditions.
a). Find which compound (B or C) exists in the unknown solution.
b). Calculate the concentration of the unknown compound.

I've figured out the molar absorptivity values at both wavelengths for both B and C. They are as follows:
B320= 8400 1/M*cm
B278= 3600 1/M*cm
C320= 4800 1/M*cm
C278= 4320 1/M*cm.
I ran stuck after figuring these. First, I thought each substance had a constant molar absorptivity, not one that varied with the wavelength of light used, so I'm not sure which of the four values I need to use. Second, it seems that there is not enough information to figure out the answer to a). I believe that if I could figure out a), I could figure out b) just by using Beer's Law. I must be missing some route, but I can not figure out what it is. Therefore, if you are willing and able to help, please do.

[Borek]

First, I thought each substance had a constant molar absorptivity

You must revise your thinking then

Molar absorptivity IS a function of wavelength. That's why you can solve this question.

[DutchGirl13]

Okey-dokey then. I have kicked myself. My thinking has been revised; I should have known that different wavelengths of light would be absorbed in different amounts. However, my confusion over the method of solving remains; I feel that I have more unknowns than I do equations. would you please give a hint as how I could solve for part a)? Once I get a), b) should be easy. I suppose my activation energy for solving this is pretty high. Sorry, I could not resist a bad joke.

[Borek]

Will the ratio of absorptivities at different wavelengths be constant for a given compound, or will it be function of its concentration?

[DutchGirl13]

Will the ratio of absorptivities at different wavelengths be constant for a given compound, or will it be function of its concentration?

The whole idea of Beer's Law is that absorptivity is proportional to concentration. In this problem, the concentrations of B and C are the same, so I believe the ratio is a function of the concentration.

[Borek]

Imagine for a GIVEN substance:

A₃₀₀ = k₃₂₀*C
A₂₆₀ = k₂₆₀*C

Calculate ratio A₃₀₀/A₂₆₀ - is it a function of a concentration?

[DutchGirl13]

I think it's not but rather a ratio of molar absorptivities. I calculated the ratio for my substance, and I think I can disregard the concentration because it's constant, but after that, I do not know how to find the molar absorptivity. Thank you for your help thus far.

[Borek]

Can you compare ratio of absorptivities of unknown with ratios for A & B?

[DutchGirl13]

I just got my homework back, and the answer I got with your guidance is correct. Thank you.