[StS]

Individual spectra of pure compounds A and B were taken using 1.00 x 10 ^-5 M solutions of each, using a cell with a 5.00 cm path length.  The transmittance data for each solution at the two given wavenumbers is as follows:

Solution         % Transmittance at Wavenumber (cm ^-1)
                     
      -------------------------------------------------------------------------------------
Pure A               31.0           79.7
Pure B               97.4           20.0

An unknown mixture of A and B in a 5.00 cm cell gave transmittance values of 50.6% at 2022 cm ^-1 and 20.1% at 1993 cm ^-1.  Find the concentrations of both A and B in the mixture.

Using the initial data I can find the molar absorptivities for the pure compounds. But this is only for the wavenumber 79.7 and 20.0. When I try to find the concentration of A and B in the mixture I have two equations, and 4 unknowns. I don't have the molar absorptivities at the wavenumbers for the total mixture, nor the substances concentration's. Is there any way to convert the molar absorptivity value from one wavenumber to another?

[fledarmus]

I think there were a couple of headings left off of your table. It looks like the column reading 31.0 and 97.4 is supposed to be at 2022 cm^-1 and the column reading 79.7 and 20.0 is supposed to be at 1993 cm_-1. Like:

Solution         % Transmittance at Wavenumber (cm -1)
                        2022          1993
      -------------------------------------------------------------------------------------
Pure A               31.0           79.7
Pure B               97.4           20.0

[StS]

Ohhh, I see now. Thanks a lot!