Question

A solution containing a mixture of the compounds X and Y had an absorbance of 0.793 at 443 nm and an absorbance of 0.681 at 520 nm when measured with a 1.00 cm cell. The molar absorptivities (ε) of X and Y at each wavelength are shown in the table below.

Answer 1

For a mixture of compounds, the beer law is as follow:

A = EbCx + EbCy

So for the first wavelength:

0.793 = 13720 * 1 * Cx + 3237 * 1 * Cy

0.793 = 13720Cx + 3237Cy (1)

For the second wavelength:

0.681 = 3338Cx + 5371Cy (2)

Now solving for Cx or Cy from any equation (In this case, I'll solve for Cy first from equation 1):

0.793 - 13720Cx / 3237 = Cy (3)

Now replacing in (3) in (2):

0.681 = 3338Cx + 5371[0.793 - 13720Cx / 3237]

0.681 - 3338Cx = 4259.2 - 73,690,120Cx / 3237

3237(0.681-3338Cx) = 4259.2 - 73,690,120Cx

2204.397 - 10,805,106Cx = 4259.2 - 73,690,120Cx

2204.937 - 4259.2 = (10,805,106 - 73,690,120)Cx

2054.263 / 62,885,014 = Cx

Cx = 3.27x10^-5 M

Now replacing in (3):

Cy = 0.793 - 13720(3.27x10^-5) / 3237

Cy = 1.07x10^-4 M

Hope this helps