Finding mixture concentration using Beer's Law

[DeadFishFactory]

Homework Statement

A 0.0450 M solution of para-aminobenzoic acid had an absorbance of 0.844 at 267 nm in a 1.00 cm cuvet, and an absorbance of 0.034 at 240 nm. A 0.0366 M solution of nicotinic acid had absorbances of 0.010 and 0.755 at 267 and 240 nm, respectively. A MIXTURE of PABA and nicotinic acid had absorbances of 0.552 and 0.403 at 267 and 240 nm, respectively. Calculate the concentration of PABA and nicotinic acid in the mixture.

Homework Equations

A = ebC

A = absorbance
b = path length
C = concentration
e = molar absorptivity

The Attempt at a Solution

I've tried, but I can't figure it out. If I try to use Beer's Law individually on the two absorbance values, then I get 2 concentration values for each species.

 

[gabriels-horn]

Homework Statement

A 0.0450 M solution of para-aminobenzoic acid had an absorbance of 0.844 at 267 nm in a 1.00 cm cuvet, and an absorbance of 0.034 at 240 nm. A 0.0366 M solution of nicotinic acid had absorbances of 0.010 and 0.755 at 267 and 240 nm, respectively. A MIXTURE of PABA and nicotinic acid had absorbances of 0.552 and 0.403 at 267 and 240 nm, respectively. Calculate the concentration of PABA and nicotinic acid in the mixture.

Homework Equations

A = ebC

A = absorbance
b = path length
C = concentration
e = molar absorptivity

The Attempt at a Solution

I've tried, but I can't figure it out. If I try to use Beer's Law individually on the two absorbance values, then I get 2 concentration values for each species.

Try taking a ratio of the known concentrations at their respective wavelengths to solve for the unknown concentrations. Beer's law is a linear relationship in this case.

 

[DeadFishFactory]

I'm still slightly confused on how that would look?

Are you saying we do:

A1/A2 = (b1C1e1)/(b2C2e2)?

 

[Borek]

From initial data calculate separately 4 values of molar absorptivity - for two substances and two wavelengths. Then you will have two equations in two unknowns for a mixture.

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