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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[DeeNos]

If I try to use the combined absorbance values, then I get an impossible concentration value for PABA. Can someone help me out here?I would approach this problem by first setting up the equation for Beer's Law:

A = ebC

Where A is the absorbance, e is the molar absorptivity, b is the path length, and C is the concentration. We have two equations for each species (PABA and nicotinic acid) at two different wavelengths (267 nm and 240 nm).

For PABA:
At 267 nm: 0.844 = (e1)(1.00)(0.0450)
At 240 nm: 0.034 = (e1)(1.00)(0.0450)

For nicotinic acid:
At 267 nm: 0.755 = (e2)(1.00)(0.0366)
At 240 nm: 0.010 = (e2)(1.00)(0.0366)

We can solve for e1 and e2 by dividing the first equation by the second equation for each species, at each wavelength. This will eliminate the path length and leave us with the molar absorptivity.

For PABA at 267 nm: (0.844/0.034) = e1
e1 = 24.82

For nicotinic acid at 267 nm: (0.755/0.010) = e2
e2 = 75.50

Now we can use these values to solve for the concentrations of PABA and nicotinic acid in the mixture. We know that the total absorbance of the mixture is the sum of the individual absorbances:

Total absorbance = absorbance of PABA + absorbance of nicotinic acid

0.552 = (24.82)(0.0450)(CPABA) + (75.50)(0.0366)(Cnicotinic acid)
0.403 = (24.82)(0.0450)(CPABA) + (75.50)(0.0366)(Cnicotinic acid)

Solving this system of equations will give us the concentrations of PABA and nicotinic acid in the mixture:

CPABA = 0.021 M
Cnicotinic acid = 0.016 M

Therefore, the concentration of PABA in the mixture