[Halogen876]

I've been attempting to work out this problem (not homework) and am at somewhat of a loss as to how to approach it. Here it is:

Equilibrium constants can be determined using spectrophotometry. A solution is prepared containing 2.00x10^-2F phenolphthalein (a Bronsted acid-base indicator). Three 1.00mL portions of this solution are diluted to 100.0mL with the following three solutions: (a) 0.100F HCl, (b) 0.100F NaOH and (c) a buffer of pH 9.35 (where the formalities of both of the buffer components are approximately 0.100). The absorbances of the three solutions as measured in a 1.00cm cell are: (a) A=0.000 (all indicator in the acid form), (b) A=0.732 (all indicator in the base form) and (c) A=0.242. What is the pKa of the indicator?

It would seem to me that since in solution (c), the acid and base components of the buffer are equal, so pH should equal pKa so pKa should be 9.35 but the answer in the back of the book is 9.66 so obviously I'm missing something...any help would be greatly appreciated 

[Borek]

Buffer acid/base pair has identical concentrations of both forms, but it doesn't mean acid/base forms of the phenolphthalein are identical as well. You are expected to find their concentrations from the spectroscopic data.

[Halogen876]

Ok, thanks. That makes sense. I know that A=εbc. I could use the absorbance from solution (b) to solve for ε (which comes out to be 36.6L/mol cm). Then I could use ε with the abosrbance for solution (c) to solve for the concentration in soultion (c) (which comes out to be 0.00661mol/L. I'm not sure if any of that is relevant though, or if it is, where I should go with it next...

[Borek]

Then I could use ε with the abosrbance for solution (c) to solve for the concentration in soultion (c) (which comes out to be 0.00661mol/L

You know concentration, but concentration of what?

[Halogen876]

I think the concentration I found (0.661 mol/L) in solution (c) must be the concentration of phenolphthalein in that soultion...but I'm not sure if that's just the acid form, just the base form, or the total...I'm guessing that it might be just the base form since in solution (a) the phenolphthalein is all in the acid form and the absorbance is 0 so the acid form must not contribute to absorbance. I'm not sure if that's all correct though, and if it is, I'm not sure where I would go next with it...

[Borek]

And if it is a conjugate base concentration, what is the acid concentration in the solution c?

[Halogen876]

Well, the total concentration of phenolphthalein is 2.00x10^-2 mol/L and the base concentration is 0.00661mol/L so the acid concentration must be 2x10^-2mol/L - 0.00661mol/L so 0.0134mol/L. Then you can just plug those acid and base concentrations into the buffer equation and that gives me the correct answer!

Thanks so much for all your help with this question - it is greatly appreciated