[Rutherford]

Barbituric acid is a monoprotic acid, in this problem indicated as HA (pKa≈4).

The value of Ka can be determined more exactly by using UV-spectroscopy. Both HA und A^- absorb UV-light with a maximum of absorbance at different wavelengths. Barbituric acid is dissolved in three buffer solutions at pH = 2.0 , pH = 3.6 and pH = 7.2 . The absorbance of the three solutions is measured at wave-lengths between 200 and 280 nm. The results of the measurements have been used to derive the molar absorption coefficient of the solutions for each wavelength. These results are given in the diagram. The graph of pH = 3.60 is incomplete. At the intersection A the wavelength is 221 nm.

a) Explain whether the graph of pH = 3.6 also intersects with point A or not.
b) Calculate Ka for barbituric acid.

I am really clueless. First to a), how can I know? Any hint is appreciated.

[UG]

Have you ever heard of the isosbestic point?

[Rutherford]

No. I will search it.

[Rutherford]

Found that it is the wavelength at which both species will have the same molar absorption, thus the graph of pH = 3.6 also intersects with point A.

Now how to calculate the K_a? I have that: pKa=pH+log(c_HA/c_A^-). At point A both HA and A^- have a molar absorption of 2000. How to combine these?

[Borek]

Hint: if you are far enough from pH=pKa, solution is dominated by one form only.

[Rutherford]

Thanks for the tip, I went a little farther.
The difference is the biggest for pH=7.2, and the dominant species is A^-, so at 257-258nm its molar absorption is 23000. For pH=2 the dominant species is HA, and at 257-258nm its molar absorption is 1000. At pH=3.6, their concentrations are close to each other, and the molar absorption coefficient is 8000. What to do now?