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If the absorbance of one of the buffer solutions (pH = 4.623) was 0.319 and the absorbance of the basic solution was 0.625, what is the $\mathrm{p}K_\mathrm{a}$ of the indicator? Include activity coefficients in the calculations.

The correct answer is 4.927, but I don’t know how to approach the problem to get the right answer. Thanks in advance!

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closed as off-topic by Martin - マーチン, Del Pate, Loong, John Snow, Jori Apr 7 '15 at 10:35

This question appears to be off-topic. The users who voted to close gave this specific reason:

If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ There is information missing in the question since it does not state what the buffer concentration is. Also, the site is not suppose to provide answers to your homework questions, but we we try to help you understand how to solve the problem. Please edit your question and state what was done in class about this type of problem. $\endgroup$ – LDC3 Apr 7 '15 at 4:13
  • $\begingroup$ I don't understand the question at all. What is this absorbance? What is the basic solution? Do you know which kind of buffer it is? $\endgroup$ – Martin - マーチン Apr 7 '15 at 4:17
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    $\begingroup$ Molar absorptivities for the protonated and deprotonated form of the indicator are needed. $\endgroup$ – Marko Apr 7 '15 at 6:54
  • $\begingroup$ If you don't know the what absorbance is, than you should first study absorption spectroscopy. $\endgroup$ – Molx Apr 8 '15 at 16:43
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The following only gives some directions!

The molar extinction coefficient (molar absorptivity) is not necessary to correlate the absorbance and the concentration of the observed species, supposed that the same species is measured at one particular wavelength at different pH values!

Using the Lambert-Beer Law, we can derive that

\[\frac{E_1}{E_2} = \frac{\epsilon\cdot c_1\cdot d}{\epsilon\cdot c_2\cdot d} = \frac{c_1}{c_2}\]

The ratio of absorbances is linear proportional to the ratio of concentrations.

  1. For a pH of 4.623, it seems fair to assume that an acetate puffer is used here. Taking this into account, you could even estimate the ratio of $\ce{HOAc}$ and $\ce{NaOAc}$ used.
  2. The species monitored by UV is either the indicator $\ce{HInd}$ or its corresponding base $\ce{Ind-}$.
  3. Since the absorbance is higher in basic solution, we might conclude that $\ce{Ind-}$ is observed. \[\ce{HInd + B <=> Ind- +BH+}\]

  4. $\ce{HInd}$ is typically a rather weak acid.

  5. Is it safe to assume that the basic solution only contains $\ce{Ind-}$, while in buffered solution $\ce{HInd}$ is present as well?
  6. Is it furthermore conceivable that $\ce{HInd}$ and $\ce{Ind-}$ constitute a buffer system for which the pH can be calculated using the Hasselbalch-Henderson equation?
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