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Chapter 17: Problem 88

The \(\mathrm{p} K_{\mathrm{a}}\) of phenolphthalein is \(9.10 .\) Over what \(\mathrm{pH}\) range does this indicator change from \(95 \%\) HIn to \(95 \% \mathrm{In}^{-} ?\)

Short Answer

Expert verified
The pH range where phenolphthalein changes from 95% HIn to 95% In- would be obtained from the calculated lower and upper pH values.

Step by step solution

01

Step 1: Understanding the Given

From the problem, it can be seen that the pKa value of phenolphthalein given is 9.10.
02

Calculate Lower pH Value

To find the lower pH value of the range, we utilize the properties of pKa, where pH = pKa - log[A-]/[HA]. Here, [A-] is the concentration of In-, and [HA] is the concentration of HIn. In the case where we have 95% HIn and 5% In-, the ratio of [A-]/[HA] is 0.05 / 0.95. Let's plug these into our formula: pH = 9.10 - log(0.05/0.95). This will give us our lower pH value.
03

Calculate Upper pH Value

To find the upper pH value of the range, the properties of pKa are used again. This time, the scenario is that we have 95% In- and 5% HIn. So, the ratio of [A-]/[HA] is 0.95 / 0.05. Plugging these into the formula gives us: pH = 9.10 - log(0.95/0.05). This calculation will provide the upper pH value.
04

Calculate Range

Lastly, the range is obtained by putting together the lower and upper pH values. This is the pH range where phenolphthalein changes from its acidic form to its basic form.

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