Phenolphthalein has a pKa of 9.7 . It is colorless in its acid form and pink in its basic form.

step 1 So now we'll work on question 80 from chapter 17. In this question, we're asked to do some calcu

Phenolphthalein has a pKa of 9.7 . It is colorless in its...

Phenolphthalein has a $\mathrm{pK}_{a}$ of $9.7 .$ It is colorless in its acid form and pink in its basic form. For each of the pH's, calculate $\left[\operatorname{In}^{-}\right] /[\operatorname{HIn}]$ and predict the color of a phenolphthalein solution. a. $\mathrm{pH}=2.0$ b. $\mathrm{pH}=5.0$ c. $\mathrm{pH}=8.0$ d. $\mathrm{pH}=11.0$

Phenolphthalein has a $\mathrm{pK}_{a}$ of $9.7 .$ It is colorless in its acid form and pink in its basic form. For each of the pH's, calculate $\left[\operatorname{In}^{-}\right] /[\operatorname{HIn}]$ and predict the color of a phenolphthalein solution.
a. $\mathrm{pH}=2.0$
b. $\mathrm{pH}=5.0$
c. $\mathrm{pH}=8.0$
d. $\mathrm{pH}=11.0$

Key Concepts

Quantitative Analysis of Indicator Species Ratio

Using the rearranged Henderson-Hasselbalch equation, one can calculate the ratio of deprotonated to protonated indicator species at any given pH. This quantitative approach helps predict the extent of the color change by calculating [In?]/[HIn]. A small ratio indicates predominantly the protonated (acid) form, while a large ratio indicates predominantly the deprotonated (base) form, which corresponds to the observable color transition in acid–base indicator systems.

Role of pKa in Indicator Color Change

The pKa of an indicator is the pH at which the concentrations of its two interconvertible forms are equal, meaning the ratio of deprotonated to protonated species is 1. This value is critical because it defines the midpoint of the indicator’s color change. When the pH is significantly lower than the pKa, the indicator remains mostly in one form (typically colorless), and when the pH is above the pKa, it shifts to the other form (typically colored).

Henderson-Hasselbalch Equation

This equation is fundamental in acid–base chemistry for relating the pH of a solution to the acid dissociation constant (pKa) and the ratio of the concentrations of deprotonated (basic) to protonated (acidic) forms of a weak acid. It is used to calculate the fraction of each form present in a solution and is especially useful in determining the behavior of buffer systems and pH-sensitive indicators.

Acid–Base Indicator Behavior

Acid–base indicators are substances that change color depending on the pH of the solution they are in. They exist in different forms, with each form exhibiting a distinct color. This duality allows for a visible transition at a specific pH range, as the equilibrium between the colored and colorless (or differently colored) forms shifts, which is the principle behind their use in titrations and pH measurements.

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