Metacresol purple is an indicator that changes from yellow...

Metacresol purple is an indicator that changes from yellow to purple at $\mathrm{pH} 8.2$
(a) What is $K_{\mathrm{a}}$ for this indicator?
(b) What is its $\mathrm{pH}$ range?
(c) What is the color of a solution with $\mathrm{pH} 9.0$ and a few drops of metacresol purple?

Key Concepts

Indicator pH Transition Range

The indicator pH transition range is the span of pH values over which the indicator changes color. It is generally about ±1 pH unit from the indicator's pKa. Within this range, significant proportions of both the protonated and deprotonated species coexist, allowing the color to gradually shift, making the indicator useful for detecting changes in pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation, pH = pKa + log([A?]/[HA]), relates the pH of a solution to the pKa of the indicator and the ratio of its deprotonated form ([A?]) to its protonated form ([HA]). This equation is fundamental in analyzing the behavior of acid-base indicators and determining the color of the solution at a specific pH.

Acid-Base Indicator

Acid-base indicators are substances that exhibit different colors depending on the pH of the environment. They are typically weak acids or bases, and their color change is due to structural changes that occur when they donate or accept protons. The color transition reflects the relative concentrations of the protonated and deprotonated forms.

Acid Dissociation Constant (Ka) and pKa

The acid dissociation constant (Ka) quantifies the extent to which an acid dissociates in solution into its conjugate base and a proton. The pKa, which is the negative logarithm of Ka, is a critical value that indicates the pH at which the concentrations of the protonated and deprotonated forms are equal. For indicators, the pKa determines the pH at which the color change occurs.

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