An indicator has a p Ka of 5.7 . It is colorless in acid...

An indicator has a $\mathrm{p} K_{\mathrm{a}}$ of $5.7 .$ It is colorless in acid solution and deep green in alkaline solution.
(a) What is its $K_{\mathrm{a}}$ ?
(b) What is its pH range?
(c) What would its color be at pH $5.7 ?$

Key Concepts

Indicator Transition Range

The indicator transition range is the span of pH values over which an acid-base indicator undergoes a noticeable color change. Typically centered around the indicator's pKa and extending about one pH unit above and below it, this range reflects the gradual shift in the ratio of the two forms of the indicator, resulting in a gradual change in the observed color.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution by measuring its ability to donate a proton. It is defined as the ratio of the concentrations of the products (the conjugate base and hydrogen ions) to the undissociated acid. This constant is crucial for understanding equilibrium processes in acid-base chemistry and is directly related to the pKa value.

pKa

The pKa is the negative logarithm of the acid dissociation constant (Ka) and serves as an indicator of the acid's strength: the lower the pKa, the stronger the acid. In the context of acid-base indicators, the pKa is especially important because it marks the pH at which the concentrations of the acid form and the base form of the indicator are equal, often corresponding to the point where the color change is most significant.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a relationship between the pH of a solution, the pKa of an acid, and the ratio of the concentrations of its conjugate base and undissociated acid (pH = pKa + log([A-]/[HA])). This equation is used to predict the pH at which an acid-base indicator will change color, essentially indicating the balance between the two forms that have different colors.

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