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

pH indicators are substances that change color in response to the acidity or basicity of their environment, making them powerful tools for measuring the pH of a solution. They are weak acids or bases that exist as natural dyes and demonstrate a distinct color change at a particular pH level. This change is due to the shift in equilibrium between the protonated (acidic) and deprotonated (basic) forms of the indicator.

When choosing a pH indicator for a particular acid-base titration or other application, it’s important to consider the pH range over which the indicator changes color. This is known as the indicator’s transition range. Ideally, it should be narrow and centered around the equivalence point or the pH value of interest in an experiment.

The pKa value is a measure of the strength of an acid. It’s defined as the negative base-10 logarithm of the acid dissociation constant (Ka) of a substance. The lower the pKa value, the stronger the acid, because it more readily donates protons (H+) to the solution. Conversely, a higher pKa value indicates a weaker acid.

Significance in pH Calculations

Understanding the pKa value of a compound is crucial for predicting and controlling the pH range in chemical reactions, especially in buffer solutions. It’s also important when using the Henderson-Hasselbalch equation to calculate the pH of a solution when concentrations of acid and conjugate base are known.

Acid-base equilibrium refers to the state of balance between the concentration of acids and bases in a chemical solution. This equilibrium is dynamic, with acids donating protons to bases and the conjugate bases (the products of this process) returning protons to the conjugate acids.

Relevance to pH

Under constant conditions, the equilibrium concentrations remain constant, hence defining the pH of the solution. This relationship is governed by the dissociation constants of the acids and bases in question. The Henderson-Hasselbalch equation, derived from the acid dissociation constant, allows for the calculation of pH based on the relative concentrations of an acid and its conjugate base.

Phenolphthalein is a common pH indicator used in many laboratory settings to visually determine the acidity or basicity of a solution. It is colorless in acidic solutions and turns pink to deep purple in basic solutions, with the color transition occurring over a pH range of approximately 8.2 to 10.0.

However, to quantify this range more precisely for a given scenario, such as a titration, we can use the Henderson-Hasselbalch equation. In the given exercise, the phenolphthalein pH range where it changes from 95 percent acid form to 95 percent base form is calculated to be from approximately pH 7.8 to 10.4. This calculation helps to more accurately predict at what pH levels a distinct color change will be observable, aiding in the determination of the endpoint of a titration.