Phenolphthalein has a pKa of 9.7. It is colorless in its acid form and pink in its basic form. For each of the following pH values, determine whether [In-] > [HIn] and predict the color of a phenolphthalein solution: a. pH = 2.0 b. pH = 5.0 c. pH = 8.0 d. pH = 11.0

Verified step by step guidance

insert step 1: Understand the relationship between pH, pKa, and the color change of phenolphthalein. Phenolphthalein changes color based on the ratio of its ionized form [In^-] to its non-ionized form [HIn].

insert step 2: Use the Henderson-Hasselbalch equation: pH = pKa + log([In^-]/[HIn]). This equation helps determine the ratio of [In^-] to [HIn] at a given pH.

insert step 3: For each pH value, compare it to the pKa of phenolphthalein (9.7) to determine the dominant form. If pH > pKa, [In^-] > [HIn]; if pH < pKa, [HIn] > [In^-].

insert step 4: a. For pH = 2.0, since 2.0 < 9.7, [HIn] > [In^-], so the solution is colorless.

insert step 5: b. For pH = 5.0, since 5.0 < 9.7, [HIn] > [In^-], so the solution is colorless.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pKa and Acid-Base Equilibrium

The pKa value of a weak acid indicates the pH at which the acid is half dissociated. It is a measure of the strength of the acid; lower pKa values correspond to stronger acids. In this context, phenolphthalein has a pKa of 9.7, meaning at pH values below this, the acid form (HIn) predominates, while above this pH, the basic form (In-) is favored.

Color Change of Indicators

Phenolphthalein is a pH indicator that changes color based on the acidity or basicity of the solution. It is colorless in its acidic form (HIn) and pink in its basic form (In-). Understanding the relationship between pH and the forms of the indicator is crucial for predicting the color of the solution at different pH levels.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of an acid and the ratio of the concentrations of its deprotonated and protonated forms. It can be expressed as pH = pKa + log([In-]/[HIn]). This equation helps determine the predominant form of the indicator at a given pH, which is essential for predicting the color of the phenolphthalein solution.

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