Ch.16 - Acid-Base Equilibria

Problem 102

Chapter 16, Problem 102

Which, if any, of the following statements are true? (a) The stronger the base, the smaller the pKb. (b) The stronger the base, the larger the pKb. (c) The stronger the base, the smaller the Kb. (d) The stronger the base, the larger the Kb. (e) The stronger the base, the smaller the pKa of its conjugate acid. (f) The stronger the base, the larger the pKa of its conjugate acid.

Verified step by step guidance

Understand the relationship between base strength and Kb: A stronger base has a larger Kb value because it dissociates more in solution, increasing the concentration of OH⁻ ions.

Relate Kb to pKb: pKb is the negative logarithm of Kb (pKb = -log(Kb)). Therefore, a larger Kb results in a smaller pKb.

Analyze statement (a): 'The stronger the base, the smaller the pKb.' This is true because a stronger base has a larger Kb, leading to a smaller pKb.

Analyze statement (b): 'The stronger the base, the larger the pKb.' This is false because a stronger base has a larger Kb, which results in a smaller pKb.

Consider the relationship between a base and its conjugate acid: A stronger base has a weaker conjugate acid, which means the conjugate acid has a larger pKa. Therefore, statement (f) is true.

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Key Concepts

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

Base Strength and pKb

The strength of a base is inversely related to its pKb value. A stronger base has a lower pKb, indicating a greater tendency to accept protons. This relationship is crucial for understanding how bases behave in chemical reactions and how their strength can be quantified.

Base Strength and Kb

The base dissociation constant (Kb) measures the strength of a base in solution. A stronger base corresponds to a larger Kb value, reflecting its ability to dissociate and produce hydroxide ions. This concept is essential for comparing the relative strengths of different bases.

Conjugate Acids and pKa

The pKa of a conjugate acid is a measure of its acidity, with lower pKa values indicating stronger acids. For a stronger base, the pKa of its conjugate acid will be smaller, as stronger bases correspond to weaker conjugate acids. Understanding this relationship helps in predicting the behavior of acids and bases in chemical equilibria.

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