Question

Which has the larger numerical value? (a) The \(\mathrm{p} K_{a}\) of a strong acid or the \(\mathrm{p} K_{\mathrm{a}}\) of a weak acid (b) The \(K_{a}\) of a strong acid or the \(K_{a}\) of a weak acid

Short answer

Question: Compare the numerical values of the pKa and Ka of strong acids and weak acids. Answer: The pKa of a strong acid has a smaller numerical value than the pKa of a weak acid, while the Ka of a strong acid has a larger numerical value than the Ka of a weak acid.

Step-by-step solution

Definition of Strong and Weak Acids

A strong acid is an acid that dissociates completely in water, releasing all of its hydrogen ions (H+) into the solution. A weak acid only partially dissociates in water, releasing only a fraction of its hydrogen ions (H+). Examples of strong acids are hydrochloric acid (HCl), nitric acid (HNO3), and sulfuric acid (H2SO4). Examples of weak acids are acetic acid (CH3COOH) and carbonic acid (H2CO3).

Definition of pKa and Ka

The pKa is a measure of the acidity of a substance and is related to the acid dissociation constant (Ka) by the equation: pKa = \(-\log _{10}(K_{a})\). The smaller the pKa, the stronger the acid; a larger Ka value indicates the stronger the acid, since it measures the tendency of an acid to dissociate into its ions in a solution.

pKa of Strong and Weak Acids

Since a strong acid dissociates completely in water, it has a higher Ka value (indicating a stronger tendency to release hydrogen ions), which means it has a smaller pKa value. Conversely, a weak acid has a lower Ka value (indicating a weaker tendency to release hydrogen ions), which means it has a larger pKa value. Therefore, the pKa of a strong acid has a smaller numerical value than the pKa of a weak acid. Answer (a): The pKa of a strong acid has a smaller numerical value than the pKa of a weak acid.

Ka of Strong and Weak Acids

Since a strong acid dissociates completely in water, it has a higher Ka value compared to a weak acid, which partially dissociates in water. Therefore, the Ka of a strong acid has a larger numerical value than the Ka of a weak acid. Answer (b): The Ka of a strong acid has a larger numerical value than the Ka of a weak acid.