Question

The \(K_{a}\) values for \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{HSO}_{3}^{-}\) are \(4.8 \times 10^{-13}\) and \(6.3 \times 10^{-8}\) respectively. Therefore, it follows the \(\mathrm{HPO}_{4}^{2-}\) is a ......... acid than \(\mathrm{HSO}_{3}^{-}\) and \(\mathrm{PO}_{4}^{3-}\) is a.......... base than \(\mathrm{SO}_{3}^{2-}\). (a) weaker, stronger (b) stronger, weaker (c) weaker, weaker (d) stronger, stronger

Short answer

\(\mathrm{HPO}_{4}^{2-}\) is a weaker acid than \(\mathrm{HSO}_{3}^{-}\) and \(\mathrm{PO}_{4}^{3-}\) is a stronger base than \(\mathrm{SO}_{3}^{2-}\), therefore the answer is (a) weaker, stronger.

Step-by-step solution

- Understand Acid Strength from Ka Values

The acid dissociation constant \(K_a\) is a measure of the strength of an acid in solution. A larger \(K_a\) value indicates a stronger acid that dissociates to a greater extent in solution.

- Compare the Ka Values of HPO4(2-) and HSO3(-)

Given that the \(K_a\) value for \(\mathrm{HPO}_{4}^{2-}\) is \(4.8 \times 10^{-13}\) and for \(\mathrm{HSO}_{3}^{-}\) is \(6.3 \times 10^{-8}\), we see that \(\mathrm{HPO}_{4}^{2-}\) has a smaller \(K_a\) value than \(\mathrm{HSO}_{3}^{-}\).

- Determine Relative Acid Strength

Since \(\mathrm{HPO}_{4}^{2-}\)'s \(K_a\) is smaller than that of \(\mathrm{HSO}_{3}^{-}\), \(\mathrm{HPO}_{4}^{2-}\) is a weaker acid compared to \(\mathrm{HSO}_{3}^{-}\).

- Understand Base Strength from Conjugate Acids

The strength of a base is directly related to the strength of its conjugate acid. A weaker conjugate acid corresponds to a stronger conjugate base.

- Deduce the Strength of Conjugate Bases

Since \(\mathrm{HPO}_{4}^{2-}\) is the conjugate acid of \(\mathrm{PO}_{4}^{3-}\) and it is a weaker acid than \(\mathrm{HSO}_{3}^{-}\) (the conjugate acid of \(\mathrm{SO}_{3}^{2-}\)), it follows that \(\mathrm{PO}_{4}^{3-}\) is a stronger base than \(\mathrm{SO}_{3}^{2-}\).

Key concepts

Acid Strength Comparison

When comparing acid strengths, the acid dissociation constant, denoted as \(K_a\), plays a critical role. The \(K_a\) value provides insight into how readily an acid donates its proton to a base in a solution. A stronger acid has a higher propensity to lose its proton, resulting in a larger \(K_a\) value.

In the context of our exercise, the \(K_a\) value for \(HPO_4^{2-}\) is significantly lower than that of \(HSO_3^{-}\), indicating that \(HPO_4^{2-}\) is less willing to give up its proton compared to \(HSO_3^{-}\). Thus, referring back to our exercise, the option stating that \(HPO_4^{2-}\) is a weaker acid than \(HSO_3^{-}\) aligns with the fundamental principle that a smaller \(K_a\) signifies a weaker acid.

Understanding and comparing acid strengths is essential for fields ranging from industrial chemistry to pharmaceuticals, as the reactivity and behavior of compounds in solution are greatly influenced by their acid-base properties.

Ka Values Interpretation

Interpreting \(K_a\) values is more than just recognizing the numerical magnitude; it's about understanding what these values tell us about the behavior of acids in solutions. The value of the acid dissociation constant, \(K_a\), quantifies the equilibrium between an acid and its ions in solution. A higher \(K_a\) value means that the acid dissociates more completely, with more protons being released into the solution.

For students studying these concepts, it's valuable to remember that \(K_a\) values typically appear in exponential notation due to their generally small size for weak acids. For example, the \(K_a\) values in the given exercise, \(4.8 \times 10^{-13}\) for \(HPO_4^{2-}\) and \(6.3 \times 10^{-8}\) for \(HSO_3^{-}\), illustrate that \(HSO_3^{-}\) is substantially more dissociated in solution, thereby classifying it as the stronger acid. Recognizing how to read and interpret these values is an essential skill for any student learning about acid-base chemistry.

Conjugate Acids and Bases

The relationship between conjugate acids and bases lies at the heart of Brønsted-Lowry acid-base theory. When an acid donates a proton in a solution, the remaining species forms its conjugate base. Conversely, when a base accepts a proton, it becomes its conjugate acid. This conjugate pair is always in equilibrium in a solution.

A significant point to grasp is that the strength of a conjugate base is inversely related to the strength of its conjugate acid. This principle means that the weaker the acid, the stronger its conjugate base will be. In our exercise, \(HPO_4^{2-}\) being a weaker acid than \(HSO_3^{-}\), indicates that its conjugate base, \(PO_4^{3-}\), is a stronger base than that of \(HSO_3^{-}\)'s conjugate base, \(SO_3^{2-}\).

Understanding the dynamic between conjugate acids and bases is crucial for predicting reaction directions, acid-base titrations, buffer solutions, and many other applications in chemistry.