Problem 89 - Chemistry: The Central Science in SI Units, Global Edition

Question

Based on their compositions and structures and on conjugate acid-base relationships, select the stronger base in each of the following pairs: (a) \(\mathrm{BrO}^{-}\) or \(\mathrm{ClO}^{-},(\mathbf{b}) \mathrm{BrO}^{-}\) or \(\mathrm{BrO}_{2}^{-}\), (c) \(\mathrm{HPO}_{4}^{2-}\) or \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\).

Step-by-Step Solution

Answer

The stronger bases in each pair are: (a) \(\mathrm{BrO}^{-}\), (b) \(\mathrm{BrO}^{-}\), and (c) \(\mathrm{HPO}_{4}^{2-}\).

Step 1: (a) Comparing Basicity of \(\mathrm{BrO}^{-}\) and \(\mathrm{ClO}^{-}\)

In this pair, both ions are from the same group (Group 17), but \(\mathrm{BrO}^{-}\) has bromine and \(\mathrm{ClO}^{-}\) has chlorine. Chlorine is more electronegative than bromine, which means it has a stronger ability to stabilize a negative charge on its conjugate acid. Therefore, the conjugate acid of \(\mathrm{ClO}^{-}\) is more stable, and \(\boldsymbol{\mathrm{BrO}^{-}}\) is the stronger base.

Step 2: (b) Comparing Basicity of \(\mathrm{BrO}^{-}\) and \(\mathrm{BrO}_{2}^{-}\)

Both of these ions contain bromine, but \(\mathrm{BrO}^{-}\) has one oxygen atom while \(\mathrm{BrO}_{2}^{-}\) has two. \(\mathrm{BrO}_{2}^{-}\) has more resonance structures that can distribute the negative charge among the multiple oxygen atoms, making its conjugate acid more stable. This leads to the conclusion that \(\boldsymbol{\mathrm{BrO}^{-}}\) is the stronger base in this pair as well.

Step 3: (c) Comparing Basicity of \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\)

In this pair, \(\mathrm{HPO}_{4}^{2-}\) has one hydrogen atom while \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) has two. When comparing the conjugate acids of these two, the \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) ion would lose a hydrogen to become \(\mathrm{H_{3}PO_{4}}\), while \(\mathrm{HPO}_{4}^{2-}\) would gain a hydrogen to become \(\mathrm{H_{2}PO_{4}^{-}\). Since \(\mathrm{H_{3}PO_{4}}\) is more acidic than \(\mathrm{H_{2}PO_{4}^{-}\), it means that the conjugate base \(\mathrm{H_{2}PO_{4}^{-}}\) is weaker than the conjugate base \(\mathrm{HPO}_{4}^{2-}\). Thus, \(\boldsymbol{\mathrm{HPO}_{4}^{2-}}\) is the stronger base in this pair.

Key Concepts

Conjugate Acid-Base Pairs

A fundamental concept in acid-base chemistry is the idea of conjugate acid-base pairs. They play a crucial role in understanding the stability and basicity of substances. A conjugate acid-base pair consists of two species that transform into each other by the gain or loss of a proton (\(\text{H}^+\)). For example, \(\text{BrO}^{-}\) is the base, and its conjugate acid is \(\text{HBrO}\). Conversely, the conjugate base of an acid is formed by removing a proton from the acid.

• The stronger the acid, the weaker its conjugate base, and vice versa.
• This relationship helps us determine which acid or base is stronger by comparing the stability of their conjugate counterparts.

In the exercise examples, where we compare \(\text{ClO}^{-}\) and \(\text{BrO}^{-}\), the focus is on stability provided by their conjugate acids. The more stable the conjugate acid, the less its ability to hold onto the proton, resulting in a weak conjugate base, thereby identifying the stronger base among the options.

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons. This concept helps us understand how different atoms influence the strengths of acids and bases. Higher electronegativity indicates a stronger pull on the electrons, which can stabilize negative charges more effectively.
This stabilization is crucial in acid-base chemistry because:

• More electronegative atoms, such as chlorine, tend to stabilize the negative charges better than less electronegative atoms, like bromine.
• If a conjugate base is associated with an atom of high electronegativity, it will be more stable relative to one with lower electronegativity.

In the steps provided, \(\text{ClO}^{-}\) is found to be associated with chlorine, which is more electronegative than bromine in \(\text{BrO}^{-}\). This makes the conjugate acid of \(\text{ClO}^{-}\) (\(\text{HClO}\)) more stable than the conjugate acid of \(\text{BrO}^{-}\) (\(\text{HBrO}\)). Consequently, \(\text{BrO}^{-}\) emerges as the stronger base.

Resonance Structures

Resonance is a concept that describes the delocalization of electrons in molecules that can have more than one valid Lewis structure. This helps in understanding the distribution of electrons within an ion or molecule, which in turn influences stability and reactivity. Resonance structures illustrate how electrons are shared between different atoms, providing insight into a molecule's behavior.

• More resonance structures often mean a more stable compound, as the negative charge can be evenly spread across several atoms.
• Stability gained through resonance can make a conjugate acid less reactive and therefore make its conjugate base weaker.

For example, \(\text{BrO}_{2}^{-}\) ion has more resonance forms relative to \(\text{BrO}^{-}\) because it has additional oxygen atoms. These additional resonance forms stabilize the negative charge better, making \(\text{BrO}_{2}^{-}\) a weaker base compared to \(\text{BrO}^{-}\). Understanding resonance helps explain why some compounds or ions are more basic or acidic based on their ability to distribute charge.