Problem 89 - Chemistry The Central Science In Si Units

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

(a) \( \text{BrO}^{-} \); (b) \( \text{BrO}^{-} \); (c) \( \text{HPO}_4^{2-} \)

Step 1: Analyze Base Pairs (a)

The given base pair is \( \text{BrO}^{-} \) and \( \text{ClO}^{-} \). To identify the stronger base, we should compare their conjugate acids: \( \text{HBrO} \) and \( \text{HClO} \). The strength of a base can be inferred from the strength of its conjugate acid – the weaker the acid, the stronger its conjugate base. Generally, more electronegative atoms make weaker acids when attached to the same group. Here, \( \text{Cl} \) is more electronegative than \( \text{Br} \), making \( \text{HClO} \) stronger than \( \text{HBrO} \). Hence, \( \text{BrO}^{-} \) is the stronger base.

Step 2: Analyze Base Pairs (b)

The given base pair is \( \text{BrO}^{-} \) and \( \text{BrO}_{2}^{-} \). Here, the number of oxygen atoms affects the conjugate acid and base strength. More oxygen atoms typically stabilize a negative charge better, thus making a compound a weaker base. \( \text{HBrO}_{2} \) is stronger than \( \text{HBrO} \), so \( \text{BrO}^{-} \) is stronger as a base than \( \text{BrO}_{2}^{-} \).

Step 3: Analyze Base Pairs (c)

The given base pair is \( \text{HPO}_4^{2-} \) and \( \text{H}_2\text{PO}_4^{-} \). Consider their conjugate acids: \( \text{H}_2\text{PO}_4^{-} \) and \( \text{H}_3\text{PO}_4 \). Since \( \text{H}_3\text{PO}_4 \) is a strong acid, \( \text{H}_2\text{PO}_4^{-} \) is a weaker base compared to \( \text{HPO}_4^{2-} \), because it retains a greater ability to donate a proton after the first deprotonation. Therefore, \( \text{HPO}_4^{2-} \) is the stronger base.

Key Concepts

Conjugate Acids and Bases

In acid-base chemistry, every acid has a conjugate base and every base has a conjugate acid, identified by the gain or loss of a proton (H⁺). When an acid donates a proton, it turns into its conjugate base.
For example, when hydrochloric acid (HCl) loses a proton, it forms its conjugate base, Cl⁻. Similarly, when a base gains a proton, it forms its conjugate acid.

• Acid: Substance that donates a proton (H⁺)
• Base: Substance that accepts a proton (H⁺)

The strength of an acid or base is inversely related to the strength of its conjugate partner. If the acid is strong, its conjugate base is weak and vice versa. Therefore, examining conjugate acids and bases helps determine the relative strength of acids and bases in a chemical equilibrium.

Electronegativity

Electronegativity is a chemical property that describes an atom's ability to attract and hold onto electrons.
It plays a crucial role in acid-base chemistry because it affects the strength of acids and bases.
Elements with higher electronegativity tend to form stronger acids when they are bonded to hydrogen.

• High electronegativity: Atoms like fluorine (F) or oxygen (O) are highly electronegative.
• Lower electronegativity: Atoms like lithium (Li) or sodium (Na) have lower electronegativity.

When considering bases like BrO⁻ and ClO⁻ in the exercise, we see that chlorine is more electronegative than bromine. This means BrO⁻ is a stronger base because its conjugate acid {HBrO} is weaker than {HClO} due to the lower electronegativity of bromine compared to chlorine.

Chemical Equilibrium

Chemical equilibrium is a state where the concentrations of reactants and products remain constant over time.
This happens because the forward and reverse reactions occur at the same rate.
In the context of acid-base reactions, equilibrium is achieved when the rate of acid dissociation equals the rate at which it recombines with its conjugate base.

• At equilibrium: The amount of acid that dissociates equals the amount that reforms.
• Equilibrium constant (K): Indicates the extent of a reaction's progression.

Understanding equilibrium helps you predict the outcome of reactions and what species are more prevalent at equilibrium. In the exercise, stronger bases in a pair find equilibrium differently, depending on the effectiveness of stabilizing a negative charge, exemplified by BrO⁻ which is the stronger base in its reactions compared to BrO₂⁻ due to less stabilization from fewer oxygen atoms.