Problem 91 - Chemistry The Central Science

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 \(\mathrm{ClO}^{-},\) (b) \(\mathrm{BrO}^{-}\) or \(\mathrm{BrO}_{2}^{-},(\mathbf{c})\) \(\mathrm{HPO}_{4}^{2-}\) or \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)

Step-by-Step Solution

Answer

In conclusion, based on the compositions, structures, and conjugate acid-base relationships, the stronger bases in each pair are: (a) \(\mathrm{BrO}^{-}\) (b) \(\mathrm{BrO}^{-}\) (c) \(\mathrm{HPO}_{4}^{2-}\)

Step 1: Recall the concept of conjugate acid-base pairs

Conjugate acids and bases are related to each other by the transfer of a proton (H+). A base is a proton acceptor, and its conjugate acid is the species formed when the base accepts a proton. The stronger the base, the weaker the conjugate acid, as a stronger base tends to have a higher affinity for protons. Therefore, we can compare the conjugate acids of the given bases to determine the stronger base.

Step 2: Compare (a) \(\mathrm{BrO}^{-}\) or \(\mathrm{ClO}^{-}\)

The conjugate acids of these two bases are HBrO and HClO, which are hypobromous acid and hypochlorous acid, respectively. In general, as we move down a group in the periodic table, the bond strength between H and the atom in the compound decreases. In this case, the H-Br bond is weaker than the H-Cl bond. This means that HBrO will be a weaker acid than HClO. Therefore, its conjugate base, \(\mathrm{BrO}^{-}\), is stronger than the \(\mathrm{ClO}^{-}\).

Step 3: Compare (b) \(\mathrm{BrO}^{-}\) or \(\mathrm{BrO}_{2}^{-}\)

In this comparison, the conjugate acids are HBrO and HBrO2 (hypobromous acid and bromous acid, respectively). When comparing conjugate acids with the same central atom but different numbers of oxygens, the acid with more oxygens is a stronger acid. In this case, HBrO2 is a stronger acid than HBrO. Thus, its conjugate base, \(\mathrm{BrO}_{2}^{-}\), is weaker than \(\mathrm{BrO}^{-}\).

Step 4: Compare (c) \(\mathrm{HPO}_{4}^{2-}\) or \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)

The conjugate acids of these two bases are H2PO4- and H3PO4 (dihydrogen phosphate and phosphoric acid, respectively). H3PO4 is a stronger acid than H2PO4-, due to the greater number of protons it can donate. Therefore, its conjugate base, \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\), is weaker than \(\mathrm{HPO}_{4}^{2-}\). In conclusion, the stronger bases in each pair are: (a) \(\mathrm{BrO}^{-}\) (b) \(\mathrm{BrO}^{-}\) (c) \(\mathrm{HPO}_{4}^{2-}\)

Key Concepts

Conjugate Acid-Base Pairs

Understanding the dynamic relationship between acids and bases is paramount for mastering chemistry concepts, particularly when comparing the strength of bases. Conjugate acid-base pairs are crucial to this comparison. These pairs are substances that transform into each other by the gain or loss of a proton (H⁺). In essence, when a base acquires a proton, it becomes its conjugate acid.

Consider water (H₂O) and the hydroxide ion (OH^-) as an example. Water acts as an acid when it donates a proton to OH^-, forming the hydronium ion (H₃O⁺) and thereby being the conjugate acid. In contrast, OH^-, which accepts the proton, is the conjugate base of water. The notable point here is that a stronger base is more inclined to accept a proton, resulting in a weaker conjugate acid and vice versa. Acidity and basicity are thus inversely correlated within these pairs.

Periodic Trends in Acidity

Acid strength can be influenced by the position of elements in the periodic table—a concept invaluable in predicting the strength of conjugate bases. Moving down a group in the periodic table, the size of atoms increases. This leads to the bonds they form with hydrogen becoming longer and weaker, which makes the release of protons easier. As a result, acids composed of these elements tend to have more strength.

Similarly, looking across a period from left to right, electronegativity increases. Atoms with higher electronegativity can stabilize the negative charge better when they become protonated. This stabilization increases the acidity of molecules. Thus, knowing the periodic trends helps in deducing whether an acid (and hence its conjugate base) is strong or weak. For example, comparing the acids HBrO and HClO, we know from periodic trends that bromine is further down the group than chlorine, giving HBrO a weaker acid strength and making its conjugate base, BrO^-, stronger.

Proton Acceptor Strength

The strength of a base is gauged by its ability to act as a proton acceptor. A powerful base is characterized by its eagerness to accept a proton. When comparing bases, especially where conjugate pairs are not immediately clear, it's helpful to consider factors such as the element's electronegativity, the charge on the base, and the stability of the resulting conjugate acid.

A base with a negative charge is typically stronger than its neutral form because the negative charge indicates a high affinity for neutralizing by gaining a proton. The stability of the conjugate acid plays a significant role as well; bases that form stable conjugate acids upon protonation are generally strong bases. For instance, in comparing BrO^- with BrO₂^-, the former is the stronger base because it forms a less stable conjugate acid, making it more willing to accept a proton.