Problem 89 - 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 \(\mathrm{BrO}_{2}^{-}\), (c) \(\mathrm{HPO}_{4}{\underline{\phantom{xx}}}^{2-}\) or \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\).

Step-by-Step Solution

Answer

The stronger bases in each pair are: a) \(\mathrm{ClO}^{-}\) b) \(\mathrm{BrO}^{-}\) c) \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\)

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

For this comparison, we should look at the basic strength in terms of their conjugate acids: hypobromous acid (\(\mathrm{HBrO}\)) and hypochlorous acid (\(\mathrm{HClO}\)). The weaker the conjugate acid, the stronger the base. From periodic trends, we know that as we go down a group on the periodic table, the acidity of the conjugate acid increases due to the larger atomic radius and poorer shielding of the positively charged nucleus. Therefore, hypobromous acid is a stronger acid than hypochlorous acid since bromine is below chlorine. Since \(\mathrm{HBrO}\) is a stronger acid than \(\mathrm{HClO}\), we can conclude that the stronger base is \(\mathrm{ClO}^{-}\).

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

This comparison deals with the presence of more oxygen atoms in these conjugate pairs. Let's consider their conjugate acids: hypobromous acid (\(\mathrm{HBrO}\)) and bromous acid (\(\mathrm{HBrO}_2\)). The more oxygen atoms present in the conjugate acid, the stronger the acid will be due to the higher electron-withdrawing nature of the oxygen atoms. This means that the strength of the acid increases as more oxygens are present, so bromous acid is stronger than hypobromous acid. Since \(\mathrm{HBrO}_2\) is a stronger acid than \(\mathrm{HBrO}\), we can conclude that the stronger base in this pair is \(\mathrm{BrO}^{-}\).

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

In this case, we have different charges on both ions. Let's look at their conjugate acids: dihydrogen phosphate (\(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\)) and hydrogen phosphate (\(\mathrm{HPO}_{4}^{2-}\)). As the negative charge of the conjugate base increases, the strength of the conjugate acid decreases because the base will be more attracted to the protons. This means that hydrogen phosphate (\(\mathrm{HPO}_{4}^{2-}\)) is a stronger acid than dihydrogen phosphate (\(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\)). Since \(\mathrm{HPO}_{4}^{2-}\) is a stronger acid than \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\), we can conclude that the stronger base is \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\), in this pair. To summarize: a) Stronger base: \(\mathrm{ClO}^{-}\) b) Stronger base: \(\mathrm{BrO}^{-}\) c) Stronger base: \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\)

Key Concepts

Conjugate Acid-Base Pairs

Understanding the relationship between acids and bases is fundamental in chemistry, and this concept is encapsulated by conjugate acid-base pairs. A conjugate base is what remains when an acid has donated a proton, while the conjugate acid is formed when a base accepts a proton. For instance, when we talk about \(\mathrm{BrO}^-\) and its conjugate acid \(\mathrm{HBrO}\), the base can garner a hydrogen ion to become its conjugate acid.

In solving for the stronger base, one must consider the strength of its conjugate acid. The general rule is: the weaker the conjugate acid, the stronger its corresponding base. This is because a strong acid is likely to donate its proton completely, leaving behind a weaker base. Conversely, a weak acid doesn't readily lose its proton, and thus its conjugate base is strong, eager to gain a proton. This understanding helps explain why in pair (c), \(\mathrm{H}_{2}\mathrm{PO}_{4}^-\) is the stronger base when compared to \(\mathrm{HPO}_{4}^{2-}\), due to it having a weaker conjugate acid.

Periodic Trends in Acidity

When comparing acids to determine relative base strengths, we need to consider periodic trends in acidity. As you move down a group in the periodic table, the size of the atoms increases, which often leads to increased acidity. This size difference affects the ability of the bond between hydrogen and the atom to release hydrogen as a proton. A larger atom like bromine (\(\mathrm{Br}\)) will generally form a weaker bond to hydrogen compared to a smaller atom like chlorine (\(\mathrm{Cl}\)), thereby making it easier to donate a hydrogen ion.

This explains our initial comparison, where the bromine-containing acid \(\mathrm{HBrO}\) is stronger than the chlorine-containing acid \(\mathrm{HClO}\). Therefore, following the aforementioned rule, the conjugate base of the weaker acid, \(\mathrm{ClO}^-\), is the stronger base among the two. Recognizing these periodic trends provides a systematic way to predict and understand the strength of acids and bases.

Effect of Oxygen on Acid Strength

Another key factor affecting acid and base strength is the effect of oxygen in the molecule. Oxygen is highly electronegative and can stabilize the positive charge developed on an acid upon releasing a proton. This feature makes an acid stronger as the number of oxygen atoms increases. When comparing \(\mathrm{HBrO}\) and \(\mathrm{HBrO}_2\), we observe that \(\mathrm{HBrO}_2\) has an additional oxygen atom, which makes it a stronger acid due to the increased electron-withdrawing effect.

Because of this additional electronegative oxygen in \(\mathrm{HBrO}_2\), its conjugate base, \(\mathrm{BrO}_2^-\), is weaker than \(\mathrm{BrO}^-\). Understanding how oxygen atoms influence acidity can help students predict acid strengths and, consequently, select the stronger base between related species.