Problem 90 - 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) \(\mathrm{NO}_{3}^{-}\) or \(\mathrm{NO}_{2}^{-},\) (b) \(\mathrm{PO}_{4}^{3-}\) or \(\mathrm{AsO}_{4}^{3-}\), (c) \(\mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}\).

Step-by-Step Solution

Answer

The stronger bases in each pair are: (a) \(\mathrm{NO}_{2}^{-}\), (b) \(\mathrm{AsO}_{4}^{3-}\), and (c) \(\mathrm{CO}_{3}^{2-}\).

Step 1: Pair (a): Compare \(\mathrm{NO}_{3}^{-}\) and \(\mathrm{NO}_{2}^{-}\)

To determine the stronger base between \(\mathrm{NO}_{3}^{-}\) and \(\mathrm{NO}_{2}^{-}\), we can look at their conjugate acids: \(\mathrm{HNO}_3\) (nitric acid) and \(\mathrm{HNO}_2\) (nitrous acid). Remember that the stronger the conjugate acid is, the weaker its corresponding base will be. Nitric acid (\(\mathrm{HNO}_3\)) is a strong acid, so its conjugate base, \(\mathrm{NO}_{3}^{-}\), will be a weak base. On the other hand, nitrous acid (\(\mathrm{HNO}_2\)) is a weak acid, so its conjugate base, \(\mathrm{NO}_{2}^{-}\), will be a stronger base. So, the stronger base in this pair is \(\mathrm{NO}_{2}^{-}\).

Step 2: Pair (b): Compare \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{AsO}_{4}^{3-}\)

To determine the stronger base between \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{AsO}_{4}^{3-}\), we can again look at their conjugate acids: \(\mathrm{H}_{3}\mathrm{PO}_{4}\) (phosphoric acid) and \(\mathrm{H}_{3}\mathrm{AsO}_{4}\) (arsenic acid). Both phosphoric acid (\(\mathrm{H}_{3}\mathrm{PO}_{4}\)) and arsenic acid (\(\mathrm{H}_{3}\mathrm{AsO}_{4}\)) are weak acids. However, the \(\mathrm{As-O}\) bond in arsenic acid is weaker due to the larger atomic size of arsenic than phosphorus, which makes the conjugate base \(\mathrm{AsO}_{4}^{3-}\) more likely to accept a proton. Thus, the stronger base in this pair is \(\mathrm{AsO}_{4}^{3-}\).

Step 3: Pair (c): Compare \(\mathrm{HCO}_{3}^{-}\) and \(\mathrm{CO}_{3}^{2-}\)

To determine the stronger base between \(\mathrm{HCO}_{3}^{-}\) and \(\mathrm{CO}_{3}^{2-}\), we can look at their conjugate acids: \(\mathrm{H}_{2}\mathrm{CO}_{3}\) (carbonic acid) and \(\mathrm{HCO}_{3}^{-}\) (hydrogen carbonate). When \(\mathrm{HCO}_{3}^{-}\) accepts a proton (H+ ion), it forms the weak acid \(\mathrm{H}_{2}\mathrm{CO}_{3}\). However, when \(\mathrm{CO}_{3}^{2-}\) accepts a proton (H+ ion), it forms \(\mathrm{HCO}_{3}^{-}\), which is a stronger acid than carbonic acid. Therefore, \(\mathrm{CO}_{3}^{2-}\) is a stronger base compared to \(\mathrm{HCO}_{3}^{-}\). Thus, the stronger base in this pair is \(\mathrm{CO}_{3}^{2-}\).

Key Concepts

Conjugate Acid-Base Pairs

In acid-base chemistry, conjugate acid-base pairs play a vital role in understanding how acids and bases interact together. Imagine an acid and a base as a pair of dancing partners, where one donates a proton (H⁺ ion) while the other accepts it. This dance is the core of what we call a conjugate acid-base pair.
When an acid donates a proton, it transforms into its conjugate base, while the base that accepts a proton becomes the conjugate acid.
Here's a simple way to identify them:

• An acid becomes a conjugate base after losing a proton.
• A base becomes a conjugate acid after gaining a proton.

This concept helps us determine the strength of acids and bases, as seen in the exercise where \( \mathrm{HNO}_3 \) (a strong acid) has a weak conjugate base \( \mathrm{NO}_{3}^{-} \), while \( \mathrm{HNO}_2 \) (a weak acid) has a stronger conjugate base \( \mathrm{NO}_{2}^{-} \).
Understanding conjugate acid-base pairs is essential to predicting the outcome of many chemical reactions and determining the strength of different substances.

Strong and Weak Acids

The strength of an acid depends on its ability to donate a proton. Strong acids are like generous givers that easily part with their protons, even in water. Weak acids, on the other hand, are more reluctant to let go of their protons.
To recognize whether an acid is strong or weak, consider the following:

• Strong acids completely dissociate in water, releasing all their protons. Examples include \( \mathrm{HNO}_3 \), \( \mathrm{HCl} \), and \( \mathrm{H}_2\mathrm{SO}_4 \).
• Weak acids only partially dissociate in water, holding onto most of their protons. Examples include \( \mathrm{HNO}_2 \) and \( \mathrm{CH}_3\mathrm{COOH} \).

In the given exercise, \( \mathrm{HNO}_3 \) is identified as a strong acid, which makes its conjugate base \( \mathrm{NO}_{3}^{-} \) weak, while \( \mathrm{HNO}_2 \) is a weak acid, resulting in a stronger conjugate base \( \mathrm{NO}_{2}^{-} \). This understanding is crucial because strong and weak acids define how their conjugate bases will behave.

Base Strength Comparison

When comparing the strength of bases, one key aspect is looking at their ability to accept protons. The stronger a base, the better it is at snatching up protons from acids.
Several factors influence base strength:

• The strength of the conjugate acid: A weaker conjugate acid usually means a stronger base.
• Electronegativity and atomic size: Less electronegative atoms in a base are better at accepting protons.

In the exercise example, let's analyze base strength through comparisons:

• \( \mathrm{NO}_{2}^{-} \) is stronger than \( \mathrm{NO}_{3}^{-} \) due to being conjugate to a weaker acid, \( \mathrm{HNO}_2 \).
• \( \mathrm{AsO}_{4}^{3-} \) is stronger than \( \mathrm{PO}_{4}^{3-} \), partly because arsenic produces a weaker acid, making its conjugate base more robust.
• \( \mathrm{CO}_{3}^{2-} \) is stronger than \( \mathrm{HCO}_{3}^{-} \) since \( \mathrm{HCO}_{3}^{-} \) is a stronger acid, thus having a weaker conjugate base.

Grasping these comparisons allows students to predict how different bases will act in reactions, which is essential for many fields of science and industry.