Problem 96 - 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) \(\mathrm{NO}_{3}^{-}\) or \(\mathrm{NO}_{2}^{-}\), (c) \(\mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}\). (b) \(\mathrm{PO}_{4}{\underline{\phantom{xx}}}^{3-}\) or \(\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\)

Step-by-Step Solution

Answer

The stronger bases in each pair are as follows: (a) \(\mathrm{NO}_{2}^{-}\) (b) \(\mathrm{PO}_{4}{\underline{\phantom{xx}}}^{3-}\) (c) \(\mathrm{CO}_{3}^{2-}\)

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

First, let's write the conjugate acids for each base by adding a proton to each of them: For \(\mathrm{NO}_{3}^{-}\): \(\mathrm{HNO}_{3}\) (nitric acid) For \(\mathrm{NO}_{2}^{-}\): \(\mathrm{HNO}_{2}\) (nitrous acid) Now, we need to compare the stability of these conjugate acids. Nitric acid, \(\mathrm{HNO}_{3}\), is a stronger acid than nitrous acid, \(\mathrm{HNO}_{2}\). Since stronger acids have weaker conjugate bases, \(\mathrm{NO}_{2}^{-}\) is the stronger base compared to \(\mathrm{NO}_{3}^{-}\).

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

First, let's write the conjugate acids for each base by adding a proton to each of them: For \(\mathrm{PO}_{4}{\underline{\phantom{xx}}}^{3-}\): \(\mathrm{HPO}_{4}{\underline{\phantom{xx}}}^{2-}\) (hydrogen phosphate) For \(\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\): \(\mathrm{HAsO}_{4}{\underline{\phantom{xx}}}^{2-}\) (hydrogen arsenate) In this case, both conjugate acids are structurally similar, containing a central atom from the same group (Group 15) of the periodic table. Generally, as we move down Group 15, the acidity of the oxoacids increases due to poorer overlap between the central atom's orbitals and oxygen's orbitals, which makes the O-H bond more readily ionizable. This means that hydrogen arsenate is a stronger acid than hydrogen phosphate. Consequently, the conjugate base \(\mathrm{PO}_{4}{\underline{\phantom{xx}}}^{3-}\) (phosphate) is stronger than \(\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\) (arsenate).

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

First, let's write the conjugate acids for each base by adding a proton to each of them: For \(\mathrm{HCO}_{3}^{-}\): \(\mathrm{H}_{2}\mathrm{CO}_{3}\) (carbonic acid) For \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\): \(\mathrm{HCO}_{3}^{-}\) (hydrogen carbonate or bicarbonate) In this case, the conjugate acid of the \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\) ion is the \(\mathrm{HCO}_{3}^{-}\) ion. Therefore, we need to compare the stability of carbonic acid, \(\mathrm{H}_{2}\mathrm{CO}_{3}\), and bicarbonate, \(\mathrm{HCO}_{3}^{-}\). Carbonic acid is a weak acid and readily loses a proton to become the bicarbonate ion. Since the \(\mathrm{HCO}_{3}^{-}\) ion still has one more acidic proton, it can lose it to become the \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\) ion. The increased charge on the \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\) ion makes it a stronger base compared to the \(\mathrm{HCO}_{3}^{-}\) ion. The conjugate acid (\(\mathrm{HCO}_{3}^{-}\)) is more stable, making the \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\) ion (carbonate) the stronger base in this pair.

Key Concepts

Conjugate Acids and Bases

In acid-base chemistry, every acid has a corresponding base, known as a conjugate base, and every base has a conjugate acid. When an acid donates a proton (\(H^+\)), it forms its conjugate base. Conversely, when a base accepts a proton, it becomes its conjugate acid.
For example, in the exercise provided, let's consider the pair \(\mathrm{NO}_3^-\) and \(\mathrm{NO}_2^-\). The conjugate acids for these are \(\mathrm{HNO}_3\) and \(\mathrm{HNO}_2\) respectively. Here, \(\mathrm{HNO}_3\) is a stronger acid than \(\mathrm{HNO}_2\), leading to \(\mathrm{NO}_2^-\) being the stronger conjugate base.
Understanding conjugate pairs is crucial because it helps to predict the strength of acids and bases. Stronger acids will have weaker conjugate bases, and similarly, weaker acids will have stronger conjugate bases. Thus, knowledge of conjugate relationships is vital for evaluating the relative strength of acids and bases.

Base Strength Comparison

Determining which base in a pair is stronger involves analyzing the strength of their respective conjugate acids. A common method is to examine the stability of the conjugate acid, as stronger acids typically produce weaker conjugate bases.
Talking about the pair \(\mathrm{PO}_4^{3-}\) and \(\mathrm{AsO}_4^{3-}\), both conjugate acids (\(\mathrm{HPO}_4^{2-}\) and \(\mathrm{HAsO}_4^{2-}\)) are oxoacids of elements from the same group. The acidity generally increases as you move down Group 15 due to atomic size and overlap of orbitals, with hydrogen arsenate being the stronger acid, making \(\mathrm{PO}_4^{3-}\) the stronger base.
To compare bases, focus primarily on the conjugate acid strength and overall molecular stability, bearing in mind that weaker acids result in stronger conjugate bases. Knowing these concepts helps in predicting and comparing the relative strengths of various bases effectively.

Periodic Trends in Acidity

Acid strength often follows periodic trends that are influenced by the position of elements in the periodic table. In a family or group of elements, acidity tends to increase as you move down the column. This trend is due to changes in atomic size and the electron distribution in the molecule.
For instance, in Group 15, as seen when comparing \(\mathrm{PO}_4^{3-}\) with \(\mathrm{AsO}_4^{3-}\), elements lower in the group have stronger oxoacids. This is attributed to the central atom's ability to hold the negative charge more stably due to larger atomic size, making the acidic proton easier to lose.
Understanding these trends is critical for predicting the behavior of acids and bases across the periodic table. This knowledge allows scientists and students to make educated guesses about the acidity or basicity of various compounds, enhancing their comprehension of chemical interactions.