Question

A hydrogen atom in the organic base pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}\) can be substituted by various atoms or groups to give \(\mathrm{XC}_{5} \mathrm{H}_{4} \mathrm{N},\) where \(\mathrm{X}\) is an atom such as \(\mathrm{Cl}\) or a group such as \(\mathrm{CH}_{3}\). The following table gives \(K_{\mathrm{a}}\) values for the conjugate acids of a variety of substituted pyridines. $$\begin{array}{ll}\text { Atom or Group } X & K_{\mathrm{a}} \text { of Conjugate Acid } \\ \hline \mathrm{NO}_{2} & 5.9 \times 10^{-2} \\\\\mathrm{Cl} & 1.5 \times 10^{-4} \\\\\mathrm{H} & 6.8 \times 10^{-6} \\\\\mathrm{CH}_{3} & 1.0 \times 10^{-6}\end{array}$$ (a) Suppose each conjugate acid is dissolved in sufficient water to give a \(0.050 \mathrm{M}\) solution. Which solution would have the highest pH? The lowest pH? (b) Which of the substituted pyridines is the strongest Bronsted base? Which is the weakest Brönsted base?

Short answer

(a) Highest pH: \(\mathrm{CH}_3\), Lowest pH: \(\mathrm{NO}_2\). (b) Strongest base: \(\mathrm{CH}_3\), Weakest base: \(\mathrm{NO}_2\).

Step-by-step solution

Understand the Problem

We need to determine the pH of solutions containing conjugate acids of various substituted pyridines and identify the strongest and weakest Brönsted bases from these substituents.

Recall the Relationship between K_a and pH

The pH of a solution is related to the strength of its acid, represented by the acid dissociation constant, \(K_a\). Stronger acids have higher \(K_a\) values and result in lower pH as they dissociate more in water, increasing the hydrogen ion concentration.

Analyze the Provided K_a Values

Review the given \(K_a\) values: \(\mathrm{NO}_2 = 5.9 \times 10^{-2}\), \(\mathrm{Cl} = 1.5 \times 10^{-4}\), \(\mathrm{H} = 6.8 \times 10^{-6}\), and \(\mathrm{CH}_3 = 1.0 \times 10^{-6}\). As \(K_a\) increases, acidity increases, leading to a lower pH.

Determine Highest and Lowest pH

Since \(\mathrm{NO}_2\) has the highest \(K_a\), it produces the lowest pH. Conversely, \(\mathrm{CH}_3\) has the lowest \(K_a\), resulting in the highest pH.

Evaluate Brönsted Base Strength

Stronger bases form weaker conjugate acids, indicated by lower \(K_a\) values. \(\mathrm{CH}_3\), with the lowest \(K_a\), is the strongest base, and \(\mathrm{NO}_2\), with the highest \(K_a\), is the weakest.

Key concepts

Acid Dissociation Constant (K_a)

The acid dissociation constant, represented as \(K_a\), is a value that provides insight into the strength of an acid. It measures how well an acid dissociates into its ions in solution. Higher \(K_a\) values demonstrate greater acidic strength because they indicate a higher concentration of hydrogen ions following dissociation. Consequently, a higher \(K_a\) means a stronger acid. In the context of substituted pyridines, examining the \(K_a\) values of their conjugate acids allows us to predict their acidity behavior when dissolved in water. For example, in the given table, the \(K_a\) of the \(\mathrm{NO}_2\) substituted pyridine is \(5.9 \times 10^{-2}\), signifying it dissociates significantly, reflecting its stronger acidic nature compared to other substituents like \(\mathrm{CH}_3\), which has a \(K_a\) of \(1.0 \times 10^{-6}\). Lower \(K_a\) values indicate weaker acids and, thus, potentially stronger basic properties in the corresponding bases.

Brönsted Base Strength

Brönsted base strength relates to how effectively a base can accept protons. It is often deduced inversely from the strength of an acid's tendency to donate protons. In the context of conjugate acids and bases, a strong base has a weak conjugate acid, characterized by a low acid dissociation constant, \(K_a\).

• The base strength can be inferred from these conjugate acid \(K_a\) values.
• A lower \(K_a\) for the conjugate acid implies the base more readily attracts protons, marking it as a strong base.
• Conversely, a higher \(K_a\) indicates a stronger acid and, thus, a weaker base.

From the table, \(\mathrm{CH}_3\) is identified as the strongest Brönsted base due to its conjugate acid's very low \(K_a\) value of \(1.0 \times 10^{-6}\), while \(\mathrm{NO}_2\), with a high \(K_a\) of \(5.9 \times 10^{-2}\), corresponds to the weakest base.

Conjugate Acids

Conjugate acids are formed when bases gain a proton, and their properties heavily influence the behavior of the originating bases. The concept of conjugate acids is central to understanding the acid-base character of a compound. For substituted pyridines, analyzing the conjugate acids' \(K_a\) values unveils their acidity levels:

• The more a conjugate acid dissociates, the weaker its corresponding base was initially.
• The difference in \(K_a\) values helps identify which bases have stronger or weaker tendencies to accept protons.
• In conjugate acid-base pairs, lower \(K_a\) values of the conjugate acid signify proficient base strength.

Substituents like \(\mathrm{H}\) and \(\mathrm{CH}_3\), with smaller \(K_a\) values, produce conjugate acids that dissociate minimally, indicating stronger original bases. This reasoning is crucial for predicting how substituted pyridines will interact in varied chemical environments.

pH and Acidity

pH is a measure of hydrogen ion concentration in a solution and gauges its acidity or basicity. A lower pH indicates higher acidity, correlating directly with higher \(K_a\) values since they signify a stronger acid that releases more hydrogen ions. In this exercise, understanding the relationship between \(K_a\) and pH helps determine which substituted pyridines will form solutions of varying pH.

• The solution with the highest \(K_a\) \,— \,\(\mathrm{NO}_2\) \,— \,will have the lowest pH, reflecting its strong acidic nature.
• Conversely, \(\mathrm{CH}_3\), with the lowest \(K_a\), results in the highest pH due to weaker acidity.
• Assessing pH values derived from \(K_a\) is essential for practical applications, including understanding a compound's reactivity and suitability for different environments.

By interpreting these relationships, one can predict how various substituted pyridines would behave in aqueous solutions, aiding in practical and theoretical chemistry applications.