Problem 106 - Chemistry and Chemical Reactivity

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?

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: 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.

Step 5: 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.