Problem 109 - Chemistry and Chemical Reactivity

Question

Sulfanilic acid, which is used in making dyes, is made by reacting aniline with sulfuric acid. (a) Is aniline a Brönsted base, a Lewis base, or both? Explain, using its possible reactions with HCl, BF \(_{3}\) or other acid. (b) Sulfanilic acid has a \(\mathrm{p} K_{\mathrm{a}}\) value of \(3.23 .\) The sodium salt of the acid, \(\mathrm{Na}\left(\mathrm{H}_{2} \mathrm{NC}_{6} \mathrm{H}_{4} \mathrm{SO}_{3}\right),\) is quite soluble in water. If you dissolve \(1.25 \mathrm{g}\) of the salt in water to give \(125 \mathrm{mL}\) of solution, what is the \(\mathrm{pH}\) of the solution?

Step-by-Step Solution

Answer

(a) Aniline is both a Brönsted and Lewis base. (b) The pH is 7.99.

Step 1: Analyzing aniline as a base

Aniline (\( ext{C}_6 ext{H}_5 ext{NH}_2 \)) has a nitrogen atom with a lone electron pair. According to Brönsted-Lowry theory, bases are substances that can accept protons, while Lewis bases are species that can donate a pair of electrons. Aniline can react with HCl to form \( ext{C}_6 ext{H}_5 ext{NH}_3^+ ext{Cl}^- \), showing it accepts a proton, thus acting as a Brönsted base. Its ability to donate the lone pair to an electron-accepting agent such as BF\(_3\) classifies it as a Lewis base. Therefore, aniline is both a Brönsted base and a Lewis base.

Step 2: Determine Molarity of Sodium Salt

First, calculate the molar mass of the sodium salt \( ext{NaH}_2 ext{NC}_6 ext{H}_4 ext{SO}_3 \): \( 23.0 + 2(1.0) + 14.0 + 6(12.0) + 4(1.0) + 32.0 + 3(16.0) = 179.0 ext{ g/mol} \). Then, the moles of salt in 1.25 g is \( \frac{1.25 ext{ g}}{179.0 ext{ g/mol}} = 0.0070 ext{ mol} \). The molarity in 125 mL (0.125 L) is \( \frac{0.0070 ext{ mol}}{0.125 ext{ L}} = 0.056 ext{ M} \).

Step 3: Calculate the \( ext{pH} \)

The sodium salt will ionize completely, giving \( ext{H}_2 ext{NC}_6 ext{H}_4 ext{SO}_3^- \), which is the conjugate base of the weak acid sulfanilic acid (\( ext{p} K_a = 3.23 \)). The formula to find \( ext{pH} \) of a basic solution is \( ext{pH} = 14 - ext{p} K_b \). First, find \( ext{K}_b \):\[ K_b = \frac{1 \times 10^{-14}}{K_a} = \frac{1 \times 10^{-14}}{5.88 \times 10^{-4}} = 1.7 \times 10^{-11} \].Knowing the equation: \( K_b = \frac{[OH^-]^2}{[HA^-]} \), we can solve for \( [OH^-] \): \( [OH^-] = \sqrt{K_b \times 0.056} = \sqrt{1.7 \times 10^{-11} \times 0.056} \approx 9.77 \times 10^{-7} \).Finally, \( ext{pOH} = - ext{log}[OH^-] \approx 6.01 \), hence \( \text{pH} = 14 - 6.01 = 7.99 \).

Key Concepts

Bronsted-Lowry_theory

The Bronsted-Lowry theory is a fundamental concept in chemistry, helping us understand acid-base reactions through the transfer of protons. This theory defines an acid as a substance that can donate a proton (H⁺), and a base as a substance that can accept a proton. For instance, when aniline is mixed with hydrochloric acid (HCl), aniline acts as a Bronsted-Lowry base by accepting a proton from HCl, forming the conjugate acid, anilinium ion (\( ext{C}_6 ext{H}_5 ext{NH}_3^+\)).
This reaction demonstrates how proton transfer categorizes substances in Bronsted-Lowry theory. By looking at the movement of protons between substances, we can determine the roles of acids and bases in reactions.
Understanding this theory is crucial, as it not only illuminates the behavior of substances in chemical reactions but also guides us in predicting outcomes of mixing different chemicals.

Lewis_acid-base_theory

The Lewis acid-base theory offers another important perspective on the behavior of acids and bases, focusing on electron pairs instead of protons. According to this theory, a Lewis acid is a substance that can accept an electron pair, while a Lewis base is a substance that can donate an electron pair.
Aniline serves as an example of a Lewis base because it possesses a nitrogen atom with a lone pair of electrons. This lone pair can be donated to an electron-deficient species, such as boron trifluoride (BF₃), which is a common Lewis acid.
When aniline interacts with BF₃, it donates its lone electron pair, demonstrating its role as a Lewis base. By understanding Lewis acid-base interactions, we can predict and explain a wide range of chemical reactions, particularly those involving coordination complexes and organic synthesis.
This theory expands our understanding beyond proton transfer, offering a richer view of how substances interact at the molecular level.

pH_calculation

Calculating the pH of a solution is essential for understanding the acidity or basicity of that solution. The pH scale, ranging from 0 to 14, is a measure of the hydrogen ion concentration in a solution, with lower values indicating more acidic solutions and higher values indicating more basic ones.
In the problem presented, the compound \( ext{NaH}_2 ext{NC}_6 ext{H}_4 ext{SO}_3\) ionizes in water to form its conjugate base, which affects the pH. Given the \( ext{p}K_a\) value of sulfanilic acid (3.23), we can determine \( ext{p}K_b\) using the relation \( ext{p}K_a + ext{p}K_b = 14 \).
Knowing the \( ext{K}_b\) and molarity of the solution allows us to calculate the hydroxide ion concentration, from which we compute the \( ext{pOH}\) and subsequently the pH. This method demonstrates how various factors including \( ext{K}_a\), \( ext{K}_b\), and molarity influence the solution’s pH.
Proficiency in pH calculation is vital for chemists, as it impacts fields such as biochemistry, agriculture, medicine, and environmental science.

molarity

Molarity is a key concept in chemistry that quantifies the concentration of a solution. It is expressed as the number of moles of solute per liter of solution.Calculating molarity involves two main steps: finding the moles of solute and dividing by the volume of the solution in liters.
For the sodium salt \( ext{NaH}_2 ext{NC}_6 ext{H}_4 ext{SO}_3\), the molar mass is calculated by summing the atomic masses of each constituent element, resulting in 179.0 g/mol. By dividing the given mass of the salt (1.25 g) by its molar mass, we find the moles of the solute.The solution's volume must be converted to liters (125 mL = 0.125 L) before calculating molarity, which provides the value 0.056 M.
Understanding molarity helps predict how solutions will behave in chemical reactions. It allows chemists to correctly prepare solutions with desired qualities, ensuring accuracy in experimentation and industrial applications.