Problem 117 - 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 Bronsted 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 pH of the solution?

Step-by-Step Solution

Answer

(a) Aniline is both a Bronsted base and a Lewis base. (b) The pH of the solution is approximately 2.27.

Step 1: Identify Aniline as a Base

Aniline, with the formula C_6H_5NH_2, has a lone pair of electrons on the nitrogen atom, which can accept a proton. Therefore, aniline acts as a Bronsted base because it can accept H^+ ions from acids, such as HCl, forming the anilinium ion (C_6H_5NH_3^+). It can also act as a Lewis base as it can donate its lone pair to electron-deficient species like BF_3.

Step 2: Calculate the Moles of the Sodium Salt in Solution

The molecular weight of the sodium salt Na(H_2NC_6H_4SO_3) is approximately 199.17 g/mol. Calculate the moles in 1.25 g using the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molecular weight}} = \frac{1.25}{199.17} \approx 0.00628 \text{ mol}. \]

Step 3: Calculate the Concentration of the Sodium Salt

The volume of the solution is 125 mL, which is 0.125 L. The concentration of the sodium salt is: \[ \text{concentration} = \frac{\text{moles}}{\text{volume}} = \frac{0.00628}{0.125} \approx 0.0502 \text{ M}. \]

Step 4: Perform Equilibrium Calculations for pH

Sulfanilic acid is a weak acid with a \( pK_a \) of 3.23. The reaction in water is: \[ \text{H}_2 ext{NC}_6 ext{H}_4 ext{SO}_3^- + ext{H}_2 ext{O} \rightleftharpoons ext{HNC}_6 ext{H}_4 ext{SO}_3^{2-} + ext{H}_3 ext{O}^+. \] The equilibrium constant (Ka) is calculated from \( pK_a \): \[ K_a = 10^{-pK_a} = 10^{-3.23} \approx 5.88 \times 10^{-4}. \] Set up the equilibrium expression: \[ K_a = \frac{[H^+][HNC_6H_4SO_3^{2-}]}{[H_2NC_6H_4SO_3^-]} \] Since the concentration of dissociated acid is equal to the concentration of H^+ ions at equilibrium, let \[ x \] represent [H^+]. The expression becomes: \[ 5.88 \times 10^{-4} = \frac{x^2}{0.0502 - x}. \] Assumption: \( x \) is small compared to the initial concentration of the anion, therefore \( 0.0502 - x \approx 0.0502 \). Solve for \( x \): \[ x^2 = 5.88 \times 10^{-4} \times 0.0502 \approx 2.95 \times 10^{-5}. \] \[ x \approx \sqrt{2.95 \times 10^{-5}} \approx 0.00543. \]

Step 5: Calculate the pH of the Solution

The pH is calculated using the concentration of H^+ ions: \[ \text{pH} = -\log[H^+] = -\log(0.00543) \approx 2.27. \]

Key Concepts

Bronsted-Lowry Theory

The Bronsted-Lowry theory provides a fundamental way of understanding acid-base behavior. In this theory, an acid is a substance that can donate a proton ( H^+ ), while a base is one that can accept a proton. For example, aniline (C_6H_5NH_2) acts as a Bronsted base because the nitrogen atom has a lone pair of electrons capable of accepting a proton. By reacting with hydrochloric acid (HCl), aniline accepts a proton and forms anilinium ion ( C_6H_5NH_3^+ ). This demonstrates aniline's role as a proton acceptor, hence a Bronsted base.

When trying to identify Bronsted acids and bases, keep an eye on reactions that involve proton ( H^+ ) transfer. This theory is all about moving protons from one molecule or ion to another, creating the foundation for understanding how many reactions work.

Lewis Theory

The Lewis theory expands our understanding of acids and bases beyond proton transfer. In this theory, acids are electron pair acceptors, and bases are electron pair donors. This approach allows for a broader classification of substances.

Aniline also acts as a Lewis base because it can donate its lone pair of electrons from the nitrogen atom. For instance, when reacting with a substance like boron trifluoride ( BF_3 ), which is electron-deficient, aniline donates its lone pair, forming a coordinate covalent bond with BF_3 .

The Lewis theory is a versatile tool for identifying acid-base interactions, especially in cases where no protons are exchanged. It highlights how electron pairs play a critical role in chemical bonding and reactions.

Equilibrium Calculations

Equilibrium calculations are essential for determining how reactions reach a state where the concentrations of reactants and products no longer change. For weak acids, like sulfanilic acid, it's important to understand the equilibrium between the acid and its ions in solution.

Using the given K_a value, which is derived from the pK_a = 3.23 , we calculate the acid dissociation constant as K_a = 10^{-3.23} . From here, we can establish an equilibrium expression and solve for the concentration of hydrogen ions ( H^+ ). Making assumptions can simplify calculations, such as assuming the change in concentration ( x ) is small compared to the initial concentration.

Equilibrium calculations help predict how different the concentrations of substances will be at equilibrium, providing insight into the reaction dynamics.

pH Determination

Determining pH is crucial for understanding the acidity or basicity of a solution. The pH scale ranges from 0 to 14, with lower values indicating acidity and higher values indicating basicity.

For the sodium salt solution of sulfanilic acid, we use the equilibrium concentration of hydrogen ions calculated from the K_a expression. The pH is found by taking the negative logarithm of the hydrogen ion concentration ( [H^+] ). In this scenario, after calculating [H^+] , we find the pH to be approximately 2.27.

Understanding pH is essential in various fields, from chemistry to biology, as it affects how molecules behave and interact. Techniques for pH calculation provide vital information for predicting and explaining the behavior of chemical systems.