Problem 14 - General Chemistry: Principles and Modern Applications

Question

What is the pH of a solution prepared by dissolving \(8.50 \mathrm{g}\) of aniline hydrochloride \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\right)\) in \(750 \mathrm{mL}\) of \(0.215 \mathrm{M}\) aniline, \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\right) ?\) Would this solution be an effective buffer? Explain.

Step-by-Step Solution

Answer

First calculate the moles of aniline and aniline hydrochloride and their respective concentrations. Then, use these values in the Henderson-Hasselbalch equation along with the pKa of aniline to find the pH of the solution. Lastly, use the buffer capacity rule to determine whether or not the solution could act as a good buffer.

Step 1: Calculate the moles of aniline hydrochloride

Firstly, calculate the number of moles of aniline hydrochloride dissolved. Use the given mass and the molar mass of aniline hydrochloride. According to the periodic table, the molar mass of aniline hydrochloride (represented by C6H5NH3+Cl-) is approximately 129.6 g/mol. Thus, the moles of aniline hydrochloride \( n_{(aniline \, hydrochloride)} = \frac{8.50 \, g}{129.6 \, g/mol}\)

Step 2: Calculate the moles of aniline

Next, calculate how many moles of aniline are in the solution prior to the addition of aniline hydrochloride. This is done by multiplying the concentration of aniline given by the volume in litres: \( n_{(aniline)} = M_{(aniline)} * V_{(aniline)} = 0.215 \, M * 0.75 \, L \)

Step 3: Determine acid and base concentrations

Then, calculate the concentrations of the aniline hydrochloride and aniline. The total volume should be used to calculate these concentrations, which will be the volume of the aniline solution plus the volume of the aniline hydrochloride solution. However, since no volume is given for the aniline hydrochloride solution, assume that its volume is negligible and calculate with only the volume of the aniline solution. \( [base] = \frac{n_{(aniline)}}{V} \) , \( [acid] = \frac{n_{(aniline \, hydrochloride)}}{V} \)

Step 4: Use the Henderson-Hasselbalch equation

Now, input the values obtained in the previous steps along with the pKa value of aniline into the Henderson-Hasselbach equation to calculate the pH of the buffer solution. The pKa of aniline is 4.63, and the Henderson-Hasselbalch equation is: \( pH = pKa + log \left(\frac{[base]}{[acid]}\right) \)

Step 5: Evaluate buffer capacity

Finally, evaluate whether the solution could act as an effective buffer by using the buffer capacity rule. This rule states that a solution can act as a good buffer if the ratio \([base]/[acid]\) falls between 0.1 and 10. Calculate this ratio and compare it to the given values.

Key Concepts

pH Calculation

Calculating the pH of a solution involves determining the acidity or basicity of the solution. In the context of buffer solutions, pH calculation is essential to verify the effectiveness of the solution to maintain pH stability. To compute the pH, you need the concentrations of the acid and base components in the buffer solution. Using this data, you can apply mathematical equations such as the Henderson-Hasselbalch equation, which simplifies the process of determining the pH by relating it to the pKa value of the acid and the ratio of the concentrations of the base and acid. This helps in understanding how the solution's components interact to resist changes in pH. When preparing the initial solution, determine moles from the provided mass and concentration, as this forms the basis for calculating the concentrations needed for pH analysis.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a crucial tool in understanding buffer solutions. This equation allows us to calculate the pH of a solution containing a weak acid and its conjugate base. The equation is represented as \( pH = pKa + \log \left(\frac{[\text{base}]}{[\text{acid}]}\right) \).

Let's break this down:

• \( pKa \): This is the logarithmic form of the acid dissociation constant, providing insight into the strength of the acid in the solution. A lower \( pKa \) indicates a stronger acid.
• \([\text{base}]\): The concentration of the base, which in the case of buffer solutions, is often a conjugate base formed alongside the weak acid.
• \([\text{acid}]\): The concentration of the acid part in the solution, typically the weak acid.

By using this equation, you can readily estimate the pH of a buffer solution by utilizing the known values for \( pKa \), and the concentrations of the acid and base. This makes the Henderson-Hasselbalch equation particularly valuable for determining buffer capacity and efficiency.

Acid-Base Equilibrium

Acid-base equilibrium is a key concept in chemistry that refers to the state at which the rates of the forward and reverse reactions of an acid-base pair equal each other, resulting in stable concentrations of the reactants and products.

In buffer solutions, understanding acid-base equilibrium is crucial because it explains how the solution resists change in pH. When an acid or a base is added to a buffer, the equilibrium shifts slightly to accommodate the added substances, thereby minimizing the change in pH. This behavior arises from the weak acid and its conjugate base reacting too less extent to maintain balance.

• A buffer works efficiently by using its conjugate acid-base pair to neutralize small amounts of added acid or base.
• The pH of the buffer remains relatively constant, within its capacity limits.

Understanding this equilibrium helps in the practical application of buffer solutions in various fields, ensuring that systems that rely on a specific pH range remain unaffected by external changes.