Question

Figure \(15.4\) shows the \(\mathrm{pH}\) curves for the titrations of six different acids by \(\mathrm{NaOH}\). Make a similar plot for the titration of three different bases by \(0.10 \mathrm{M} \mathrm{HCl}\). Assume \(50.0 \mathrm{~mL}\) of \(0.20 M\) of the bases and assume the three bases are a strong base \((\mathrm{KOH})\), a weak base with \(K_{\mathrm{b}}=1 \times 10^{-5}\), and another weak base with \(K_{\mathrm{b}}=1 \times 10^{-10}\).

Short answer

To generate a pH titration plot for the titration of three different bases by 0.10 M HCl, first calculate the initial pH for each base using their concentrations and Kb values. For KOH, find the hydroxide ion concentration and calculate the pH using \( pH = 14 - pOH \). For the weak bases, use the relation \( K_b = \frac{[BH^+][OH^-]}{[B]} \) to solve for [OH^-] and calculate the pH. Then, calculate the pH during titration by finding moles of base and HCl, moles of the conjugate acid formed, and applying the Henderson-Hasselbalch equation for the weak bases. Finally, plot the titration curves using the calculated pH values against the volume of HCl added. The resulting plot will show different curves for the strong base (KOH) and the two weak bases with different buffering phases and equivalence points.

Step-by-step solution

1. Calculate Initial pH for each base

First, find the initial pH for each of the three bases using their concentrations and Kb values: For KOH (strong base), find the hydroxide ion concentration and then find the pOH using the following formula: \( pOH = -log[OH^-] \) Then, calculate the pH using the formula: \( pH = 14 - pOH \) For the weak base with Kb of 1×10^-5, use the relation: \( K_b = \frac{[BH^+][OH^-]}{[B]} \) Solve for [OH^-] and then find the pH as described above. Repeat the same process for the weak base with a Kb of 1×10^-10.

2. Calculate pH during titration

Calculate the pH at different volumes of 0.10 M HCl added during the titration process for each base. Use the following steps: a. Calculate moles of the base and moles of HCl at each step, b. Calculate the moles of the conjugate acid formed, c. For strong base, calculate the [OH^-] and pH, d. For weak bases, use the Henderson-Hasselbalch equation for calculating pH: \( pH = pK_a + log \frac{[B]}{[BH^+]} \) Plot these pH values against the volume of HCl added to observe the titration curve.

3. Plot the resulting titration curves

Finally, plot the titration curves for all three bases using the pH calculated in step 2. For each curve, you should observe the following: - For the strong base (KOH), the titration curve will have a sharp rise at the equivalence point. - For the weak base with Kb = 1×10^-5, there will be a buffering phase before the equivalence point and a sharp rise at the equivalence point. - For the weak base with Kb = 1×10^-10, the buffering phase will be wider and shallower, with a more gradual rise at the equivalence point. These plots should help us understand how titration curves vary for different bases and how the pH of the solution changes during the titration process.

Key concepts

pH Calculation

Understanding the pH calculation is crucial for interpreting titration curves. pH is a scale used to specify the acidity or basicity of an aqueous solution.

pH is calculated using the concentration of hydrogen ions \( [H^+] \) in the solution, with the formula: \( pH = -\log[H^+] \) For bases, the concentration of hydroxide ions \( [OH^-] \) is used to calculate the pOH first: \( pOH = -\log[OH^-] \). The pH is then derived by subtracting the pOH from 14: \( pH = 14 - pOH \).

In a titration, the initial pH of the solution is determined by the base's concentration. Strong bases, like KOH, dissociate completely and their initial pH can be calculated directly from their concentration. Weak bases, however, only partially dissociate, requiring a different approach using the base dissociation constant \( K_b \). For weak bases, we must first determine \( [OH^-] \) by solving the equilibrium expression before finding the pH.

Acid-Base Titration

Acid-base titration is a method used to determine the concentration of an acid or a base in a solution. During the titration, a solution of known concentration (titrant) is gradually added to a known volume of a solution with an unknown concentration (analyte).

The point at which the titrant has neutralized all of the analyte is known as the equivalence point. A pH indicator or a pH meter can be used to detect the equivalence point in the titration process. By measuring the volume of the titrant needed to reach the equivalence point, we can calculate the concentration of the analyte.

The pH of the solution changes as the titration progresses, which can be plotted on a graph to produce a titration curve. Strong acids and bases typically show a sharp change in pH at the equivalence point, while weak acids and bases exhibit a more gradual change due to the presence of buffering species.

Strong and Weak Bases

Bases are substances that can accept hydrogen ions or release hydroxide ions when dissolved in water.

Strong bases, such as potassium hydroxide \( (KOH) \), dissociate completely in water, meaning they release all of their hydroxide ions into the solution. This results in a high \( [OH^-] \) and consequently a higher initial pH, which we can easily calculate using \( pOH \).

Weak bases, on the other hand, do not fully dissociate in water and have a lower \( [OH^-] \). Their degree of dissociation is represented by the base dissociation constant \( K_b \). A larger \( K_b \) indicates a stronger weak base, capable of accepting more hydrogen ions, while a smaller \( K_b \) represents a weaker base. Weak bases also possess a buffering capacity due to the equilibrium between the weak base and its conjugate acid, affecting the shape of the titration curve. Understanding the distinction between strong and weak bases is vital when interpreting their behavior during a titration.