Problem 24 - Chemical Principles: The Quest for Insight

Question

Sketch reasonably accurately the \(\mathrm{pH}\) curve for the titration of \(20.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq})\) with \(0.20 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\). Mark on the curve (a) the initial \(\mathrm{pH}\); (b) the \(\mathrm{pH}\) at the stoichiometric point.

Step-by-Step Solution

Answer

The initial pH is high due to the \(OH^-\) concentration from the strong base. The pH at the stoichiometric point corresponds to the excess acid present in the solution after all \(OH^-\) is neutralized. Sketch a curve that starts from the initial pH, decreases and then drops sharply at the stoichiometric point then continues to fall as more acid is added.

Step 1: Determine the initial pH

To find the initial pH, you need to determine the concentration of \(OH^-\) ions in the solution of \(Ba(OH)_2\). Since \(Ba(OH)_2\) is a strong base, it will dissociate completely in water. For \(Ba(OH)_2\), which has a stoichiometry of 1:2 for \(Ba^{2+}\) to \(OH^-\), the concentration of hydroxide will be twice that of the initial concentration of barium hydroxide, thus \(0.10 \, M \times 2 = 0.20 \, M\) \(OH^-\). Now use the formula \(\text{pOH} = - \log[OH^-]\) and \(\text{pH} + \text{pOH} = 14\) to find the initial pH.

Step 2: Calculate the volume of HCl required to reach the stoichiometric point

The stoichiometric (equivalence) point is reached when the number of moles of acid equals the number of moles of \(OH^-\) ions from the base. Calculate the initial moles of \(OH^-\) in the barium hydroxide solution. Using the molarity of HCl and the stoichiometry of the reaction (1:2 moles of HCl to Ba(OH)2), calculate the volume of \(0.20 \, M\) HCl required to reach the stoichiometric point.

Step 3: Determine the pH at the stoichiometric point

At the stoichiometric point, a solution of barium chloride, water, and excess HCl will be present. Since all the \(OH^-\) will have reacted, the excess \(H^+\) will determine the pH. Calculate the remaining concentration of \(H^+\) after the stoichiometric point is reached and use this to calculate the pH.

Step 4: Sketch the pH curve

On a graph, plot the initial pH (Step 1) at the volume of 0 mL of added HCl. Then, plot the pH at the stoichiometric point (Step 3). The curve should start high since we are titrating a strong base, decrease gradually as HCl is added, and then drop sharply at the stoichiometric point, given that we reach a neutral solution of water and salt before starting to accumulate excess \(H^+\) ions. Extend the curve to show the decrease in pH as more HCl is added past the stoichiometric point.

Step 5: Mark the requested points on the curve

On the curve, mark point (a) the initial pH calculated from Step 1, and point (b) the pH at the stoichiometric point calculated from Step 3. Label the axis appropriately with volume of HCl on the x-axis and pH on the y-axis.

Key Concepts

Stoichiometric Point

The stoichiometric point in a titration is the moment when the quantity of titrant added exactly neutralizes the analyte solution. In the context of acid-base titrations, it signifies the moment when the number of moles of acid equals the number of moles of base, leading to complete neutralization.

In our titration example, barium hydroxide, a strong base, reacts with hydrochloric acid, a strong acid. Since the stoichiometric point involves a strong acid-strong base reaction, the resulting solution will be neutral (pH of 7) at 25°C, assuming no other reactions occur. To determine the volume of HCl needed to reach this point, we use the molarity of the acid and base and the volume of the base present. Accurately identifying the stoichiometric point is crucial for the correct interpretation of the pH titration curve, and it is typically indicated by a sudden change of pH in the curve.

pH Calculation

Calculating pH is a fundamental aspect of understanding acid-base chemistry. The pH scale ranges from 0 to 14 and measures the acidity or basicity of an aqueous solution. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution. pH is calculated using the formula \( \text{pH} = -\log [H^+] \), where \( [H^+] \) represents the molar concentration of hydrogen ions. For basic solutions, the calculation requires finding the pOH first, using \( \text{pOH} = -\log [OH^-] \) and then utilizing the relationship \( \text{pH} + \text{pOH} = 14 \) to obtain the pH.

In our exercise, we start by calculating the initial pH of the barium hydroxide solution prior to any acid addition. By determining the concentration of hydroxide ions and using the pOH and pH relationship, we can precisely obtain the initial pH. The pH at the stoichiometric point is likewise found using pH calculations based on the remaining concentration of hydrogen ions after neutralization.

Strong Base Titration

Titration of a strong base, such as barium hydroxide (\(Ba(OH)_2\)), with a strong acid involves neutralization reactions where the strong base completely dissociates to produce hydroxide ions \( (OH^-) \) in the solution. The initial pH of the strong base solution will typically be quite high (greater than 7) since barium hydroxide is a strong, fully dissociative base.

The titration curve of a strong base titration initially decreases slowly as acid is added because the large amount of available \( OH^- \) ions buffers the addition of \( H^+ \) ions. As more acid is introduced and we approach the stoichiometric point, the curve sharply declines, reflecting the rapid neutralization of the remaining hydroxide ions. At this point, the addition of just a small volume of acid results in a significant pH change, and this substantial deflection in the curve is a clear indicator of the stoichiometric point.

Acid-Base Titration

Acid-base titration is an analytic procedure used to determine the concentration of an unknown acid or base solution by adding a measured volume of a titrant of known concentration until the reaction reaches neutralization. The titration process is typically monitored with the aid of pH indicators or pH meters to trace the pH changes that occur as the titrant is added.

A key feature of an acid-base titration is the titration curve, which plots pH against the volume of titrant added. The curve provides valuable insights into the reaction's stoichiometry, the strength of the acid or base, and the equivalence or stoichiometric point. For a strong acid-strong base titration, the curve exhibits a sharp change in pH at the stoichiometric point, whereas for weak acid-strong base or weak base-strong acid titrations, the curve will be more gradual and exhibit a buffer region before reaching the equivalence point. Each type of titration produces a characteristic curve shape that can be used to infer details about the acid or base's strength and concentration.