Question

Sketch a \(\mathrm{pH}\) curve for the titration of a weak acid (HA) with a strong base \((\mathrm{NaOH})\). List the major species and explain how you would go about calculating the \(\mathrm{pH}\) of the solution at various points, including the halfway point and the equivalence point.

Short answer

To sketch a pH curve for the titration of a weak acid (HA) with a strong base (NaOH), identify the major species at various points during the titration process and determine the pH using the Ka and Kw expressions. The major species at significant points are: HA (initial point), HA, A-, OH- (before equivalence point), HA, A- (halfway point), A-, H2O (equivalence point), and A-, OH- (after equivalence point). Use stoichiometry and Ka/Kb expressions to calculate the pH at each point: for the initial point and before equivalence point, use Ka; for the halfway point, -log(Ka); for the equivalence point, use Kb; and for after equivalence point, use the concentration of excess OH- ions. Lastly, plot the pH values on the y-axis and the volume of NaOH added on the x-axis to create the pH curve, showing the gradual increase in the buffering region and the steep rise around the equivalence point.

Step-by-step solution

Analyze the given problem

We are given a weak acid (HA) titrated with a strong base (NaOH). First, we should write down the chemical reactions and formulas for calculating the pH of the solution. Dissociation of HA: HA ⇌ H+ + A- Neutralization reaction: HA + OH- → H2O + A- We will use the dissociation constant (Ka) and the ion-product constant of water (Kw) to calculate the pH. Ka = [H+][A-]/[HA] Kw = [H+][OH-]

Major species at various points

At different points during a titration process, we will have various major species present in the solution. Here, we will identify these major species at each significant point. 1. Initial point (no base added): HA (only the weak acid) 2. Before equivalence point (less base added): HA, A-, and OH- 3. At the halfway point (halfway to equivalence point): HA and A- 4. Equivalence point (equal amounts of acid and base): A- and H2O 5. After equivalence point (more base added): A- and OH-

Calculating the pH

With the major species identified, we'll calculate the pH at various points during the titration process. 1. Initial point: As no base has been added, we will use the Ka expression to calculate the [H+], then the pH. 2. Before equivalence point: To determine the pH, we will use the stoichiometry of the titration reaction and the Ka expression. 3. Halfway point: Since we know that Ka = [H+], we can directly use the -log of Ka to find the pH. 4. Equivalence point: At this point, all the weak acid has reacted with the base and only the A- ion is left. We'll use the Kb expression and the concentration of A- to calculate the OH- concentration, then pH. Kb = Kw/Ka 5. After equivalence point: Since there is an excess of NaOH at this point, we will use the concentration of the excess OH- ions to find the pOH, then the pH.

Sketching the pH curve

With the pH values calculated for various points, we can now sketch the pH curve. On the x-axis, we will plot the volume of NaOH added, and on the y-axis, we will plot the pH of the solution. The curve starts with the initial pH of the weak acid, increases gradually in the buffering region, then rises steeply around the equivalence point before leveling off again once we are past the equivalence point.

Key concepts

Weak Acid

A weak acid is a type of acid that does not completely dissociate in water. This means that only a small percentage of its molecules release hydrogen ions \((H^+)\). Understanding weak acids is crucial when analyzing pH titration curves.

For a weak acid \((HA)\), the dissociation can be represented by the equation: \[ HA \rightleftharpoons H^+ + A^- \]

It's important to note the presence of the equilibrium arrow, indicating that the reaction reaches a balance, not completion.

• At the starting point of a titration, HA is the predominant species.
• As titration progresses, HA molecules react with strong base molecules.

The weak acid characteristics lead to a buffering region in the pH curve where the pH changes gradually. This will occur before and slightly after the halfway point.

Strong Base

A strong base, like sodium hydroxide \((NaOH)\), fully dissociates in water to release hydroxide ions \((OH^-)\). This complete dissociation is a key factor during titration with a weak acid.

The reaction with a strong base can be outlined as follows:

• \(NaOH \rightarrow Na^+ + OH^-\)
• OH- ions react with H+ ions from HA, neutralizing them.

This leads to the production of water and the conjugate base \((A^-)\) of the weak acid.
As more base is added, it drives the equilibrium of \(HA\) dissociation to the right, impacting the pH by increasing it as the base neutralizes the acid.

Equivalence Point

The equivalence point in a titration is where the amount of titrant added exactly neutralizes the analyte solution. In our case, it is when the moles of \(NaOH\) added equal the moles of \(HA\) initially present.

At this significant juncture, the predominant species switches:

• The solution mainly contains the conjugate base \((A^-)\) and water.
• The solution pH is not neutral (pH=7) since \((A^-)\) can still affect pH.

The steepest portion of the pH curve occurs near this point, illustrating the rapid change in pH. After the equivalence point, excess \(OH^-\) ions from further \(NaOH\) additions dominate the solution.

Dissociation Constant (Ka)

The dissociation constant \((K_a)\) is a measure of the strength of a weak acid in solution. It represents the equilibrium constant for the acid's dissociation into ions.

This constant is defined by the equation:
\[ K_a = \frac{[H^+][A^-]}{[HA]} \]

The value of \(K_a\) is pivotal in calculating the pH of the acid solution, especially during:

• Initial titration points: where \(K_a\) helps find the concentration of \([H^+]\).
• Halfway points: where pH equals \(-\log(K_a)\) as \([HA] = [A^-]\).

A lower \(K_a\) value indicates a weaker acid. Understanding \(K_a\) helps determine where the buffering region lies and its efficacy.

Ion-Product Constant of Water (Kw)

The ion-product constant for water \((K_w)\) is a crucial concept when dealing with any acid-base chemistry. This constant represents the relationship between hydrogen and hydroxide ions in water at a temperature of 25°C.

Defined as: \[ K_w = [H^+][OH^-] = 1.0 \times 10^{-14} \]

This relationship is essential for relating \([H^+]\) and \([OH^-]\) concentrations:

• Used during calculations at the equivalence point to find \(OH^-\) concentration from \([A^-]\) using \(K_b = \frac{K_w}{K_a}\).
• Post-equivalence point: when calculating \(pH\) from known \(OH^-\) concentrations.

Understanding \(K_w\) assists in connecting various elements of the titration, ensuring accurate pH calculations at different stages.