Question

Sketch the titration curve for the titration of a generic weak base B with a strong acid. The titration reaction is $$\mathbf{B}+\mathbf{H}^{+} \rightleftharpoons \mathbf{B H}^{+}$$ On this curve, indicate the points that correspond to the following: a. the stoichiometric (equivalence) point b. the region with maximum buffering c. \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}\) d. \(\mathrm{pH}\) depends only on \([\mathrm{B}]\) e. \(\mathrm{pH}\) depends only on \(\left[\mathrm{BH}^{+}\right]\) f. \(\mathrm{pH}\) depends only on the amount of excess strong acid added

Short answer

To sketch the titration curve of a weak base (B) with a strong acid, follow these steps: 1. Draw the initial curve that represents the pH change as a function of the added strong acid's volume. 2. Identify point "a" as the stoichiometric (equivalence) point, where moles of B equal moles of the strong acid added. 3. Label region "b" as the maximum buffering region, where B and its conjugate acid (BH⁺) are in equal amounts. 4. Identify point "c" (inside region "b") as the pH = pKa point, where moles of B equal moles of BH⁺. 5. Label point "d" on the left end, where pH depends only on [B] with no strong acid added yet. 6. Identify point "e" immediately after the equivalence point, where pH depends only on [BH⁺]. 7. Label point "f" on the far right end, where pH depends only on the amount of excess strong acid added.

Step-by-step solution

Draw the initial curve

Begin by sketching a generic titration curve that rises slowly at first, then rapidly in the middle, and finally levels off gradually. This curve represents the pH change as a function of the volume of added strong acid.

Identify the stoichiometric (equivalence) point

The stoichiometric (equivalence) point occurs when the moles of the weak base B equate the moles of the strong acid added. At this point, the curve shows the most significant change (usually a steep slope). Label this point as "a" on the curve.

Identify the region with maximum buffering

The region with maximum buffering occurs when the weak base (B) and its conjugate acid (BH⁺) are present in equal amounts. In this region, the system is highly resistant to pH changes and the slope of the curve is relatively flat. Label this region as "b" on the curve.

Identify the pH = pKa point

The point where pH = pKa occurs when the moles of the weak base (B) equal the moles of the conjugate acid (BH⁺). This is also the same point in the buffering region that you labeled in Step 3. Label this point as "c" on the curve, inside the region "b."

Identify the point where pH depends only on [B]

At the beginning of the titration, the pH depends only on [B] because the strong acid has not been added yet. Locate the point at the left end of the curve before any acid has been added, which represents the highest pH value. Label this point as "d" on the curve.

Identify the point where pH depends only on [BH⁺]

At the stoichiometric (equivalence) point (point "a"), all weak base (B) has been consumed, and only the conjugate acid (BH⁺) remains. Locate the point on the curve immediately after the equivalence point when the curve starts to level off. Label this point as "e" on the curve.

Identify the point where pH depends only on the amount of excess strong acid added

When the acid addition significantly surpasses the stoichiometric (equivalence) point (point "a"), the pH of the solution mainly depends on the concentration of the excess strong acid added. Locate the point at the extreme right end of the curve where the pH is lowest. Label this point as "f" on the curve.

Key concepts

Weak Base

A weak base is a chemical that partially accepts protons (H⁺) when dissolved in water. Unlike strong bases, which fully dissociate, weak bases only partially ionize in solution. This means that the reaction:

• \[ \text{B} + \text{H}^+ \leftrightarrows \text{BH}^+ \]

reaches an equilibrium where both the base (B) and its conjugate acid (BH⁺) coexist. The incomplete ionization is due to the weak electrostatic attraction between the weak base and the proton.
This property makes weak bases more resistant to pH changes, especially in buffering scenarios.

Strong Acid

A strong acid is known for its complete dissociation in water. This property means that a strong acid readily donates all its available protons (H⁺) to the solution. For example, hydrochloric acid (HCl) dissociates completely as:

• \( \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \)

The introduction of a strong acid in a titration with a weak base results in the formation of the conjugate acid of the base, affecting the pH change observed in the titration curve.
Over the course of the titration, the strong acid reacts with the weak base until it reaches the stoichiometric point, where the moles of acid added equal the moles of base present.

Stoichiometric Point

The stoichiometric point, also known as the equivalence point, is a crucial moment in a titration. It occurs when the amount of titrant (strong acid, in this case) added is exactly equal to the amount of the substance (weak base) being titrated. At the stoichiometric point:

• All the weak base has reacted, forming the conjugate acid (BH⁺).
• The pH usually experiences a sharp change, indicated by a steep slope on the titration curve.
• This point can be identified by observing the largest pH shift on the graph.

Recognizing the stoichiometric point is key for determining the concentration of the weak base in the original solution.

Buffering Region

The buffering region is where the solution resists small changes in pH. This occurs before the stoichiometric point in a titration curve involving a weak base and a strong acid. In this region:

• The weak base and its conjugate acid are present in significant, comparable quantities.
• The pH experiences minimal change despite the addition of more acid.
• At this point, pH equals the pKa of the weak acid formed, displaying optimal buffering capacity.

This characteristic makes buffer solutions incredibly useful in maintaining stable conditions in various chemical and biological systems.

pH

pH is a measure of the acidity or basicity of a solution. It is calculated as the negative logarithm of the hydrogen ion concentration:

• \( \text{pH} = -\log [ \text{H}^+ ] \)

In the context of a titration with a weak base and strong acid, the pH value changes predictably through different phases:

• At the start, influenced only by the concentration of the weak base.
• In the buffering region, stabilized at around the pKa value.
• At the stoichiometric point, where it shifts significantly due to the formation of the conjugate acid.
• Beyond this point, strongly dependent on the excess strong acid added.

Understanding the pH evolution during titration is crucial for interpreting and anticipating reactions involving weak bases and acids.