Consider the curve shown here for the titration of a weak base with a strong acid and answer each question.
c. At what volume of added acid does pH = 14 - pK_b?

Verified step by step guidance

1. Identify the relationship between pH, pK_b, and pK_a. Recall that pK_a + pK_b = 14 for a conjugate acid-base pair.
2. Recognize that when pH = 14 - pK_b, it implies that the pH is equal to pK_a.
3. Understand that at the point where pH = pK_a, the solution is at the half-equivalence point in the titration of a weak base with a strong acid.
4. Determine the volume of added acid at the half-equivalence point, which is half of the volume required to reach the equivalence point.
5. Use the titration curve to find the equivalence point, then calculate half of that volume to find the volume of added acid at the half-equivalence point.

Key Concepts

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (a solution of known concentration) to a sample until a reaction reaches its endpoint, which is often indicated by a color change or a pH change. In this case, the titration of a weak base with a strong acid will show a characteristic curve that reflects the pH changes as the acid is added.

pH and pK_b

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. The pK_b is the negative logarithm of the base dissociation constant (K_b) and indicates the strength of a weak base. The relationship between pH and pK_b is crucial in titration, as it helps determine the pH at various points during the titration process, particularly at the equivalence point.

Equivalence Point

The equivalence point in a titration is the stage at which the amount of titrant added is stoichiometrically equivalent to the amount of substance in the sample. For a weak base titrated with a strong acid, this point is characterized by a significant change in pH. At this point, the weak base has been completely neutralized, and the resulting solution's pH can be calculated using the relationship between pH, pK_b, and the concentrations of the resulting species.