Half-Equivalence Point

Carson West

Half-Equivalence Point

The half-equivalence point is a specific point in a Titration where exactly half of the analyte has reacted with the titrant. This point is particularly important when titrating a weak acid or a weak base, as it provides a direct way to determine the $ pK_a $ or $ pK_b $ of the weak acid or base.

Definition

The half-equivalence point is the point in a titration where:

Significance

The key significance of the half-equivalence point lies in its relationship to the Acid Dissociation Constant ( $ K_a $ ) and the Base Dissociation Constant ( $ K_b $ ).

Weak Acids

At the half-equivalence point, the pH of the solution is equal to the $ pK_a $ of the weak acid. This can be derived from the Henderson-Hasselbalch Equation:

$ pH = pK_a + log\frac{[A^-]}{[HA]} $

Since $ [A^-] = [HA] $ at the half-equivalence point, the log term becomes $ log(1) = 0 $ . Therefore:

$ pH = pK_a $

Weak Bases

Similarly, for weak bases, at the half-equivalence point, the pOH of the solution is equal to the $ pK_b $ of the weak base:

$ pOH = pK_b + log\frac{[BH^+]}{[B]} $

Since $ [BH^+] = [B] $ at the half-equivalence point, the log term becomes $ log(1) = 0 $ . Therefore:

$ pOH = pK_b $

Calculations

To find the pH at the half-equivalence point:

  1. Determine the $ pK_a $ (or $ pK_b $ ). If not given, it can be looked up.
  2. Calculate the pH (or pOH). $ pH = pK_a $ or $ pOH = pK_b $
  3. If needed, convert pOH to pH. $ pH + pOH = 14 $

Example

Suppose you are titrating a 50.0 mL solution of 0.10 M acetic acid ( $ CH_3COOH $ , $ K_a = 1.8 \times 10^{-5} $ ) with 0.10 M NaOH.

  1. Half-Equivalence Point: This will occur when half of the acetic acid has been neutralized.
  2. Calculate $ pK_a $ : $ pK_a = -log(K_a) = -log(1.8 \times 10^{-5}) = 4.74 $
  3. pH at Half-Equivalence Point: At the half-equivalence point, $ pH = pK_a = 4.74 $

Importance in Titration Curves

In a titration curve for a weak acid or weak base, the half-equivalence point is located at the midpoint of the buffer region. The buffer region is the relatively flat portion of the titration curve where the pH changes slowly upon addition of titrant. The buffering capacity is greatest at or near the half equivalence point.