Titration curve of weak acid with strong base is a fundamental concept in analytical chemistry that illustrates how the pH of a solution changes as a strong base is gradually added to a weak acid. Day to day, understanding this curve enables chemists to determine the acid’s dissociation constant (Ka), locate the equivalence point accurately, and select appropriate indicators for precise measurements. The shape of the curve reflects the buffering action of the weak acid/conjugate base pair and provides a visual representation of the acid‑base reaction progress That alone is useful..
Understanding the Titration Process
When a weak acid, represented as HA, is titrated with a strong base such as NaOH, the hydroxide ions (OH⁻) react with the acid to form its conjugate base (A⁻) and water:
[ \text{HA} + \text{OH}^- \rightarrow \text{A}^- + \text{H}_2\text{O} ]
Because the acid only partially dissociates in solution, the initial pH is higher than that of a strong acid at the same concentration. As base is added, HA is consumed and A⁻ accumulates, creating a buffer system that resists pH changes. The titration curve of weak acid with strong base therefore shows a gradual slope in the buffer region, a steep rise near the equivalence point, and a relatively flat high‑pH region after excess base has been added.
The Shape of the Titration Curve
A typical titration curve of weak acid with strong base plots pH (y‑axis) against the volume of base added (x‑axis). The curve can be divided into five distinct sections:
- Initial pH – before any base is added.
- Buffer region – where HA and A⁻ coexist in comparable amounts.
- Half‑equivalence point – the volume at which exactly half of the acid has been neutralized.
- Equivalence point – the volume where moles of added base equal the initial moles of acid.
- Post‑equivalence region – excess strong base dominates the solution.
Each section provides valuable information about the acid’s strength and the reaction’s progress Less friction, more output..
Initial pH
At the start, the solution contains only the weak acid. Its pH can be approximated using the acid dissociation expression:
[ K_a = \frac{[H^+][A^-]}{[HA]} ]
Assuming that the change in HA concentration due to dissociation is small, the hydrogen ion concentration is:
[ [H^+] \approx \sqrt{K_a \cdot C_{HA}} ]
where (C_{HA}) is the initial acid concentration. Taking the negative log gives the initial pH. This value is higher than that of a strong acid of equal concentration because only a fraction of HA dissociates.
Buffer Region and the Henderson‑Hasselbalch Equation
As base is added, the solution contains both HA and its conjugate base A⁻. The pH in this region is best described by the Henderson‑Hasselbalch equation:
[ \text{pH} = \text{p}K_a + \log\frac{[A^-]}{[HA]} ]
Here, (\text{p}K_a = -\log K_a). On top of that, the buffer region appears as a relatively gentle slope on the titration curve of weak acid with strong base because changes in the ratio ([A^-]/[HA]) produce only modest pH shifts. The region extends roughly from about 10 % to 90 % of the equivalence volume Less friction, more output..
Not the most exciting part, but easily the most useful.
Half‑Equivalence Point
When exactly half of the weak acid has been neutralized, ([A^-] = [HA]). Substituting into the Henderson‑Hasselbalch equation yields:
[ \text{pH} = \text{p}K_a ]
Thus, the pH at the half‑equivalence point directly gives the pKa of the acid. This point is easily identified on the curve as the location where the curve’s slope is at its minimum in the buffer region.
Equivalence Point
At the equivalence point, all HA has been converted to A⁻. The solution now contains the conjugate base of a weak acid, which hydrolyzes water to produce OH⁻:
[ \text{A}^- + \text{H}_2\text{O} \rightleftharpoons \text{HA} + \text{OH}^- ]
The pH is therefore greater than 7. It can be calculated from the base hydrolysis constant (K_b):
[ K_b = \frac{K_w}{K_a} \quad\text{and}\quad [OH^-] \approx \sqrt{K_b \cdot C_{A^-}} ]
where (C_{A^-}) is the concentration of the conjugate base at equivalence (total volume accounted for). The pH follows from (pOH = -\log[OH^-]) and (pH = 14 - pOH). The equivalence point appears as a sharp, near‑vertical rise on the titration curve of weak acid with strong base.
Post‑Equivalence Region
Beyond the equivalence point, excess strong base determines the pH. The contribution of the weak acid’s conjugate base becomes negligible, and the pH can be approximated by:
[ [OH^-] = \frac{C_{\text{excess OH}^-}}{\text{total volume}} \quad\text{then}\quad pH = 14 + \log[OH^-] ]
This region shows a gradual increase in pH as more base is added, eventually approaching the pH of the titrant itself.
Calculating pH at Different Points
To construct or interpret a titration curve of weak acid with strong base, one can follow these stepwise calculations:
- Determine initial moles of HA: (n_{HA,0} = C_{HA} \times V_{HA}).
- For each added volume of base (V_{b}), calculate moles of OH⁻ added: (n_{OH^-} = C_{b} \times V_{b}).
- Compare (n_{OH^-}) to (n_{HA,0}):
- If (n_{OH^-} < n_{HA,0}): solution contains HA and A⁻; use Henderson‑Hasselbalch.
- If (n_{OH^-} = n_{HA,0}): at equivalence; calculate pH from A⁻ hydrolysis.
- If (n_{OH^-} > n_{HA,0}): excess OH⁻ dominates; compute pH from excess base.
- Convert ([H^+]) or ([OH^-]) to pH using (pH = -\log[H^+]) or (pH = 14 + \log[OH^-]).
These calculations can be performed manually for a few points or programmed into a spreadsheet to generate the full curve.
Choosing an Indicator
An indicator must change color within the pH range of the steep portion of the titration curve of weak acid with strong base. Because the equivalence point pH is above 7 (typically 8–10 depending on the acid’s strength), indicators such as phenolphthalein (pH range
