Acid/Base Titration - Theory

 

Fig. Acid/Base Titration. Screenshot from CHEMIX School.

Chemistry Software Download

ACID/BASE TITRATION — THEORY AND BACKGROUND

──────────────────────────────────────────────

1. PURPOSE OF TITRATION
An acid–base titration is a laboratory technique used to determine the unknown concentration of an acid or a base by neutralizing it with a titrant of known concentration.
During the titration, the pH of the solution changes gradually and then sharply near the equivalence point.
Plotting pH versus added titrant volume (V) produces the characteristic titration curve.

---

2. KEY DEFINITIONS

Acid: A substance that donates hydrogen ions (H⁺) in solution.
Base: A substance that accepts hydrogen ions (H⁺) or releases hydroxide ions (OH⁻).
Titrant: The solution of known concentration added from a burette (often a strong acid or strong base).
Analyte: The unknown solution in the flask being analyzed.
Equivalence Point: The point at which chemically equivalent amounts of acid and base have reacted — all acid or base has been neutralized.
Endpoint: The point observed experimentally when the indicator changes color. Ideally, this coincides with the equivalence point.
Indicator: A weak acid or base that changes color depending on pH, used to signal the endpoint.
pKa: The negative logarithm of the acid dissociation constant, Ka.
 pKa = –log₁₀(Ka)
It describes how strongly an acid dissociates in water:
• small pKa → strong acid (more dissociation)
• large pKa → weak acid (less dissociation)

---

3. THE TITRATION CURVE
The titration curve shows how pH changes as titrant volume increases.
Typical regions on the curve:

1. Initial region: Before titration starts — pH is characteristic of the analyte.

2. Buffer region: The pH changes slowly because both acid and conjugate base are present (especially for weak acid/strong base titrations).

3. Equivalence region: The steep, nearly vertical part where the solution changes rapidly in pH.

4. After-equivalence region: Excess titrant dominates, and pH levels off.

The first derivative (d(pH)/dV) of the curve shows a peak at the equivalence point, allowing more precise determination of that volume.

---

4. pH CALCULATION PRINCIPLES

Strong Acid + Strong Base:
Reaction goes to completion. pH can be calculated from the excess of H⁺ or OH⁻ ions remaining after neutralization.

Before equivalence:
 [H⁺] = (n_acid – n_base) / total_volume

After equivalence:
 [OH⁻] = (n_base – n_acid) / total_volume

pH = –log[H⁺]   pOH = –log[OH⁻]   pH + pOH = 14

Weak Acid + Strong Base:
Before equivalence, use the Henderson–Hasselbalch equation:
 pH = pKa + log([A⁻]/[HA])
At half-equivalence, [A⁻] = [HA], so
 pH = pKa
— a simple way to determine pKa experimentally.

Weak Base + Strong Acid:
Use analogous relations:
 pOH = pKb + log([BH⁺]/[B]) and pH = 14 – pOH

---

5. EQUIVALENCE POINT CHARACTERISTICS

For polyprotic acids (like H₂SO₄ or H₃PO₄), there are multiple equivalence points — one for each ionizable proton — each associated with its own pKa.

---

6. CHOOSING A PROPER INDICATOR
An indicator should change color within ±1 pH unit of the equivalence point.
Common indicators:

For computer-based titrations (like CHEMIX School), the equivalence point is located automatically from derivative peaks, but knowing the correct indicator helps confirm the real endpoint in lab experiments.

---

7. BUFFER ACTION AND HALF-EQUIVALENCE
A buffer solution resists changes in pH when small amounts of acid or base are added.
At the half-equivalence point, the concentrations of acid and conjugate base are equal, and pH equals pKa.
The slope of the curve is minimal here, forming the flat “buffer region.”

---

8. COMMON SOURCES OF ERROR
• Misreading burette or pH meter.
• Poor electrode calibration.
• Too large titrant increments near equivalence point.
• Contaminated glassware or diluted titrant.
• Air bubbles in burette tip or electrode drift.

To reduce error, add titrant dropwise near equivalence and record data at fine intervals.

---

9. USING SPLINE SMOOTHING AND DERIVATIVES
Experimental data often includes random “noise.”
Spline smoothing creates a continuous curve that passes close to all data points while minimizing error.
By differentiating this smoothed curve, the software identifies maxima in d(pH)/dV — the equivalence points — and estimates the pKa values at half-equivalence.

---

10. SUMMARY OF KEY RELATIONSHIPS
pH = –log[H⁺]
pKa = –log(Ka)
Ka = [H⁺][A⁻] / [HA]
Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA])
At half-equivalence: pH = pKa
At equivalence: moles acid = moles base

---

11. INTERPRETING TITRATION RESULTS
• Determine equivalence volume (Ve): where the slope is steepest or derivative is maximum.
• Calculate analyte concentration:
 C_analyte = (C_titrant × V_equivalence) / V_analyte
• Estimate pKa:
 pKa ≈ pH at half of equivalence volume (Ve/2).
• Compare theory vs. experiment:
 Overlay simulated and experimental curves; adjust completion factor to align them.

---

12. PRACTICAL SUMMARY

1. Calibrate pH electrode.

2. Add titrant slowly, record small increments.

3. Observe curve shape; locate equivalence point.

4. Derive pKa from half-equivalence.

5. Use indicator matching the expected pH range.

6. Compare with simulation to evaluate accuracy.

──────────────────────────────────────────────

In short:
Titration teaches how acids and bases neutralize each other, how to find pKa and equivalence points, and how curve shape reveals chemical properties. The CHEMIX School tool helps visualize these reactions, improving both theoretical understanding and experimental accuracy.

──────────────────────────────────────────────