Titration Curves: A Level Chemistry Guide

Titration curves are graphs that show how the pH of a solution changes as you add a titrant (a solution of known concentration) from a burette. You plot pH on the y-axis against the volume of titrant added on the x-axis, and the resulting curve lets you identify the equivalence point, choose the correct indicator, and understand the strength of the acid and base involved. This guide explains the shapes of the four main types of titration curves, how to sketch them, and how to read them for A Level exam questions.

Formula

The Henderson-Hasselbalch equation relates pH, pKa, and the ratio of conjugate base to acid concentrations:

pH = pKa + log([A⁻]/[HA])

where:

• pH = negative logarithm of hydrogen ion concentration (unitless)
• pKa = negative logarithm of the acid dissociation constant (unitless)
• [A⁻] = concentration of conjugate base (mol/L)
• [HA] = concentration of weak acid (mol/L)

At the half-equivalence point, [A⁻] = [HA], so the log term becomes zero and pH = pKa. For a weak base, the analogous equation gives pOH = pKb at half-equivalence, and pH = 14 − pKb.

Worked Example

Using the calculator defaults: titrating a 50 mL sample of 0.1 mol/L acetic acid (pKa = 4.76) with a strong base. At the half-equivalence point, you have added 25 mL of base, so [A⁻] = [HA]. Plug into the equation:

pH = 4.76 + log(1) = 4.76 + 0 = 4.76

The calculator shows pH = 4.76 at half-equivalence, matching the pKa. The equivalence point pH for this weak acid–strong base titration is above 7 (around 8.7 for these concentrations), because the conjugate base hydrolyzes water to produce OH⁻. The calculator’s first output shows 7.00 as a simplified default—for a real weak acid–strong base curve, the equivalence pH is always above 7.

Why the Curve Shape Matters

The shape of a titration curve reveals the relative strengths of the acid and base. A strong acid–strong base curve starts at a low pH (around 1), rises slowly, then jumps steeply near pH 7, and levels off at a high pH (around 13). The vertical section—often called the “break”—is where the equivalence point lies. For a weak acid–strong base titration, the curve starts higher (pH 2–4), has a buffer region where pH changes slowly, then a shorter vertical jump centered above pH 7. Weak base–strong acid curves mirror this, starting basic and ending acidic. Weak acid–weak base curves have no sharp break at all, which is why they are rarely used in practical titrations—no indicator changes color sharply enough.

How to Sketch a Curve from Data

Exam questions often ask you to sketch a curve given only the concentrations and volumes. Follow these steps:

1. Calculate the initial pH from the acid’s concentration and Ka (or from pH = −log[H⁺] for a strong acid).
2. Calculate the pH at the half-equivalence point using pH = pKa (for a weak acid).
3. Calculate the pH at the equivalence point using the salt hydrolysis formula (for weak acid–strong base, pH = 7 + ½(pKa + log C) where C is the salt concentration).
4. Calculate the pH after adding excess base (for strong base, pH = 14 − pOH, where pOH comes from the excess OH⁻ concentration).
5. Plot these four points and connect them smoothly, making the steepest part pass through the equivalence point.

For a strong acid–strong base, the equivalence pH is exactly 7, and the curve is symmetric around that point. For a weak acid–strong base, the equivalence pH is above 7, and the curve is steeper on the acidic side before the jump.

Choosing the Right Indicator

An indicator changes color over a narrow pH range (about 2 pH units). For a sharp end point, the indicator’s pKa should be within 1–2 units of the equivalence point pH. Common indicators and their ranges:

• Methyl orange: pH 3.1–4.4 (good for strong acid–weak base)
• Bromothymol blue: pH 6.0–7.6 (good for strong acid–strong base)
• Phenolphthalein: pH 8.3–10.0 (good for weak acid–strong base)

For a weak acid–weak base titration, no indicator gives a sharp color change because the pH changes too gradually. In practice, you would use a pH meter or a conductivity probe instead.

Common Mistakes and Misconceptions

One frequent error is confusing the equivalence point with the end point. The equivalence point is the theoretical point where moles of acid equal moles of base; the end point is where the indicator actually changes color. They differ by a small volume, called the titration error. Another mistake is assuming the equivalence point is always pH 7—this is only true for strong acid–strong base. For a weak acid–strong base, the equivalence pH is above 7; for a strong acid–weak base, it is below 7.

A third misconception is that the half-equivalence point occurs at half the volume of the equivalence point. That is true, but only when the acid and base react in a 1:1 mole ratio. For polyprotic acids like H₃PO₄, there are multiple equivalence points and multiple half-equivalence points, each with its own pKa value.

Real-World Applications

Titration curves are not just exam exercises—they are used to determine the pKa of unknown acids, to calibrate pH meters, and to design buffer solutions. In biochemistry, the curve of an amino acid shows two or three breaks, each corresponding to a different ionizable group. In environmental chemistry, titration curves help measure the alkalinity of water samples. The same principles apply to redox titrations, where the y-axis is electrode potential instead of pH, but the curve shape is similar.

Frequently Asked Questions

Why does the pH jump so suddenly near the equivalence point?

Just before the equivalence point, the solution contains very little unreacted acid or base. Adding one drop of titrant consumes the last of the analyte, leaving a tiny excess of the titrant. That tiny excess produces a large change in [H⁺] or [OH⁻], which translates into a large pH change. The effect is most dramatic for strong acid–strong base because both are fully dissociated.

How do I find the equivalence point from the curve?

Find the midpoint of the steep vertical section. You can draw two parallel lines along the flat parts of the curve, then draw a line halfway between them—the equivalence point is where this middle line crosses the curve. Alternatively, use the first derivative (ΔpH/ΔV); the maximum of that derivative corresponds to the equivalence point.

What is the difference between a titration curve and a pH curve?

They are the same thing. “Titration curve” is the standard term in chemistry, but some textbooks and exam boards call it a “pH curve” because the y-axis is pH. Both refer to the plot of pH against volume of titrant added.

Can I use a titration curve to find the concentration of an unknown acid?

Yes. From the curve, read the volume of base at the equivalence point. Then use the equation C₁V₁ = C₂V₂ (where C is concentration and V is volume) to solve for the unknown concentration, provided you know the concentration of the base and the stoichiometry of the reaction. For a monoprotic acid, the mole ratio is 1:1.

Why is the half-equivalence point important?

At the half-equivalence point, the concentrations of the weak acid and its conjugate base are equal, so the Henderson-Hasselbalch equation simplifies to pH = pKa. This gives you a direct experimental measurement of the acid’s pKa, which is a key property used to predict how the acid behaves in solution.

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in v | Volume of titrant added | mL | 25 | 0
in pka | pKa of weak acid (or pKb of weak base) | - | 4.76 | 0
in c | Concentration of analyte (mol/L) | mol/L | 0.1 | 0
in v0 | Initial volume of analyte | mL | 50 | 0
out ph | pH at equivalence point | - | 7 | 2
out half | pH at half-equivalence | - | pka | 2