Add alkali to acid a drop at a time and plot the pH. Almost nothing happens, almost nothing happens, and then the pH leaps by seven units in the space of a single drop. That leap is the whole point of the graph.
📚 What you need to know
A pH curve plots pH against the volume of the solution added from the burette.
All pH curves are S-shaped, with a nearly vertical section.
The equivalence point is the midpoint of that vertical section — where the acid and base have reacted in exactly the ratio of the equation.
From a curve you can read the starting pH, the equivalence volume and the pH at equivalence.
Weak acid + weak base gives no sharp section, so the end point cannot be seen clearly.
An indicator is suitable if its colour change falls inside the vertical section.
How the curve is produced
Put a known volume of acid in a flask with a pH probe in it, add alkali from a burette in small portions, and record the pH after each addition. Near the equivalence point you switch to adding a drop at a time, because that is where everything happens.
Every point on this curve was calculated from the amounts of acid and base present. The near-vertical section spans roughly one drop of solution.
Reading the four regions
At the start: only acid is present, so the pH comes straight from its concentration.
Acid in excess: each addition removes some H+, but plenty remains, so the pH creeps up slowly.
Around equivalence: only a trace of acid is left, so one more drop wipes it out and then puts base into excess. The pH leaps.
Base in excess: the pH is set by the excess OH–, and further additions change it very little.
The steep part is not magic, it is arithmetic. Just before equivalence there might be 0.0001 mol of acid left in the flask; one more drop of alkali removes it entirely and leaves 0.0001 mol of alkali instead. Because pH is logarithmic, going from a tiny excess of one to a tiny excess of the other swings the reading enormously.
🧩 Calculating the pH at any point
Find moles of acid and moles of base added so far.
Subtract to find which is in excess, and by how much.
Divide by the total volume — both solutions, added together.
If acid is in excess, take –log[H+]. If base is in excess, find pOH first and subtract from 14.00.
At exact equivalence with a strong acid and strong base, the answer is simply 7.00.
WORKED EXAMPLE
25.0 cm3 of 0.100 mol dm–3 HCl is titrated with 0.100 mol dm–3 NaOH. Calculate the pH after adding (a) 10.0 cm3 (b) 24.0 cm3 (c) 26.0 cm3 of NaOH.
Moles of acid at the startn(HCl) = 0.0250 × 0.100 = 2.50 × 10⁻³ mol(a) after 10.0 cm³n(NaOH) = 0.0100 × 0.100 = 1.00 × 10⁻³excess acid = 1.50 × 10⁻³ mol in 0.0350 dm³[H⁺] = 0.04286 → pH = 1.37pH = 1.37(b) after 24.0 cm³excess acid = 2.50 × 10⁻³ − 2.40 × 10⁻³ = 1.00 × 10⁻⁴ mol[H⁺] = 1.00 × 10⁻⁴ ÷ 0.0490 = 2.04 × 10⁻³pH = 2.69(c) after 26.0 cm³excess base = 2.60 × 10⁻³ − 2.50 × 10⁻³ = 1.00 × 10⁻⁴ mol[OH⁻] = 1.00 × 10⁻⁴ ÷ 0.0510 = 1.96 × 10⁻³pOH = 2.71, so pH = 14.00 − 2.71pH = 11.29Look at (b) and (c). Two cubic centimetres of alkali — roughly forty drops — move the pH by more than eight units. That is the vertical section.
The other three combinations
The shape survives, but the equivalence point moves. The reason is the salt left in the flask: it is not always neutral.
All four cross the same equivalence volume of 25.0 cm3, because the stoichiometry is identical. What differs is the pH there, and how sharply the curve rises through it.
Combination
pH at equivalence
Why
Vertical section
strong acid + strong base
7
the salt is neutral; neither ion reacts with water
very long, about pH 3 to 11
strong acid + weak base
below 7
the salt contains the conjugate acid of a weak base, e.g. NH4+
shorter, at the acidic end
weak acid + strong base
above 7
the salt contains the conjugate base of a weak acid, e.g. CH3COO–
shorter, at the alkaline end
weak acid + weak base
around 7
the two effects roughly cancel
almost none — avoid this titration
Notice that a weak acid curve does not start at pH 1. Ethanoic acid at 0.100 mol dm–3 begins near pH 2.9, because only a fraction of it has dissociated. If a question shows you a curve starting around 3, the acid is weak before you read anything else.
Choosing an indicator
An indicator is a weak acid whose two forms have different colours, and it changes over a range of about two pH units. It is only useful if that range lies inside the vertical section, because that is the only way one drop can flip the colour.
Indicator
pH range of colour change
Suitable for
methyl orange
3.1 – 4.4
strong acid + strong base; strong acid + weak base
phenolphthalein
8.3 – 10.0
strong acid + strong base; weak acid + strong base
Keep two terms apart. The equivalence point is where the amounts match the equation — a fact about the chemistry. The end point is where the indicator changes colour — a fact about what you can see. A well-chosen indicator makes them close enough to be treated as the same.
WORKED EXAMPLE
A pH curve for 25.0 cm3 of sodium hydroxide titrated with 0.100 mol dm–3 hydrochloric acid has its equivalence point at 22.5 cm3. Calculate the concentration of the sodium hydroxide.
Step 1 — moles of acid at equivalencen(HCl) = 0.0225 × 0.100 = 2.25 × 10⁻³ molStep 2 — the ratio is 1 : 1n(NaOH) = 2.25 × 10⁻³ molStep 3 — divide by the volume in the flaskc = 2.25 × 10⁻³ ÷ 0.02500.0900 mol dm⁻³The equivalence volume is read from the middle of the vertical section, not from where it begins or ends.
WORKED EXAMPLE
A titration curve starts at pH 2.9, rises gradually, and has a vertical section running from about pH 7 to pH 11. Identify the acid and base as strong or weak, and choose a suitable indicator.
The starting pHA 0.1 mol dm⁻³ strong acid would start at pH 1. Starting at 2.9 means only a fraction has dissociated.the acid is weakThe equivalence pHThe midpoint of the vertical section is around pH 9, which is alkaline.the base is strongThe indicatorphenolphthalein, range 8.3 – 10.0Methyl orange would change colour at pH 3–4, long before the equivalence point, and would give a badly wrong titre.
💡 Exam tip
Read the equivalence point from the midpoint of the steep section, and say so if asked how you found it.
Use the starting pH to identify a weak acid, and the equivalence pH to identify a weak base.
When calculating, always divide by the combined volume of both solutions.
For excess base, go through pOH — it is quicker and safer than dividing by Kw.
Justify an indicator by saying its range falls within the vertical section, and quote both numbers.
Label a sketched curve with the starting pH, equivalence volume and equivalence pH.
⚠️ Common mix-up
Assuming every equivalence point is at pH 7. That holds only for a strong acid with a strong base.
Forgetting to add the volumes when working out a concentration mid-titration.
Starting a weak acid curve at pH 1. It begins much higher.
Choosing an indicator by the colour you like rather than by its range.
Confusing the equivalence point with the end point. They are close, not identical.
Reading the equivalence volume off the top or bottom of the steep part instead of its midpoint.
Up next: Electron Transfer Reactions — that completes proton transfer. The other great family of reactions moves electrons instead of protons, and almost everything you have just learned has a mirror image there.
Want this explained one-to-one?
Book a free session with an experienced IB Chemistry tutor and get your trickiest topics made simple.
