TL;DR:
A titration curve plots pH against the volume of base added. Its shape tells you the starting pH, the equivalence point and the strength of the acid.
For 25.0 mL of 0.100 M HCl and 0.100 M NaOH, the start is pH 1.00, the equivalence point is at 25.0 mL and pH 7, and pH jumps from 3.70 to 10.30 within 0.2 mL.
A weak acid starts higher, has a flatter middle and an equivalence point above pH 7.
In a titration you add a solution of known concentration, drop by drop, to a measured amount of another solution until the reaction is exactly complete. Plot the pH as you go and you get an S-shaped curve. Learning to read that curve tells you what was in the flask.
Lab safety first: Do titrations only in a supervised lab. Wear splash goggles, gloves and a lab coat. Acids and bases burn skin and eyes, so rinse spills with plenty of water and tell your teacher at once. Never pipette by mouth, and when diluting acid always add the acid to the water.
What is happening in the flask
A strong acid such as HCl is fully split into ions in water. A strong base such as NaOH is too. When you add base, the hydroxide ions react with hydrogen ions: H⁺ + OH⁻ → H₂O. The pH rises as hydrogen ions are used up.
The equivalence point is when the moles of base added exactly equal the moles of acid that were there. The endpoint is when the indicator changes colour. A good indicator is chosen so the two are close together.
Worked example: 25.0 mL of 0.100 M HCl with 0.100 M NaOH
Moles of acid at the start: 0.0250 L × 0.100 mol/L = 0.00250 mol. That fixes where everything happens. We calculate pH at five points, using pH = −log[H⁺], and pH + pOH = 14 at 25 °C.
NaOH added | What is left | Concentration | pH |
|---|---|---|---|
0 mL | 0.00250 mol H⁺ in 25.0 mL | 0.100 M H⁺ | 1.00 |
12.5 mL | 0.00125 mol H⁺ in 37.5 mL | 0.0333 M H⁺ | 1.48 |
24.9 mL | 0.0000100 mol H⁺ in 49.9 mL | 2.00 × 10⁻⁴ M H⁺ | 3.70 |
25.0 mL | Neither in excess | Pure water and salt | 7.00 |
25.1 mL | 0.0000100 mol OH⁻ in 50.1 mL | 2.00 × 10⁻⁴ M OH⁻ | 10.30 |
30.0 mL | 0.000500 mol OH⁻ in 55.0 mL | 9.09 × 10⁻³ M OH⁻ | 11.96 |
Work one row in full. At 24.9 mL, base added is 0.0249 L × 0.100 = 0.00249 mol. Acid left: 0.00250 − 0.00249 = 0.0000100 mol. Total volume: 25.0 + 24.9 = 49.9 mL = 0.0499 L. So [H⁺] = 0.0000100 / 0.0499 = 2.00 × 10⁻⁴ M and pH = −log(2.00 × 10⁻⁴) = 3.70.
After equivalence, the leftover is base. At 25.1 mL, excess OH⁻ is 0.0000100 mol in 0.0501 L, so [OH⁻] = 1.996 × 10⁻⁴ M, pOH = 3.70 and pH = 14.00 − 3.70 = 10.30.
Reading the shape
Start. The pH is set by the acid alone: 1.00 for 0.100 M strong acid.
Gentle rise. For most of the run, pH climbs slowly. From 0 to 24.9 mL it goes from 1.00 to only 3.70, because each drop barely changes the hydrogen ion concentration compared with the amount left.
The steep jump. Between 24.9 and 25.1 mL, just 0.2 mL, the pH leaps from 3.70 to 10.30. This is why the endpoint can be seen so sharply.
Equivalence. The middle of the jump, at 25.0 mL and pH 7.00, for a strong acid with a strong base.
Levelling off. After the jump the pH approaches the pH of the base you are adding.
The strong-strong curve has no buffer region, meaning no flat stretch where added base barely moves the pH. That is why it is so steep at equivalence.
How a weak acid curve differs
A weak acid, such as acetic acid, only partly splits into ions. Compared with a strong acid of the same concentration, its curve differs in four ways.
It starts at a higher pH, since fewer H⁺ ions are present.
It has a buffer region that rises slowly, where the acid and its conjugate base are both present.
At half the equivalence volume,
pH = pKa, which is how pKa is read off the graph.The equivalence point is above pH 7, since the leftover conjugate base is slightly basic.
Because the equivalence point is above 7, the indicator must change colour in the basic range. Phenolphthalein, which changes around pH 8 to 10, suits a weak acid with a strong base.
How to check your answer
Mole check. Equivalence is where
moles acid = moles base. Here0.100 × V = 0.00250givesV = 0.0250 L.Symmetry. For a strong-strong curve with equal concentrations, pH 3.70 and pH 10.30 sit equally far from 7 at equal distances either side of equivalence.
Total volume. Always include both solutions in the volume after mixing.
Direction. pH must rise as base is added.
Mistakes that cost marks
Dividing by the starting volume instead of the total volume.
Calling the endpoint and equivalence point the same thing.
Saying equivalence is always at pH 7. That is only for strong with strong.
Taking the log of moles instead of concentration.
Using pH = 14 − pOH after, but forgetting pOH is −log[OH⁻] for excess base.
Where you will use it next
Titrations measure unknown concentrations in labs. The mole bookkeeping behind them is in the mole, explained with a dozen and balancing chemical equations by counting atoms.
Frequently asked questions
Why is pH 7 only for strong acid with strong base?
The salt that forms, here sodium chloride, does not react with water to make acidic or basic ions. With a weak acid, the conjugate base does, so the pH differs.
How many drops are too many near the endpoint?
Slow down near the endpoint and add single drops. As the table shows, 0.2 mL is enough to swing the pH from 3.70 to 10.30.
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