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At equivalence the protons given equal the hydroxide added; the pH there depends on which partner is weak.
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By the end of this lesson you will be able to use the proton count to find a volume or concentration at equivalence, process titration readings into concordant titres, balance an acid–hydroxide equation, predict whether the solution at equivalence is acidic, neutral or alkaline, and find the pH or the heat released when one reagent is in excess.
Chemistry 1 gave you titration as a procedure and the calculation amount $=$ concentration $\times$ volume. This unit has given you acids as proton donors, conjugate bases, and pH for acids and bases. This lesson puts them together to say what is conserved when an acid meets a base, and what the pH is when they have exactly cancelled.
Neutralisation is the reaction of an acid with a base; with a hydroxide the net ionic equation is $\mathrm{H_3O^+ + OH^- \rightarrow 2H_2O}$. The equivalence point is where the amount of base added exactly matches the protons the acid can give. The end point is where an indicator changes colour, chosen to be as close to equivalence as possible. A titre is the volume delivered from the burette in one titration; concordant titres agree within $0.10$ mL. A salt is the ionic compound left when the acid's anion and the base's cation stay in solution.
Every neutralisation is proton transfer. A hydroxide ion accepts one proton and becomes a water molecule, so at the equivalence point
$$\text{amount of hydroxide added} = \text{amount of protons the acid can give}$$
For an acid that gives $p$ protons per unit,
$$c_b V_b = p \times c_a V_a$$
with both volumes in the same unit. $25.0$ mL of $0.100$ mol/L sulfuric acid holds $0.00250$ mol, which can give $0.00500$ mol of protons, so it needs $50.0$ mL of $0.100$ mol/L sodium hydroxide — twice the volume hydrochloric acid of the same concentration would need.
Strength does not enter this count. $0.100$ mol/L ethanoic acid needs exactly the same volume of alkali as $0.100$ mol/L hydrochloric acid: as the hydroxide removes hydronium ions, the weak acid's equilibrium shifts right and gives up more, until every molecule has reacted.
The pH at equivalence is a different question, and here strength matters. At equivalence the flask holds water and a salt. The salt's ions are the acid's conjugate base and the base's conjugate acid:
| Acid + base | Ions left | pH at equivalence (25 °C) |
|---|---|---|
| strong + strong (HCl + NaOH) | $\mathrm{Na^+}$, $\mathrm{Cl^-}$ — neither reacts with water | 7 |
| weak + strong (ethanoic acid + NaOH) | ethanoate, a weak base | above 7, about 8.7 |
| strong + weak (HCl + ammonia) | ammonium, a weak acid | below 7, about 5.3 |
The conjugate base of a strong acid is too feeble to take a proton back — that is what made the acid strong — so chloride is a spectator. The conjugate base of a weak acid is a real base: $\mathrm{CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-}$ leaves hydroxide in the solution.
Another way: picture
Two teams exchange tokens until one team has none left to give. That moment is equivalence. Whether the room is then calm depends on who is left standing: if one team's leftover players still want to snatch tokens back, the room is not neutral, even though the exchange is over.
Another way: steps
For any neutralisation calculation:
Before equivalence one reagent is in excess, and the pH is set by what is left of it. Mixing $55.0$ mL of $0.100$ mol/L hydrochloric acid with $45.0$ mL of $0.100$ mol/L sodium hydroxide:
| acid | hydroxide | |
|---|---|---|
| amount added, mmol | 5.50 | 4.50 |
| reacted, mmol | 4.50 | 4.50 |
| left, mmol | 1.00 | 0 |
The $1.00$ mmol of acid left is in $100.0$ mL — the total volume, because the two solutions are now one — so $[\mathrm{H_3O^+}] = 0.0100$ mol/L and the pH is 2. Reverse the volumes and $1.00$ mmol of hydroxide is left: pOH 2, pH 12.
Neutralisation is also exothermic. For any strong acid with any strong base the reaction is the same one, $\mathrm{H_3O^+ + OH^- \rightarrow 2H_2O}$, so the enthalpy change is the same too: about $-57$ kJ for each mole of water formed. The heat released is set by the limiting reagent, because only as much water forms as it allows.
One titration is never trusted. A rough run finds the end point to within a millilitre, and careful runs follow until at least two agree within $0.10$ mL. Only the concordant titres are averaged; the rough one was deliberately overshot and is left out. Each titre is final reading minus initial reading, and burette readings are recorded to $0.05$ mL, the nearest half-division.
When a sample is diluted before titrating, the dilution must be undone at the end: if $25.0$ mL of vinegar is made up to $250$ mL and $25.0$ mL of that is titrated, the titrated portion holds a tenth of the acid from the original sample.
Neutralisation always gives pH 7. Only a strong acid with a strong base does, at 25 °C. With a weak acid the equivalence point is alkaline; with a weak base, acidic.
A weak acid needs less alkali. Equal amounts of acid need equal amounts of alkali, per proton. The weak acid gives its protons up as they are taken.
Every acid needs one hydroxide per unit. Sulfuric acid needs two and phosphoric acid three.
The excess is divided by its own volume. After mixing, everything is in the total volume.
The rough titre goes in the mean. It is a first estimate and is left out; only concordant titres are averaged.
$25.0$ mL of sulfuric acid needs $20.00$ mL of $0.150$ mol/L sodium hydroxide.
The alkali's concentration and volume are both known, so start there.
Hydroxide: $0.150 \times 0.02000 = 0.00300$ mol. Sulfuric acid gives two protons, so the acid is $0.00150$ mol.
Scale by the equation: one acid to two hydroxide.
Concentration: $0.00150 \div 0.0250 = 0.0600$ mol/L.
Amount over volume in litres.
Hydrochloric acid is titrated with ammonia solution to equivalence.
One strong partner and one weak one.
The solution holds ammonium chloride. Chloride is a spectator; ammonium is the conjugate acid of a weak base.
Look for the ion that is a real acid or base.
$\mathrm{NH_4^+ + H_2O \rightleftharpoons NH_3 + H_3O^+}$, so the solution is acidic, about pH 5.
The weak partner's conjugate decides.
Nitric acid: $0.100 \times 0.0200 = 0.00200$ mol, one proton each.
Amount of the known solution first.
Hydroxide needed: $0.00200$ mol, so the volume is $0.00200 \div 0.200 = \ldots$
…$0.0100$ L, which is $10.0$ mL.
$25.0$ mL of hydrochloric acid at $0.2$ mol/L is titrated with sodium hydroxide solution at $0.4$ mol/L. Each unit of the acid gives $1$ proton(s). What volume of the alkali reaches the equivalence point?
Answer: unit: L / mL
A learner's burette readings, in mL, from four titrations of the same acid with the same alkali are below. The first run was a rough one. Work out each titre, and say whether it belongs in the mean: only concordant titres, within $0.10$ mL of each other, are averaged.
| initial reading in mL | final reading in mL | titre in mL | used in the mean | |
|---|---|---|---|---|
| rough | 0 | 21.1 | ||
| run 1 | 0.5 | 21.05 | ||
| run 2 | 1.2 | 21.65 | ||
| run 3 | 0.3 | 20.8 |
Balance the equation for phosphoric acid neutralised by potassium hydroxide: acid plus hydroxide gives a salt and water.
This task has no paper form; do it on a device.
$25$ mL of ethanoic acid is titrated with sodium hydroxide solution exactly to the equivalence point. What is the pH of the solution there, at 25 °C?
Each pair is titrated exactly to its equivalence point. Say whether the solution there is acidic, neutral or alkaline at 25 °C.
| solution at the equivalence point | |
|---|---|
| hydrochloric acid and sodium hydroxide | |
| ethanoic acid and sodium hydroxide | |
| hydrochloric acid and ammonia | |
| nitric acid and potassium hydroxide |
$55.0$ mL of hydrochloric acid is mixed with $45.0$ mL of sodium hydroxide solution. Both are $0.100$ mol/L. What is the pH of the mixture at 25 °C?
Answer:
A self-heating food pack is being designed around a neutralisation. In a test, $80$ mL of $1.00$ mol/L hydrochloric acid is mixed with $90$ mL of $1.00$ mol/L sodium hydroxide solution. Each mole of water formed releases $57$ kJ. How much heat is released?
Answer: unit: J / kJ
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A $25.0$ mL sample of vinegar is diluted to $250$ mL with water. $25.0$ mL of the diluted solution needs $22.00$ mL of $0.100$ mol/L sodium hydroxide to reach equivalence. What mass of ethanoic acid, $\mathrm{CH_3COOH}$ ($60$ g/mol), was in the original $25.0$ mL of vinegar, in grams?
Answer: g
You can calculate reacting amounts in a neutralisation and you know neutralised does not mean neutral. Say out loud why ethanoic acid and sodium hydroxide give an alkaline solution at equivalence. Next: following the pH through the whole titration — the titration curve.
10. Your turn: what volume of $0.200$ mol/L potassium hydroxide neutralises $20.0$ mL of $0.100$ mol/L nitric acid?, step 3