The shape of the lesson
By the end of the lesson, learners can
- The pH scale: pH is a logarithmic scale: one unit is a factor of ten in hydrogen ion concentration.
- Four curves: Run all four combinations in the simulator, adding 0.100 mol dm −3 base to 25.0 cm 3 of 0.100 mol dm −3 acid.
- Choosing an indicator: An indicator changes colour over a range of about two pH units.
- pH = −log[H+]; strong acid [H+] = concentration.
- Strong/weak base: equivalence below 7, methyl orange.
- Weak acid/strong base: above 7, phenolphthalein.
- Weak/weak: no sharp end point.
One picture every idea returns to
pH = −log10[H+]. For a strong monobasic acid, [H+] equals the acid concentration, so 0.0100 mol dm−3 HCl has pH 2.00; each tenfold dilution raises the pH by one. A titration curve plots pH against volume added. Near the equivalence point the pH changes sharply, and the vertical section sits around pH 7 for strong acid/strong base, below 7 for strong acid/weak base, and above 7 for weak acid/strong base. A suitable indicator must change colour entirely within that vertical section: methyl orange (3.1 to 4.4) for strong acid/weak base, phenolphthalein (8.3 to 10.0) for weak acid/strong base, either for strong/strong, and none for weak/weak.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Watch the pH jump.. Add alkali to acid one drop at a time and the pH hardly moves, then leaps by several units in a fraction of a cubic centimetre. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: The pH scale | pH is a logarithmic scale: one unit is a factor of ten in hydrogen ion concentration. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Four curves | Run all four combinations in the simulator, adding 0.100 mol dm −3 base to 25.0 cm 3 of 0.100 mol dm −3 acid. Project tab 6 of the lab (Equilibria lab, titration curves) and let a student drive it while the class predicts. | Pairs |
| 21 to 30 min | Teach and check: Choosing an indicator | An indicator changes colour over a range of about two pH units. | Cooperative Concept Mapping |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 13 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Choosing an indicator, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Cooperative Concept Mapping
Teams receive the key terms on cards and arrange them on a large sheet, drawing and labelling the links. Compare maps between teams before showing the model map.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| The equivalence point is where the acid and base have reacted in exactly the ratio of the equation; it is not always pH 7. | And the end point of an indicator is where it changes colour, which is only a good estimate of equivalence if the indicator's range lies inside the steep part of the curve. |
pH, strong and weak acids, titration curves: worksheet
6 questions, 13 marks. Written in the style of the papers; no past paper question is reproduced.
Calculate the pH of (a) 0.100 mol dm−3 HCl and (b) 0.00100 mol dm−3 HNO3.
A solution of hydrochloric acid has pH 0.60. Calculate its concentration.
Sketch the pH curve for adding 0.100 mol dm−3 NaOH to 25.0 cm3 of 0.100 mol dm−3 ethanoic acid. Label the starting pH, the equivalence volume and the approximate pH range of the vertical section.
Explain why phenolphthalein is suitable for titrating ethanoic acid with sodium hydroxide but methyl orange is not.
Explain why the pH at the equivalence point is below 7 when hydrochloric acid is titrated with aqueous ammonia.
Suggest how the end point of a titration between ethanoic acid and aqueous ammonia could be found, and why.
Answer key and marking notes
- (a) pH = −log(0.100) = 1.00.
- (b) pH = −log(0.00100) = 3.00.
- [H+] = 10−0.60 = 0.251 mol dm−3.
- HCl is fully dissociated, so [HCl] = 0.251 mol dm−3.
- Starts at about pH 3 and rises gradually.
- Vertical section at 25.0 cm3, from about pH 7 to 11 (equivalence above 7).
- Levels off at about pH 13 as excess NaOH is added.
- The vertical section is at about pH 7 to 11; phenolphthalein changes over 8.3 to 10.0, inside this range.
- Methyl orange changes at 3.1 to 4.4, where the pH is still rising slowly, so it would change colour gradually well before equivalence.
- At equivalence the solution contains ammonium chloride.
- NH4+ is a weak acid (it donates H+ to water), so the solution is slightly acidic.
- Use a pH meter (or a conductivity meter) and plot the curve.
- There is no sharp vertical section, so no indicator would change colour at a precise volume.
8 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
What is the pH of 0.0100 mol dm−3 hydrochloric acid?
- A2.00
- B0.0100
- C12.0
- D1.00
What is the pH of 0.0500 mol dm−3 hydrochloric acid?
- A1.30
- B3.00
- C12.7
- D1.00
A solution of a strong acid has a pH of 3.40. What is the hydrogen ion concentration?
- A3.98 × 10−4 mol dm−3
- B2.51 × 103 mol dm−3
- C0.531 mol dm−3
- D3.40 × 10−3 mol dm−3
The graph shows the pH curve when 0.100 mol dm−3 NaOH is added to 25.0 cm3 of 0.100 mol dm−3 HCl. The shaded bands are the colour-change ranges of two indicators. Which indicator(s) would be suitable?
- Aboth methyl orange and phenolphthalein
- Bphenolphthalein only
- Cmethyl orange only
- Dneither indicator
Ethanoic acid is titrated with sodium hydroxide solution. What is the pH at the equivalence point?
- Agreater than 7, because the ethanoate ions formed act as a weak base
- Bexactly 7, because the acid has been exactly neutralised
- Cless than 7, because ethanoic acid is a weak acid
- Dless than 7, because some ethanoic acid is left undissociated
The graph shows the pH curve when 0.100 mol dm−3 NaOH is added to 25.0 cm3 of 0.100 mol dm−3 ethanoic acid. Which indicator should be used, and why?
- Aphenolphthalein, because its range (8.3 to 10.0) lies within the vertical section (about 7 to 10)
- Bmethyl orange, because its range (3.1 to 4.4) lies within the vertical section
- Cmethyl orange, because ethanoic acid is an acid
- Deither indicator, because the equivalence point is at 25.0 cm3
The graph shows the pH curve when 0.100 mol dm−3 aqueous ammonia is added to 25.0 cm3 of 0.100 mol dm−3 HCl. What is the pH at the equivalence point and which indicator is suitable?
- Abelow 7; methyl orange
- Bbelow 7; phenolphthalein
- Cexactly 7; either indicator
- Dabove 7; phenolphthalein
Why is no indicator suitable for titrating ethanoic acid with aqueous ammonia?
- Athe pH changes only gradually near the equivalence point, so there is no vertical section for an indicator to match
- Bthe equivalence point is at exactly pH 7, where no indicator changes colour
- Ca weak acid and a weak base do not react with each other
- Dthe vertical section is too long, so every indicator changes colour at once
Quiz key
HCl is fully dissociated, so [H+] = 0.0100 = 1.00 × 10−2 mol dm−3 and pH = −log(0.0100) = 2.00. 0.0100 is the [H+], not the pH. 12.0 is 14 − 2.00, which would be the pH of 0.0100 mol dm−3 NaOH, an alkali. 1.00 is the pH of 0.100 mol dm−3 HCl; it comes from misreading the power of ten.
[H+] = 0.0500 mol dm−3, so pH = −log10(0.0500) = 1.30. 3.00 uses the natural logarithm (−ln 0.0500 = 3.00) instead of log base 10. 12.7 is 14 − 1.30, treating the solution as an alkali. 1.00 doubles [H+] to 0.100 as if HCl were dibasic; HCl releases only one proton per molecule.
[H+] = 10−3.40 = 3.98 × 10−4 mol dm−3. 2.51 × 103 uses 10+3.40, forgetting the minus sign. 0.531 is log(3.40), taking the log again instead of the inverse log. 3.40 × 10−3 just places the pH digits in front of a power of ten, which is not how logarithms work.
For a strong acid and a strong base, the pH rises almost vertically from about 3.7 to about 10.3 at 25.0 cm3, and the equivalence point is at pH 7. Both ranges (methyl orange 3.1 to 4.4, phenolphthalein 8.3 to 10.0) fall essentially within this steep section, so either changes colour within a drop of the equivalence point. Phenolphthalein only is the answer for a weak acid with a strong base. Methyl orange only is the answer for a strong acid with a weak base. Neither is the answer for a weak acid with a weak base, which has no steep section.
At the equivalence point the solution is sodium ethanoate. The ethanoate ion is the conjugate base of a weak acid, so it accepts protons from water (CH3COO− + H2O ⇌ CH3COOH + OH−), making the solution alkaline, with a pH of about 8.7. Exactly 7 is true only for a strong acid with a strong base. The acid being weak is the reason the pH is above 7, not below. At the equivalence point all the acid has reacted with NaOH; none is left over to lower the pH.
For a weak acid with a strong base, the steep section runs from about pH 7 to 10 and the equivalence point is about 8.7. Phenolphthalein changes colour between 8.3 and 10.0, inside this section, so it gives a sharp end point at 25.0 cm3. Methyl orange changes between 3.1 and 4.4, which on this curve is passed within the first few cm3 of NaOH, long before 25.0 cm3, so it would give a very early and gradual colour change. The choice depends on the shape of the curve, not simply on the substance being an acid. The equivalence volume is the same for any indicator, but only one of them changes colour at that volume.
At equivalence the solution contains NH4+ ions, which donate protons to water (NH4+ ⇌ NH3 + H+), so the pH is below 7 (about 5.3). The steep section runs from about pH 3.7 to 7, which includes the methyl orange range (3.1 to 4.4). Phenolphthalein needs pH 8.3 to 10.0, which is only reached gradually after the equivalence point. Exactly 7 applies only to strong acid with strong base. Above 7 is the case for a weak acid with a strong base, the reverse situation.
With a weak acid and a weak base the curve has no steep section: the pH changes gradually through the equivalence point, so any indicator would change colour slowly over several cm3 and give no sharp end point. (A pH meter or a conductivity method is used instead.) Indicators exist that change colour around pH 7 (for example bromothymol blue), so a pH of 7 is not the problem. Weak acids and weak bases do react (ethanoic acid and ammonia form ammonium ethanoate). A long vertical section would make indicator choice easy, not impossible.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.