E. Chemical Systems and Equilibrium · Acid-Base and Solubility EquilibriaChoosing Indicators and Solving Titration Problems
E2.5 E2.1 A1.2 A1.4 A1.5 A1.8 A1.13About 75 minutes
Learning goals- I can explain how an acid-base indicator works as a weak acid whose two forms have different colours.
- I can choose a suitable indicator for a titration from the pH at its equivalence point.
- I can solve titration problems: concentration, percentage purity, molar mass and back titration.
- I can describe how to carry out a pH titration safely and identify sources of error.
Words to know
acid-base indicator
A weak acid, HIn, whose acid form and conjugate base form In⁻ have different colours.
transition range
The pH range over which an indicator changes colour, usually about pKIn ± 1.
back titration
A method in which an excess of a reagent is added to the sample, and the unreacted excess is then titrated.
standardization
Titrating a solution against a very pure substance (a primary standard) to find its exact concentration.
The colour has to change at the right moment
A pH meter shows the whole titration curve, but most titrations in school, industry and the field still use a few drops of an indicator. The indicator only helps if its colour changes at (or very near) the equivalence point. Choose the wrong one and your result can be off by several millilitres, even if your technique is perfect. This lesson connects indicators to the curves from the last two lessons and then puts titration data to work on real problems.
How an indicator works
An indicator is itself a weak acid, HIn, whose acid form and conjugate base form have different colours:
HIn(aq) + H₂O(l) ⇌ H₃O⁺(aq) + In⁻(aq)
HIn has one colour and In⁻ has another.
By Le Châtelier's principle, adding acid shifts it left (colour 1) and adding base shifts it right (colour 2). From the Henderson-Hasselbalch equation, pH = pKIn + log([In⁻] ÷ [HIn]). Your eye sees a clear change only when one form is about 10 times more plentiful than the other, so the colour changes over roughly pKIn − 1 to pKIn + 1, the indicator's transition range. Because only a few drops are added, the indicator does not use up a meaningful amount of titrant.
The red cabbage indicator you made in the first lesson is a mixture of natural pigments (anthocyanins) that change colour several times, which is why it shows so many colours.
Choosing the right indicator
Pick an indicator whose transition range falls inside the steep part of the curve, as close as possible to the equivalence-point pH:
- Strong acid + strong base (equivalence pH 7.00, jump from about 4 to 10 at 0.1 mol/L): bromothymol blue is ideal; methyl red and phenolphthalein also work because the jump is so tall.
- Weak acid + strong base (equivalence above 7, about 8.7 for acetic acid): phenolphthalein. An indicator that changes in the acidic range would change in the buffer region, long before equivalence.
- Weak base + strong acid (equivalence below 7, about 5.3 for ammonia): methyl red. Phenolphthalein would change far too early.
For a polyprotic substance there can be more than one equivalence point. For example, when sodium carbonate is titrated with HCl, CO₃²⁻ → HCO₃⁻ happens first (equivalence near pH 8.3, detected with phenolphthalein), and then HCO₃⁻ → H₂CO₃ (equivalence near pH 4, detected with methyl orange). A chemist can use both indicators in one titration.
| Indicator | Range (pH) | Colour change (low → high pH) | Typical use |
|---|
| methyl orange | 3.1 to 4.4 | red → yellow | strong acid with weak base; second point of carbonate |
| methyl red | 4.4 to 6.2 | red → yellow | weak base titrated with strong acid |
| bromothymol blue | 6.0 to 7.6 | yellow → blue | strong acid with strong base |
| phenolphthalein | 8.2 to 10.0 | colourless → pink | weak acid titrated with strong base |
Doing a pH titration in the lab
A school-lab version of the titrations in this unit looks like this (your teacher will provide the exact procedure and safety rules):
- Safety: splash goggles, a lab coat and gloves. NaOH and HCl solutions are corrosive; read their safety data sheets and WHMIS labels. Rinse spills with lots of water and tell the teacher.
- Calibrate the pH meter with standard buffers (often pH 4.00, 7.00 and 10.00).
- Prepare the burette: rinse with the NaOH titrant, fill, and remove the air bubble from the tip. Read the bottom of the meniscus to ±0.01 mL (two decimal places).
- Pipette the analyte into a beaker with a stir bar, and lower the clean pH electrode into it.
- Add titrant in 1 mL portions far from equivalence and 0.10 to 0.20 mL portions near it. Record volume and pH after each addition, once the reading is steady.
- Plot pH against volume, find the equivalence point (middle of the jump), and use the half-equivalence point for pKa.
Common sources of error: a meter that was not calibrated; air bubbles in the burette tip; readings taken before the pH settles; titrant that has absorbed CO₂ from air (NaOH should be standardized, for example against pure potassium hydrogen phthalate); and, with an indicator, an endpoint that does not match the equivalence point (choose the indicator well).
Worked exampleExample 1: Percentage purity
A 0.400 g aspirin tablet is dissolved in an ethanol-water mixture and titrated with 0.1000 mol/L NaOH, using phenolphthalein. The endpoint is at 17.85 mL. Aspirin (acetylsalicylic acid, C₉H₈O₄, M = 180.16 g/mol) is monoprotic. Find the mass of aspirin and its percentage of the tablet's mass.
- n(NaOH) = 0.1000 × 0.01785 = 1.785 × 10⁻³ mol. The ratio is 1 : 1, so n(aspirin) = 1.785 × 10⁻³ mol.
- m = 1.785 × 10⁻³ × 180.16 = 0.3216 g.
- Percentage = 0.3216 ÷ 0.400 × 100% = 80.4%. (The rest of the tablet is binder and filler.)
- Indicator check: aspirin is a weak acid, so the equivalence point is basic, and phenolphthalein is the right choice.
0.322 g of aspirin, 80.4% of the tablet.
Worked exampleExample 2: Identifying an acid by its molar mass
0.2500 g of a pure, solid, monoprotic acid needs 20.47 mL of 0.1000 mol/L NaOH to reach the equivalence point. Find its molar mass and suggest what it could be.
- n(NaOH) = 0.1000 × 0.02047 = 2.047 × 10⁻³ mol = n(acid).
- M = m ÷ n = 0.2500 ÷ 2.047 × 10⁻³ = 122.1 g/mol.
- Benzoic acid, C₆H₅COOH, has M = 7(12.01) + 6(1.01) + 2(16.00) = 122.13 g/mol.
M = 122.1 g/mol, consistent with benzoic acid. Measuring pKa at half-equivalence (4.20) would confirm it.
Worked exampleExample 3: A back titration
A 0.500 g antacid tablet is crushed and added to 50.00 mL of 0.200 mol/L HCl (an excess). After the reaction, the leftover HCl needs 13.40 mL of 0.150 mol/L NaOH. Find the percentage of CaCO₃ (M = 100.09 g/mol) in the tablet. CaCO₃ + 2 HCl → CaCl₂ + H₂O + CO₂.
- Total HCl added = 0.200 × 0.05000 = 1.000 × 10⁻² mol.
- HCl left over = n(NaOH) = 0.150 × 0.01340 = 2.010 × 10⁻³ mol.
- HCl that reacted with CaCO₃ = 1.000 × 10⁻² − 2.010 × 10⁻³ = 7.990 × 10⁻³ mol.
- n(CaCO₃) = 7.990 × 10⁻³ ÷ 2 = 3.995 × 10⁻³ mol; m = 3.995 × 10⁻³ × 100.09 = 0.3999 g.
- Percentage = 0.3999 ÷ 0.500 × 100% = 80.0%.
80.0% CaCO₃. A back titration is used here because CaCO₃ is a solid that reacts slowly and gives off CO₂, so titrating it directly would give a poor endpoint.
Just for funRed cabbage juice is a one-pot indicator kit: as the pH rises it runs through red, pink, purple, blue, green and finally yellow. That is about as close to a rainbow as a vegetable gets.
Hands-on activityA kitchen titration of vinegar
You need: white vinegar (label: 5% acetic acid), baking soda, a kitchen scale (if you have one), a 250 mL (1 cup) measuring cup, red cabbage indicator, a clear glass, a 10 mL oral medicine syringe (from a pharmacy) or measuring spoons, a spoon for stirring, and white paper.
Grown-up note: an adult should supervise and help prepare the cabbage indicator (knife, hot water). Don't drink the mixtures.
- Make the titrant. Dissolve 8.4 g of baking soda (0.10 mol of NaHCO₃) in water and add water to make 250 mL (1 cup). Its concentration is about 0.40 mol/L. (Without a scale, use 2 level teaspoons, about 9 to 10 g, and treat the result as a rough estimate.)
- Prepare the sample. Measure 10.0 mL of vinegar into the glass, add about 50 mL of water and 2 tablespoons of cabbage indicator. It should be pink-red.
- Titrate. Add the baking soda solution 1 mL at a time, stirring well (it will fizz). As the colour starts to shift toward purple, add it 0.5 mL at a time. Stop when the colour turns to purple-blue and stays that way after stirring for 30 seconds. Record the total volume.
- Repeat twice more and average the trials that agree best.
- Calculate. CH₃COOH + HCO₃⁻ → CH₃COO⁻ + H₂O + CO₂ (1 : 1). n(HCO₃⁻) = c × V; c(acetic acid) = n ÷ 0.0100 L. Convert to % (g per 100 mL) with M = 60.05 g/mol.
What to look for: about 20 to 21 mL of 0.40 mol/L baking soda solution should be needed for 10.0 mL of 5% vinegar (0.83 mol/L). Your result will be less precise than a lab titration: the CO₂ bubbles and the gradual colour change of cabbage indicator make the endpoint fuzzy, and kitchen measures are less accurate than a burette. List these as sources of error, and decide whether each would make your answer too high or too low.
Your turn
1Choose an indicator for the titration of HF with KOH. Explain.
HF is a weak acid, so the equivalence point is basic (above 7). Choose phenolphthalein (8.2 to 10.0), whose range lies in the steep part of the curve.
2Choose an indicator for the titration of NH₃ with HNO₃. Explain.
The equivalence point is acidic (NH₄⁺ is a weak acid, pH about 5.3), so choose methyl red (4.4 to 6.2).
3An indicator HIn has pKIn = 5.0. Over what pH range will it change colour?
About pKIn ± 1: pH 4.0 to 6.0.
4What colour is bromothymol blue in a solution of pH 9? In pH 4?
Above its range it is blue (pH 9); below its range it is yellow (pH 4).
5A 25.00 mL sample of vinegar needs 34.20 mL of 0.5000 mol/L NaOH. Find the acetic acid concentration in mol/L and in g/100 mL.
n(NaOH) = 0.5000 × 0.03420 = 1.710 × 10⁻² mol = n(CH₃COOH). c = 1.710 × 10⁻² ÷ 0.02500 = 0.6840 mol/L. Mass per litre = 0.6840 × 60.05 = 41.07 g/L, so 4.107 g/100 mL (about 4.1%).
6Why does using methyl orange in the acetic acid titration give a result that is far too low?
Methyl orange changes colour between pH 3.1 and 4.4, which the curve passes in the first few millilitres (in the buffer region). The student would stop long before equivalence, measure a volume that is far too small, and calculate a concentration that is far too low.
More practice: warm-up
1What kind of substance is an acid-base indicator?
A weak acid whose acid and base forms have different colours.
2What colour is phenolphthalein in an acidic solution?
3Which indicator is best for a strong acid-strong base titration?
Bromothymol blue (range 6.0 to 7.6).
4What is the name for the pH range over which an indicator changes colour?
5Why do you add only a few drops of indicator?
So the indicator (itself a weak acid) uses up a negligible amount of titrant.
More practice: on your own
10.3150 g of potassium hydrogen phthalate (KHP, KHC₈H₄O₄, M = 204.22 g/mol, monoprotic) needs 15.62 mL of NaOH to reach the endpoint. Find [NaOH].
n(KHP) = 0.3150 ÷ 204.22 = 1.5425 × 10⁻³ mol = n(NaOH). c = 1.5425 × 10⁻³ ÷ 0.01562 = 0.09875 mol/L.
20.1800 g of an unknown monoprotic acid needs 24.00 mL of 0.0750 mol/L NaOH. Find its molar mass.
n = 0.0750 × 0.02400 = 1.800 × 10⁻³ mol. M = 0.1800 ÷ 1.800 × 10⁻³ = 100.0 g/mol.
3A student overshoots the endpoint of a vinegar titration and the solution turns dark pink. Will the calculated acetic acid concentration be too high or too low? Explain.
Too high. The recorded volume of NaOH is larger than needed, so the calculated moles of acid, and its concentration, are too large.
4A sample of sodium carbonate is titrated with HCl using phenolphthalein first, then methyl orange. The first endpoint needs 12.40 mL. How much more acid (approximately) is needed to reach the second endpoint? Explain.
About 12.40 mL more (24.80 mL in total). The first endpoint converts CO₃²⁻ to HCO₃⁻ (1 H⁺ per ion); the second converts the same number of HCO₃⁻ ions to H₂CO₃, which needs the same number of moles of acid again.
5In a pH titration, why should titrant be added in smaller portions near the equivalence point?
The pH changes very quickly there. Small portions (0.10 to 0.20 mL) give enough points to locate the middle of the steep jump precisely; large portions could skip over it.
Challenge
1Show why an indicator changes colour over about pKIn ± 1. (Use pH = pKIn + log([In⁻] ÷ [HIn]) and assume the eye sees one colour when that form is 10 times the other.)
When [In⁻] ÷ [HIn] = 1/10, pH = pKIn + log(0.1) = pKIn − 1 (acid colour). When the ratio is 10, pH = pKIn + 1 (base colour). Between these, the eye sees a mixture, so the transition range is about pKIn ± 1.
2A 1.00 g sample of impure Mg(OH)₂ is dissolved in 50.00 mL of 0.500 mol/L HCl (excess). The excess acid needs 11.60 mL of 0.250 mol/L NaOH. Find the percentage of Mg(OH)₂ (M = 58.33 g/mol). Mg(OH)₂ + 2 HCl → MgCl₂ + 2 H₂O.
HCl added = 0.02500 mol. Excess = 0.250 × 0.01160 = 2.900 × 10⁻³ mol. Reacted = 0.02210 mol. n(Mg(OH)₂) = 0.01105 mol; m = 0.01105 × 58.33 = 0.6445 g. Percentage = 64.5%.
3Thymol blue changes colour twice: red → yellow at pH 1.2 to 2.8, and yellow → blue at pH 8.0 to 9.6. Could it replace phenolphthalein in the acetic acid titration? Could it replace bromothymol blue in the HCl titration? Explain.
For acetic acid: yes, its second change (8.0 to 9.6) lies in the steep jump around pH 8.7. For HCl with NaOH: its second change is also inside the very tall strong-strong jump (about 4 to 10), so it would work too. (Its first change, 1.2 to 2.8, happens before equivalence as the pH climbs from 1.00 to about 3, so you would ignore it and watch for the yellow-to-blue change.)
Quiz
1. Which indicator is best for titrating acetic acid with sodium hydroxide?
2. An indicator works because
3. What is the approximate transition range of an indicator with pKIn = 7.1?
4. 0.2500 g of a monoprotic acid needs 25.00 mL of 0.1000 mol/L NaOH. What is its molar mass?
5. In a back titration, the volume of NaOH used measures
6. A student used phenolphthalein to titrate NH₃ with HCl. What happens?
Big idea (E2.5): an indicator is a weak acid that changes colour over about pKIn ± 1, so it must be chosen so that its range falls in the steep part of the titration curve: bromothymol blue for strong-strong, phenolphthalein for weak acid-strong base, methyl red for weak base-strong acid. Titration data then give concentrations, purity, molar mass and Ka.
How to help: Ask your teen to sketch the right kind of curve before choosing an indicator: "Where is the equivalence point? Which range fits inside the jump?" For the kitchen titration, an adult should supervise the indicator preparation; a pharmacy oral syringe makes measuring much easier. Encourage your teen to write down the volumes from each trial and explain why they differ.
Common difficulties:
- Choosing an indicator by its name or colour rather than its range.
- Forgetting mole ratios (CaCO₃ and Mg(OH)₂ react 1 : 2 with HCl).
- In back titrations, forgetting to subtract the excess from the total.
- Thinking the indicator's colour change is the equivalence point; it is only a signal that should be close to it.