Redox titrations

Finding an unknown concentration

A bottle of iron tablets says that each tablet holds 60 mg of iron. A teacher asks: is that true? We dissolve a tablet in acid, so that all the iron is iron(II). Then we measure it with a solution whose strength we know well. That measurement is a titration.

In a titration, a burette lets one solution run slowly into a flask that holds the other. We add it drop by drop until the reaction just finishes. That moment is the end point. The volume run in, read from the burette, is the titre.

A redox titration uses a redox reaction. The oxidising agent and the reducing agent meet in an exact ratio, and the balanced equation gives that ratio.

Permanganate is its own indicator

Potassium permanganate, $\text{KMnO}_4$, is a deep purple. In acid it changes to $\text{Mn}^{2+}$, which is almost colourless. So the liquid in the burette also shows the end point.

• Before the end point, iron(II) is still in the flask. Each drop of purple vanishes at once.
• At the end point, the last iron(II) has reacted. The next drop has nothing to react with, so a faint pink stays.

Three rules make a good titration:

• Acidify with dilute sulfuric acid. Hydrochloric acid is no good, because permanganate oxidises chloride ions and some of it is wasted. Nitric acid is no good either, because it is an oxidising agent itself.
• Read the top of the meniscus. The liquid is so dark that the bottom of the curve cannot be seen.
• Warm the flask for oxalic acid, to about $60\ ^\circ\text{C}$. The first drops react slowly. Once a little $\text{Mn}^{2+}$ has formed, it speeds the reaction up, and the later drops vanish quickly.

Dichromate, and iodine with thiosulfate

Potassium dichromate, $\text{K}_2\text{Cr}_2\text{O}_7$, is orange. In acid it changes to green $\text{Cr}^{3+}$, but the change of colour is gradual. So we add an indicator, such as diphenylamine, which turns blue-violet at the end point. A dichromate solution can be made by weighing the pure salt, so its strength is exact. A permanganate solution cannot be made this way, because traces of dust slowly use it up. It is checked against oxalic acid first.

Some oxidising agents, such as bleach, are measured in two steps. First the sample is added to excess iodide, which frees iodine. Then the iodine is titrated with sodium thiosulfate:

Near the end we add starch. Starch turns blue-black with iodine, and the blue disappears at the end point.

From titre to concentration

Follow these four steps:

1. Write the balanced equation and read the mole ratio.
2. Find the moles of the solution in the burette: concentration in mol/L times volume in litres. A volume in mL divided by 1000 is in litres.
3. Use the ratio to find the moles of the unknown.
4. Divide by the volume of the unknown solution, in litres.

Worked example 1. A flask holds $25.0\ \text{mL}$ of iron(II) sulfate solution. It needs $20.0\ \text{mL}$ of $0.0200\ \text{mol/L}$ potassium permanganate in acid.

• Ratio. $1\ \text{MnO}_4^-$ reacts with $5\ \text{Fe}^{2+}$.
• Permanganate. $0.0200 \times 0.0200\ \text{L} = 0.000400\ \text{mol}$.
• Iron(II). $5 \times 0.000400 = 0.00200\ \text{mol}$.
• Concentration. $\dfrac{0.00200\ \text{mol}}{0.0250\ \text{L}} = 0.0800\ \text{mol/L}$.

Practise with new numbers

Worked example 2: standardising permanganate. A student weighs $0.630\ \text{g}$ of oxalic acid crystals, $\text{H}_2\text{C}_2\text{O}_4 \cdot 2\text{H}_2\text{O}$, with a molar mass of $126\ \text{g/mol}$. The crystals are dissolved and made up to $250\ \text{mL}$. A $25.0\ \text{mL}$ portion is warmed with acid. It needs $20.0\ \text{mL}$ of the permanganate solution. The balanced equation is

• Oxalic acid in all. $\dfrac{0.630}{126} = 0.00500\ \text{mol}$ in $250\ \text{mL}$, so $0.000500\ \text{mol}$ in the $25.0\ \text{mL}$ portion.
• Permanganate. The ratio is $2 : 5$, so $\dfrac{2}{5} \times 0.000500 = 0.000200\ \text{mol}$.
• Concentration. $\dfrac{0.000200\ \text{mol}}{0.0200\ \text{L}} = 0.0100\ \text{mol/L}$.

The n-factor and equivalents

There is a shorter road for a titration. The n-factor of a substance is the number of electrons that one formula unit gains or loses in the reaction. Equivalents are moles times the n-factor.

• $\text{KMnO}_4$ in acid: $n = 5$. $\text{K}_2\text{Cr}_2\text{O}_7$ in acid: $n = 6$.
• $\text{FeSO}_4$: $n = 1$. Oxalic acid, $\text{H}_2\text{C}_2\text{O}_4$: $n = 2$.

At the end point, the equivalents of the oxidising agent equal the equivalents of the reducing agent:

Use it for example 1, with $n_1 = 5$ for permanganate and $n_2 = 1$ for iron(II): $5 \times 0.0200 \times 20.0 = 1 \times M_2 \times 25.0$. So $M_2 = 0.0800\ \text{mol/L}$, the same as before.

Try it in Python

The program turns a titre into a concentration in the three steps. The volumes are in mL, so it divides by 1000.

Common mistakes

• Forgetting the mole ratio. One permanganate ion does not react with one iron(II) ion. The ratio is 1 to 5.
• Leaving volumes in mL. Concentration is in mol/L, so divide a volume in mL by 1000.
• Using hydrochloric acid with permanganate. The chloride is oxidised, and the titre comes out too large.
• Missing the end point. The first faint pink that stays for half a minute is the end point. A deep pink is far past it.
• Mixing up the two volumes. The volume of the unknown solution goes at the bottom of the final division.

Remember these

• The balanced equation gives the mole ratio. Never guess it.
• Moles = concentration in mol/L times volume in litres.
• Permanganate is its own indicator, and sulfuric acid is the acid to use.
• Dichromate needs an indicator. Iodine needs starch, and thiosulfate turns it colourless.
• At the end point, $n_1 M_1 V_1 = n_2 M_2 V_2$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why is hydrochloric acid not used to acidify a permanganate titration?

2. In a titration, $0.000200\ \text{mol}$ of permanganate reacts with iron(II). How many moles of iron(II) were in the flask?

3. What is the n-factor of potassium dichromate in acid?

4. Why can a dichromate solution be made by weighing, but a permanganate solution must be checked first?

5. In the iodine and thiosulfate titration with starch, what is the colour change at the end point?