Standard solutions, indicators and acid and base titrations

How much is there?

A chemist who wants to know the concentration of an acid in vinegar does not weigh it. She adds a base of known concentration from a burette until the acid is just used up. Then she knows how much base reacted, and so how much acid there was. This is volumetric analysis, or a titration.

Standard solutions and primary standards

A standard solution has a concentration that we know accurately. We make one by weighing a pure solid, dissolving it, and making the solution up to a mark in a volumetric flask.

The solid must be a primary standard. It must be pure, stable, not take up water or carbon dioxide from air, and have a large molar mass, so that weighing errors are small. Good examples are:

• oxalic acid dihydrate, $\text{H}_{2}\text{C}_{2}\text{O}_{4}\cdot 2\text{H}_{2}\text{O}$, $126\ \text{g/mol}$
• anhydrous sodium carbonate, $\text{Na}_{2}\text{CO}_{3}$, $106\ \text{g/mol}$
• potassium hydrogenphthalate
• Mohr's salt, $\text{FeSO}_{4}(\text{NH}_{4})_{2}\text{SO}_{4}\cdot 6\text{H}_{2}\text{O}$, $392\ \text{g/mol}$

Sodium hydroxide is not a primary standard. It takes up water and carbon dioxide. Potassium permanganate is not one either: it always holds a little manganese(IV) oxide and decomposes in light. We fix their concentrations by titrating them against a primary standard.

The molarity of a standard solution is $c = \dfrac{m}{M \times V}$, with $m$ in grams, $M$ in g/mol and $V$ in litres.

The steps of a titration

Apparatus. A burette, a pipette, a conical flask, a funnel, a white tile and a wash bottle of distilled water.

Steps.

1. Rinse the burette with a little of the solution it will hold. Fill it above the zero mark through a funnel, and remove the funnel.
2. Let the solution run through the tip so that no air bubble is left in it. Set the level at or near zero.
3. Rinse the pipette with a little of the solution it will measure. Pipette 25.00 mL into the conical flask.
4. Rinse the conical flask with distilled water only. Add two or three drops of indicator.
5. Place the flask on a white tile under the burette. Add the solution slowly, with swirling.
6. Near the end point, add one drop at a time. Stop at the first permanent change of colour.
7. Read the bottom of the meniscus with your eye at the level of the liquid. The difference of the two readings is the titre.
8. Repeat until two titres agree within $0.10\ \text{mL}$. These are concordant titres. Use their mean.

Why distilled water in the flask? Water does not change the number of moles in the flask, so it does not change the titre. A rinse with the solution would add extra moles.

Indicators and the end point

The equivalence point is where the moles of acid and base are exactly equal. The end point is where the indicator changes colour. We choose an indicator that changes colour at the pH of the equivalence point.

• Phenolphthalein changes at pH 8.3 to 10.0, from colourless in acid to pink in alkali.
• Methyl orange changes at pH 3.1 to 4.4, from red in acid to yellow (orange at the middle) in alkali.
• Methyl red changes at pH 4.4 to 6.2, from red to yellow.

• Strong acid and strong base. The pH at the equivalence point is 7. Either indicator works.
• Weak acid and strong base. The pH at the equivalence point is above 7. Use phenolphthalein.
• Strong acid and weak base. The pH at the equivalence point is below 7. Use methyl orange or methyl red.
• Weak acid and weak base. There is no sharp jump. No indicator works well.

Look at the red curve. For a weak acid, the pH rises gently at first, and at the half-way point (12.5 mL) it equals the $\text{p}K_a$ of the acid. The steep part is short and sits above pH 7. Methyl orange changes colour long before that steep part. So methyl orange gives a wrong end point for a weak acid, and phenolphthalein is right.

The calculation

For an acid and a base that react $a : b$ in the equation $a\ \text{A} + b\ \text{B}$, the amounts are in the same ratio at the equivalence point.

• Hydrochloric acid and sodium hydroxide react 1 : 1.
• Oxalic acid and sodium hydroxide react 1 : 2, because oxalic acid has two acidic hydrogen atoms.
• Sodium carbonate and hydrochloric acid react 1 : 2 to carbon dioxide: $\text{Na}_{2}\text{CO}_{3}\ +\ 2\text{HCl}\ \rightarrow \ 2\text{NaCl}\ +\ \text{H}_{2}\text{O}\ +\ \text{CO}_{2}$. Use methyl orange.

Percentage purity. Find the mass of the pure compound from the titration. Then

Try it in Python

The program works out the molarity of an oxalic acid solution and the molarity of sodium hydroxide from three burette readings. It keeps only the concordant titres.

Common mistakes

• Rinsing the conical flask with the solution. It adds extra moles, and the titre is too small.
• Not removing the air bubble from the burette tip. The reading then counts a volume of air that is not delivered.
• Reading the top of the meniscus. For a colourless liquid, read the bottom.
• Using the wrong indicator. Methyl orange with a weak acid gives an end point that is too early.
• Forgetting the ratio. Oxalic acid needs two moles of sodium hydroxide for each mole.
• Weighing sodium hydroxide to make a standard solution. It is not a primary standard.

Remember these

• A primary standard is pure, stable and heavy. A standard solution is made in a volumetric flask.
• Rinse the burette and pipette with their own solutions, and the flask with water only.
• Concordant titres agree within $0.10\ \text{mL}$.
• Weak acid and strong base: phenolphthalein. Strong acid and weak base: methyl orange or methyl red.
• At the half-way point of a weak acid titration, pH equals $\text{p}K_a$.

References

• NCERT Chemistry Lab Manual for Class 11, the experiments on volumetric analysis.
• OpenStax Chemistry 2e, Chapter 14, section 14.7 Acid-Base Titrations.

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 the conical flask rinsed with distilled water and not with the solution it will hold?

2. Which indicator would you choose for a titration of ethanoic acid with sodium hydroxide? Why?

3. Why is sodium hydroxide not weighed to make a standard solution?

4. 20.00 mL of a hydrochloric acid solution needs 25.00 mL of a sodium hydroxide solution of concentration $0.0800\ \text{mol/L}$. What is the concentration of the acid?