Quantitative Analysis: Acid-Base Titrations

Note on indicators: OCR requires you to use specific indicators like phenolphthalein (pink in alkali, colourless in acid) or methyl orange (yellow in alkali, red in acid). Universal indicator is explicitly not suitable because it produces a gradual colour change rather than a single, sharp shift at the exact point of neutralisation. A white tile is placed under the flask to make this sharp change easier to see, and the flask must be continuously swirled to ensure thorough mixing.

Calculating the Mean Titre

You wouldn't trust a single measurement to build a house, and chemists do not trust a single titration run either. Burette readings must be highly precise, recorded to two decimal places and always ending in '0' or '5' (e.g., $23.40\text{ cm}^3$ or $23.45\text{ cm}^3$).

To find an accurate average volume, you must repeat the titration until you get concordant results. These are titre volumes that are within $0.10\text{ cm}^3$ of each other. The initial "rough" trial is strictly excluded from your mean calculation unless it coincidentally falls within this $0.10\text{ cm}^3$ range.

The Concentration Formula

To calculate an unknown concentration from your titration results, you need the fundamental relationship between moles, concentration, and volume:

$$n = c \times V$$

Where $n$ is the number of moles ($\text{mol}$), $c$ is the concentration ($\text{mol/dm}^3$), and $V$ is the volume measured in a decimetre cubed (dm³).

Because burettes measure volume in $\text{cm}^3$, you must always divide your volume by $1000$ to convert $\text{cm}^3$ to $\text{dm}^3$.

Often, exam questions will ask for the concentration in $\text{g/dm}^3$ rather than $\text{mol/dm}^3$. To convert a molar concentration to a mass concentration, simply multiply your $\text{mol/dm}^3$ answer by the solute's relative formula mass (Mᵣ).

Stoichiometry in Titrations

You cannot assume one mole of acid always reacts with exactly one mole of alkali. Stoichiometry refers to the exact molar ratio of reactants and products, shown by the large numbers (coefficients) in a balanced chemical equation.

While hydrochloric acid ($HCl$) and sodium hydroxide ($NaOH$) react in a simple 1:1 ratio, a diprotic acid like sulfuric acid ($H_2SO_4$) requires two moles of alkali to neutralise it, creating a 1:2 ratio. You must use this molar ratio from the balanced equation to link the moles of your known solution to your unknown solution.

Worked Example: Multi-Step Titration Calculation

25.0 cm³ of sulfuric acid ($H_2SO_4$) of unknown concentration was titrated against a 0.150 mol/dm³ potassium hydroxide ($KOH$) standard solution. The mean titre of $KOH$ added from the burette was 24.80 cm³. Calculate the concentration of the acid in mol/dm³ and g/dm³.

Step 1: Write the balanced symbol equation to find the mole ratio.

$$H_2SO_4(aq) + 2KOH(aq) \rightarrow K_2SO_4(aq) + 2H_2O(l)$$

(The stoichiometric ratio of $H_2SO_4 : KOH$ is $1 : 2$)

Step 2: Calculate the moles of the known solution ($KOH$).

• Convert volume to $\text{dm}^3$: $V = 24.80 \div 1000 = 0.0248\text{ dm}^3$
• Use the formula:

Step 3: Use the stoichiometry ratio to find the moles of the unknown ($H_2SO_4$).

• The ratio is $1:2$, meaning we need exactly half the amount of acid.
• $n(\text{acid}) = 0.00372 \div 2 = 0.00186\text{ mol of }H_2SO_4$

Step 4: Calculate the concentration of the unknown acid in mol/dm³.

• Convert acid volume to $\text{dm}^3$: $V = 25.0 \div 1000 = 0.025\text{ dm}^3$
• Rearrange formula to

Step 5: Convert the final concentration to g/dm³.

• Calculate $M_r$ of $H_2SO_4$: