Titrations and Solution Calculations: AQA A-Level Chemistry 3.1.2

Solutions are formed when a solute dissolves in a solvent. Because we measure solutions by volume rather than mass, we use concentration to link solution volumes with amount in moles.

Concentration Equations

Concentration is the amount of solute dissolved in a unit volume of solution. It can be expressed in two ways:

Moles per cubic decimeter (\( \text{mol dm}^{-3} \))
Grams per cubic decimeter (\( \text{g dm}^{-3} \))

\[ n = \frac{C \times V}{1000} \]

Where:

\( n \) = amount of substance in moles (\( \text{mol} \))
\( C \) = concentration in moles per cubic decimeter (\( \text{mol dm}^{-3} \))
\( V \) = volume of solution in cubic centimeters (\( \text{cm}^3 \))

🔑 Key Principle

To convert from \( \text{mol dm}^{-3} \) to \( \text{g dm}^{-3} \), multiply the concentration by the relative molecular mass (\( M_r \)) of the solute: \[ \text{Concentration in g dm}^{-3} = \text{Concentration in mol dm}^{-3} \times M_r \]

Preparing a Standard Solution

A standard solution is a solution of known concentration. Preparing one is the first part of AQA Required Practical 1 (RP1):

Weigh the solute in a weighing boat on a balance.
Transfer the solid to a beaker and reweigh the weighing boat (weighing by difference).
Dissolve the solid in a beaker using distilled water, stirring with a glass rod.
Transfer the solution to a volumetric flask using a funnel. Rinse the beaker, glass rod, and funnel with distilled water and transfer the washings to the flask.
Fill the flask with distilled water until the bottom of the meniscus lies exactly on the graduation mark. Use a pipette for the last few drops.
Stopper the flask and invert it several times to ensure thorough mixing.

Titration Calculations

A titration is used to find the concentration of an unknown solution by reacting it with a standard solution. The three-step roadmap below outlines the titration calculation process:

✏️ Worked Example 1: Titration Calculation

A student performs a titration to find the concentration of a sulfuric acid solution. They find that \( 25.0 \text{ cm}^3 \) of \( 0.100 \text{ mol dm}^{-3} \) sodium hydroxide (\( \text{NaOH} \)) requires exactly \( 20.0 \text{ cm}^3 \) of sulfuric acid (\( \text{H}_2\text{SO}_4 \)) to reach the neutralisation point. Calculate the concentration of the sulfuric acid. \[ 2\text{NaOH(aq)} + \text{H}_2\text{SO}_4\text{(aq)} \to \text{Na}_2\text{SO}_4\text{(aq)} + 2\text{H}_2\text{O(l)} \]

Step 1: Calculate the moles of sodium hydroxide used.

\[ n(\text{NaOH}) = \frac{C \times V}{1000} = \frac{0.100 \times 25.0}{1000} = 2.50 \times 10^{-3} \text{ mol} \]

Step 2: Use the reaction stoichiometry to find the moles of sulfuric acid.

The equation shows that \( 2 \text{ moles of NaOH} \) react with \( 1 \text{ mole of } \text{H}_2\text{O}_4 \). The ratio is \( 2 : 1 \).

\[ n(\text{H}_2\text{SO}_4) = \frac{2.50 \times 10^{-3}}{2} = 1.25 \times 10^{-3} \text{ mol} \]

Step 3: Calculate the concentration of the sulfuric acid.

\[ C(\text{H}_2\text{SO}_4) = \frac{n \times 1000}{V} = \frac{1.25 \times 10^{-3} \times 1000}{20.0} = 0.0625 \text{ mol dm}^{-3} \]

📝 AQA Examiner Tip

When selecting results to calculate the mean titre, only use concordant titres. Concordant titres are those within \( 0.10 \text{ cm}^3 \) of each other. Never include a rough titration titre in your mean titre calculation!

Percentage Uncertainty in Measurements

Every piece of apparatus used in a titration has an uncertainty. You must be able to calculate the percentage uncertainty associated with a measurement using the formula:

\[ \text{Percentage Uncertainty} = \frac{\text{Absolute Uncertainty} \times \text{Number of Readings}}{\text{Measured Value}} \times 100 \]

✏️ Worked Example 2: Uncertainty in Burette Titres

A burette has an absolute uncertainty of \( \pm 0.05 \text{ cm}^3 \) for each reading. A student performs a titration and delivers a titre volume of \( 20.00 \text{ cm}^3 \). Calculate the percentage uncertainty for this titre.

Note: A titre volume requires two readings: an initial volume reading and a final volume reading. Therefore, the number of readings is 2.

\[ \text{Total Absolute Uncertainty} = 2 \times 0.05 = 0.10 \text{ cm}^3 \]

\[ \text{Percentage Uncertainty} = \frac{0.10}{20.00} \times 100 = 0.50\% \]

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