Yields, atom economy and experimental errorsEdexcel A-Level Chemistry: Revision notes

Every measurement has an uncertainty, the interval within which the true value is expected to lie. Apparatus uncertainties are often given as ±: for example a burette ±0.05 cm³ per reading, a 25.0 cm³ pipette ±0.06 cm³, a balance ±0.001 g per reading.

Percentage uncertainty = (absolute uncertainty ÷ measured value) × 100.

When a value is found from two readings (a titre, or a mass by difference) the absolute uncertainties add: a titre has ±0.10 cm³, so for 20.00 cm³ the percentage uncertainty is 0.10 ÷ 20.00 × 100 = 0.50%.

Percentage error compares the result with an accepted value: (|result − accepted value| ÷ accepted value) × 100.

Random errors cause scatter in repeats and are reduced by repeating and averaging. Systematic errors, such as a balance that is not zeroed or heat lost in calorimetry, shift every result the same way and are not reduced by repeating.

To reduce percentage uncertainty:

• use a larger quantity, because the same absolute uncertainty is a smaller fraction;
• use apparatus with a smaller uncertainty, such as a balance reading to 0.001 g or a pipette instead of a measuring cylinder;
• weigh by difference, noting that this doubles the absolute uncertainty.

If the difference between a result and the accepted value is larger than the total percentage uncertainty, a systematic error is probably present. Quantities in excess, such as acid in excess, do not need to be measured precisely.

The percentage yield compares the mass of product actually obtained with the maximum possible:

percentage yield = (actual mass ÷ theoretical mass) × 100.

Worked example: 5.00 g of salicylic acid (138.0 g mol⁻¹) gives 4.80 g of aspirin (180.0 g mol⁻¹), 1 : 1. n = 5.00 ÷ 138.0 = 0.0362 mol; theoretical mass = 0.0362 × 180.0 = 6.52 g; yield = 4.80 ÷ 6.52 × 100 = 73.6%.

Yields are below 100% because of incomplete reactions, side reactions, losses in transferring and purifying, and equilibrium.

Percentage atom economy = (molar mass of desired product ÷ sum of molar masses of all products) × 100.

It is calculated from the balanced equation alone. It measures how much of the reactant mass ends up as the desired product, so a high atom economy means less waste. It is not the same as yield: a reaction can have a high yield but a low atom economy.

Worked example: CH₄ + H₂O → CO + 3H₂. Desired product H₂ = 3 × 2.0 = 6.0. Total products = 28.0 + 6.0 = 34.0. Atom economy = 6.0 ÷ 34.0 × 100 = 17.6%.

Addition reactions, in which everything joins into one product, have an atom economy of 100%. Uses for by-products raise the sustainability of a process.

A hazard is something with the potential to cause harm; a risk is the chance that the harm occurs, combined with its severity. In practical work:

• identify the hazards (for example irritant 2.0 mol dm⁻³ HCl, corrosive concentrated acids, flammable solvents, hot apparatus, glassware, gas pressure);
• decide how likely and how serious harm is;
• choose precautions: eye protection, gloves, a fume cupboard for toxic fumes, heating flammable liquids with a water bath, supporting glassware, not sealing a flask that is heated or producing gas.

A good risk assessment concludes whether the risk is acceptably low once the precautions are taken.