Experimental Errors, Yield, and Atom Economy

Specification Reference Topic 5: Formulae, Equations and Amounts of Substance (Points 12–16)

Quick Notes

Uncertainty = half the smallest division on a measuring instrument.
% Uncertainty = (uncertainty ÷ reading) × 100
Errors can come from measurement mistakes or method limitations, such as heat loss or incomplete reactions.
Percentage yield compares actual product made to the theoretical maximum.

Edexcel A-Level Chemistry box formula showing percentage yield equals actual yield divided by theoretical yield times 100.

Atom economy shows how much of the reactants become the desired product, based on the balanced reaction equation.

Edexcel A-Level Chemistry box formula showing atom economy equals Mr of desired product over total Mr of all products times 100.

Observations and equations for reactions must match e.g., precipitate = solid (s) forms, effervescence = gas (g) given off.

Full Notes

Measurement Uncertainty

Every measuring instrument has an uncertainty, usually ± the smallest scale division.

Burette reading: ±0.05 cm³ per reading
Balance reading: ±0.01 g
Thermometer: ±0.5 °C

Because of this, all experiments and data values have a certain degree of uncertainty. It is more useful to express the uncertainty in experimental values as percentages.

% Uncertainty formula: % uncertainty = (absolute uncertainty ÷ measured value) × 100

where:

absolute uncertainty is the uncertainty of the apparatus (for example ±0.5)
measured value is the measurement made using the apparatus

Matt’s exam tip

If you take two readings to get a single measurement (e.g. temperature change or titre volume), the absolute uncertainty doubles because the instrument is used twice. This is especially important in titrations, where the burette is read at both the start and end.

Example Applying percentage uncertainty to a titre

If titre volume = 25.0 cm³ (burette uncertainty ±0.05 cm³ per reading):

Total uncertainty = ±0.10 cm³
% uncertainty = (0.10 ÷ 25.0) × 100 = 0.40%

Reducing Percentage Uncertainty

You can’t change the absolute uncertainty of a piece of apparatus however you can reduce percentage uncertainty by:

Use larger volumes or masses.
Changing the apparatus (e.g., a balance with more decimal places).

Sources of Error

There are lots of potential sources of error in an experiment. Common examples include:

Heat loss in calorimetry and enthalpy change experiments.
Product loss during isolation and purification.
Side reactions forming undesired products.
Incomplete reaction or impure reactants.

Percentage Yield

Percentage yield compares the actual amount of product obtained to the maximum possible amount (theoretical yield).

Worked Example

Simple Percentage Yield Calculation
In the reaction: Mg + 2HCl → MgCl₂ + H₂, if 2.40 g of Mg is reacted with excess HCl, and only 5.80 g of MgCl₂ is obtained, what is the percentage yield?

Atom Economy

Atom economy is a measure of a reactions efficiency. Essentially how much of the reactants end up as the desired product rather than waste.

Atom economy is theoretical, it is based only on the balanced reaction equation it isn’t based on experimental data.

Edexcel A-Level Chemistry formula graphic for atom economy equals Mr of desired product divided by total Mr of products times 100.

Worked Example

Calculating Atom Economy
Find the percentage atom economy for the production of Iron (Fe) from the reaction between Iron (III) Oxide and Carbon Monoxide.

If there is only one product in the reaction, then the atom economy must be 100%.

Example Ethanol from ethene and water

Find the percentage atom economy for the production of ethanol (CH₃CH₂OH) from the reaction between ethene (CH₂CH₂) and water (H₂O).

Edexcel A-Level Chemistry example showing 100% atom economy for hydration of ethene to ethanol.

This reaction is 100% atom efficient because all reactants are converted into the desired product.

Matt’s exam tip

Remember that atom economy and percentage yield are different. Just because a reaction has a 100% atom economy doesn’t mean it will have a high yield. Ideally, a reaction would have a high atom economy and the practical process used would give a high percentage yield.

Relating Equations to Observations

It is important to able to relate observations in the real world to written reactions and equations.

Displacement reactions

Observation: Colour change or solid metal forms

Example:
Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s)

Acid reactions

Observation: Effervescence (CO₂ or H₂), temperature change

Examples:
HCl(aq) + Mg(s) → MgCl₂(aq) + H₂(g)
2HCl(aq) + CaCO₃(s) → CaCl₂(aq) + CO₂(g) + H₂O(l)

Precipitation reactions

Observation: Formation of a solid from two solutions

Example:
AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)

Always include state symbols and match observations to the type of reaction.

Summary

Uncertainty comes from instrument resolution and is best compared using percentage uncertainty.
Percentage uncertainty can be reduced by using larger measurements or more precise apparatus.
Common errors include heat loss, product loss, side reactions and incomplete reaction.
Percentage yield compares actual to theoretical yield.
Atom economy measures how efficiently reactants become the desired product.
Observations such as effervescence or precipitate must align with state symbols in equations.