Balanced Equations, Atom Economy, and Percentage Yield
Quick Notes
- Balanced Equations ensure that the number of moles of each atom of each element remains the same on both sides of a reaction.
- Atom Economy (%) measures the efficiency of a reaction based on relative molecular masses of reactants and products:
- Percentage Yield (%) measures how much product is obtained compared to the theoretical maximum amount:
- High atom economy and high percentage yield are desirable in industry to maximise efficiency and reduce waste.
Full Notes:
Understanding Balanced Equations
Balanced equations ensure that the law of conservation of mass is obeyed – no atoms are lost or created during a reaction.
Steps to Balance a Chemical Equation
- Write down the unbalanced equation.
- Count the number of moles of atoms for each element in reactants and products.
- Adjust coefficients (big numbers in front of the formula) to balance atoms (never change the small number subscripts!).
- Check that the number of each atom type is equal on both sides.
It's important to understand that balanced equations show molar ratios.
For example, 0.5Cl2 means 0.5 moles worth of Cl2, it doesn't mean half a Cl2 molecule.
Unbalanced: H2 + O2 → H2O
- There are 2 moles of oxygen atoms in O2 but only 1 in H2O.
- To balance oxygen, place 2 moles of H2O molecules on the right: H2 + O2 → 2H2O
- Now there are 4 moles of hydrogen atoms on the right, so we need 2 moles of H2 molecules on the left: 2H2 + O2 → 2H2O
Balanced Equation: 2H2 + O2 → 2H2O
Understanding Atom Economy
Atom economy is a measure of a reactions efficiency - 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.
Formula for Atom Economy:
- Higher atom economy = more efficient process.
- Low atom economy = more waste, less sustainable.
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%. For example, Find the percentage atom economy for the production of ethanol (CH3CH2OH) from the reaction between ethene (CH2CH2) and water (H2O).
This reaction is 100% atom efficient because all reactants are converted into the desired product.
Understanding Percentage Yield
Percentage yield compares the actual amount of product obtained to the maximum possible amount (theoretical yield).
Unlike atom economy, percentage yield is calculated using experimental (actual) data.
Formula for Percentage Yield
Actual yield = Mass of product obtained in an experiment.
Theoretical yield = Maximum amount of product predicted by the balanced equation.
Matt’s Exam Tip - Remember that atom economy is theoretical and based on the balanced reaction equation whereas percentage yield is experimental and based on actual experimental data - it can’t be determined before a reaction has happened.
Steps to Calculate Percentage Yield
- Write the balanced chemical equation.
- Calculate the theoretical yield (use mole ratios).
- Compare actual and theoretical yields.
- Use the percentage yield formula.
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?
Why Percentage Yield is always Less Than 100%
In reality, percentage yields are rarely 100% because of:
- Incomplete reactions (some reactants don’t fully convert to products).
- Side reactions (other products may form).
- Loss of product during filtration, transfer, or evaporation.
Industrial Importance of Atom Economy and Percentage Yield
- Higher yield & atom economy = more efficient process giving lower costs and less waste.
- Low yield = more raw material needed giving higher costs and a potentially negative environmental impact.
- Pharmaceutical industry aims for high percentage yields to minimise expensive reactant waste.
Summary
- Balance equations by adjusting coefficients only; never change subscripts.
- Atom economy is theoretical and uses the balanced equation: Atom economy = (Mr of desired product ÷ total Mr of all reactants) × 100.
- Percentage yield is experimental: % yield = (actual yield ÷ theoretical yield) × 100.
- High atom economy and high percentage yield minimise waste and cost.
- Deviations from 100% yield arise from incomplete reactions, side reactions, and practical losses.