Atom Economy Calculations

Atom economy measures how efficiently a chemical reaction converts reactant atoms into the desired product. Unlike percentage yield (which depends on experimental performance), atom economy is determined entirely by the balanced equation and is therefore a property of the reaction pathway itself.

The method

1. Write the balanced equation.
2. Identify the desired product.
3. Calculate the Mr of the desired product (multiplied by its coefficient if greater than 1).
4. Calculate the total Mr of all products (each multiplied by its coefficient).
5. Apply the atom economy formula.

The formula

atom economy = (Mr of desired product x its coefficient / total Mr of all products) x 100

Equivalently, since mass is conserved:

atom economy = (Mr of desired product x its coefficient / total Mr of all reactants) x 100

Worked examples

Example 1: Thermal decomposition of calcium carbonate

Question: Calculate the atom economy for producing calcium oxide from the thermal decomposition of calcium carbonate: CaCO3 -> CaO + CO2. The desired product is CaO. (Ar: Ca = 40, C = 12, O = 16)

Working:

• Mr of CaO = 56
• Total Mr of all products = Mr of CaO + Mr of CO2 = 56 + 44 = 100
• Atom economy = (56 / 100) x 100 = 56%

Answer: 56%

Examiner note: 44% of the mass ends up as CO2 waste. This is an inherent limitation of this reaction pathway.

Example 2: Neutralisation (high atom economy)

Question: Calculate the atom economy for producing sodium chloride: NaOH + HCl -> NaCl + H2O. The desired product is NaCl. (Ar: Na = 23, Cl = 35.5, O = 16, H = 1)

Working:

• Mr of NaCl = 58.5
• Total Mr of all products = 58.5 + 18 = 76.5
• Atom economy = (58.5 / 76.5) x 100 = 76.5%

Answer: 76.5%

Examiner note: Even a simple neutralisation does not achieve 100% atom economy because water is a by-product.

Example 3: Addition reaction (100% atom economy)

Question: Calculate the atom economy for the addition of hydrogen to ethene: C2H4 + H2 -> C2H6. The desired product is C2H6. (Ar: C = 12, H = 1)

Working:

• Mr of C2H6 = 30
• Total Mr of all products = 30 (only one product)
• Atom economy = (30 / 30) x 100 = 100%

Answer: 100%

Examiner note: Addition reactions have 100% atom economy because all reactant atoms end up in a single product. This is why addition reactions are preferred in green chemistry.

Example 4: Extraction of iron

Question: Calculate the atom economy for extracting iron from iron(III) oxide: Fe2O3 + 3CO -> 2Fe + 3CO2. The desired product is Fe. (Ar: Fe = 56, C = 12, O = 16)

Working:

• Mr of desired product = 2 x 56 = 112 (two moles of Fe)
• Total Mr of all products = (2 x 56) + (3 x 44) = 112 + 132 = 244
• Atom economy = (112 / 244) x 100 = 45.9%

Answer: 45.9%

Examiner note: More than half the product mass is CO2 waste. When comparing extraction methods, atom economy helps evaluate environmental impact.

Example 5: Comparing two routes to the same product

Question: Compare the atom economy of two routes to produce ethanol:

Route 1 (fermentation): C6H12O6 -> 2C2H5OH + 2CO2 Route 2 (hydration of ethene): C2H4 + H2O -> C2H5OH

(Ar: C = 12, H = 1, O = 16)

Working:

Route 1:

• Mr of desired product = 2 x 46 = 92
• Total Mr of all products = 92 + (2 x 44) = 92 + 88 = 180
• Atom economy = (92 / 180) x 100 = 51.1%

Route 2:

• Mr of desired product = 46
• Total Mr of all products = 46 (only one product)
• Atom economy = (46 / 46) x 100 = 100%

Answer: Route 1 = 51.1%, Route 2 = 100%

Examiner note: Route 2 (hydration) has a much higher atom economy. However, Route 1 uses a renewable feedstock (glucose from plants), so the comparison involves trade-offs. Examiners may ask you to discuss both atom economy and sustainability.

Common mistakes

1. Confusing atom economy with percentage yield. Atom economy comes from the equation. Percentage yield comes from experimental data. They measure different things.
2. Forgetting to multiply by coefficients. If the equation produces 2 moles of the desired product, use 2 x Mr, not just Mr.
3. Using only one product in the denominator. The total must include all products, not just the desired one.
4. Not identifying the desired product. The question must specify which product is desired. Read carefully.

When this appears

Atom economy is Extended tier content and appears on Paper 4. It connects to green chemistry and sustainability discussions. See the stoichiometry topic for context.