Atom economy calculations: formula and examples
Quantitative chemistry • Yield and atom economy
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Key concepts
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Definition of atom economy
Atom economy equals the percentage of the combined mass of reactants that ends up in the desired product. The calculation uses relative formula masses (Mr) and the balanced chemical equation so that all atoms are accounted for. A higher atom economy indicates fewer atoms form unwanted by-products, which reduces waste and improves resource efficiency.
Formula and calculation steps
Atom economy uses the formula: (Mr of desired product / sum of Mr of all reactants) × 100. Calculation steps follow: 1) Write the balanced equation so stoichiometric coefficients are correct. 2) Identify the desired product. 3) Calculate the Mr of the desired product and the Mr sum of all reactants (apply coefficients). 4) Substitute values into the formula and calculate the percentage. Correct use of the balanced equation is essential because coefficients change the mass contribution of each substance.
Worked example: hydration of ethene to ethanol
Reaction: C2H4 + H2O → C2H5OH. Mr(C2H4) = 28, Mr(H2O) = 18, total Mr reactants = 46. Mr(product C2H5OH) = 46. Substituting into the formula gives (46 / 46) × 100 = 100%. The cause is that all atoms from reactants become atoms in the desired product, and the effect is a perfect atom economy of 100%.
Worked example: chlorination of methane (one-step product)
Reaction: CH4 + Cl2 → CH3Cl + HCl, desired product = CH3Cl. Mr(CH4) ≈ 16, Mr(Cl2) ≈ 71, total Mr reactants ≈ 87. Mr(CH3Cl) ≈ 50.5. Substituting into the formula gives (50.5 / 87) × 100 ≈ 58.0%. The cause is formation of a significant by-product (HCl), and the effect is a lower atom economy because many atoms end up in the unwanted product.
Relation to green chemistry and limitations
High atom economy reduces waste and aligns with green chemistry principles by maximising useful product from reactants. Atom economy does not measure reaction yield, reaction rate, energy use, or safety; therefore, a process can have high atom economy but low yield or poor sustainability for other reasons. Limiting factors include necessary reagents that form unavoidable by-products, reaction conditions that require excess reagents, and separations that consume energy or generate waste.
Common pitfalls and clarifications
Common errors include using unbalanced equations, forgetting stoichiometric coefficients, and mixing percentage yield with atom economy. Percentage yield compares actual product mass to theoretical mass based on limiting reagent, while atom economy compares masses from a balanced equation regardless of how much product actually forms. Correct calculation requires relative formula masses and careful accounting of all reactants.
Key notes
Important points to keep in mind