What atom economy measures
Atom economy, introduced by Barry Trost in 1991, measures how much of the mass of the reactants ends up in the desired product, assuming a perfect yield. It is one of the twelve principles of green chemistry: a reaction with high atom economy wastes fewer atoms as by-products.
Atom economy (%) = (molar mass of desired product × its coefficient) ÷ (sum of molar masses of all reactants × their coefficients) × 100
The equation must be balanced. Catalysts are not counted, because they are not consumed, but solvents and reagents that end up as by-products are.
Example: making iron
In a blast furnace, Fe₂O₃ + 3 CO → 2 Fe + 3 CO₂.
- Desired product: 2 × 55.845 = 111.69 g of iron.
- Reactants: 159.69 + 3 × 28.01 = 243.72 g.
- Atom economy = 111.69 ÷ 243.72 × 100 ≈ 45.8%.
More than half of the reactant mass leaves as carbon dioxide: about 1.18 kg of by-product for each kilogram of iron.
Typical values
| Reaction type | Atom economy |
|---|---|
| Addition (e.g. hydrogenation, Diels-Alder) | 100% |
| Rearrangement | 100% |
| Substitution | moderate |
| Elimination | moderate to low |
| Wittig reaction | often under 30% |
A classic case: ibuprofen
The original Boots process for ibuprofen took six steps and had an atom economy of about 40%. The BHC process, developed in the 1990s, takes three catalytic steps and reaches about 77%, or almost 99% when the acetic acid by-product is recovered. It won a Presidential Green Chemistry Challenge Award.
Atom economy versus yield
Yield tells you how much product you actually obtained compared with the theoretical maximum. Atom economy tells you how much waste the reaction makes even when it works perfectly. A reaction can have a 95% yield and still produce more waste than product. Multiplying the two gives a quick measure of overall efficiency.
Other green metrics
- E-factor (Roger Sheldon): kilograms of waste per kilogram of product, including solvents and losses. Pharmaceuticals often have E-factors of 25 to over 100.
- Reaction mass efficiency: the mass of product divided by the mass of all reactants actually used, accounting for yield and excess reagents.