Atom Economy Calculator (green chemistry: % of reactant atoms in the product)

Understanding the atom economy calculator — concept and principle

Atom economy measures how much of the mass of the reactants ends up in the desired product, assuming the balanced equation goes to completion. It is a core metric of green chemistry, used to compare synthetic routes by how much waste they inherently produce.

How it is calculated

• Atom economy (%) = (coefficient × M of the desired product) ÷ Σ(coefficient × M of each reactant) × 100.
• By-product (waste) mass = reactant mass − desired product mass.
• Waste per kg of product = by-product mass ÷ product mass.
• Atom economy × yield gives a rough overall mass efficiency.

The principle

Barry Trost introduced atom economy in 1991 to highlight that a reaction can have a 100% yield and still waste much of its starting material, if most atoms leave as by-products. Mass is conserved, so whatever is not in the desired product leaves as something else. Addition and rearrangement reactions can reach 100%; substitutions and eliminations always produce a by-product. Atom economy depends only on the equation, not on lab technique.

Worked example

Default inputs: Fischer esterification, acetic acid (60.05 g/mol) + ethanol (46.07 g/mol) → ethyl acetate (88.11 g/mol) + water; yield 100%.

1. Reactant mass = 60.05 + 46.07 = 106.12 g per mol of reaction.
2. Desired product mass = 88.11 g.
3. Atom economy = 88.11 ÷ 106.12 × 100 ≈ 83%.
4. By-product (water) = 106.12 − 88.11 = 18.01 g; waste per kg of product = 18.01 ÷ 88.11 ≈ 0.204 kg.
5. With 100% yield, atom economy × yield = 83%. 2 reactants counted.

How to read the result

Higher is better: 83% means 17% of the reactant mass becomes water. Compare routes to the same product: a route with fewer protecting groups or stoichiometric reagents usually scores higher. Atom economy ignores solvents, catalysts and excess reagents; metrics such as the E-factor and process mass intensity capture those.

Common mistakes

• Using an unbalanced equation.
• Forgetting coefficients when a reactant appears twice.
• Including catalysts as reactants.
• Treating atom economy as the actual yield.

Frequently asked questions

How do you calculate atom economy?

Divide the molar mass of the desired product (times its coefficient) by the total molar mass of the reactants, then multiply by 100.

What reactions have 100% atom economy?

Additions and rearrangements, where all reactant atoms end up in the product.

How is atom economy different from percent yield?

Yield measures how much product you actually got; atom economy measures how much of the reactant mass could ever end up in it.

Sources: Trost, B. M. (1991). The Atom Economy—A Search for Synthetic Efficiency. Science, 254(5037), 1471–1477. · Anastas, P. T. & Warner, J. C. (1998). Green Chemistry: Theory and Practice. Oxford University Press