Atom Economy Calculator
Inputs
| Molar Mass of Desired Product | 100 g/mol |
|---|---|
| Total Molar Mass of All Reactants | 180 g/mol |
Atom Economy Calculator
Calculate the atom economy of a reaction — the percentage of reactant mass that ends up in the desired product — using molar masses multiplied by stoichiometric coefficients.
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Details
This reaction has a low atom economy — less than 50% of the reactant mass becomes the desired product. A large fraction of starting materials is lost as by-products, which increases waste and cost.
Understanding atom economy
Atom economy measures how efficiently a chemical reaction uses its starting materials. Introduced by Barry Trost in 1991, it is one of the twelve principles of green chemistry. Rather than asking only whether a reaction works, atom economy asks how much of the input mass actually becomes the desired product and how much becomes waste.
A reaction that converts nearly all of its reactants into the target molecule is inherently cleaner and cheaper to run than one that discards most of them as by-products, regardless of how carefully the experiment is performed.
The atom economy formula
Atom Economy=MreactantsMproduct×100%where:
- is the molar mass of the desired product multiplied by its stoichiometric coefficient
- is the sum of (molar mass × stoichiometric coefficient) for every reactant in the balanced equation
The waste fraction follows directly:
W=100%−Atom Economy| Quantity | Meaning |
|---|---|
| Stoichiometrically weighted molar mass of the desired product (g/mol) | |
| Total stoichiometrically weighted molar mass of all reactants (g/mol) | |
| Atom Economy | Fraction of reactant mass incorporated into the product (%) |
| Waste Fraction | Fraction of reactant mass lost to by-products (%) |
Worked example
Consider the synthesis of ethanol by hydration of ethylene:
C2H4+H2O→C2H5OHThe reactant molar masses are 28.05 g/mol (ethylene) and 18.02 g/mol (water), giving a total of 46.07 g/mol. The product ethanol has a molar mass of 46.07 g/mol.
MreactantsMproductAtom Economy=28.05+18.02=46.07 g/mol=46.07 g/mol=46.0746.07×100%=100%This is an addition reaction — every atom in the reactants ends up in the product — so the atom economy is 100%.
Compare that with the Grignard synthesis of an alcohol, which uses reagents, a solvent, and produces a magnesium salt as a by-product. The wasted mass lowers the atom economy well below 100% even though the desired alcohol can be isolated in high yield.
Atom economy vs. percent yield
These two metrics measure different things:
| Atom Economy | Percent Yield | |
|---|---|---|
| What it measures | How much of the reactant mass can become product | How much of the possible product was obtained |
| Depends on | The balanced equation only | Experimental conditions |
| Can be 100% | Yes, for addition/rearrangement reactions | Yes, in principle |
| Reflects waste from by-products | Yes | No |
A reaction can have a 95% yield but a 20% atom economy — meaning only one fifth of the starting materials contributed to the product, even though almost all of that theoretical product was collected. Both metrics together give a fuller picture of efficiency.
Reaction types ranked by atom economy
Addition reactions combine all reactants into one product, so their atom economy is always 100%. Rearrangement reactions reorganize atoms within a molecule and also achieve 100%. Substitution reactions produce a by-product alongside the desired molecule, giving an atom economy between 0% and 100% that depends on the relative molar masses. Elimination reactions expel a small molecule — often water or HX — as waste, typically giving moderate atom economies. Multi-step syntheses multiply the inefficiencies of each step, so a long synthetic route through several low-atom-economy transformations can waste most of the starting material even when each individual yield is acceptable.
Practical implications
Raw material cost scales with the mass of reactants purchased, not with the mass of product collected. When atom economy is low, the reaction consumes extra starting materials and generates extra waste, both of which increase cost. Waste disposal — especially for hazardous by-products — can exceed the cost of the starting materials themselves. For industrial processes, improving atom economy by even a few percent across millions of kilograms of product per year translates into substantial savings and a smaller environmental footprint.
Frequently Asked Questions (FAQ)
What is the atom economy formula?
Atom economy = (molar mass of desired product ÷ total molar mass of all reactants) × 100%. Each molar mass is first multiplied by its stoichiometric coefficient in the balanced equation. For example, if a reaction uses 180 g/mol of reactants and produces 100 g/mol of the wanted product, the atom economy is (100 ÷ 180) × 100% ≈ 55.6%.
How does atom economy differ from percent yield?
Atom economy is a theoretical measure of how much of the starting-material mass can, in principle, end up in the desired product — it depends only on the balanced equation, not on how the reaction is run. Percent yield measures how much of the theoretically possible product was actually obtained in a specific experiment. A reaction can have a high percent yield but a low atom economy if the balanced equation itself produces large amounts of by-products.
Why does atom economy matter in green chemistry?
Atom economy is one of the twelve principles of green chemistry, introduced by Trost in 1991. It quantifies waste at the molecular level: every atom that does not end up in the desired product must be disposed of, treated, or recycled, all of which cost money and energy and generate environmental impact. Reactions with high atom economy reduce raw-material consumption, lower waste-disposal costs, and decrease the overall environmental footprint of a chemical process.
Which reaction types have high vs. low atom economy?
Addition reactions, where two or more molecules combine to form a single product with no atoms left over, have the highest possible atom economy of 100%. Rearrangement reactions also tend to be close to 100%. Substitution reactions produce one product and one by-product, giving a lower atom economy that depends on the molecular weights involved. Elimination reactions, which produce a small molecule such as water as a by-product, typically have moderate atom economies. Multi-step syntheses accumulate the losses of each step, so a long route through low-atom-economy steps can waste the majority of starting material.
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