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Green Chemistry Metrics Calculator
In short: This green chemistry calculator works out atom economy from a balanced equation, with molar masses from the formulas, and then percent yield, E-factor, process mass intensity (PMI), reaction mass efficiency (RME) and carbon efficiency from the masses you used. It includes the Boots and BHC ibuprofen routes, a Diels-Alder reaction and a Wittig reaction. It is free and works in your web browser.
Type a balanced equation with formulas such as C5H6 + C4H2O3 → C9H8O3 and pick the desired product to get the atom economy. Add the mass of each reactant, the mass of product you isolated and any solvents, water, reagents or catalysts to get the waste metrics.
Other materials used (solvents, water, reagents, catalysts)
Green chemistry metrics and formulas
Atom economy (%) = ν × M(desired product) / Σ ν × M(reactants) × 100
Percent yield (%) = actual mass / theoretical mass × 100 RME (%) = mass of product / Σ mass of reactants × 100
E-factor = (total mass in − mass of product) / mass of product PMI = total mass in / mass of product = E-factor + 1
Carbon efficiency (%) = mol of C in product / mol of C in reactants × 100
| Metric | Based on | Ideal | What it misses |
|---|---|---|---|
| Atom economy | Balanced equation | 100% | Yield, excess reagents, solvents |
| Percent yield | Lab result | 100% | By-products and other waste |
| Reaction mass efficiency | Masses of reactants and product | 100% | Solvents and work-up |
| Carbon efficiency | Carbon atoms in and out | 100% | Non-carbon waste such as salts |
| E-factor (simple) | All inputs except solvents and water | 0 | Solvent waste |
| E-factor (complete) and PMI | Every material used | 0 and 1 | Hazard and energy use |
Typical E-factors by industry
| Sector | Annual output (tonnes) | E-factor (kg waste/kg product) |
|---|---|---|
| Oil refining | 10⁶ to 10⁸ | under 0.1 |
| Bulk chemicals | 10⁴ to 10⁶ | under 1 to 5 |
| Fine chemicals | 10² to 10⁴ | 5 to over 50 |
| Pharmaceuticals | 10 to 10³ | 25 to over 100 |
The 12 principles of green chemistry
- Prevention: avoid making waste rather than treating it.
- Atom economy: build as much of the reactants as possible into the product.
- Less hazardous syntheses: use and make substances with little toxicity.
- Safer chemicals: design products that work but are less toxic.
- Safer solvents and auxiliaries: use fewer and safer solvents.
- Energy efficiency: run reactions near room temperature and pressure.
- Renewable feedstocks: use raw materials from biomass where practical.
- Reduce derivatives: avoid protecting groups and other temporary steps.
- Catalysis: catalysts beat stoichiometric reagents.
- Design for degradation: products should break down harmlessly after use.
- Real-time analysis: monitor reactions to stop pollution before it forms.
- Accident prevention: choose substances and conditions that cut the risk of fires, explosions and releases.
Worked examples
Esterification
CH₃COOH + C₂H₅OH → CH₃COOC₂H₅ + H₂O. 60.05 + 46.07 = 106.12 g/mol in, 88.11 g/mol of ester out.
12.0 g acid and 11.5 g ethanol give 13.2 g ester (theoretical 17.6 g).
AE 83.0%, yield 75.0%, RME 56.2%
Diels-Alder
Cyclopentadiene + maleic anhydride → adduct: C₅H₆ + C₄H₂O₃ → C₉H₈O₃.
66.10 + 98.06 = 164.16 g/mol, the same as the product.
AE 100%
Wittig reaction
Ph₃P=CH₂ + cyclohexanone → methylenecyclohexane + Ph₃PO.
96.17 / (276.32 + 98.14) × 100. Triphenylphosphine oxide (278.29 g/mol) is waste.
AE 25.7%
Ibuprofen: Boots route (6 steps)
Reagents over all steps: C₁₀H₁₄, C₄H₆O₃, C₄H₇ClO₂, C₂H₅ONa, H₃O⁺, NH₂OH and 2H₂O = 515.0 g per 206.3 g of ibuprofen.
AE 40.1%
Ibuprofen: BHC route (3 steps)
C₁₀H₁₄ + C₄H₆O₃ + H₂ + CO → C₁₃H₁₈O₂ + CH₃COOH. 266.3 g in per 206.3 g out.
AE 77.5% (often quoted as 77%; about 99% with acetic acid recovered)
E-factor and PMI
Esterification above with 1.0 g H₂SO₄, 20 g carbonate solution and a 50 g water wash: 94.5 g in, 13.2 g out.
Complete E-factor 6.16, PMI 7.16
Common mistakes
- Using an unbalanced equation. Coefficients change the reactant mass. Balance first.
- Confusing atom economy with yield. A 95% yield Wittig reaction still wastes about three quarters of the reactant mass.
- Counting catalysts and solvents in atom economy. They are left out of AE but belong in the E-factor and PMI.
- Forgetting the coefficient of the product. If the equation makes 2 mol of product, use 2 × M in the top line.
- Mixing simple and complete E-factors. Say whether solvents and water are included. They often dominate the total.
- Using the excess reagent for the theoretical yield. The theoretical yield comes from the limiting reagent.
Comparing synthetic routes? Draw each route, with reagents over the arrows, in MolDraw, a free online chemical structure editor.
Open MolDraw editorFrequently asked questions
What is atom economy and how is it calculated?
Atom economy is the percentage of the mass of all reactants that ends up in the desired product, assuming 100% yield. Atom economy = (coefficient × molar mass of desired product) / (sum of coefficient × molar mass of all reactants) × 100. For CH3COOH + C2H5OH → CH3COOC2H5 + H2O it is 88.11 / 106.12 × 100 = 83.0%.
What is the difference between atom economy and percent yield?
Atom economy comes from the balanced equation alone and says how much of the reactant mass can end up in the product. Percent yield is measured in the lab and says how much product you actually got compared with the theoretical yield. A reaction can have 100% yield and still a low atom economy, as the Wittig reaction does.
What is a good E-factor?
Lower is better and the ideal is 0. Typical values are under 0.1 for oil refining, under 1 to 5 for bulk chemicals, 5 to over 50 for fine chemicals and 25 to over 100 for pharmaceuticals. Most of the waste in fine chemicals and drugs is solvent.
How is process mass intensity related to the E-factor?
PMI is the total mass of everything used divided by the mass of product. The complete E-factor is the mass of waste divided by the mass of product. Since waste = total input − product, PMI = E-factor + 1.
Why does the Diels-Alder reaction have 100% atom economy?
It is an addition: the diene and the dienophile join into one product and nothing is lost. For cyclopentadiene + maleic anhydride, 66.10 + 98.06 = 164.16 g/mol, exactly the molar mass of the adduct. Rearrangements and most additions also reach 100%.
Why is the BHC ibuprofen synthesis greener than the Boots synthesis?
The Boots route takes six steps and has an atom economy of about 40%. The BHC route takes three catalytic steps and reaches 77.5%, and about 99% when its acetic acid by-product is recovered. It also produces far less waste salt and uses recyclable catalysts.
What is reaction mass efficiency?
RME is the mass of product isolated divided by the total mass of reactants used, times 100. It combines atom economy, yield and the use of excess reagents in one number: RME = atom economy × yield ÷ excess factor.
Related chemistry tools
Want the full method with more examples? Read the green chemistry metrics guide. Need to sketch molecules for a report? Draw chemical structures online with MolDraw.
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