Library / Foundations: Chemistry / FCH-09
Foundations: Chemistry
Atom economy
The share of reactant mass that ends up in the useful product.
- Ref
- FCH-09
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- % [%]
AE is atom economy as a percentage, Mr,d the desired product and ΣMr,R the sum over all reactants. Use relative formula masses multiplied by the coefficients in the balanced equation. Atom economy is about the reaction design, not how well it was carried out in the lab.
It shows how much of what you put in is turned into what you want rather than waste.
Calculator
- Mass of waste per 100 g of reactants44 g
- Atom economy as a fraction0.56
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Addition reactions that put every atom into the product have 100% atom economy.
- A reaction can have a high yield and still waste most of the atoms if the by-product is large.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (%) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Mr total Total mass of reactants | 1 to 1,000 g/mol | 5.6 | 5,600 | 5,594 | +10% | −9.09 % |
| Mr desired Mass of desired product | 1 to 1,000 g/mol | 1 | 1,000 | 999 | +10% | +10 % |
Sweep of Mass of desired product
| Mass of desired product (g/mol) | Atom economy (%) |
|---|---|
| 1 | 1 |
| 2.371 | 2.371 |
| 5.623 | 5.623 |
| 13.34 | 13.34 |
| 31.62 | 31.62 |
| 74.99 | 74.99 |
| 177.8 | 177.8 |
| 421.7 | 421.7 |
| 1,000 | 1,000 |
Sweep one variable
Variables and how each one contributes
Atom economy
What the equation gives you. Everything else feeds it.
Mass of desired product
Total Mr of the wanted product (CaO = 56). Directly proportional.
Total mass of reactants
Sum of all reactant Mr values (CaCO₃ = 100). Inversely proportional.
Worked example with the values above
- Desired: 56; total reactants: 100.
- Ratio: 56 / 100 = 0.56.
- Atom economy = 56 % (CaCO₃ → CaO + CO₂).
Assumptions and limits
- Balanced equation used.
- Single desired product.
Common mistakes
- Forgetting the coefficients.
- Mixing it up with percentage yield.
Statistics and uncertainty
Atom economy is calculated, not measured, so it carries no experimental error beyond the Ar values used.
Where it is used
- Choosing sustainable synthesis routes.
- Waste reduction in manufacture.
Maths you need
- Relative formula mass: Mr
- Balanced equations: coefficients