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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

Solve for
%
g/mol
11,000
g/mol
11,000
  • 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.

Atom economy (%) current value 56 %
Mr totalTotal mass of reactantsKey driver
5.65,600
Mr desiredMass of desired product
11,000
  • 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

VariableTypical rangeLowest resultHighest resultSwing (%)Local stepChange in result
Mr total Total mass of reactants1 to 1,000 g/mol5.65,6005,594+10%−9.09 %
Mr desired Mass of desired product1 to 1,000 g/mol11,000999+10%+10 %

Sweep of Mass of desired product

Mass of desired product (g/mol)Atom economy (%)
11
2.3712.371
5.6235.623
13.3413.34
31.6231.62
74.9974.99
177.8177.8
421.7421.7
1,0001,000

Sweep one variable

Atom economy (%)Hover, touch, or use the arrow keys on the chart
02004006008001000 1520100500 Mass of desired product (g/mol), log scale now 56

Variables and how each one contributes

%

Atom economy

Result · %

What the equation gives you. Everything else feeds it.

Mr desired

Mass of desired product

g/mol · typical 1 to 1,000

Total Mr of the wanted product (CaO = 56). Directly proportional.

Mr total

Total mass of reactants

g/mol · typical 1 to 1,000

Sum of all reactant Mr values (CaCO₃ = 100). Inversely proportional.

Worked example with the values above

  1. Desired: 56; total reactants: 100.
  2. Ratio: 56 / 100 = 0.56.
  3. 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

Related formulas

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