Atom is economy is defined as the % of atoms in the reagents which are present in the product (measured by RMM, rather than the number of atoms). This metric only requires a balanced equation and can be measured before any lab work. It does not take into account solvent, the use of excess reagents or catalysts. Likewise work-up reagents and solvents are ignored. However, it is very useful to evaluate different routes to the same molecule.

Calculating atom economy

The calculation for 

Examples

Diels-Alder

Michael addition

Both these reactions are addition reactions, a class of reactions which have 100% AE. However, most reactions have AE less than 100%.

Friedel Crafts acylation

The Friedel Crafts acylation of aromatics can be carried out (in principle at least) with acid chlorides, anhydrides and acids. Each gives a different AE:

AE (X = Cl) = 150 / (108 + 78.5) = 80.4%

AE (X = OAc) = 150 / (108 + 102) = 71.4%

AE (X = OH) = 150 / (108 + 60) = 89.3%

So here we can use AE to evaluate the attractiveness of these three options for making our product. Using ethanoic acid gives the highest atom economy, and therefore (other things being equal) the cleanest reaction. It also gives water as a by-product, which is also better than HCl or ethanoic acid, the products form the other reagents. However, it is the least reactive of the three and thus may require more energy or a more powerful catalyst.

Swern oxidation

The Swern Oxidation is an old but widely used method for the oxidation of primary alcohols to aldehydes, which requires the use of dimethyl sulfoxide, oxalyl chloride and triethylamine as reagents.

Thus AE – 112 / (114 + 78 + 127 + 101) = 26.7% (so an effective oxidation method, but very wasteful, especially given that we are only removing two hydrogen atoms from the alcohol!