Atom economy measures how much of the product mass is wanted

1. A reaction usually makes more than one product, and only one of them is the desired product.
2. Atom economy compares the mass of that product with the mass of everything formed: $$atom\; economy=\frac{M_{r}of\; the\; desired\; product}{sum\; of\; the{M}_{r}of\; all\; products}\times 100$$
3. The masses come from the balanced equation, with each $M_r$ multiplied by its balancing number.
4. A high atom economy means little of the starting material ends up as waste.
5. The answer is a percentage and carries no unit.

Working out an atom economy step by step

1. Write the balanced equation and identify which product is wanted.
2. Find the $M_r$ of that product and multiply it by its balancing number.
3. Do the same for every other product, then add all the products together.
4. Divide the desired figure by the total and multiply by $100$.
5. The reactants never enter the calculation, since conservation of mass makes their total the same.

A worked atom economy: extracting iron

1. The equation for reducing iron(III) oxide with carbon monoxide is: $${Fe}_2{O}_3+3CO\to 2Fe+3{CO}_2$$
2. The desired product is iron, of $A_r$ $56$: $$2\times 56=112$$
3. The only by-product is carbon dioxide, of $M_r$ $44$: $$3\times 44=132$$
4. The atom economy follows from the two totals: $$\frac{112}{112+132}\times 100=45.9\%$$
5. Less than half the mass formed is iron, and the rest leaves the process as carbon dioxide.

Why a high atom economy matters

1. A reaction with a low atom economy converts much of its raw material into waste.
2. That waste has to be separated, treated or disposed of, which costs money.
3. Raw materials are often finite, so wasting them shortens the supply.
4. A route with a higher atom economy is usually more sustainable for the same product.
5. A useful by-product softens the objection, because the waste can be sold rather than discarded.

Comparing two routes to the same product

1. Two reactions that give the same product can have very different atom economies.
2. The route that forms fewer by-products keeps more of the mass in the wanted product.
3. An addition reaction, which joins everything into one product, scores highest of all.
4. A route with a lower atom economy may still be chosen if it is faster or cheaper to run.
5. Comparing routes fairly means quoting both figures and the reason for preferring one.