Atom Economy

Higher tier only: This whole lesson is Higher tier. Foundation candidates do not need atom economy, but should be confident with percentage yield from the previous lesson.

Percentage yield tells you how much of the possible product you actually collected, but it says nothing about how much of your starting material ends up as waste. A reaction can have a high yield and still be wasteful if much of the reactant mass turns into unwanted by-products. Atom economy measures this — what proportion of the reactant atoms end up in the desired product. It has become one of the most important ideas in green, sustainable chemistry. This lesson, part of Topic C5 of OCR Gateway Science A, defines atom economy, shows how to calculate it, and explains why a high value matters.

By the end of this lesson you should be able to define atom economy, calculate it from a balanced equation, explain why a high atom economy is desirable, and compare two routes to the same product.

Atom economy is a relatively modern idea, but it has quickly become one of the central measures of how "green" a chemical process is. Where percentage yield asks how much product you obtained, atom economy asks a deeper question — how much of your starting material was even capable of becoming the product you wanted, rather than being destined to end up as waste.

What Atom Economy Means

The atom economy of a reaction is the proportion of the mass of the reactants that ends up as the desired product. It is calculated from the balanced equation:

$\% \text{ atom economy} = \dfrac{M_r \text{ of the desired product}}{\text{total } M_r \text{ of all the reactants}} \times 100$

Because mass is conserved (from C3), the total $M_r$ of the reactants equals the total $M_r$ of all the products. So the bottom of the fraction can also be read as the total $M_r$ of everything made. Anything that is not the desired product is by-product or waste.

A reaction that makes only one product has an atom economy of 100% — every atom of the reactants ends up in the product, with nothing wasted.

The word "economy" is a good guide to the meaning: just as an economical car makes the most of its fuel, an atom-economical reaction makes the most of its atoms, turning as many of them as possible into the useful product rather than into waste. A reaction with a low atom economy is wasteful in principle, because much of the reactant mass is destined to become by-product no matter how perfectly the reaction is run — the waste is built into the equation itself.

Exam Tip: Atom economy is worked out entirely from the balanced equation — it does not depend on how carefully you carry out the reaction. Put the $M_r$ of the wanted product on top and the total $M_r$ of the reactants on the bottom.

Calculating Atom Economy

Worked Example 1 — Extracting iron

Iron is extracted by reducing iron(III) oxide with carbon: $2\text{Fe}_2\text{O}_3 + 3\text{C} \rightarrow 4\text{Fe} + 3\text{CO}_2$ . Calculate the atom economy for making iron. ( $A_r$ : Fe = 56, O = 16, C = 12.)

Step 1 — $M_r$ of the desired product (Fe). There are 4 Fe in the equation:

$4 \times 56 = 224$

Step 2 — total $M_r$ of the reactants. $2\text{Fe}_2\text{O}_3 = 2 \times (2 \times 56 + 3 \times 16) = 2 \times 160 = 320$ ; and $3\text{C} = 3 \times 12 = 36$ :

$320 + 36 = 356$

Step 3 — atom economy:

$\% \text{ atom economy} = \dfrac{224}{356} \times 100 = 62.9\%$

Answer: the atom economy is $62.9\%$ (to 3 s.f.). The rest of the mass ends up as the by-product carbon dioxide.

Check: the products' total $M_r = 224 + (3 \times 44) = 224 + 132 = 356$ , which equals the reactants' total — confirming conservation of mass.

Worked Example 2 — A reaction with only one product

Calculate the atom economy for making ammonia: $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$ . ( $A_r$ : N = 14, H = 1.)

Step 1 — $M_r$ of the desired product ( $2\text{NH}_3$ ): $2 \times (14 + 3) = 2 \times 17 = 34$ .

Step 2 — total $M_r$ of the reactants: $\text{N}_2 = 28$ and $3\text{H}_2 = 6$ , so $28 + 6 = 34$ .

Step 3 — atom economy: $\dfrac{34}{34} \times 100 = 100\%$ .

Answer: $100\%$ . Ammonia is the only product, so every reactant atom ends up in it — there is no waste.

Exam Tip: When a reaction makes a single product, its atom economy is 100%. Watch the big numbers: $2\text{NH}_3$ means the product's $M_r$ is doubled to $34$ , and $3\text{H}_2$ means $6$ , not $2$ .

Comparing Two Routes to the Same Product

Atom economy lets you judge which of two ways of making the same substance is less wasteful.

Worked Example 3 — Two routes to copper

Copper can be made (a) by reducing copper(II) oxide with carbon, or (b) by displacing it from copper(II) sulfate solution with iron. Calculate the atom economy of each route for making copper. ( $A_r$ : Cu = 64, O = 16, C = 12, Fe = 56, S = 32.)

Route (a): $2\text{CuO} + \text{C} \rightarrow 2\text{Cu} + \text{CO}_2$ .

$M_r$ of desired product ( $2\text{Cu}$ ) $= 2 \times 64 = 128$ .
Total $M_r$ of reactants $= 2\text{CuO} (2 \times 80 = 160) + \text{C} (12) = 172$ .
Atom economy $= \dfrac{128}{172} \times 100 = 74.4\%$ .

Route (b): $\text{Fe} + \text{CuSO}_4 \rightarrow \text{FeSO}_4 + \text{Cu}$ .

$M_r$ of desired product (Cu) $= 64$ .
Total $M_r$ of reactants $= \text{Fe} (56) + \text{CuSO}_4 (64 + 32 + 64 = 160) = 216$ .
Atom economy $= \dfrac{64}{216} \times 100 = 29.6\%$ .

Answer: route (a) has the higher atom economy ( $74.4\%$ vs $29.6\%$ ), so it wastes less of the reactant mass as by-products and is the more atom-efficient route.

Route to copper	Atom economy	More or less wasteful?
(a) $2\text{CuO} + \text{C}$	$74.4\%$	Less wasteful (preferred)
(b) $\text{Fe} + \text{CuSO}_4$	$29.6\%$	More wasteful

Exam Tip: To compare two routes, calculate the atom economy of each and pick the higher one as the more sustainable. Always identify the desired product first — it is whatever the question says you want to make.

Why a High Atom Economy Matters

A high atom economy means most of the reactant atoms end up in the useful product and little is wasted as by-products. This is desirable for several linked reasons:

Less waste is produced, so there is less to dispose of (and less pollution).
It uses raw materials more efficiently, so fewer reactants are needed for the same amount of product.
It is more economic — less is spent on reactants, and less on separating and disposing of unwanted by-products.
It is more sustainable, conserving finite resources.

Industry therefore prefers reactions with a high atom economy, and may try to find a use for any by-products (selling them rather than discarding them) to make a lower-atom-economy process more economic.

Atom Economy

Atom Economy

What Atom Economy Means

Calculating Atom Economy

Worked Example 1 — Extracting iron

Worked Example 2 — A reaction with only one product

Comparing Two Routes to the Same Product

Worked Example 3 — Two routes to copper

Why a High Atom Economy Matters

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