GCSE & A level chemical calculations notes and practise questions

ATOM ECONOMY CALCULATIONS (and a mention of the related % yield too)

So also see % YIELD calculation notes too

[Author ©  Dr Phil Brown PhD: Doc Brown's exam revision notes suitable for students of GCSE level chemistry and advanced level pre-university/college chemistry courses: teach yourself chemical calculations - atom economy calculations [updated Mar 21st 2026 *]

Advanced UK A/AS level, IB and US grade 11-12 pre-university chemistry

14. Chemical calculations ATOM ECONOMY CALCULATIONS

Keywords: Quantitative chemistry calculations What is atom economy? Help on how to do atom economy calculations. What is the formula to calculate the 'atom economy' of a chemical reaction? Calculating the atom economy of a chemical reaction is explained on this page - fully worked out examples of atom economy calculations. Online practice exam chemistry CALCULATIONS and solved problems for KS4 Science GCSE/IGCSE CHEMISTRY and basic starter chemical calculations for A level AS/A2/IB courses.  These revision notes and practice questions on how to do atom economy chemical calculations and worked examples should prove useful for the new AQA, Edexcel and OCR GCSE (9–1) chemistry science courses.

Spotted any careless error? EMAIL query ? comment or request a type of calculation not covered?

14.2b The Atom economy of a chemical reaction

The atom economy (a measure of atom utilisation or efficiency) is a measure of the amount of starting materials that end up as useful products.

It is important for sustainable development and for good economic reasons to use reactions with high atom economy.

A chemical reaction may give, and often does, more than one product, but of the mixture of products, perhaps only one of them is the desired useful product.

The percentage atom economy of a reaction is readily calculated using the balanced equation for the reaction expressed in reacting masses.

You need to be able to calculate the atom economy of a reaction to form a desired product from the balanced equation and ...

... perhaps explain why a particular reaction pathway is chosen to produce a specified product given appropriate information such as atom economy, percent yield, rate of reaction, equilibrium position and usefulness of by-products.

The atom economy of a reaction is a theoretical percentage measure of the amount of starting materials that ends up as the 'desired' useful reaction products. Its sometimes referred to as atom utilisation.

In atom economy calculations you can say REACTANTS or PRODUCTS because of the law of conservation of mass which states that in a chemical reaction you cannot lose or gain mass overall.

The greater the % atom economy of a reaction, the more 'efficient' or 'economic' it is likely to be, though this is a gross simplification when complex and costly chemical synthesis are looked at.

Many reactions give more than one product, and not all of them are useful, so it is useful to calculate what % of the products is theoretically useful, and we call this the atom economy of the reaction.

The reactions that only give one product, have the maximum atom economy of 100% and these are the most economic reactions e.g. synthesis of ammonia and reacting ethene with water to make ethanol.

N₂ + 3H₂ ==> 2NH₃    and    CH₂=CH₂  +  H₂O  ===>  CH₃CH₂OH

These are simple addition reactions where two reactants give one product e.g. synthesis of ammonia from nitrogen and hydrogen and the synthesis of ethanol from ethene and water.

100 minus the % atom economy gives you the % waste, but reactions with only one product will always give the highest atom economy

If a reaction gives more than one product it may be possible to use and sell these other products, thereby making the process more economic overall.

Whatever, waste products have to be dealt with and disposed of in some safe way, and this costs money!

Reactions with a low atom economy can be very wasteful and use up resources at faster rate than high atom economy reactions.

They are usually less sustainable in the long run and the cost of raw materials will increase over time.

e.g. the process may involve non-renewable raw materials which will increase in costs as reserves become depleted.

BUT take care on this 'low economy' point, e.g. many products can be recycled and, as already mentioned, the waste products may have some economic value after further separation and processing, known as useful by-product.

The less waste there is, the higher the atom economy, the less materials are wasted, less energy used, so making the process more economic, 'greener' and more sustainable.

Quite simply, the larger the atom economy of a reaction, the less waste products are produced and hopeful the waste is easy and cheap to deal with, or even better, some use can be found for these waste 'by-products'.

It can be defined numerically in words in several ways, all of which amount to the same theoretical % number!

The chemical industry is continuously working on chemical synthetic routes that have the highest atom economy and give the highest % yield (see section 14.2a % reaction yield)

If a chemical reaction that has a low atom economy or gives a low yield of useful product research would be undertaken to find ways the reaction can been improved to increase the yield of useful product.

Note that there are other factors when considering industrial production.

% reaction yield and theoretical yield calculations and why you can't actually get 100% yield in practice

The factors affecting the rate of a reaction - is the chemical process fast enough to be economic?

Is the reaction reversible?  and 

Does it involve a chemical equilibrium? - can you alter reaction conditions to increase the yield of the desired product?

CALCULATING the ATOM ECONOMY of a chemical reaction

You can do the calculation in any mass units you want, or non at all by simply using the atomic/formula masses of the reactants and products as appropriate , and I suggest you just think like that.

Make sure your calculations are based on a fully numerically balanced equation.

The formula to calculate atom economy can be written in several different ways and they are ALL equivalent to each other because of the law of conservation of mass e.g.

THEY ALL GIVE THE SAME ANSWER!

As long as you take into account ANY balancing numbers in the equation, which itself should be balanced!

but they are theoretical values, you don't get these results in real life chemistry,

see also % purity of a product  and  % reaction yield

Examples of how to work out atom economy calculations

Atom economy calculation Example 14.2b (atom economy 1)

See Extraction of Iron and Steel Making for detailed chemistry

This is illustrated by using the blast furnace reaction from example 14.2a.3 above.

Fe₂O_3(s) + 3CO_(g) ===> 2Fe_(l) + 3CO_2(g)

Using the atomic masses of Fe = 56, C = 12, O = 16, we can calculate the atom economy for extracting iron.

the reaction equation can be expressed in terms of theoretical reacting mass units

[(2 x 56) + (3 x 16)] + [3 x (12 + 16)] ===> [2 x 56] + [3 x (12 + 16 + 16)]

[160 of Fe₂O₃] + [84 of CO] ===> [112 of Fe] + [132 of CO₂]

so there are a total of 112 mass units of the useful/desired product iron, Fe,

out of a total mass of reactants or products of 160 + 84 = 112 + 132 = 244.

Therefore the atom economy = 100 x 112 / 244 = 45.9%

Note: It doesn't matter whether you use the total mass of reactants or the total mass products in the calculations, they are the same due to the law of conservation of mass

Atom economy calculation Example 14.2b (atom economy 2) See Ethanol Chemistry

The fermentation of sugar to make ethanol ('alcohol') and (b) converting ethanol to ethene

(a) glucose (sugar) == enzyme ==> ethanol + carbon dioxide

C₆H₁₂O_6(aq) ==> 2C₂H₅OH_(aq) + 2CO_2(g) 

atomic masses: C = 12, H = 1 and O = 16

formula mass of glucose reactant = 180 (6x12 + 12x1 + 6x16)

formula mass of ethanol product = 46 (2x12 + 5x1 + 1x16 + 1x1)

relative mass of desired useful product in the equation = 2 x 46 = 92

Atom economy = 100 x 92/180 = 51.1%

 

(b) ethanol === heat/catalyst ===> ethene + water

It possible to use ethanol from fermentation to produce ethene for plastics (polymers) manufacture instead of relying on the cracking of crude oil fractions (e.g. a country like Brazil with a huge agriculture system but no oil deposits.

CH₃CH₂OH  ===>  CH₂=CH₂  +  H₂O

formula masses: ethanol = 46, ethene = 28, water = 18

% atom economy = 100 x 28/46 = 60.9%

 

(c) ethene + water ===> ethanol

 CH₂=CH₂  +  H₂O ====>  CH₃CH₂OH

BUT, it is also possible to manufacture ethanol by catalytically reacting steam with ethene from cracking oil fractions.

Since this is a 'simple' addition reaction, the atom economy is 100%.

This is a much cleaner and efficient process than fermentation which only has a 51% atom economy.

Atom economy calculation Example 14.2b (atom economy 3)

All about making hydrogen See Ammonia Synthesis

In these three examples, Reactions 1 to 3:

Relative atomic masses used: C = 12.0,  H = 1.0,  O = 16.0

Hydrogen is used in synthesising ammonia and making margarine, and is made on a large scale from reacting methane with water

methane + water  ==>  hydrogen + carbon monoxide

Reaction equation 1.: CH₄(g) + H₂O(g)  ==>  3H₂(g)  +  CO(g)

using formula masses gives the ratios gives

16 + 18 ==> (3 x 2) + 28

34 mass units of reactants ==> 6 mass units of useful product

Atom economy = 100 x 6 / 34 = 17.6%

BUT, the 82.4% of waste toxic carbon monoxide must be dealt with in some way!

It seems a very inefficient process BUT ...

(i) hydrogen has very small molecular mass and 75% of the molecules are the desired product

(ii) you can actually burn the carbon monoxide as a fuel to provide energy for power generation.

(iii) methane is readily available from the petrochemical industry and is much cleaner to work with than impure coal (see reactions 2. and 3.), which must be converted to coke first - an extra process.

So, a low atom economy doesn't always mean the process is not economically viable or necessarily produces undue waste.

 

Hydrogen can also be made from reacting water with coke (a form of carbon made by roasting coal)

A second reaction used to manufacture hydrogen

carbon  +  water  ===> hydrogen + carbon monoxide

Reaction equation 2.: C(s)  + H₂O(g)  ===>  H₂(g) +  CO(g)

formula masses:  12 + 18 (= 30) ==> 28 + 2 (= 30)

% atom economy = 100 x 2 / 30 = 6.67 %

This is a much lower atom economy than reaction, and only 50% of the molecules are useful product.

 

However, the carbon monoxide can be made to react further with water to form more hydrogen

carbon monoxide  +  water  ===>  hydrogen  +  carbon dioxide

Reaction equation 3.: CO(g)  +  H₂O(g)  ===>  H₂(g)  +  CO₂(g)

formula masses:  28 + 18 (= 46)  ===> 2 + 44 (= 46)

% atom economy = 100 x 2 / 46 = 4.35 %

This is an even lower atom economy than reaction, and again, only 50% of the molecules are useful product.

However: (a) it does take care of poisonous carbon monoxide, but there is also something else you can do ...

(b) You can combine these process, so combining equations 2. and 3. we get ...

C(s)  + H₂O(g)  ===>  H₂(g) +  CO(g)   plus

CO(g)  +  H₂O(g)  ===>  H₂(g)  +  CO₂(g)   gives

------------------------------------------------------------------

C(s)  + 2H₂O(l)  ====>  2H₂(g)  +  CO₂(g)

------------------------------------------------------------------

formula masses:  12 + 2x18 (= 48)  ===> 4 + 44 (= 48)

% atom economy = 100 x 4 / 48 = 8.33 %

This is a higher atom economy than reactions 2 or 3, and 67% of the molecules are useful product.

Only 50% of the molecular products are the desired product in reactions 2. and 3.

Therefore employing a secondary process improves the efficiency of this particular process for making hydrogen.

It should be noted that carbon monoxide is a water insoluble toxic gas and not easy to deal with.

As already mentioned, you can burn it as a fuel for power generation or heating a reactor vessel.

BUT, carbon dioxide is not toxic (as long as plenty of air is around!) and importantly, it readily dissolves in sodium hydroxide solution in gas flow 'scrubbers' to leave hydrogen as the only remaining gas.

This greatly reduces the cost of purifying the hydrogen to use e.g. in the Haber Synthesis of ammonia and the hydrogenation of unsaturated plant fats to make spreadable margarine.

Also, the reaction between steam and carbon monoxide is exothermic, this reduces the energy needs of the overall process.

 

Making hydrogen using electrolysis

(I'm only interested in atom economy here - see other notes on electrolysis for details)

Relative atomic masses: Na = 23.0,  Cl = 35.5,  H = 1.0,  O = 16.0

Process A. Electrolysis of aqueous sodium chloride solution (brine)

Overall change: 2NaCl(aq)  +  2H₂O(l)  ====>  2NaOH(aq)  +  Cl₂(g)  +  H₂(g)

total masses for reactants or products = (2 x 58.5) + (2 x 18) =

mass of desired product 2

% atom economy = 100 x 2 / = 153 = 1.31%

Very low atom economy and much waste to deal with?, BUT, sodium hydroxide and chlorine are useful saleable chemicals.

The low atom economy percentage for hydrogen production is very misleading here because it is a very useful product that just happens to have a very low molecular mass.

Process B. Electrolysis of acidified water

Overall change: 2H₂O(l)  ===> 2H₂(g)  +  O₂(g)

total masses for reactants or products = (2 x 18) = (4 + 32) = 36

mass of desired product 2

% atom economy = 100 x 4 / = 36 = 11.1%

This has a much greater atom economy than process B and no waste products, no pollution.

This is an ideal process, especially if you can use green energy e.g. from wind turbine, solar cell or hydroelectric sources of electricity.

BUT, both processes have their place in the chemical industry - from Process A we do need sodium hydroxide and chlorine to manufacture other products e.g. soap from NaOH + plant oil and PVC from ethene and chlorine.

---

Note 1: These reactions contrast with the 100% atom economy of ammonia production (for which much of the hydrogen is made),

because its an addition reaction with no extra waste products

N₂ + 3H₂ ==> 2NH₃

mass of reactants = mass of useful products = 100% atom economy

 

Note 2: In organic chemistry, these three types of reaction can never have a 100% atom economy because there are always at least two products - desired useful product and often a waste product e.g.

(i) condensation reaction - a small molecule formed in joining two molecules to make a larger molecule e.g.

n HOOC-[][][][]-COOH + n H₂N-[][][][]-NH₂ ==> -(-OC[][][][]-CONH-[][][][]-NH-)_n-+  2n H₂O

a schematic example of condensation polymerisation where n is a very large number and water is the waste product

 

(ii) elimination reaction - a group of atoms eliminated from a molecule

e.g. CH₃CH₂OH  ===>  CH₂=CH₂  +  H₂O

water eliminated from ethanol to form ethene (very useful), and water is the waste product

(iii) substitution reaction - one or more atoms substituted by another atom or group of atoms

e.g. CH₃CH₂Br  +  NaOH  ===>  CH₃CH₂OH  +  NaBr

-Br group substituted by an -OH group in organic chemistry, ethanol is the useful product, sodium bromide is a waste product - but maybe useful, the word 'waste' can be over-used!

FOR YOU TO DO AS A PRACTICE QUESTION

Atom economy calculation Example 14.2b (atom economy 4)

The extraction of copper by reducing copper(II) with a reducing agent.

You can use either (a) hydrogen or (b) a hydrocarbon gas like methane to reduce the oxides of metals of low reactivity to obtain the metal itself.

Using the relative atomic masses: Cu = 63.5,  H = 1,  O =16,  C = 12

(a) CuO  + H₂  ==>  Cu  +  H₂O

Calculate the atom economy of the reaction to produce copper by reduction of copper(II) oxide with hydrogen.

(b) 4CuO  +  CH₄  ==>  4Cu  +  2H₂O  +  CO₂

Calculate the atom economy of the reaction of copper(II) oxide with methane to extract copper.

Formula masses: CuO = 79.5,  CH₄ = 16,  Cu = 63.5,  H₂O = 18,  CO₂ = 44

(c) Which reaction has the higher atom economy? BUT, with reasons, would this be the preferential method used?

ANSWERS

Rather than here, I've added more atom economy calculations to the Reacting mass ratio calculations of reactants and products from equations page.

Chemical & Pharmaceutical Industry Economics & Sustainability, Life Cycle Assessment, Recycling

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OTHER CALCULATION PAGES

1. What is relative atomic mass?, relative isotopic mass and calculating relative atomic mass

2. Calculating relative formula/molecular mass of a compound or element molecule

3. Law of Conservation of Mass and simple reacting mass calculations

4. Composition by percentage mass of elements in a compound

5. Empirical formula and formula mass of a compound from reacting masses (easy start, not using moles)

6. Reacting mass ratio calculations of reactants and products from equations (NOT using moles) and brief mention of actual percent % yield and theoretical yield, atom economy and formula mass determination

   • Reacting masses, concentration of solution and volumetric titration calculations (NOT using moles)

7. Introducing moles: The connection between moles, mass and formula mass - the basis of reacting mole ratio calculations (relating reacting masses and formula mass)

8. Using moles to calculate empirical formula and deduce molecular formula of a compound/molecule (starting with reacting masses or % composition)

9. Moles and the molar volume of a gas, Avogadro's Law

10. Reacting gas volume ratios, Avogadro's Law and Gay-Lussac's Law (ratio of gaseous reactants-products)

11. Molarity, volumes and solution concentrations (and diagrams of apparatus)

12. How to do acid-alkali titration calculations, diagrams of apparatus, details of procedures

13. Electrolysis products calculations (negative cathode and positive anode products)

14. Other calculations e.g. % purity, % percentage & theoretical yield, dilution of solutions (and diagrams of apparatus), water of crystallisation, quantity of reactants required, atom economy

    • 14.1 % purity of a product

    • 14.2a % reaction yield

    • 14.2b atom economy

    • 14.3 dilution of solutions

    • 14.4 water of crystallisation calculation 

    • 14.5 how much of a reactant is needed?

15. Energy transfers in physical/chemical changes, exothermic/endothermic reactions

16. Gas calculations involving PVT relationships, Boyle's and Charles Laws

17. Radioactivity & half-life calculations including dating materials

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