# Atom Economy Calculator

Created by Davide Borchia
Reviewed by Purnima Singh, PhD and Adena Benn
Based on research by
B.M. TROST The Atom Economy—A Search for Synthetic Efficiency Science, Volume 254, Issue 5037 (6/12/1991)
Last updated: Mar 10, 2023

Table of contents:

Calculate the greenness of a chemical reaction with our atom economy calculator. With this short article, you will get an introduction to an important topic in green chemistry: the wastefulness of a process. Forget about yield, and start considering how efficient your reaction is. Keep reading to learn:

• What the atom economy is;
• Basics of green chemistry: how do I calculate the atom economy in any reaction;
• What is the difference between yield and atom economy;
• Examples of calculations of the atom economy in green chemistry;
• And much more.

What are you waiting for? Learn how to make our world greener with science!

## What is atom economy?

Atom economy is a measure of the performance of a chemical reaction. The concept originated pretty recently, in 1991, thanks to the work of Barry M. Trost, following the growing popularity of green chemistry: atom economy fits the principles of the field like a glove! Let's see the definition, then!

Atom economy measures the degree to which the reactant atoms are transformed in the desired product. There's a lot to unpack here. First, in which context do we use atom economy?

Atom economy, in green chemistry, applies to any chemical reaction in the form:

$\mathrm{aA}+\mathrm{bB}\rightleftharpoons \mathrm{cC}+\mathrm{dD}$

Obviously, we are not limited to two reactants and products!

Atom economy targets a single product, the desired result of our reactions. To be more specific, consider the slight distinctions between products and byproducts! Most of the time, we ignore the latter, and in some situations, they are a complete nuisance we must get rid of. Atom economy puts the accent on the waste of byproducts, which is why it became an essential metric of green chemistry: a more sustainable approach to industry and technology is a key value of the field.

## How do I calculate atom economy in green chemistry?

To calculate the atom economy, we use either the masses or the molecular weights of the chemical species appearing in the reaction — it depends on whether you are considering a theoretical or experimental setting. In both cases, however, the formula for the atom economy remains the same!

The generic formula for atom economy, as per Trost, is:

$\footnotesize\mathrm{AE} = \frac{w_\mathrm{m,desired\ product}}{w_{\mathrm{m,total\ reactants}}}\times100\%$

Where we used the molecular weights of the species, but we can substitute them with the experimental masses.

🔎 You can't use the moles in the calculations for the atom economy: check our mole calculator if you need to convert the moles into grams!

Notice that, theoretically, we can substitute the products' total masses or molecular weights: we assume a yield of $100\%$. You can find both definitions in books and online, often used interchangeably. In fact, in most experimental situations, we prefer to use the latter since it excludes the detrimental effects of the process on the number of products we obtain. The expression for the atom economy in this case is:

$\footnotesize\mathrm{AE} = \frac{w_\mathrm{m,desired\ product}}{w_{\mathrm{m,total\ product}}}\times100\%$

As before, you can substitute the molecular weights with the masses of the species. Did you notice how these formulas are similar to the ones we used in the mass percent calculator? You can consider the atom economy as a measure of the "dilution" of the desired products in the total output of a reaction!

⚠️ Remember to consider the stoichiometric coefficients in your formulas: if you are using molecular weights, multiply each species' weight by their coefficient!

## How calculating the atom economy gives information on the greenness of a reaction

The atom economy easily differentiates between types of reactions, something that is not immediate when we calculate the yield. The distinction, moreover, helps classify reactions according to their greenness.

Consider an isomerization reaction, a transformation of a molecule into chemical species with the same atoms but a different structure. Since the desired product corresponds to the total products, the atom economy is $100\%$

Catalytic reactions follow suit. The presence of the catalyst, which enters and exits the reaction unmodified, does not influence the atom economy. The result is a lower percentage result than the not-catalyzed reaction.

Reactions where groups or portions of the molecules are eliminated result in lower values of the atom economy and are thus disregarded by "green" chemists. The best way to reach your desired product is through additions and rearrangements, which are preferred over substitutions and eliminations.

## Examples of calculations of the atom economy

Take a simple chemical reaction. We consider the decomposition of glucose into ethanol.

$\footnotesize\mathrm{C_6H_{12}O_6}\!\rightleftharpoons\! 2\mathrm{C_2H_5OH}+2\mathrm{CO_2}$

The molecular weights of the species involved in the reactions are:

• $\mathrm{C_6H_{12}O_6}$ (glucose): $180.16\ \mathrm{g/mol}$;
• $\mathrm{C_2H_5OH}$ (ethanol): $46.07\ \mathrm{g/mol}$; and
• $\mathrm{CO_2}$ (carbon dioxide): $44.01\ \mathrm{g/mol}$.

Apply the formula for the atom economy:

$\footnotesize\begin{split} \mathrm{AE} &= \frac{w_\mathrm{m,desired\ product}}{w_{\mathrm{m,total\ reactants}}}\times100\%\\[1em] &=\frac{2w_{\mathrm{ethanol}}}{w_{\mathrm{glucose}}}\times100\%\\[1em] &=\frac{2\times 46.07\ \mathrm{g/mol}}{180.16\ \mathrm{g/mol}}\\[1em] &=51.14\% \end{split}$

Almost half of the material we poured into the vessel has been wasted. Is there another way to obtain ethanol? Yes!

$\mathrm{C_2H_4}+\mathrm{H_2O}\rightleftharpoons\mathrm{C_2H_5OH}$

The new compound we see in the reactants is the ethene, with molecular weight $28.05\ \mathrm{g/mol}$; water has weight $18.02\ \mathrm{g/mol}$ Let's check the atom economy in this case:

$\footnotesize\begin{split} &\mathrm{AE} = \frac{w_\mathrm{m,desired\ product}}{w_{\mathrm{m,total\ reactants}}}\times100\%\\[1em] &=\frac{w_{\mathrm{ethanol}}}{w_{\mathrm{ethene}}+w_{\mathrm{water}}}\times100\%\\[1em] &=\frac{46.07\ \mathrm{g/mol}}{28.05\ \mathrm{g/mol}\!+\!18.02\ \mathrm{g/mol}}\times100\%\\[1em] &=\frac{46.07\ \mathrm{g/mol}}{46.07\ \mathrm{g/mol}}\times100\%\\[1em] &=100% \end{split}$

Impressive! This equation has no byproducts, and its atom economy reflects this fact.

## What is the difference between atom economy and yield?

There is a substantial difference between yield and atom economy: the first one calculates the effectiveness of a chemical reaction (the amount of desired product obtained compared to the theoretical quantity), while the atom economy calculates the amount of desired product obtained in a chemical reaction compared to the total amount of products of the reaction.

A chemical reaction conducted with extreme care may have a relatively high yield (i.e., obtain as much product as possible). However, if the desired product is a small fraction of the total output of the reaction, the atom economy would be meager!

Omni has tools you can use to calculate the yield: visit our percent yield calculator and theoretical yield calculator, and compare the results there to the atom economy calculator.

## FAQ

### What is the atom economy?

Atom economy is a measure of the wastefulness (or lack thereof) of a chemical reaction. A useful concept in green chemistry, we use the atom economy to measure the fraction of the total reagents (or products, under the assumptions of mass equivalence) that transform into the desired product. In contrast, the yield measures the effectiveness with which we performed the reaction, ignoring eventual wastes.

### How do I calculate the atom economy if I know the molecular weights?

To calculate the atom economy if you know the molecular weights, follow these steps:

1. Write the reaction. For example:

aA + bB ⇌ cC + dD

2. Choose the desired product. We will choose C.

3. Calculate the total molecular weights of the reactants. Multiply the weights by the stoichiometric coefficients:

w(tot) = a × w(A) + b × w(B)

4. Divide the molecular weight of C (adjusted by its coefficient) by the total weight of the reactants. Multiply by 100%:

AE = (c × w(C)/w(tot)) × 100%

### What is the atom economy of the production of hydrogen from methane?

The reaction we are considering is:

CH4 + H2O → 3 H2 +CO

The compounds have molecular weights:

• CH4 = 16.04 g/mol;
• H2O = 18.02 g/mol;
• H2 = 2.02 g/mol; and
• CO = 28.01 g/mol.

Calculate the atom economy using the sum of the reagents' weights at the denominator:

AE = (3 × 2.02)/(16.04 + 18.02) × 100% = 17.80%

Notice that we would find the same result even using the products' weights as the denominator.

### Why is a high atom economy better?

A high atom economy is an indicator of a chemical reaction where the output is mainly composed of the intended and desired product(s). Synthesis with a single product has a high atom economy, ideally of 100%: we will use all the products created in the reaction.

Eliminations or substitutions are the origins of wastes (byproducts) that lower the atom economy. Calculating the atom economy helps design reactions with a focus on their sustainability.

Davide Borchia
I know...
the masses
Reagents
Reagent 1
g
Reagents (total)
g
Products
Desired product
g
Atom economy
Atom economy
%
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