# Calculating the Percentage Atom Economy of a Reaction

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• 0:03 How Much Waste?
• 0:52 Percentage Atom…
• 1:47 Steps to the Equation
• 2:34 Example
• 5:14 Lesson Summary
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Lesson Transcript
Instructor: Hemnath (Vikash) Seeboo

Taught Science (mainly Chemistry, Physics and Math) at high school level and has a Master's Degree in Education.

In this lesson, we'll explore the meaning of atom economy as applied to a chemical reaction. You'll learn to calculate the percentage atom economy of a reaction and how to calculate it to form a desired product.

## How Much Waste?

Peter bought one pound of potatoes from the supermarket. Upon reaching home, he asked his two daughters what they would like him to do with them. His first daughter, Saanya, asked him to prepare some potato wedges while his second daughter, Youkey, wanted to have French fries. In the kitchen, Peter divided the potatoes into two equal halves to make both wedges and French fries.

For the first batch, he simply washed the potatoes and cut them into wedges. For the second, he peeled off the skin to prepare the French fries. Which batch had the maximum use of raw potatoes? In other words, which choice is more economical and involves less waste? I bet you got it right, the potato wedges! By keeping the skin, there is no waste of raw potato! Waste is undesirable, and this concept, as you will see, also applies to chemical reactions.

## Percentage Atom Economy Formula

Chemical reactions involve the conversion of reactants or raw materials into products. At the very base of a chemical reaction, there are atoms that are being rearranged. At this point, an American chemist, named Barry M. Trost asked a question: What atoms of the reactants are incorporated into the final desired product(s), and what atoms are wasted? This question, and eventually its answers, became the basis behind the concept of atom economy and also part of the principles behind green chemistry.

Atom economy, or atom efficiency, is the measurement of desired useful products formed from reactants. It is often measured in terms of percent, known as percentage atom economy. To calculate the percent atom economy, we divide the atoms of desired product by the total atoms in the reactants (which is the same as the total atoms in the product):

## Steps to the Equation

Consider the general equation that uses reactants X and Y to form products Z and W. If the desired product is Z, W is a waste for the reaction.

If the reaction has a higher atom economy, that means more of the desired product is formed and there is less waste.

A general way to proceed in order to calculate the atom economy is to use the following steps:

1. Construct a chemical equation for the given reaction.
2. Balance the equation.
3. Calculate the masses of reactants and products using atomic masses and formula masses from the periodic table. Notice that for a properly balanced equation, the total mass of reactants on the left side is always equal to the total mass of the products on the right side.
4. Calculate the percentage atom economy.

## Example

Let's look at Henry, who is a businessman who wants to build a new factory that would manufacture hydrogen. In order to maximize profit, he ponders which reaction he would use to produce hydrogen with the least waste possible. His chemical engineer proposed two different ways that could be used to obtain the desired product: by steam reforming or by electrolysis of water. Henry applied the four steps mentioned above for both reactions.

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