# Percentage yield and atom economy

### Percentage yield and atom economy

#### Lessons

In this lesson, we will learn:
• To understand the definitions of atom economy and percentage yield and the difference between them.
• To calculate atom economy and percentage yield from example chemical reactions.
• To explain the importance of atom economy as a chemist when planning chemical reactions and processes.

Notes:

• The atom economy of a reaction is the percentage of atomic mass of useful products in a reaction. It is calculated by: $Atom\;Economy \;$(%)$\;= \frac{Atomic\;mass\;of\;useful\;products}{Total\;atomic\;mass\;of\;products} * 100$

• A high atom economy means that most of what the chemical process makes is useful! In the same way, a low atom economy tells you that a reaction is mostly producing unwanted waste products.

The atom economy is used to show an efficient reaction that makes lots of valuable chemicals and not much waste product that will require disposal.

• A quick tip – reactions with a single product have a 100% atom economy because the only chemical being produced is the desired product.

• The percentage yield of a reaction is the mass of products formed as a percentage of how much could have been formed given the mass of reactants used.

• A low percentage yield means that not much of the reactants you used has become products. A high percentage yield therefore means that a lot of the reactant chemicals you used successfully reacted to make the products.

• Know the difference between the two! Atom economy is about how wasteful the reaction is, and yield is about how much reactant was successfully converted to products!

• Introduction
Why do chemists do chemical reactions?
a)
Things that happen during a chemical reaction.

b)
The definitions of atom economy and percentage yield.

c)
The difference between atom economy and percentage yield.

d)
Environmental and economic chemistry.

• 1.
Find the atom economy and percentage yield of chemical reactions.
Water can be produced by reaction of hydrogen and oxygen gas according to this equation:
2 H$_2 +$O$_2$→2 H$_2$O
a)
What is the atom economy of this reaction?

b)
If the reaction was performed and 150 g was the theoretical yield of water and the actual yield was only 92 g, what is the percentage yield?

• 2.
Find the atom economy and percentage yield of chemical reactions.
The reaction to make iron metal by reduction uses carbon. CO$_2$ is an unwanted side-product. The reaction is as follows:
2 Fe$_2$O$_3 +$3 C→3 CO$_2 +$4 Fe
a)
What is the atom economy of this reaction?

b)
280 g of Fe$_2$O$_3$ was used in this reaction and 104 g of Fe metal was collected. Calculate the theoretical yield and then the percentage yield of this reaction.

c)
This reaction was done again and a percentage yield of 90% was achieved this time. If 250 g of Fe was collected this time, how much Fe$_2$O$_3$ was used up?

• 3.
Compare the viability of two reactions by finding the atom economy and percentage yield.
Magnesium reacts with hydrochloric acid as shown in the following equation:
Mg$+$2 HCl→MgCl$_2 +$H$_2$
a)
If this reaction was performed to make hydrogen gas, what would be the atom economy?

b)
55 g of Mg metal was used in this reaction with HCl in excess. Only 4.21 g of H$_2$ gas was produced from this reaction. What is the percentage yield of this reaction?

c)
Hydrogen gas could also be made by electrolysis of water, in the following reaction:
2 H$_2$O→2 H$_2 +$O$_2$

Find the atom economy of this reaction. Is it a better or worse way to make hydrogen than reacting magnesium with hydrochloric acid?