# 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 them.

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?