Atom economy and percentage yield
In a nutshell
The percentage yield and atom economy can be calculated for reactions. These two calculations show how much of the potential product is wasted during the reaction.
Equations
Percentage yield=theoretical yieldactual yield×100
Atom economy=sum of molecular mass of all productsmolecular mass of desired product×100
Percentage yield
Definition
The percentage yield is the amount of product collected during a reaction. Percentage yield tells you how wasteful the process is and how much product is lost.
Percentage yield can be calculated by:
Percentage yield=theoretical yieldactual yield×100
The theoretical yield is the amount of product that should be made if nothing is lost during the reaction. Where as the actual yield is the amount of product collected once the reaction has completed.
Note: The theoretical yield can be calculated from masses by using a balanced equation to find molar ratios.
procedure
1. | Write the balanced equation for the reaction to find the molar ratios of both the reactants and products. |
2. | Find the number of moles of the reactant by using the mass and the equation: n=Mm |
3. | Use the moles of the reactant and molar ratios found from the balanced equation to find the number of moles of the desired product. |
4. | Use the moles calculated to find the theoretical mass of the product using: m=n×M |
5. | Finally, use the actual mass gathered and the theoretical mass calculated to find the percentage yield: Percentage yield=theoretical yieldactual yield×100 |
Example
2.56g of sodium chloride is reacted with sulfuric acid. 2.45g of sodium sulfate is produced. What is the percentage yield?
First, write down the equation you will use to find the percentage yield:
Percentage yield=theoretical yieldactual yield×100
You need to find the theoretical yield.
Write out the balanced equation for the reaction:
2NaCl(s)+H2SO4(aq)→Na2SO4(s)+2HCl(aq)
Next, write down the equation you will use to find the number of moles of
NaCl:
n=Mm
Find the molar mass for NaCl:
M(NaCl)=23+35.5=58.5gmol−1
Calculate the number of moles of NaCl but substituting the mass and molar mass into the equation:
n=58.52.56=0.0438mol
Use the balanced equation to find a molar ratio between NaCl and Na2SO4:
The mole ratio from NaOH to Na2SO4 is 2:1.
Use the mole ratio to find the number of moles of Na2SO4:
n=20.0438=0.0219mol
Find the mass (theoretical yield) of Na2SO4 using the equation:
m=n×M
Find the molar mass of Na2SO4:
M(Na2SO4)=(23×2)+32.1+ (16×4)=142.1gmol−1
Substitute in the values for the molar mass and number of moles to find the mass of Na2SO4:
m=0.0219×142.1=3.11g
Substitute your values for actual yield (given in the question) and theoretical yield calculated to find the percentage yield:
Percentage yield=3.112.45×100=78.8%
The percentage yield for this reaction is 78.8%.
Atom economy
Definition
Atom economy is a measure of the proportion of atoms in the reactants that are in the desired product. Atom economy tells you how wasteful the reaction itself is.
Atom economy can be calculated by:
Atom economy=sum of molecular mass of all productsmolecular mass of desired product×100
Example
Find the atom economy for the sodium chloride product of the reaction below.
Na2S(s)+2HCl(aq)→2NaCl(s)+H2S(g)
First, write down the equation you will use to find atom economy:
Atom economy=sum of molecular mass of all productsmolecular mass of desired product×100
Find the molecular mass of all the products:
M(2NaCl)=2×(23+35.5)=117gmol−1M(H2S)=2+32.1=34.1gmol−1Total=117+34.1=151.1gmol−1
Find the molecular mass for the desired product (NaCl):
M(2NaCl)=2×(23+35.5)=117gmol−1
Substitute the molecular masses for the products and desired product to find the atom economy:
Atom economy=151.1117×100=77.4%
The atom economy is 77.4%.
When a reaction has one product the percentage atom economy will always be 100%.
Example
Addition reactions will always form one product, leaving these reactions with an atom economy of 100%.
Sustainability
Chemists will choose reactions with high atom economies to reduce wastage. If a reaction has a low atom economy more money is needed to separate and dispose of the waste products. It is also expensive to purchase reactants when they are not all being used to make the desired product.
Reactions that require high amounts of energy (high temperatures and pressures) are very costly. These conditions are not good for the environment. Raw materials sourced renewably are much better for the environment.