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Percentage yield and atom economy

Percentage yield and atom economy

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Summary

Percentage yield and atom economy

In a nutshell

Percentage yield calculates the conversion of theoretical yield to actual yield. Atom economy is the measure of atoms in reactants compared to atoms in useful products. 


Equations


mass of productsmax theoretical mass of products ×100 =% yield\frac{mass\ of\ products}{max\ theoretical\ mass\ of\ products}\ \times 100\ = \% \ yield



Mr of desired productsMr of reactants × 100 = % atom economy\frac{M_r\ of\ desired\ products}{M_r\ of\ reactants}\ \times\ 100\ =\ \% \ atom\ economy​​


Percentage yield

Theoretical yield is if 100%100\% of the reactants react to form the products. In practice, yield is never 100%100\%​ and therefore ways of calculating yields are required.

 

There are several ways in which a product can be lost, therefore lowering the yield. Loss in transfer is one way, a solution might not be completely emptied or residue can be left behind. Certain chemicals can evaporate more easily than others so the reaction may not have gone to completion.


Calculating percentage yield


mass of productsmax theoretical mass of products ×100 =% yield\frac{mass\ of\ products}{max\ theoretical\ mass\ of\ products}\ \times 100\ = \% \ yield


100%100\%​ means that only the product was made and 0%0\%​ means that no product was formed. 


Procedure

1.
Find the mass of products in the question, typically this will be the smaller number. This is the numerator (top of the fraction).
2.
Find the theoretical maximum mass of the products, which is typically the bigger number. This is the denominator (bottom of the fraction).
3.
Multiply the fraction, which should be a value between zero and one, by 100100​. This will give your percentage yield.


Example

The theoretical maximum yield of a reaction results in 2.0 g2.0\ g​ of CuSO4CuSO_4 product. After the reaction and transfer, 1.2 g1.2\ g of CuSO4CuSO_4 is collected.


Mass of products achieved:


1.2 g CuSO4 (real)1.2\ g\ CuSO_4\ (real)

​​

Theoretical maximum mass of product:


2.0 g CuSO4 (theoretical)2.0\ g\ CuSO_4\ (theoretical)​​


Insert the given values into the equation for percentage yield:


mass of productsmax theoretical mass of products ×100 =% yield\frac{mass\ of\ products}{max\ theoretical\ mass\ of\ products}\ \times 100\ = \% \ yield​​


1.2 g (real)2.0 g (theoretical) = 0.6\frac{1.2\ g\ (real)}{2.0\ g\ (theoretical)}\ =\ 0.6


Multiply by 100100​ to convert the fraction to a percentage:


0.6 × 100 = 60%0.6 \ \times\ 100\ =\ \underline{60\%}​​


The percentage yield achieved for this reaction was 60%\underline{60\%}​.



Atom economy 

Definition

Atom economy compares the total amount of atoms used in the reactants to the amount of atoms present in the desired product. Whilst no atoms are lost in a chemical reaction they may end up as wasted a product. 


Calculating atom economy


Mr of desired productsMr of reactants × 100 = % atom economy\frac{M_r\ of\ desired\ products}{M_r\ of\ reactants}\ \times\ 100\ =\ \% \ atom\ economy

​​

Procedure

1.
Calculate molecular mass (Mr)(M_r) of both the desired products and of the reactants.
2.
Divide the molecular mass of the desired products by the molecular mass of the total reactants. The result should be between zero and one.
3.
Multiply by 100100​ to achieve your percentage atom economy. 


Example 

The electrolysis of water is seen as a route to produce eco-friendly H2H_2 for industrial processes. O2O_2 is a waste product. Calculate the atom economy for:


2H2O  2H2 + O22H_2O\ \rightarrow\ 2H_2\ +\ O_2 


Calculate the molecular mass of the reactants and the desired product:


Mr(H2O) = (1 × 2) +(16 × 1)=18Mr(H2)=(1×2) = 2M_r(H_2O)\ = \ (1\ \times\ 2)\ + (16\ \times\ 1) = 18 \\ M_r(H_2) = (1 \times2)\ =\ 2


Multiply the molecular mass of the reactants and the desired product by the stoichiometry:


Mr(2H2O) = 18 (Mr) × 2 = 36Mr(2H2) = 2 (Mr) ×2 = 4M_r(2H_2O)\ =\ 18\ (M_r)\ \times \ 2\ =\ 36 \\M_r(2H_2)\ =\ 2\ (M_r)\ \times 2\ =\ 4​​


Note: Stoichiometry means the ratio of each substance in the balanced equation.


Insert the calculated values into the equation for percentage atom economy:


Mr of desired productsMr of reactants × 100 = % atom economy\frac{M_r\ of\ desired\ products}{M_r\ of\ reactants}\ \times\ 100\ =\ \% \ atom\ economy​​


4 36  = 0.111\frac{4\ }{36\ }\ =\ 0.111


Multiply by 100100​ to convert the fraction to a percentage:


0.111 × 100 = 11.1%0.111\ \times\ 100 \ = \ 11.1\%


The percentage atom economy for the H2H_2 production is 11.1%\underline{11.1\%}.



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