# The yield of a chemical reaction

## Example 1

A diesel engine provides only 45 % of the power which it could provide if the whole energy liberated by the combustion was transformed to usable energy.
The losses have multiple causes which are mostly anavoidable.

## Example 2

To make an apple cake , you need 3 apples, 2 eggs and enough flour.
Unfortunately this time three apples were rotten and with your 12 apples you can make only 3 cakes, while you had planned for 4 !
The yield with respect to the apples is
$\rho$ $=$ $\frac{3}{4}$ $=$
$0.75$
or
$\rho$ $=$ $75\%$
(from the $100\%$ that you should have made).
Unfortunately this time 3 eggs were broken and with 9 eggs you realise only 3 cakes, while you had planned for $\frac{9}{2}$ ! !
The yield with respect to the eggs is
$\rho$ $=$ $\frac{3}{\frac{9}{2}}=0.666$
or
$\rho$ $=$ $66.6\%$
(from the $100\%$ that you should have made).

## Definition of yield in chemistry

The yield of a chemical reaction is the ration of the number of moles of a product obtained actually by the number of moles of this producttheoretically obtainable.
$\rho=\frac{n_{actually\; obtained}}{n_{theoretically\; obtainable}}$
The yield is often given in %, then $\rho$ is multiplied by 100:
$\rho_{\%}$ $=$ $\frac{n_{actually\; obtained}\cdot 100}{n_{theoretically\; obtainable}}$

## Example

3 molecules $H_2$ should give 3 molecules $H_2O$ but actually they produce only 2 (because of losses while water is collected, lack of watertight integrity of the containers, etc...)
The yield with respect to hydrogen is therefore
$\rho$ $=$ $\frac{2}{3}$ $=$
$0.666$
or
$\rho$ $=$ $66.6\%$

.