Editing Limiting reagent (section)

==Method 2: Comparison of product amounts which can be formed from each reactant==
In this method the chemical equation is used to calculate the amount of one product which can be formed from each reactant in the amount present. The limiting reactant is the one which can form the smallest amount of the product considered. This method can be extended to any number of reactants more easily than the first method.

===Example===

20.0 g of [[iron (III) oxide]] (Fe<sub>2</sub>O<sub>3</sub>) are reacted with 8.00 g [[aluminium]] (Al) in the following [[thermite reaction]]:

:<chem>Fe2O3(s) + 2 Al(s) -> 2 Fe(l) + Al2O3(s)</chem>

Since the reactant amounts are given in grams, they must be first converted into moles for comparison with the chemical equation, in order to determine how many moles of Fe can be produced from either reactant.
* Moles of Fe which can be produced from reactant Fe<sub>2</sub>O<sub>3</sub>
*: <math chem>\begin{align}
 \ce{mol~Fe2O3} &= \frac{\ce{grams~Fe2O3}}{\ce{g/mol~Fe2O3}}\\
 &= \frac{20.0~\ce g}{159.7~\ce{g/mol}} = 0.125~\ce{mol}
\end{align}</math>
*: <math chem> \ce{mol~Fe} = 0.125 \ \ce{mol~Fe2O3} \times \frac{\ce{2~mol~Fe}}{\ce{1~mol~Fe2O3}} = 0.250~\ce{mol~Fe}</math>
* Moles of Fe which can be produced from reactant Al
*: <math chem>\begin{align}
 \ce{mol~Al} &= \frac\ce{grams~Al}\ce{g/mol~Al}\\
 & = \frac{8.00~\ce g}{26.98~\ce{g/mol}} = 0.297~\ce{mol}
\end{align}</math>
*: <math chem> \ce{mol~Fe} = 0.297~\ce{mol~Al} \times \frac\ce{2~mol~Fe}\ce{2~mol~Al} = 0.297~\ce{mol~Fe}</math>
There is enough Al to produce 0.297&nbsp;mol Fe, but only enough Fe<sub>2</sub>O<sub>3</sub> to produce 0.250&nbsp;mol Fe. This means that the amount of Fe actually produced is limited by the Fe<sub>2</sub>O<sub>3</sub> present, which is therefore the limiting reagent.

===Shortcut===
It can be seen from the example above that the amount of product (Fe) formed from each reagent X (Fe<sub>2</sub>O<sub>3</sub> or Al) is proportional to the quantity

<math>\frac{\mbox{Moles of Reagent X }}{\mbox{Stoichiometric Coefficient of Reagent X}}</math>

This suggests a shortcut which works for any number of reagents. Just calculate this formula for each reagent, and the reagent that has the lowest value of this formula is the limiting reagent. We can apply this shortcut in the above example.