Limiting reagent

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 (Fe₂O₃) are reacted with 8.00 g aluminium (Al) in the following thermite reaction:

${\displaystyle {\text{Fe}}_2^{}{\text{O}}_3^{}(\text{s})+2\text{Al}(\text{s})⟶2\text{Fe}(\text{l})+{\text{Al}}_2^{}{\text{O}}_3^{}(\text{s})}$

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 Fe₂O₃

  ${\displaystyle \begin{array}{cc}\text{mol}{\text{Fe}}_2^{}{\text{O}}_3^{}& =\frac{\text{grams}{\text{Fe}}_2^{}{\text{O}}_3^{}}{\text{g}/\text{mol}{\text{Fe}}_2^{}{\text{O}}_3^{}}\\ & =\frac{20.0\text{g}}{159.7\text{g}/\text{mol}}=0.125\text{mol}\end{array}}$

  ${\displaystyle \text{mol}\text{Fe}=0.125\text{mol}{\text{Fe}}_2^{}{\text{O}}_3^{}\times \frac{2\text{mol}\text{Fe}}{1\text{mol}{\text{Fe}}_2^{}{\text{O}}_3^{}}=0.250\text{mol}\text{Fe}}$

• Moles of Fe which can be produced from reactant Al

  ${\displaystyle \begin{array}{cc}\text{mol}\text{Al}& =\frac{\text{grams}\text{Al}}{\text{g}/\text{mol}\text{Al}}\\ & =\frac{8.00\text{g}}{26.98\text{g}/\text{mol}}=0.297\text{mol}\end{array}}$

  ${\displaystyle \text{mol}\text{Fe}=0.297\text{mol}\text{Al}\times \frac{2\text{mol}\text{Fe}}{2\text{mol}\text{Al}}=0.297\text{mol}\text{Fe}}$

There is enough Al to produce 0.297 mol Fe, but only enough Fe₂O₃ to produce 0.250 mol Fe. This means that the amount of Fe actually produced is limited by the Fe₂O₃ 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 (Fe₂O₃ or Al) is proportional to the quantity

${\displaystyle \frac{\text{Moles of Reagent X }}{\text{Stoichiometric Coefficient of Reagent X}}}$

This value is the extent of reaction required to deplete each reagent to zero. The reagent that decreases to zero moles with the lowest extent of reaction is the limiting reagent. The extent value can be multiplied by the stoichiometric coefficients of the other reagents and products to determine the amounts of each chemical once the reaction is complete.