= Limiting reagent
{wiki}
= Limiting reactant
{synonym}
The <limiting reagent> is the <reactant> exhausted first if the specified <chemical reaction> proceeds to the maximum conversion permitted by <stoichiometry>. With initial values of <amount of substance> $n_{i,0}$ for the <reactants> and positive consumption coefficients $a_i$, the largest forward <extent of reaction> is $\xi_{\max}=\min_i(n_{i,0}/a_i)$. Compare these quotients, rather than simply choosing the smallest initial quantity. This calculation predicts the maximum <reaction product> quantity and identifies which <reactant> supply must increase to raise it. See https://openstax.org/books/chemistry-2e/pages/4-4-reaction-yields[Flowers et al., Chemistry 2e, limiting reactants].
Start with $3\,\mathrm{mol}$ of <molecular hydrogen>, $1\,\mathrm{mol}$ of <molecular oxygen> and no <water>. Assume complete conversion by the displayed <chemical reaction>, without competing reactions. Then
$$
\xi_{\max}=\min\left(\frac{3\,\mathrm{mol}}2,\frac{1\,\mathrm{mol}}1\right)=1\,\mathrm{mol}.
$$
The <molecular oxygen> is the <limiting reagent>. Consumption of $2\,\mathrm{mol}$ of <molecular hydrogen> and $1\,\mathrm{mol}$ of <molecular oxygen> forms $2\,\mathrm{mol}$ of <water>, leaving $1\,\mathrm{mol}$ of <molecular hydrogen>. Initially there are $1.806642228\times10^{24}$ <molecular hydrogen> <molecules> and $6.02214076\times10^{23}$ <molecular oxygen> <molecules>; after conversion there are $1.204428152\times10^{24}$ <water> <molecules> and $6.02214076\times10^{23}$ leftover <molecular hydrogen> <molecules>.
\Image[/limiting-reagent-amounts.png]
{title=Oxygen runs out while one mole of molecular hydrogen remains}
{description=The horizontal axis is <extent of reaction>, rather than time. The endpoint assumes complete conversion by one <chemical reaction>; the curves express <stoichiometry>.}
As a check, the initial inventory has $6\,\mathrm{mol}$ of <hydrogen> <chemical atoms> and $2\,\mathrm{mol}$ of <oxygen> <chemical atoms>. The final <water> contains $4\,\mathrm{mol}$ of <hydrogen> <chemical atoms>, and leftover <molecular hydrogen> supplies the remaining $2\,\mathrm{mol}$. The atom totals balance even though the total <amount of substance> of <molecules> falls from four to three <moles>.
Back to article page
