Identifying the Limiting Reactant

Reaction Yields Continued: Identifying the Limiting Reactant

This is an follow-up example from the first lesson on reaction yields showing how to identify the limiting reactant.

Silicon nitride is a very hard, high-temperature-resistant ceramic used as a component of turbine blades in jet engines. It is prepared according to the following equation:

$$\mathrm{3Si}(s) + \mathrm{2N_2}(g) \longrightarrow \mathrm{Si_3N_4}(s)$$

Which is the limiting reactant when 2.00 g of Si and 1.50 g of N2 react?

Solution

Compute the provided molar amounts of reactants, and then compare these amounts to the balanced equation to identify the limiting reactant.

$$\require{cancel}\text{mol Si} = \mathrm{2.00 \; \cancel{g \; Si}} × \cfrac{\text{1 mol Si}}{\mathrm{28.09 \; \cancel{g \; Si}}} = \text{0.0712 mol Si}$$

$$\require{cancel}\mathrm{mol \; N_2} = \mathrm{1.50 \; \cancel{g \; N_2}} × \cfrac{\text{1 mol N_2}}{\mathrm{28.02 \; \cancel{g \; N_2}}} = \mathrm{0.0535 \; mol \; N_2}$$

The provided Si:N2 molar ratio is:

$$\cfrac{\mathrm{0.0712 \; mol \; Si}}{\mathrm{0.0535 \; mol \; N_2}} = \cfrac{\mathrm{1.33 \; mol \; Si}}{\mathrm{1 \; mol \; N_2}}$$

The stoichiometric Si:N2 ratio is:

$$\cfrac{\mathrm{3 \; mol \; Si}}{\mathrm{2 \; mol \; N_2}} = \cfrac{\mathrm{1.5 \; mol \; Si}}{\mathrm{1 \; mol \; N_2}}$$

Comparing these ratios shows that Si is provided in a less-than-stoichiometric amount, and so is the limiting reactant.

Alternatively, compute the amount of product expected for complete reaction of each of the provided reactants. The 0.0712 moles of silicon would yield

$$\mathrm{mol \; Si_3N_4 \; produced} = \mathrm{0.0712 \; mol \; Si} × \cfrac{\mathrm{1 mol \; Si_3N_4}}{\mathrm{3 \; mol \; Si}} = \mathrm{0.0237 \; mol \; Si_3N_4}$$

while the 0.0535 moles of nitrogen would produce

$$\mathrm{mol \; Si_3N_4 \; produced} = \mathrm{0.0535 \; mol \; N_2} × \cfrac{\mathrm{1 mol \; Si_3N_4}}{\mathrm{2 \; mol \; N_2}} = \mathrm{0.0268 \; mol \; Si_3N_4}$$

Since silicon yields the lesser amount of product, it is the limiting reactant.