Solved Examples on Limiting Reagent Formula

Question 1: If you have 6 moles of iron (Fe) and 4 moles of sulfur (S), which one is the limiting reactant in the following reaction:

Fe + S → FeS

Determine the limiting reactant for this reaction.

Solution:

The balanced chemical equation is already given as:

Fe + S → FeS

Using Reaction Stoichiometry Method,

We determine the mole ratio for each reactant:

Mole ratio of Fe = 6/1 = 6

Mole ratio of S = 4/1 =4

As the mole ratio of S is lesser in this case, S is the limiting reactant in this case.

Question 2: Consider the reaction of the formation of ammonia from nitrogen and hydrogen. We have 14 grams of Nitrogen gas and 12 grams of Hydrogen gas. Determine the limiting reactant for this case.

Solution: 

The balanced chemical equation for the reaction:

N₂ + 3H₂ → 2NH₃

Find the moles of the reactant,

n(N₂) = 14/14 = 1 mole

n(H₂) = 12/2 = 6 moles

Using the Product Yield Method,

We observe that 1 mole of Nitrogen is required to form 2 moles of Ammonia and 3 moles of Hydrogen gas are required for the same.

In the given problem, we have 1 mole of Nitrogen which can produce 2 moles of ammonia.

6 moles of hydrogen which can produce 4 moles of ammonia.

Thus, in this case, the reaction would stop when 1 mole of Nitrogen and 3 moles from the available 6 moles of hydrogen would react completely. Thus, Nitrogen(N₂) becomes the limiting reactant in this case. The other reactant H₂, which would remain after the reaction will be called an excess reactant.

Question 3: Determine the limiting reagent if 32 grams of methane reacts with 32 grams of oxygen gas.

Solution:

The balanced chemical equation for the above reaction is as follows:

CH₄ + 2O₂ →  CO₂ + 2H₂O

We have, 

n(CH₄) = 32/16 = 2 moles

n(O₂) = 32/16 = 2 moles

Using Product Yield Method,

2 moles of methane(CH₄) can produce 2 moles of carbon dioxide(CO₂).

2 moles of oxygen(O₂) can produce 1 mole of carbon dioxide(CO₂).

We know that the reactant which produces the least amount of product is the limiting reactant. Thus, in this case, oxygen(O₂) gas will be the limiting reactant.

Question 4: Consider the chemical reaction that produces silver chloride from silver nitrate and hydrochloric acid. If you have 2 moles of silver nitrate and 1 mole of hydrochloric acid, determine the limiting reactant by the Mole-Ratio method.

Solution:

The balanced chemical equation for the reaction is as follows,

AgNO₃ + HCl → AgCl + HNO₃

Using Reaction Stoichiometry Method,

Mole ratio of AgNO₃ = 2/1 = 2

Mole ratio of HCl = 1/1 = 1

As the mole ratio of HCl is less in this case, HCl is the limiting reactant in this case.

Question 5: Consider the chemical reaction between magnesium metal and oxygen gas to form magnesium oxide. If you have 4 moles of magnesium and 3 moles of oxygen gas, determine the limiting reactant by the Product Yield method.

Solution:

The balanced chemical equation for the reaction is as follows:  

2Mg + O₂ -> 2MgO

Using Product Yield Method,

We observe that 2 moles of Mg produces 2 moles of MgO and 1 Mole of O₂ produces 2 moles of MgO. 

We have 4 moles of Mg, so 4 moles of MgO can be produced from them. And, we have 3 moles of oxygen gas, which can produce 6 moles of MgO. As Mg produces the least amount of product in this case, Mg becomes the limiting reactant for this reaction.

A chemical reaction occurs when one or more reactants undergo some chemical changes to form new products. If the reaction involves two or more reactants, one of the reactants becomes the limiting reactant, when the reaction occurs practically. As, theoretically, a chemical reaction occurs in a stoichiometric proportion of the number of moles of reactants and products, but when a chemical reaction is carried out practically, it is impossible to have exact proportions of reactant moles due to limitations in the measuring instruments. Thus, the reactant which gets exhausted first and stops the reaction from proceeding further is termed a limiting reagent. 

In this article, we will explore the definition, examples, formula, and some examples of limiting reactants.