Question

In a reaction $A + {B_2} \to A{B_2}$, identify the limiting reagent, if any, in the following reaction mixtures.
(A) 300 atoms of $A$ + 200 molecules of ${B_2}$
(B) 2 mol of $A$ + 3 mol ${B_2}$
(C) 100 atoms of $A$+ 100 molecules of ${B_2}$
(D) 5 mol of $A$ + 2.5 mol of ${B_2}$
(E) 2.5 mol of $A$ + 5 mol of ${B_2}$

Answer 1

Hint: A limiting reagent is a reagent in a reaction which is used up completely in a reaction. It determines the amount of the product formed after the reaction because the reaction cannot proceed
without it. Once we calculate the number of mol of each reactant in the reaction, the limiting reagent can be determined.

Complete step by step answer:
A limiting reagent in a reaction is the reagent which is used completely in the reaction. It is present in less quantity as compared to the other reagent. It determines the amount of the product formed because without the limiting reagent the reaction cannot proceed further.
To identify the limiting reagent in a reaction we first need to balance the chemical equation of the reaction then calculate the number of mol of each reactant present in the reaction and compare how many mol of each reactant are required to produce the product. Thus, the reactant which is being used completely for producing the product is the limiting reagent.
So, for the above given question,
$A + {B_2} \to A{B_2}$
(A) According to the equation, 1 atom of $A$ reacts with 1 molecule of ${B_2}$.
So, 200 molecules of ${B_2}$ will react with 200 atoms of $A$ and thus, 100 atoms of $A$ will remain unreacted and ${B_2}$ here is the limiting reagent.
(B) According to the equation, 1 mol of $A$ reacts with 1 mol of ${B_2}$.
So, 2 mol of $A$ will react with 2 mol of ${B_2}$ and thus, I mol of ${B_2}$ remains unreacted and therefore, $A$ is the limiting reagent.
(C) According to the equation, 1 atom of $A$ reacts with 1 molecule of ${B_2}$.
So, 100 atoms of $A$ react with 100 molecules of ${B_2}$ So, there is no limiting reagent in the reaction and the reactants are said to be present in stoichiometric amount.
(D) According to the equation, 1 mole of $A$ reacts with 1 mol of ${B_2}$.
So, 2.5 mol of ${B_2}$ react with 2.5 mol of $A$ and thus, 2.5 mole of $A$ are lest unreacted and thus, ${B_2}$ is the limiting reagent.
(E) According to the equation, 1 mole of $A$ reacts with 1 mol of${B_2}$.
So, 2.5 mol of $A$ react with 2.5 mol of ${B_2}$ and 2.5 mol of ${B_2}$ remain unreacted and thus, $A$ is the limiting reagent.

Note: Stoichiometry is the branch that deals with the calculation of masses or volumes of the reactants and products in the reaction. It is measured with the help of a balanced chemical equation. Whenever a chemical change takes place a chemical reaction occurs. Stoichiometry measures the elements in the reaction.