Consider the generic chemical equation: $$ \mathrm{A}+3 \mathrm{~B} \longrightarrow \mathrm{C} $$ What is the limiting reactant when each of the initial quantities of \(\mathrm{A}\) and \(\mathrm{B}\) is allowed to react? (a) \(1 \mathrm{~mol} \mathrm{~A} ; 4 \mathrm{~mol} \mathrm{~B}\) (b) \(2 \mathrm{~mol} \mathrm{~A} ; 3 \mathrm{~mol} \mathrm{~B}\) (c) \(0.5 \mathrm{~mol} \mathrm{~A} ; 1.6 \mathrm{~mol} \mathrm{~B}\) (d) \(24 \mathrm{~mol} \mathrm{~A} ; 75 \mathrm{~mol} \mathrm{~B}\)

Stoichiometry is a crucial concept in chemistry that deals with the quantitative relationships of substances as they participate in chemical reactions. By understanding stoichiometry, one can determine the amounts of reactants or products that are involved in a chemical reaction.

A stoichiometric calculation often begins with a balanced chemical equation, which tells us the proportions in which reactants combine to form products. It involves the use of the mole concept, as it is the standard unit for measuring the amount of substance. Stoichiometry is pivotal when dealing with problems related to limiting reactants because it allows the prediction of how much of a reactant is needed and how much product can be formed from given quantities of reactants.

In the context of our exercise, stoichiometry helps us to understand that 1 mole of reactant A requires 3 moles of reactant B to form product C, establishing the basis for finding the limiting reactant in various scenarios.

The mole ratio, an integral part of stoichiometry, is derived from the coefficients of a balanced chemical equation. It reflects the relative amounts of reactants needed to produce products. For the chemical reaction given as \( A + 3B \rightarrow C \), the mole ratio of A to B is 1:3.

This ratio means that for every mole of A, three moles of B are required for the reaction to proceed to completion. Understanding this allows chemists to calculate how much of each reactant is necessary when given certain amounts, which is particularly helpful in determining the limiting reactant. It's crucial to comprehend that any deviation from the established mole ratio could either leave excess reactant or insufficient reactant, affecting the amount of product formed.

A chemical reaction is a process where reactants transform into products. It involves making and breaking chemical bonds, resulting in the formation of one or more new substances. The reactions abide by the laws of conservation of mass and energy, meaning that the number of atoms for each element is conserved during the reaction.

The generic equation \( A + 3B \rightarrow C \) symbolizes such a transformation, with A and B being the initial reactants and C being the final product. Familiarity with the nature of the reactants and the conditions under which they react can provide further insight into the reaction mechanism and the characteristics of the resulting products.

In chemistry, the relationship between reactants and products in a chemical reaction is defined by the law of conservation of mass, as well as by the stoichiometric coefficients of a balanced chemical equation. These coefficients tell us exactly how much of each reactant is needed to form the desired products without any leftovers.

When dealing with limitations, understanding which reactant will be used up first (the limiting reactant) is essential. The limiting reactant is the substance that will be completely consumed in the reaction first, thus determining the maximum amount of product that can be formed. Once this reactant is exhausted, the reaction stops, regardless of the presence of excess amounts of the other reactants.

In the solutions provided for the various scenarios (a to d), identifying the limiting reactant allows to predict the extent to which the chemical reaction will proceed and how much product will ultimately be produced.