A mixture of \(1.0\) mole of \(\mathrm{Al}\) and \(3.0\) mole of \(\mathrm{Cl}_{2}\) are allowed to react as: $$ 2 \mathrm{Al}_{(\mathrm{s})}+3 \mathrm{Cl}_{2} \longrightarrow 2 \mathrm{AlCl}_{3(\mathrm{~s})} $$ (a) Which is limiting reagent? (b) How many moles of \(\mathrm{AlCl}_{3}\) are formed? (c) Moles of excess reagent left unreacted.

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It is built upon the law of conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed. With stoichiometry, it becomes possible to predict how much product will form from given reactants, as well as to determine the amount of reactants needed for a reaction to occur.

In stoichiometry, equations must be balanced, meaning the number of atoms for each element should be the same on both sides of the equation. This balance is based on the mole concept, where a mole represents Avogadro's number of particles, or approximately 6.022 \(\times\) 10²³ atoms, molecules, or ions. Through the balanced equation, the ratios of the moles of reactants and products can then be determined, leading to accurate stoichiometric calculations.

A chemical reaction is a process where substances, called reactants, transform into new substances, known as products. Chemical reactions are described by chemical equations, which use chemical formulas to represent the substances involved. These equations provide a concise way to show the conversion of reactants to products, indicating the physical states of the compounds with symbols like (s) for solids, (l) for liquids, (g) for gases, and (aq) for aqueous solutions.

The equation for a chemical reaction must be balanced; this means it complies with the law of conservation of mass. The balancing of an equation involves ensuring that there are equal numbers of each type of atom on both sides of the equation. This is crucial for stoichiometric calculations, as it sets the stage for determining the mole ratios of reactants and products.

The mole ratio is a key concept in stoichiometry, as it defines the proportion of reactants that react with each other and the proportion of products formed. It is determined from the coefficients in a balanced chemical equation, which provide the ratio by which reactants combine and products form.

For instance, in the reaction of aluminum with chlorine to form aluminum chloride (\(\mathrm{2 Al + 3 Cl}_2 \longrightarrow 2 \mathrm{AlCl}_3\)), the mole ratio between aluminum and chlorine is 2:3, and the mole ratio between aluminum and aluminum chloride is 1:1. These ratios are used to calculate the amount of product that can be formed from given amounts of reactants (stoichiometry) and to establish which reactant will run out first (limiting reagent problem).

In a chemical reaction, the excess reagent is the substance that remains after the limiting reagent has been completely consumed. The limiting reagent is the one that will be used up first and limits the amount of product that can be formed in the reaction.

By comparing the amount of each reactant with the mole ratios from the balanced equation, we can identify the limiting reagent. The other reagents will be in excess, meaning that there will be leftover amounts after the reaction has completed. Calculating the excess reagent remaining involves determining how much of it was needed to react with the limiting reagent and subtracting this from the initial amount. This calculation is crucial in determining the efficiency of a reaction and for planning the use of reagents in practical applications.