For the reaction shown, find the limiting reactant for each of the initial quantities of reactants. $$ 4 \mathrm{Cr}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s) $$ (a) \(1 \mathrm{~mol} \mathrm{Cr} ; 1 \mathrm{~mol} \mathrm{O}_{2}\) (b) \(4 \mathrm{~mol} \mathrm{Cr} ; 2.5 \mathrm{~mol} \mathrm{O}_{2}\) (c) \(12 \mathrm{~mol} \mathrm{Cr} ; 10 \mathrm{~mol} \mathrm{O}_{2}\) (d) \(14.8 \mathrm{~mol} \mathrm{Cr} ; 10.3 \mathrm{~mol} \mathrm{O}_{2}\)

Stoichiometry is at the heart of every chemical reaction, acting as a quantitative bridge between reactants and products in a chemical equation. Imagine it as a recipe in chemistry; it tells you how much of each substance you need to create a certain amount of product, just like a cooking recipe specifies quantities of ingredients for a dish.

When dealing with chemical reactions, stoichiometry allows us to calculate the amount of reactants needed to carry out the reaction to completion or predict the amount of product formed from given reactants. It's based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. As such, the atoms that start as reactants must equal the atoms found in the products, although they may be arranged differently.

Importance in Chemical Reactions

Understanding stoichiometry is essential for chemists to ensure that reactions have enough material to proceed and to calculate how much product can be expected. Without it, we would be like chefs trying to bake a cake without knowing how much flour or sugar is required. By calculating molar ratios - the proportion of one compound to another as dictated by the balanced equation - we can accurately align our quantities with the prescribed 'recipe' of the chemical reaction.

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. It involves breaking of old bonds and formation of new ones, resulting in different substances (products) than you started with (reactants).

The balanced chemical equation provided in our exercise $$4 \text{Cr}(s)+3 \text{O}_{2}(g) \rightarrow 2 \text{Cr}_{2}\text{O}_{3}(s)$$ shows a synthesis reaction, where a compound is formed from simpler materials. Balancing this equation is crucial as it ensures the law of conservation of mass is obeyed, indicating that atoms are neither created nor destroyed, only rearranged.

Identifying Limiting Reactants

In such reactions, the limiting reactant is the substance that is totally consumed when the chemical reaction is complete. Once it's used up, the reaction stops, and no more products can form, regardless of the remaining quantities of other reactants. In our example, identifying the limiting reactant is critical since it determines the maximum yield of chromium(III) oxide that can be produced.

The mole concept is a fundamental pillar of chemistry because it relates the macroscopic world we can measure, to the microscopic world of atoms and molecules. One mole is defined as exactly 6.022 x 10^23 particles, which is Avogadro's number, and can be atoms, molecules, ions, or electrons.

In the context of our chemical reaction, we use the mole concept to count atoms in terms of moles to carry out stoichiometric calculations. Using moles allows chemists to 'count' atoms by weighing, since weighing atoms individually is impossible due to their minuscule mass.

Applying the Mole Concept

During a chemical reaction, you're often given quantities in moles, allowing you to use the stoichiometric relationships established by the balanced equation to calculate the amounts of products formed or reactants needed. In the provided exercise, you can see the practical application where amounts of reactants are given in moles, aligning perfectly with the stoichiometry of the reaction to find the limiting reactant.