Consider the reaction between reactants \(\mathrm{S}\) and \(\mathrm{O}_{2}\) : $$ 2 \mathrm{~S}(\mathrm{~s})+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g) $$ If a reaction vessel initially contains \(5 \mathrm{~mol} \mathrm{~S}\) and \(9 \mathrm{~mol} \mathrm{O}_{2}\), how many moles of \(\mathrm{S}, \mathrm{O}_{2}\), and \(\mathrm{SO}_{3}\) will be in the reaction vessel after the reactants have reacted as much as possible? (Assume \(100 \%\) actual yield.)

Stoichiometry is the quantitative relationship between the reactants and products in a chemical reaction. It allows us to predict how much product will be formed from given amounts of reactants or how much of the reactants are needed to create a certain amount of product.

When solving a stoichiometry problem, such as the one provided, the first step is to ensure that we have a balanced chemical equation. From there, we can use the coefficients from the balanced equation to determine the proportions with which the reactants combine and compare this to the amounts we have. Using the mole concept (which we'll discuss in more detail later), we convert all given information into moles, as this is the unit used in stoichiometry calculations.

In the provided example, the balanced equation is our roadmap, giving us the ratio of sulfur to oxygen to sulfur trioxide. Understanding stoichiometry is crucial as it forms the basis for much of the calculations in chemistry.

Chemical reactions involve the transformation of one or more substances into new substances. The equation representing the reaction between sulfur (S) and oxygen (O₂) to form sulfur trioxide (SO₃) is a representation of such a transformation.

These equations not only describe the substances involved in the reaction but also give insight into the reactants' and products' physical states (solid, liquid, gas), depicted by the symbols (s), (l), (g), respectively. The balanced reaction equation indicates how many molecules or moles of each reactant are needed to create a certain amount of product. In this particular case, for every 2 moles of pure sulfur used, 3 moles of oxygen gas are required to produce 2 moles of sulfur trioxide gas. Knowing this, we can begin to understand the concept of limiting and excess reactants.

The mole concept is a fundamental aspect of chemistry that relates the macroscopic amounts of substances to their constituent particles. One mole is Avogadro's number (\(6.022 \times 10^{23}\) particles) of substance. The mole allows chemists to count atoms, ions, and molecules in a way that makes it possible to predict the mass of substances used and produced in a reaction.

In the context of the limiting reactant problem, we use the mole concept to describe amounts of reactants and products. We often start with the mass of substances and convert these to moles using molar masses. With moles, we can make direct comparisons using the balanced equation to find the limiting reactant and determine the amounts of substances after the reaction. This is crucial in the exercise provided, where we work entirely in moles to ascertain the amounts of S, O₂, and SO₃ before and after the reaction.

Balanced equations are essential in chemistry, as they ensure that the Law of Conservation of Mass is upheld, meaning matter cannot be created or destroyed in a chemical reaction. Thus, the number of atoms of each element must be the same on both sides of the reaction. Understanding how to balance equations is critical for stoichiometry, as it gives us the stoichiometric coefficients that relate the amounts of reactants to products.

In the equation for the reaction of sulfur with oxygen, we see the coefficients 2 and 3 before S and O₂, respectively. These numbers are used directly to solve stoichiometry problems, including limiting reactant problems, as they tell us the exact ratio in which substances react. For example, in the given exercise, the balanced equation informed us that for every 2 moles of S, 3 moles of O₂ were required, which was the crux in identifying the limiting reactant.