Consider the following reaction: $$ 4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ It takes \(2.00 \mathrm{~L}\) pure oxygen gas at STP to react completely with a certain sample of aluminum. What is the mass of aluminum reacted?

Understanding chemical reaction stoichiometry is pivotal when dealing with reactions, as it ties together the proportion of reactants and products. Stoichiometry is grounded in the law of conservation of mass which states that matter cannot be created or destroyed in an isolated system. The balance in a chemical equation represents this, ensuring that the number of atoms for each element is equal on the reactant and product sides.

For instance, in the reaction provided in the exercise, the coefficients 4, 3, and 2 tell us directly the molar ratio in which aluminum (\text{Al}) and oxygen (\text{O\(_2\)}) react to form aluminum oxide (\text{Al\(_2\)O\(_3\)}). This ratio allows us to solve complex chemistry problems by calculating the amount of reactants needed or products formed.

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. One mole of any substance contains Avogadro's number (\text{6.022 x 10\(^{23}\)}) of particles, which could be atoms, molecules, ions, or electrons.

In the exercise, moles are utilized to convert the volume of oxygen gas to a quantity that can be used alongside the stoichiometric coefficients of the chemical equation. Understanding this concept allows the student to manipulate quantities of substances in a chemical reaction with precision.

The gas laws are a series of laws that relate the pressure, volume, temperature, and number of moles of a gas. At standard temperature and pressure (0°C and 1 atm), one mole of any gas occupies 22.4 liters. This is a key point from the ideal gas law, which is a cornerstone of understanding how gases behave under different conditions.

In the context of our exercise, the gas law is applied to determine that 2 liters of oxygen gas at STP corresponds to 0.0893 moles. Knowledge of gas laws is also essential in predicting how gases will react under changing conditions.

The molar mass is the mass of one mole of a substance, typically measured in grams per mole (g/mol). It is numerically equivalent to the atomic or molecular weight of a substance but gives us a way to translate moles to grams, an invaluable step for practical lab work.

As seen in the final calculation step for the aluminum mass in our exercise, the molar mass of aluminum (26.98 g/mol) is crucial for converting the calculated moles of aluminum into grams, thus providing the mass of aluminum that reacted with the oxygen.