Determine the volume of \(0.225 \mathrm{M} \mathrm{KOH}\) solution required to neutralize each sample of sulfuric acid. The neutralization reaction is: $$ \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{KOH}(a q) \longrightarrow \mathrm{K}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) \(45 \mathrm{~mL}\) of \(0.225 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) (b) \(185 \mathrm{~mL}\) of \(0.125 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) (c) \(75 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\)

Chemical stoichiometry is the branch of chemistry that deals with determining the relative quantities of reactants and products involved in a chemical reaction. It is rooted in the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Thus, the amount of each element must be the same in the reactants and products.

Starting with a balanced chemical equation, like the neutralization reaction between sulfuric acid \( \mathrm{H}_{2} \mathrm{SO}_{4} \) and potassium hydroxide \( \mathrm{KOH} \) given in the exercise, stoichiometry allows us to calculate the exact amount of reactants needed to react completely without excess, or to predict the amount of product produced.

To perform these calculations in the context of neutralization, we identify that one mole of sulfuric acid reacts with two moles of potassium hydroxide. Knowing this ratio is crucial for determining the volumes of KOH solution required to neutralize given volumes of sulfuric acid solution, an application of stoichiometry.

Molarity, denoted by \( M \), is a measurement of the concentration of a solute in a solution. It is defined as the number of moles of solute dissolved in one liter of solution. The molarity equation is: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]

Understanding molarity is essential for preparing solutions in a lab and for conducting reactions that require precise reactant concentrations, such as the neutralization reaction described in the exercise. By using the molarity and volume of the sulfuric acid, \( \text{moles} = \text{molarity} \times \text{volume in liters} \), we calculated the moles of acid, which was subsequently used to calculate the volume of KOH needed for neutralization based on the stoichiometry of the reaction.

Acid-base titration is a laboratory procedure used to determine the concentration of an unknown acid or base by neutralizing it with a base or acid of known concentration, respectively.

In a typical titration, the known solution (the titrant) is added gradually from a burette to the unknown solution (the analyte) until the reaction reaches the endpoint, signifying neutralization. An indicator is often used to visually signify the endpoint of the titration.

The exercise illustrates the concept through a hypothetical titration process where KOH, the titrant, is added to sulfuric acid, the analyte, until neutralization. The volume of KOH required gives us information about the amount of sulfuric acid present, which can be used to determine its concentration if it were unknown.

The mole concept is a fundamental building block in chemistry that relates mass to number of atoms or molecules. One mole contains exactly \(6.022 \times 10^{23}\) entities (Avogadro’s number), whether they are atoms, ions, or molecules.

In the context of the exercise problem, we use the mole concept to convert between moles and volumes using the molarity of the solutions. As the problems deal with a liquid solution, understanding the relationship between moles, molarity, and volume is crucial for solving for the unknown volumes of KOH required for neutralization.

By finding the number of moles of sulfuric acid in each sample and knowing that the stoichiometry of the reaction requires twice the number of moles of KOH, we directly apply the mole concept to find the volumes of a KOH solution of a certain molarity that will neutralize those amounts of sulfuric acid.