What volume of a \(0.500 M\) HCl solution is needed to neutralize each of the following? (a) \(10.0 \mathrm{~mL}\) of a \(0.300 \mathrm{M} \mathrm{NaOH}\) solution (b) \(10.0 \mathrm{~mL}\) of a \(0.200 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) solution

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In the context of neutralization reactions, such as those between acids and bases, stoichiometry involves using the balanced equation for the reaction to determine the exact amounts of reactants needed to completely react with each other.

For example, when an acid neutralizes a base, the stoichiometric relationship is often a one-to-one ratio, meaning one mole of acid will react with one mole of base. This knowledge allows us to calculate the required volume of an acid solution to neutralize a known amount of a base, as shown in the exercise. Understanding stoichiometry is essential in chemical analysis and industry, where precise amounts of substances must be mixed to yield the desired product.

Molarity represents the concentration of a solution and is defined as the number of moles of solute dissolved in one liter of solution, commonly expressed in moles per liter (M). It is an integral part of the stoichiometry in acid-base titrations because it directly relates the volume of solution to the number of moles of solute.

When calculating volume or molarity in a neutralization reaction, you can rearrange the relationship molarity (M) = moles of solute (n) / volume of solution (V) depending on what information you have and what you need to find. In the given exercise, molarity helps in calculating the number of moles of base initially present and the volume of acid solution needed for neutralization. Molarity is very practical, as it allows chemists to easily scale reactions up or down by simply adjusting the volumes of solutions they use.

Acid-base titration is a laboratory method used to determine the concentration of an acid or base in a solution by neutralization. A measured volume of an acid or base of known concentration (the titrant) is gradually added to a volume of the other with unknown concentration (the analyte), until the reaction reaches an end-point, typically indicated by a color change in an added indicator or by reaching a certain pH value measured by a pH meter.

During the titration, the stoichiometry of the neutralization reaction guides the amount of titrant needed to reach the end-point. As demonstrated in the original exercise, we use stoichiometry and molarity to calculate the exact volumes of an HCl solution required to neutralize given amounts of NaOH and Ba(OH)2 solutions. Through acid-base titration, students learn to execute precise techniques to measure and analyze solutions, an essential skill in many branches of chemistry.