A \(25.00-\mathrm{mL}\) sample of hydrochloric acid solution requires \(24.16 \mathrm{mL}\) of \(0.106 \mathrm{M}\) sodium hydroxide for complete neutralization. What is the concentration of the original hydrochloric acid solution?

Stoichiometry is an area of chemistry that deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction. It is based on the conservation of mass and the principle of fixed proportions stated in the law of definite proportions. For a neutralization reaction, like the one involving hydrochloric acid (HCl) and sodium hydroxide (NaOH), stoichiometry tells us how much of one reactant is needed to react completely with a given amount of the other.

Understanding stoichiometry involves interpreting the coefficients in a balanced chemical equation. For example, in the equation \( HCl (aq) + NaOH (aq) \to H_{2}O (l) + NaCl (aq) \), the coefficients imply a 1:1 molar ratio between HCl and NaOH. This means that one mole of HCl will neutralize one mole of NaOH. Applying this to problem-solving, once you know the amount of NaOH, you can directly find the equivalent amount of HCl needed for neutralization because of their 1:1 stoichiometric relationship.

Molarity is a measure of concentration in chemistry, expressed as the number of moles of a solute divided by the volume of the solution in liters. The unit of molarity is moles per liter (M). To calculate the molarity of a solution, the formula used is:\[ Molarity = \frac{moles \text{ of solute}}{volume \text{ of solution in liters}} \]

In the context of the given problem, once you have determined the moles of NaOH used in the titration, you can calculate the molarity of the HCl solution. Since the exercise provides the volume of the acid in milliliters (mL), it's crucial to convert this volume into liters before using it in the molarity equation. Dividing the moles of HCl by the volume of the HCl solution (expressed in liters) will yield its concentration in molarity.

Balancing a chemical equation is essential because it ensures that the law of conservation of mass is obeyed in a chemical reaction. It means that atoms are neither created nor destroyed, and the same number of each type of atom must be present on both sides of the equation. A balanced chemical equation has the same number of each element's atoms on both the reactant and product sides.

For the reaction presented in the exercise, \( HCl (aq) + NaOH (aq) \to H_{2}O (l) + NaCl (aq) \), the equation is already balanced. Each side has one chloride (Cl), one sodium (Na), one hydrogen (H), and one oxygen (O) atom. When using this balanced equation to solve problems, it ensures that the stoichiometric ratios reflect the true proportions of substances involved in the reaction.

Acid-base titration is a quantitative analytical technique used to determine the concentration of an unknown acid or base by neutralizing it with a base or acid of known concentration. The point at which the neutralization is complete is known as the equivalence point, and it is often marked by a color change if an indicator is used, or by a sudden change in pH monitored with a pH meter.

In a titration exercise like the one we have, you typically have a known volume of an acid (HCl) and you add a base (NaOH) of known concentration until neutralization is achieved. By recording the volume of the base added to reach the equivalence point, and knowing the stoichiometry of the reaction (from a balanced equation), you can calculate the concentration of the original acid solution. This technique combines knowledge of stoichiometry, molarity, and balancing equations to accurately determine the unknown concentration.