A \(20.0\)-mL portion of an HBr solution of unknown strength is diluted to exactly \(240 \mathrm{~mL}\). If \(100.0 \mathrm{~mL}\) of this diluted solution requires \(88.4 \mathrm{~mL}\) of \(0.37 \mathrm{M} \mathrm{NaOH}\) to achieve complete neutralization, what was the strength of the original \(\mathrm{HBr}\) solution?

Understanding molarity is essential when dealing with solutions in chemistry. Molarity represents the concentration of a solution, defined as the number of moles of solute per liter of solution. Mathematically, it's described by the equation:
\( M = \frac{n}{V} \)
where \( M \) is the molarity, \( n \) is the number of moles of solute, and \( V \) is the volume of the solution in liters. In the scenario of titration calculations, determining the molarity of each reactant allows us to understand how much of one substance will react with a given amount of another substance. By using the equation, we can quantify the amount of reactant needed to achieve a complete reaction, which is particularly useful in neutralization reactions.

A neutralization reaction occurs when an acid and a base react to form water and a salt. This type of reaction is important in titration calculations. For instance, when sodium hydroxide (NaOH), a base, is added to hydrobromic acid (HBr), they undergo a neutralization reaction.
In a balanced equation, NaOH and HBr react in a 1:1 mole ratio, meaning one mole of NaOH will neutralize one mole of HBr. During a titration, the point at which all the acid has been neutralized by the base is called the equivalence point, and it is at this point we are able to perform calculations to determine concentrations of the solutions involved in the reaction.

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It based on the law of conservation of mass and the concept of the mole, allows chemists to predict the amounts of substances consumed and produced in a given reaction.
In the context of titration, stoichiometry enables us to use the known molarity and volume of one reactant to find the unknown concentration of another, by employing the mole ratio from the balanced chemical equation. It's this stoichiometric conversion that is key to solving titration problems, ensuring that the moles of one reactant are equal to the moles of another reactant as defined by the chemical equation.

Dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent. The dilution equation is a mathematical way to express the relationship between the concentrations and volumes before and after the dilution process:
\( M_1V_1 = M_2V_2 \)
where \( M_1 \) and \( M_2 \) are the molarities of the solution before and after dilution, and \( V_1 \) and \( V_2 \) are the respective volumes. This equation shows that the product of the initial concentration and volume is equal to the product of the final concentration and volume. In titration calculations, understanding dilution is critical, especially when determining the concentration of the original solution prior to dilution. Dilution does not change the amount of substance present; it only spreads it out into a greater volume of solvent.