Four solutions of unknown \(\mathrm{HCl}\) concentration are titrated with solutions of \(\mathrm{NaOH}\). The following table lists the volume of each unknown \(\mathrm{HCl}\) solution, the volume of \(\mathrm{NaOH}\) solution required to reach the equivalence point, and the concentration of each \(\mathrm{NaOH}\) solution. Calculate the concentration (in M) of the unknown HCl solution in each case.

Titration is a laboratory method used to determine the concentration of an unknown solution by reacting it with a solution of known concentration. It involves the gradual addition of one solution (the titrant) to another, until the chemical reaction between the two solutions is complete. This point of completion is known as the equivalence point, where the amount of titrant added stoichiometrically matches the quantity of the substance in the unknown solution. A common indicator used turns a specific color at the equivalence point, signaling the end of the titration.

Throughout the titration process, careful measurements of the volumes of the solutions are crucial. These measurements play a central role in the calculations and the final determination of the unknown concentration.

The equivalence point in a titration is the exact point at which the amount of titrant added equals the amount of substance in the sample; in other words, when the number of moles of the acid equals the number of moles of the base. At this point, the reaction is complete. Identifying the equivalence point accurately is vital for a precise titration.

For acid-base reactions, the equivalence point is typically indicated by a pH change, which can be identified using pH meters or indicators that change color at certain pH levels. Understanding the equivalence point is important for calculating concentrations, as it relates directly to the stoichiometry of the reaction being analyzed.

Molarity is a unit of concentration that measures the number of moles of a solute per liter of solution, denoted as M. It is calculated using the formula \( \text{M} = \frac{\text{n (moles)}}{\text{V (liters of solution)}} \).

Molarity is an essential concept in titration since it relates the volume of the solution to the quantity of the substance dissolved in it. In the context of the textbook exercise problem, molarity helps determine the concentration of the unknown HCl solution. When the molarity and volume of the titrant are known, they can be used to calculate the molarity of the unknown solution by applying the stoichiometry of the balanced equation for the acid-base reaction.

Stoichiometry is the part of chemistry that deals with the quantitative relationships that exist between reactants and products in a chemical reaction. These relationships are based on the balanced chemical equation and the mole concept. It allows chemists to predict the amounts of substances consumed and produced in a given reaction.

In a titration, stoichiometry is used to derive the relationship between the molarity and volume of the titrant and the analyte (the substance being analyzed). The balanced chemical equation provides the mole ratio needed to perform these calculations. Factors like the coefficients in the equation affect how the mole ratio is applied when using stoichiometry to solve for concentrations.

An acid-base reaction is a type of chemical reaction that occurs between an acid and a base. It typically forms water and a salt. In the context of our problem, when hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH), it forms sodium chloride (NaCl) and water (H2O). The reaction can be represented by the balanced chemical equation: \( \text{HCl}_{(aq)} + \text{NaOH}_{(aq)} \rightarrow \text{NaCl}_{(aq)} + \text{H}_2\text{O}_{(l)} \).

Understanding the nature of this reaction is crucial for performing a titration because it defines the mole ratio that is used in the calculations. For every mole of HCl that reacts, one mole of NaOH is required, representing a 1:1 mole ratio. This simple stoichiometry allows for straightforward calculation of the unknown concentration, once the equivalence point is reached and provided, that all of the necessary volume and concentration data are known.