A student titrates an unknown monoprotic acid with a \(\mathrm{NaOH}\) solution from a buret. After the addition of \(12.35 \mathrm{~mL}\) of \(\mathrm{NaOH},\) the \(\mathrm{pH}\) of the solution read 5.22. The equivalence point is reached at \(24.70 \mathrm{~mL}\) of \(\mathrm{NaOH}\). What is the \(K_{\mathrm{a}}\) of the acid?

Titration is a laboratory technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration, called the titrant. The process involves adding the titrant to the unknown solution incrementally until a reaction completion criteria, often indicated by a color change by an indicator or a pH meter reading, is reached. This point in the titration is known as the equivalence point.

In acid-base titrations, the titrant is a standard solution of a strong acid or base, which reacts with the acid or base in the unknown solution. The equivalence point is reached when the number of moles of acid equals the number of moles of base, essentially neutralizing each other. Understanding titration curves, which graphically represent the pH of the solution as a function of the volume of titrant added, helps in identifying the equivalence point and thus, plays a crucial role in interpreting titration data.

The equivalence point in a titration is the juncture at which the quantity of titrant added is stoichiometrically equivalent to the quantity of substance present in the sample. For acid-base titrations, this is when the number of moles of acid is equal to the number of moles of base. Detecting the equivalence point precisely is crucial to determining the concentration of the unknown solution.

Indicators or pH meters are commonly employed to detect the equivalence point. The choice of an indicator, if used, is dependent on the acid and base's strength and the expected pH at the equivalence point. Slight color changes in indicators signal the approach toward the equivalence point, however, the use of a pH meter allows for a more accurate determination by monitoring the sudden change in pH that occurs at this critical point in the titration process.

A monoprotic acid is an acid that is capable of donating one proton (hydrogen ion, H+) per molecule during the process of dissociation. Common examples of monoprotic acids include hydrochloric acid (HCl) and acetic acid (CH3COOH). In the titration of a monoprotic acid with a strong base, such as NaOH, each acid molecule reacts with one hydroxide ion (OH-), resulting in a 1:1 molar ratio.

Understanding the concept of monoprotic acids is critical for calculating the equivalence point in titrations because it simplifies stoichiometric calculations. When dealing with monoprotic acids, one can assume that the number of moles of base added will be equal to the number of moles of acid present at the equivalence point, thereby facilitating the concentration determination of the acid.

pH is a logarithmic measure of the hydrogen ion concentration in a solution and is used to denote the acidity or basicity of an aqueous solution. The pH scale ranges from 0 to 14, with 7 being neutral, values below 7 acidic, and values above 7 basic. The pH of a solution is calculated using the equation \( pH = -\log [H^+] \) where \( [H^+] \) is the concentration of hydrogen ions in moles per liter.

During a titration, calculating the pH at different stages allows for the understanding of how the acid-base reaction progresses. Prior to the equivalence point, the pH can give information about the acid's dissociation and after the equivalence point, the pH can indicate the excess amount of titrant. These calculations are fundamental to determining the equivalence point accurately and understanding the buffer capacity of the solution, guiding the selection of indicators.

A conjugate base is the species that remains after an acid has donated a proton during a chemical reaction. It corresponds to the acid minus the proton. For example, the conjugate base of acetic acid (CH3COOH) is the acetate ion (CH3COO-). In the context of titration, as the monoprotic acid reacts with the strong base, it gradually dissociates, forming its conjugate base.

The ratio of the conjugate base to the acid before the equivalence point is reached can be used to calculate the pH of the solution, and the acid dissociation constant (Ka). The Ka value helps in quantifying the strength of the acid, with a smaller Ka indicating a weaker acid, and a larger Ka a stronger acid. This ratio plays an integral role in determining the pH at any given point in an acid-base titration before reaching the equivalence point.