Suppose that \(0.483 \mathrm{~g}\) of an unknown monoprotic weak acid, HA, is dissolved in water. Titration of the solution with \(0.2 .50 \mathrm{M}\) \(\mathrm{NaOH}\) (aq) required \(42.0 \mathrm{~mL}\) to reach the stoichiometric point. After the addition of \(21.0 \mathrm{~mL}\), the \(\mathrm{pH}\) of the solution was found to be \(3.75\). (a) What is the molar mass of the acid? (b) What is the value of \(\mathrm{p} K_{\mathrm{a}}\) for the acid? Can you identify the acid?

Titration is a technique in chemistry used to determine the concentration of a solution by reacting it with a solution of known concentration, called the titrant. In the context of a weak acid titration, the weak acid (HA) in solution is titrated with a strong base, such as sodium hydroxide (NaOH). Unlike strong acids, weak acids do not completely dissociate in water; they establish an equilibrium between the undissociated acid (HA) and the dissociated form (A- and H+).

During the titration of a weak acid with a strong base, there is a point known as the equivalence or stoichiometric point where the amount of base added equals the amount of the substance being titrated. In this exercise, the stoichiometric point is reached when the moles of NaOH added equal the moles of the weak acid present.

Another significant point during the titration is the halfway point, also called the midpoint, where exactly half of the acid has been neutralized. This is the point where the concentrations of HA and A- are equal, which is where the pH of the solution equals the pKa, the negative log of the acid dissociation constant (Ka).

The molar mass of a compound is the mass of one mole of that substance and is expressed in grams per mole (g/mol). It's a fundamental property used to determine the mass of particles in a given substance. To calculate the molar mass of an unknown acid in a titration exercise, as described in the given problem, one would first need to establish the amount of titrant used to reach the stoichiometric point.

As mentioned in the solution, by utilizing the molarity of the NaOH solution and the volume used, we can determine the moles of NaOH at the equivalence point. Given that the reaction between a monoprotic weak acid and NaOH is a 1:1 stoichiometry, the moles of the unknown acid (HA) will match the moles of NaOH. Then the molar mass of the acid is found by dividing the initial mass of HA (in grams) by the moles of HA.

This calculation is a crucial step in identifying the acid. It can be used along with other properties, such as the pKa value, to compare against known acids, helping us determine the chemical identity of the unknown acid.

The acidity constant, Ka, is a quantitative measurement of the strength of an acid in solution. The pKa is the negative base-10 logarithm of Ka and provides a more convenient way to express acid strength. A smaller pKa value indicates a stronger acid because it implies a larger acidity constant. In the context of the titration of a weak acid with a strong base, we can calculate the pKa using the pH at the midpoint of the titration.

In the exercise, the pH at the midpoint (when half the molar amount of the acid has been neutralized by the base) is given, and this pH is numerically equal to the pKa of the acid. Knowing the pKa is extremely valuable because it gives us insight into the acid's behavior in the solution and can help us identify the acid from a list of potential candidates with known pKa values.

To summarize, the process of calculating pKa in this exercise is straightforward – the pH value at the midpoint is taken to be the pKa of the weak acid. When considering the pH of a solution of a weak acid and its conjugate base at equilibrium, the Henderson-Hasselbalch equation can also be applied, but this is not necessary for this specific problem as the pH measurement directly provides the needed pKa value.