A 0.1276 -g sample of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.0633 \mathrm{M} \mathrm{NaOH}\) solution. The volume of base required to bring the solution to the equivalence point was \(18.4 \mathrm{~mL}\). (a) Calculate the molar mass of the acid. (b) After \(10.0 \mathrm{~mL}\) of base had been added during the titration, the \(\mathrm{pH}\) was determined to be 5.87 . What is the \(K_{\mathrm{a}}\) of the unknown acid?

Understanding how to calculate the molar mass of a substance is a fundamental skill in chemistry that allows us to convert between mass and moles. It is especially important in the context of a titration analysis, where precise measurements are necessary to determine the concentration and mass of analytes.

In an acid-base titration, when an unknown acid reacts with a known base, we can determine the molar mass of the acid by first finding the number of moles of base that reacted at the equivalence point - the point where the number of moles of acid is equal to the number of moles of base. Once the moles of base are calculated from its concentration and volume used, the moles of the unknown acid are determined, since they are stoichiometrically equivalent at the equivalence point.

Steps to Calculate Molar Mass

• Calculate moles of the titrant (base or acid) from volume and concentration.
• Assuming a 1:1 reaction stoichiometry, moles of the unknown substance (acid or base) will be equal to the moles of the titrant.
• Calculate the molar mass of the unknown substance by dividing its mass (in grams) by moles.

This calculated molar mass enables us to determine the molecular weight of the unknown acid and therefore identify it.

The equivalence point in a titration is a crucial moment that denotes the exact point at which the amount of titrant added is chemically equivalent to the substance being titrated. In other words, it's where the moles of acid and base in the reaction are equal. This is particularly important when working with monoprotic acids and bases, as they have a 1:1 mole ratio.

To identify the equivalence point, chemists often use indicators that change color at a certain pH or employ instruments to graph the titration curve and determine the inflection point where neutralization is achieved. Knowing the volume of the titrant used to reach the equivalence point allows us to calculate related quantities of the analyte, such as its molarity or mass.

Characteristics of the Equivalence Point

• Stoichiometrically equal amounts of the reactants are present.
• In monoprotic acid-base titrations, the moles of acid equal the moles of base.
• It is accompanied by a noticeable change in the pH of the solution, often detected by a pH indicator or a pH meter.

Recognizing the equivalence point is a key step for accurate molar mass calculation and the subsequent determination of the chemical’s identity or concentration in a solution.

The Henderson-Hasselbalch equation provides a direct relationship between the pH of a solution and the pKa (which is the negative log of the acid dissociation constant, Ka) of a buffer when an acid (or its conjugate base) is partially neutralized. It's an invaluable tool in the world of chemistry for estimating the pH of a buffer solution.

The equation is given by:
\[\begin{equation}\text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)\end{equation}\]
where \([\text{A}^-]\) is the concentration of the conjugate base and \([\text{HA}]\) is the concentration of the weak acid. By rearranging the equation, you can solve for Ka if you know the pH and the ratio of the concentrations of the conjugate base and the acid.

In a practical sense, the Henderson-Hasselbalch equation lets us deduce the acid dissociation constant of an unknown acid during a titration by using the pH at a point before the equivalence is reached. This can further aid in identifying the unknown acid based on its dissociation characteristics.

Application in Titration

• Useful for finding the pH of buffer systems during a titration.
• Allows the calculation of the dissociation constant (Ka) of weak acids.
• Helps to understand how the pH changes as the conjugate acid-base pair concentration changes.

Understanding how to apply the Henderson-Hasselbalch equation is powerful because it enables us to control the pH during chemical processes and helps in the characterization of acid-base properties of compounds.