A sample of 0.1687 g of an unknown monoprotic acid was dissolved in 25.0 mL of water and titrated with 0.1150 M NaOH. The acid required 15.5 mL of base to reach the equivalence point. (b) After 7.25 mL of base had been added in the titration, the pH was found to be 2.85. What is the Ka for the unknown acid?

Verified step by step guidance

1. First, calculate the number of moles of NaOH that have been added at the point where the pH is 2.85. This can be done using the formula: moles = Molarity * Volume (in liters). In this case, the molarity of NaOH is 0.1150 M and the volume added is 7.25 mL or 0.00725 L.
2. Next, calculate the initial number of moles of the unknown acid before any base was added. This can be done using the equivalence point volume of NaOH, which is 15.5 mL or 0.0155 L. The number of moles of acid is equal to the number of moles of base at the equivalence point.
3. Then, calculate the number of moles of the unknown acid that remain after 7.25 mL of base has been added. This is done by subtracting the moles of base added from the initial moles of acid.
4. Subsequently, calculate the concentration of the unknown acid that remains after 7.25 mL of base has been added. This is done by dividing the remaining moles of acid by the total volume of the solution at this point (25.0 mL of water + 7.25 mL of base = 32.25 mL or 0.03225 L).
5. Finally, use the pH and the concentration of the remaining acid to calculate the Ka of the unknown acid. The formula for Ka is: Ka = [H+]*[A-]/[HA], where [H+] is the concentration of hydrogen ions (which can be calculated from the pH), [A-] is the concentration of the base (which is equal to the initial moles of acid minus the remaining moles of acid), and [HA] is the concentration of the remaining acid.

Key Concepts

Monoprotic Acids

Monoprotic acids are acids that can donate only one proton (H+) per molecule during a chemical reaction. This characteristic simplifies the calculation of their dissociation constants, as they only have one equilibrium expression to consider. Understanding the behavior of monoprotic acids is essential for determining their strength and the pH of their solutions.

Titration and Equivalence Point

Titration is a quantitative analytical method used to determine the concentration of a solute in a solution. The equivalence point occurs when the amount of titrant added is stoichiometrically equivalent to the amount of substance being titrated. In this case, it indicates that all the monoprotic acid has reacted with the NaOH, allowing for calculations of the acid's concentration and dissociation constant.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) is a measure of the strength of an acid in solution, defined as the equilibrium constant for the dissociation of the acid into its conjugate base and a proton. It is calculated using the concentrations of the products and reactants at equilibrium. For monoprotic acids, knowing the pH at various points in a titration helps in determining Ka, especially at the half-equivalence point where pH = pKa.