Final answer:
To calculate the pH at the equivalence point of the titration between HCO₂H and KOH, the formate ion concentration is determined to be 0.50 M, and using the pKa calculated from the given Ka value, the pH is found to be 3.74.
Step-by-step explanation:
Calculating pH at the Equivalence Point in a Weak Acid/Strong Base Titration
To calculate the pH at the equivalence point in the titration of 50.0 mL of 0.50 M HCO₂H with 1.0 M KOH, one must understand that at the equivalence point, the weak acid has been completely neutralized by the strong base, producing the weak acid's conjugate base in solution. In this case, the acid is formic acid (HCO₂H), and its conjugate base is the formate ion (HCO₂⁻).
Since the concentration of the weak acid and the strong base are given, we can calculate the moles of each:
Moles of HCO₂H = Volume (L) × Concentration (M) = 0.050 L × 0.50 M = 0.025 moles.
Moles of KOH at equivalence point = 0.025 moles (same as moles of HCO₂H).
At the equivalence point, all the formic acid has reacted to form formate ions. Therefore, the concentration of formate ions in the solution is equal to:
Concentration of HCO₂⁻ = Moles of HCO₂⁻ / Total Volume = 0.025 moles / (50 mL + Volume of KOH added) = 0.025 moles / 0.050 L = 0.50 M (since the KOH volume was not specified, we assume it is sufficient to neutralize exactly the acid).
The pH of the solution is now dependent on the dissociation of the formate ion in water, which can be found using the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]). In this equation, A⁻ is the conjugate base (formate) and HA is the weak acid (formic acid).
Since [A⁻] is 0.50 M and the weak acid has been neutralized, [HA] is 0. Therefore, plugging in the given Ka value:
pKa = -log(Ka) = -log(1.8 × 10⁻⁴) = 3.74
Since [HA] is negligible, the equation simplifies to pH = pKa, which gives the pH at the equivalence point as 3.74.