A 20.0-mL sample of 0.115 M sulfurous acid (H₂SO₃) solution is titrated with 0.1014 M KOH. At what added volume of base solution does each equivalence point occur?

Verified step by step guidance

1. Identify the reaction: Sulfurous acid (H2SO3) is a diprotic acid, meaning it can donate two protons (H+). The reaction with KOH, a strong base, occurs in two steps: H2SO3 + KOH -> KHSO3 + H2O and KHSO3 + KOH -> K2SO3 + H2O.
2. Calculate the moles of H2SO3: Use the concentration and volume of the sulfurous acid solution to find the initial moles of H2SO3. Moles of H2SO3 = 0.115 M * 0.020 L.
3. Determine the moles of KOH needed for the first equivalence point: At the first equivalence point, all H2SO3 is converted to KHSO3. This requires an equal number of moles of KOH as there are moles of H2SO3.
4. Calculate the volume of KOH for the first equivalence point: Use the moles of KOH needed and the concentration of the KOH solution to find the volume. Volume (L) = moles of KOH / 0.1014 M.
5. Determine the volume of KOH for the second equivalence point: At the second equivalence point, all KHSO3 is converted to K2SO3. This requires an additional equal number of moles of KOH as the initial moles of H2SO3. Calculate the total volume of KOH needed for both equivalence points.

Key Concepts

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (in this case, KOH) to a solution of the analyte (H2SO3) until the reaction reaches its equivalence point, where stoichiometrically equivalent amounts of acid and base have reacted.

Equivalence Point

The equivalence point in a titration is the stage at which the amount of titrant added is exactly enough to completely neutralize the analyte solution. For a diprotic acid like sulfurous acid, there are two equivalence points corresponding to the neutralization of each acidic proton, which must be calculated based on the stoichiometry of the reaction.

Molarity and Volume Relationship

Molarity (M) is defined as the number of moles of solute per liter of solution. In titration calculations, the relationship between the molarity and volume of the acid and base solutions is crucial. The formula M1V1 = M2V2 allows us to determine the volume of titrant needed to reach the equivalence point, where M1 and V1 are the molarity and volume of the acid, and M2 and V2 are those of the base.