Final answer:
The Ka value for sulfurous acid is calculated by converting the given pH to a hydronium ion concentration and using the equilibrium expression for its dissociation in water. The concentration of the conjugate base is assumed to be equal to the hydronium ion concentration, and the initial concentration of H2SO3 remains mostly unchanged.
Step-by-step explanation:
Determination of Ka for Sulfurous Acid from pH Data
To calculate the Ka value for sulfurous acid (H₂SO₃), we start by converting the measured pH of 1.46 to a hydrogen ion concentration [H+⁺]. This is done by using the formula [H+⁺] = 10−pH, which gives us a hydronium ion concentration of approximately 3.47 × 10−3 M. Sulfurous acid partially dissociates in water according to the equation:
H₂SO₃(aq) → HSO₃⁻(aq) + H₃O+(aq)
Assuming that the concentration of HSO₃⁻ is equal to the concentration of H₃O+ and that the initial concentration of H2SO3 is only slightly reduced by the small amount of ionization, the equilibrium constant Ka can be written as:
Ka = [H₃O+][HSO₃⁻]/[H₂SO₃]
Substituting the measured concentrations into the Ka expression, we can solve for Ka. For this problem, since the solution is 0.12 M and the ionization is minor, we can assume 0.12 M as the initial concentration of H2SO3.