Question

{"given":"A weak acid HA with $pK_a = 4.5$ forms a buffered solution where 50% of the acid is ionized. We need to find the pOH of this buffer solution. ","key_observation":"When 50% of a weak acid is ionized in a buffer solution, the concentrations of the acid and its conjugate base (salt) become equal: [Salt] = [Acid]. This condition allows us to use the Henderson-Hasselbalch equation where the log term becomes zero, making pH equal to pKa.","option_analysis":[{"label":"(A)","text":"4.5","verdict":"incorrect","explanation":"This is the pKa value and would be the pH of the solution, not the pOH. Since pH + pOH = 14, the pOH cannot equal the pKa when pH equals pKa."},{"label":"(B)","text":"2.5","verdict":"incorrect","explanation":"This value has no theoretical basis. It appears to be an arbitrary distractor that doesn't follow from any buffer equation or relationship."},{"label":"(C)","text":"9.5","verdict":"correct","explanation":"Using Henderson-Hasselbalch equation: pH = $pK_a$ + log$\\frac{[Salt]}{[Acid]}$ = 4.5 + log(1) = 4.5. Since pH + pOH = 14, we get pOH = 14 - 4.5 = 9.5."},{"label":"(D)","text":"7.0","verdict":"incorrect","explanation":"This would be the pOH of a neutral solution where pH = 7. However, this buffer solution has pH = 4.5 (acidic), so pOH ≠ 7."}],"answer":"(C)","formula_steps":[]}