Exactly of an unknown weak base is being titrated with a strong acid . When exactly of the strong ac — Ionic Equilibrium Chemistry Question
Question
Exactly $20 \text{ mL}$ of an unknown weak base $BOH$ is being titrated with a strong acid $HA$. When exactly $10 \text{ mL}$ of the strong acid has been added, the pH of the mixed solution is measured to be $9.0$. If the equivalence point is reached when exactly $20 \text{ mL}$ of the strong acid is added in total, calculate the exact $pK_b$ of the weak base $BOH$ at the titration temperature.
💡 Solution & Explanation
The true equivalence point requires $20 \text{ mL}$ of the acid. Therefore, adding exactly $10 \text{ mL}$ corresponds to the exact half-neutralization point. At this specific half-equivalence point, half of the weak base has been neutralized to form its conjugate acid salt, meaning $[BOH] = [B^+]$. According to the Henderson-Hasselbalch equation for basic buffers: $pOH = pK_b + \log\frac{[Salt]}{[Base]}$. Since the ratio is 1, $\log 1 = 0$, directly yielding $pOH = pK_b$. The measured pH is 9.0, meaning the $pOH = 14.0 - 9.0 = 5.0$. Thus, $pK_b = 5$.