A visually plotted fractional composition diagram for a weak monoprotic acid () and its conjugate ba — Ionic Equilibrium Chemistry Question
Question
A visually plotted fractional composition diagram for a weak monoprotic acid ($HA$) and its conjugate base ($A^-$) reveals that the two curves intersect exactly at pH = 4.4. What is the exact value of the acid dissociation constant ($K_a$) expressed as $K_a \times 10^5$?
💡 Solution & Explanation
The visual intersection of the protonated fraction curve ($HA$) and the deprotonated fraction curve ($A^-$) represents the point where $[HA] = [A^-]$. According to the Henderson-Hasselbalch equation, $pH = pK_a + \log\frac{[A^-]}{[HA]}$. When the concentrations are strictly equal, the log term is zero, making $pH = pK_a$. The visual intersection occurs at pH 4.4, meaning $pK_a = 4.4$. Therefore, $K_a = 10^{-4.4} = 10^{0.6} \times 10^{-5}$. Since $\log 3.98 \approx 0.6$, $K_a \approx 3.98 \times 10^{-5}$. Thus, the value is 3.98.