Part (d): Explain why in a strong acid solution, the hydronium ion concentration doubles as the total acid concentration doubles, whereas in a weak acid solution, it increases only slightly to abo

Let's explain part (d).

Part (d): Explain why in a strong acid solution, the hydronium ion concentration doubles as the total acid concentration doubles, whereas in a weak acid solution, it increases only slightly to about a factor 1.4.

• Strong Acid: Strong acids dissociate completely ($HA \to H^+ + A^-$). Thus, the hydronium ion concentration, $[H_3O^+]$, is directly proportional to the initial acid concentration. Doubling the initial acid concentration therefore doubles $[H_3O^+]$.
• Weak Acid: Weak acids only partially dissociate, establishing an equilibrium ($HA \rightleftharpoons H^+ + A^-$). The equilibrium expression is $K_a = \frac{[H_3O^+]^2}{[HA]_0}$ (assuming $[H_3O^+] \ll [HA]_0$). This implies $[H_3O^+] \propto \sqrt{[HA]_0}$.
• Therefore, doubling the initial weak acid concentration increases $[H_3O^+]$ by a factor of $\sqrt{2} \approx 1.4$.