Which of the following equations correctly represents the relationship between the hydrogen ion concentration [H+] and the dissociation constants (Ka1 and Ka2) for a diprotic acid H2A?

• A. [H+] = Ka1 + Ka2
• B. [H+]^2 = Ka1 + Ka2
• C. [H+]^2 = Ka1 * Ka2
• D. [H+]^2 = Ka1 * [H+] + Ka1 * Ka2

Answer: (D)

Verified step by step guidance

1. Understand that a diprotic acid, H2A, can dissociate in two steps: first, it loses one proton to form HA-, and then it loses a second proton to form A2-. Each step has its own dissociation constant, Ka1 and Ka2 respectively.
2. Write the dissociation reactions: H2A ⇌ H+ + HA- with dissociation constant Ka1, and HA- ⇌ H+ + A2- with dissociation constant Ka2.
3. Recognize that the overall concentration of hydrogen ions [H+] in solution is influenced by both dissociation steps.
4. Consider the equilibrium expressions: For the first dissociation, Ka1 = [H+][HA-]/[H2A], and for the second dissociation, Ka2 = [H+][A2-]/[HA-].
5. Combine these expressions to find a relationship between [H+], Ka1, and Ka2. The correct relationship is derived from the equilibrium conditions and is given by [H+]^2 = Ka1 * [H+] + Ka1 * Ka2, which accounts for the contributions of both dissociation steps to the hydrogen ion concentration.