Question

Arrange the dissociation constant of phosphoric acid in increasing order. \[\begin{aligned} \text{H}_3\text{PO}_4 + \text{H}_2\text{O} &\rightleftharpoons \text{H}_3\text{O}^+ + \text{H}_2\text{PO}_4^- \quad (K_{\text{a1}}) \\ \text{H}_2\text{PO}_4^- + \text{H}_2\text{O} &\rightleftharpoons \text{H}_3\text{O}^+ + \text{HPO}_4^{2-} \quad (K_{\text{a2}}) \\ \text{HPO}_4^{2-} + \text{H}_2\text{O} &\rightleftharpoons \text{H}_3\text{O}^+ + \text{PO}_4^{3-} \quad (K_{\text{a3}}) \\ \end{aligned}\]

• (1) \( K_{\text{a1}} = K_{\text{a2}} = K_{\text{a3}} \)
• (2) \( K_{\text{a1}} > K_{\text{a2}} > K_{\text{a3}} \)
• (3) \( K_{\text{a1}} < K_{\text{a2}} < K_{\text{a3}} \)
• (4) \( K_{\text{a3}} > K_{\text{a2}} > K_{\text{a1}} \)

Hint:

For triprotic acids like phosphoric acid, the dissociation constants decrease with each successive proton loss.

Answer 1

The Correct Option is B

Step 1: Understanding Dissociation Constants.
Phosphoric acid (\( H_3PO_4 \)) is a triprotic acid, meaning it dissociates in three steps. Each step has a dissociation constant: \( K_{\text{a1}}, K_{\text{a2}}, K_{\text{a3}} \). The first dissociation constant (\( K_{\text{a1}} \)) is the strongest, as phosphoric acid dissociates more easily to form \( H_2PO_4^- \). The second dissociation constant (\( K_{\text{a2}} \)) is smaller because it involves the dissociation of \( H_2PO_4^- \) to \( HPO_4^{2-} \), which is less acidic. The third dissociation constant (\( K_{\text{a3}} \)) is the smallest since \( HPO_4^{2-} \) dissociates very weakly to form \( PO_4^{3-} \).

Step 2: Conclusion.
Therefore, the dissociation constants for phosphoric acid are arranged in the order \( K_{\text{a1}} > K_{\text{a2}} > K_{\text{a3}} \), which matches option (2).

Final Answer: \[ \boxed{\text{(2) } K_{\text{a1}} > K_{\text{a2}} > K_{\text{a3}}} \]