Question

Which of the following patterns is true about the relationship between three pKa values of triprotic phosphoric acid?

• A. pKa1 \(<\) pKa2 \(<\) pKa3
• B. pKa1 \(>\) pKa2 \(>\) pKa3
• C. pKa1 = pKa2 = pKa3
• D. pKa3 = (pKa1 + pKa2)/2

Hint:

For any polyprotic acid, it is always true that \(\text{p}K_{a1} < \text{p}K_{a2} < \text{p}K_{a3}\), because removing a proton from an increasingly negative anion is thermodynamically unfavorable.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Phosphoric acid (\(\text{H}_3\text{PO}_4\)) is a triprotic acid, meaning it can donate three protons sequentially.
Each proton dissociation step has its own characteristic acid dissociation constant (\(K_a\)) and associated \(\text{p}K_a\).

Step 2: Detailed Explanation:
The ionization of phosphoric acid occurs in three distinct stages:
1. \(\text{H}_3\text{PO}_4 \rightleftharpoons \text{H}^+ + \text{H}_2\text{PO}_4^-\) with dissociation constant \(K_{a1}\)
2. \(\text{H}_2\text{PO}_4^- \rightleftharpoons \text{H}^+ + \text{HPO}_4^{2-}\) with dissociation constant \(K_{a2}\)
3. \(\text{HPO}_4^{2-} \rightleftharpoons \text{H}^+ + \text{PO}_4^{3-}\) with dissociation constant \(K_{a3}\)
In each step, the proton must be removed from a species carrying a greater negative charge.
The electrostatic attraction between the negative charge of the acid anion and the positive charge of the leaving proton (\(\text{H}^+\)) increases with each successive step.
This makes it progressively more difficult to release the proton, meaning:
\[ K_{a1} > K_{a2} > K_{a3} \] Because \(\text{p}K_a = -\log_{10}(K_a)\), a larger \(K_a\) value results in a smaller \(\text{p}K_a\) value.
Therefore, the relationship among the \(\text{p}K_a\) values is: \[ \text{p}K_{a1} < \text{p}K_{a2} < \text{p}K_{a3} \] The actual values are approximately \(\text{p}K_{a1} \approx 2.15\), \(\text{p}K_{a2} \approx 7.20\), and \(\text{p}K_{a3} \approx 12.35\).

Step 3: Final Answer:
This relationship is correctly represented by option (A).