`K_(a_(1)), K_(a_(2)) and K_(a_(3))` are the three dissociation constants of `H_3PO_4`. Which of the following is a correct order

Options

A. `K_(a_(1)) gt K_(a_(2)) lt K_(a_(3))`
B. `K_(a_(1)) gt K_(a_(2)) gt K_(a_(3))`
C. `K_(a_(3)) gt K_(a_(2)) gt K_(a_(1))`
D. None of these

Answer

To determine the correct order of the dissociation constants \( K_{a1}, K_{a2}, \) and \( K_{a3} \) for the triprotic acid \( H_3PO_4 \), we can analyze the dissociation steps of the acid and the factors affecting the dissociation constants.

### Step-by-Step Solution:

1. **Identify the Dissociation Steps:**
- The dissociation of \( H_3PO_4 \) occurs in three steps:
1. \( H_3PO_4 \rightleftharpoons H^+ + H_2PO_4^- \) (First dissociation)
2. \( H_2PO_4^- \rightleftharpoons H^+ + HPO_4^{2-} \) (Second dissociation)
3. \( HPO_4^{2-} \rightleftharpoons H^+ + PO_4^{3-} \) (Third dissociation)

2. **Write the Expressions for \( K_a \):**
- The dissociation constants for each step can be expressed as:
- \( K_{a1} = \frac{[H^+][H_2PO_4^-]}{[H_3PO_4]} \)
- \( K_{a2} = \frac{[H^+][HPO_4^{2-}]}{[H_2PO_4^-]} \)
- \( K_{a3} = \frac{[H^+][PO_4^{3-}]}{[HPO_4^{2-}]} \)

3. **Analyze the Strength of Each Step:**
- The first dissociation \( H_3PO_4 \) is the strongest because it releases the first proton easily. The presence of \( H^+ \) ions in the solution from the first dissociation makes the second and third dissociation steps less favorable due to the common ion effect.
- As we move to the second and third dissociation steps, the equilibrium shifts to the left due to the increased concentration of \( H^+ \) ions already present. This results in lower dissociation constants for the second and third steps.

4. **Establish the Order of \( K_a \):**
- Since \( K_{a1} \) is the largest due to the strong dissociation of the first proton, followed by \( K_{a2} \) which is smaller, and \( K_{a3} \) being the smallest due to the common ion effect, we can conclude:
\[ K_{a1} > K_{a2} > K_{a3} \]

5. **Final Answer:**
- The correct order of the dissociation constants is \( K_{a1} > K_{a2} > K_{a3} \).