For a polyprotic acid, `H_(3)PO_(4)` its three dissociation constanst `K_(1),K_(2)` and `K_(3)` are in the order

Options

A. `K_(1) = K_(2) gt K_(3)`
B. `K_(1) = K_(2) = K_(3)`
C. `K_(1) gt K_(2) gt K_(3)`
D. `K_(1) lt K_(2) lt K_(3)`

Explanation

To determine the order of the dissociation constants \( K_1, K_2, \) and \( K_3 \) for the polyprotic acid \( H_3PO_4 \) (phosphoric acid), we need to analyze the dissociation steps and the corresponding equilibrium constants.

### Step-by-Step Solution:

1. **Identify the Dissociation Steps:**
- The dissociation of \( H_3PO_4 \) occurs in three steps:
1. \( H_3PO_4 \rightleftharpoons H^+ + H_2PO_4^- \) (Dissociation constant \( K_1 \))
2. \( H_2PO_4^- \rightleftharpoons H^+ + HPO_4^{2-} \) (Dissociation constant \( K_2 \))
3. \( HPO_4^{2-} \rightleftharpoons H^+ + PO_4^{3-} \) (Dissociation constant \( K_3 \))

2. **Write the Expressions for the Dissociation Constants:**
- For the first dissociation:
\[ K_1 = \frac{[H^+][H_2PO_4^-]}{[H_3PO_4]} \]
- For the second dissociation:
\[ K_2 = \frac{[H^+][HPO_4^{2-}]}{[H_2PO_4^-]} \]
- For the third dissociation:
\[ K_3 = \frac{[H^+][PO_4^{3-}]}{[HPO_4^{2-}]} \]

3. **Analyze the Strength of Each Step:**
- The first dissociation \( K_1 \) is the strongest because it involves the release of the first proton from a fully protonated acid, which is typically more favorable.
- The second dissociation \( K_2 \) is weaker than the first because the remaining species \( H_2PO_4^- \) is a weaker acid than \( H_3PO_4 \).
- The third dissociation \( K_3 \) is the weakest because \( HPO_4^{2-} \) is even less acidic than \( H_2PO_4^- \).

4. **Establish the Order of the Dissociation Constants:**
- Based on the analysis, we can conclude that:
\[ K_1 > K_2 > K_3 \]

5. **Select the Correct Option:**
- The order of the dissociation constants for \( H_3PO_4 \) is \( K_1 > K_2 > K_3 \), which corresponds to option number 3.

### Final Answer:
The correct order of the dissociation constants for \( H_3PO_4 \) is:
\[ K_1 > K_2 > K_3 \]