In `H_(3)PO_(4)` which of the following is true?

Options

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

Explanation

To analyze the question regarding the dissociation of phosphoric acid (H₃PO₄), we will break down the steps involved in understanding the dissociation constants and their relationships.

### Step-by-Step Solution:

1. **Understanding the Dissociation of H₃PO₄:**
- Phosphoric acid (H₃PO₄) can lose three protons (H⁺) in a stepwise manner. The dissociation can be represented as:
- First dissociation: H₃PO₄ ⇌ H⁺ + H₂PO₄⁻
- Second dissociation: H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻
- Third dissociation: HPO₄²⁻ ⇌ H⁺ + PO₄³⁻

2. **Defining the Dissociation Constants:**
- Each step has a dissociation constant (Kₐ):
- Kₐ₁ for the first dissociation
- Kₐ₂ for the second dissociation
- Kₐ₃ for the third dissociation

3. **Relationship Between Kₐ and Kₐ Values:**
- The overall dissociation constant (Kₐ) for the complete ionization of H₃PO₄ can be expressed as:
\[ K_a = K_{a1} \times K_{a2} \times K_{a3} \]
- This means that the overall dissociation constant is the product of the individual dissociation constants.

4. **Order of Successive Dissociation:**
- The strength of the acid decreases with the removal of each successive proton. This is due to the increasing negative charge on the ion, which makes it harder to remove another proton.
- Therefore, the order of the dissociation constants is:
\[ K_{a1} > K_{a2} > K_{a3} \]

5. **Conclusion:**
- From the analysis, we conclude that:
- The first option (Kₐ = Kₐ₁ × Kₐ₂ × Kₐ₃) is correct.
- The third option (Kₐ₁ > Kₐ₂ > Kₐ₃) is also correct.

### Final Answer:
- The correct statements about H₃PO₄ are:
1. Kₐ = Kₐ₁ × Kₐ₂ × Kₐ₃
2. Kₐ₁ > Kₐ₂ > Kₐ₃