1 mole of `Ba(OH)_(2)` will exactly neutralize :

Options

A. 0.5 mole HCL
B. 1 mole of `H_(2)SO_(4)`
C. 1 mole of `H_(3)PO_(3)`
D. 2 mole of `H_(3)PO_(2)`

Answer

To solve the question of how many moles of various acids can be exactly neutralized by 1 mole of barium hydroxide (Ba(OH)₂), we need to follow these steps:

### Step-by-Step Solution

1. **Identify the Reaction**:
Barium hydroxide is a strong base that dissociates in water to produce Ba²⁺ and OH⁻ ions. The dissociation can be represented as:
\[ \text{Ba(OH)}_2 \rightarrow \text{Ba}^{2+} + 2 \text{OH}^- \]

2. **Determine the Number of Equivalents of Ba(OH)₂**:
The number of equivalents of a substance is calculated as:
\[ \text{Number of equivalents} = \text{Number of moles} \times n \text{ factor} \]
For barium hydroxide, since it produces 2 hydroxide ions (OH⁻), the n factor is 2. Therefore, for 1 mole of Ba(OH)₂:
\[ \text{Number of equivalents of Ba(OH)}_2 = 1 \text{ mole} \times 2 = 2 \text{ equivalents} \]

3. **Analyze Each Acid Option**:
We will calculate the number of equivalents for each acid option provided.

- **Option A: 0.5 moles of HCl**:
HCl dissociates to produce 1 H⁺ ion:
\[ \text{Number of equivalents of HCl} = 0.5 \text{ moles} \times 1 = 0.5 \text{ equivalents} \]
This is not enough to neutralize 2 equivalents of Ba(OH)₂.

- **Option B: 1 mole of H₂SO₄**:
H₂SO₄ dissociates to produce 2 H⁺ ions:
\[ \text{Number of equivalents of H}_2\text{SO}_4 = 1 \text{ mole} \times 2 = 2 \text{ equivalents} \]
This exactly neutralizes 2 equivalents of Ba(OH)₂.

- **Option C: 1 mole of H₃PO₃**:
H₃PO₃ can release 2 H⁺ ions:
\[ \text{Number of equivalents of H}_3\text{PO}_3 = 1 \text{ mole} \times 2 = 2 \text{ equivalents} \]
This also exactly neutralizes 2 equivalents of Ba(OH)₂.

- **Option D: 2 moles of H₃PO₂**:
H₃PO₂ can release only 1 H⁺ ion:
\[ \text{Number of equivalents of H}_3\text{PO}_2 = 2 \text{ moles} \times 1 = 2 \text{ equivalents} \]
This also exactly neutralizes 2 equivalents of Ba(OH)₂.

4. **Conclusion**:
The acids that can exactly neutralize 1 mole of Ba(OH)₂ are:
- 1 mole of H₂SO₄
- 1 mole of H₃PO₃
- 2 moles of H₃PO₂

### Final Answer:
1 mole of Ba(OH)₂ will exactly neutralize:
- 1 mole of H₂SO₄
- 1 mole of H₃PO₃
- 2 moles of H₃PO₂