0.1 mol of a basic substance (X) requires `25cm^(3)` of 8.0 `mol//dm^(3)` hydrochloric acid for complete neutralisation .X could be
1. `Al(OH)_(3)`
2. `CuO`
3 . `K_(2)O`
4 . `NaOH`

Options

A. 1 and 2
B. 2 and 3
C. 1 and 4
D. 2 and 4

Explanation

To solve the problem, we need to determine which of the given basic substances (X) can react with hydrochloric acid (HCl) in the specified mole ratio. Let's break this down step by step.

### Step 1: Calculate the moles of HCl used
We are given the molarity and volume of hydrochloric acid:
- Molarity of HCl = 8.0 mol/dm³
- Volume of HCl = 25 cm³ = 25 × 0.001 dm³ = 0.025 dm³

Using the formula for moles:
\[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume} = 8.0 \, \text{mol/dm}^3 \times 0.025 \, \text{dm}^3 = 0.2 \, \text{mol} \]

### Step 2: Determine the mole ratio of the base to acid
We know that 0.1 mol of the basic substance (X) reacts with 0.2 mol of HCl. The mole ratio of base (X) to acid (HCl) is:
\[ \text{Mole ratio} = \frac{\text{Moles of X}}{\text{Moles of HCl}} = \frac{0.1}{0.2} = \frac{1}{2} \]

### Step 3: Analyze each option for the mole ratio
Now we will check each of the given substances to see if they react with HCl in a 1:2 ratio.

1. **Al(OH)₃ (Aluminum hydroxide)**:
\[ \text{Reaction: } \text{Al(OH)}_3 + 3 \text{HCl} \rightarrow \text{AlCl}_3 + 3 \text{H}_2\text{O} \]
- Mole ratio: 1 mol Al(OH)₃ reacts with 3 mol HCl (1:3). **Not suitable.**

2. **CuO (Copper(II) oxide)**:
\[ \text{Reaction: } \text{CuO} + 2 \text{HCl} \rightarrow \text{CuCl}_2 + \text{H}_2\text{O} \]
- Mole ratio: 1 mol CuO reacts with 2 mol HCl (1:2). **Suitable.**

3. **K₂O (Potassium oxide)**:
\[ \text{Reaction: } \text{K}_2\text{O} + 2 \text{HCl} \rightarrow 2 \text{KCl} + \text{H}_2\text{O} \]
- Mole ratio: 1 mol K₂O reacts with 2 mol HCl (1:2). **Suitable.**

4. **NaOH (Sodium hydroxide)**:
\[ \text{Reaction: } \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
- Mole ratio: 1 mol NaOH reacts with 1 mol HCl (1:1). **Not suitable.**

### Conclusion
The substances that can react with HCl in the required 1:2 mole ratio are **CuO** and **K₂O**.

### Final Answer
**X could be CuO or K₂O.**

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