Equal volumes of `1M HCI` and `1M H_(2)SO_(4)` are neutralised by `1M NaOH` solution and `x` and `y kJ//` equivalent of heat are liberated, respectively. Which of the following relations is correct?

Options

A. `x = 2y`
B. `x = 3y`
C. `x = 4y`
D. `x = (1)/(2)y`

Explanation

To solve the problem, we need to analyze the neutralization reactions of hydrochloric acid (HCl) and sulfuric acid (H₂SO₄) with sodium hydroxide (NaOH) and determine the relationship between the heat liberated (x and y kJ) during these reactions.

### Step-by-Step Solution:

1. **Identify the Neutralization Reactions:**
- The neutralization reaction of HCl with NaOH is:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
- The neutralization reaction of H₂SO₄ with NaOH is:
\[ \text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O} \]

2. **Calculate Moles of H⁺ Ions:**
- For HCl:
- Since HCl is a monoprotic acid, it furnishes 1 mole of H⁺ per mole of HCl.
- If the volume of HCl is \( V \) liters, the moles of H⁺ from HCl:
\[ \text{Moles of H⁺ from HCl} = V \times 1\, \text{M} = V \]

- For H₂SO₄:
- H₂SO₄ is a diprotic acid, which means it furnishes 2 moles of H⁺ per mole of H₂SO₄.
- If the volume of H₂SO₄ is also \( V \) liters, the moles of H⁺ from H₂SO₄:
\[ \text{Moles of H⁺ from H₂SO₄} = V \times 1\, \text{M} \times 2 = 2V \]

3. **Heat Released During Neutralization:**
- For HCl:
- The heat released during the neutralization of HCl can be expressed as:
\[ \text{Heat} = \text{Moles of H⁺} \times \Delta H_{\text{neutralization}} = V \times \Delta H_{\text{neutralization}} = x \]
- Therefore, we can express \( x \) as:
\[ x = V \times \Delta H_{\text{neutralization}} \]

- For H₂SO₄:
- The heat released during the neutralization of H₂SO₄ can be expressed as:
\[ \text{Heat} = \text{Moles of H⁺} \times \Delta H_{\text{neutralization}} = 2V \times \Delta H_{\text{neutralization}} = y \]
- Therefore, we can express \( y \) as:
\[ y = 2V \times \Delta H_{\text{neutralization}} \]

4. **Relate x and y:**
- From the equations derived, we can relate \( x \) and \( y \):
\[ y = 2x \]

5. **Conclusion:**
- The correct relationship between the heat liberated during the neutralization of HCl and H₂SO₄ by NaOH is:
\[ y = 2x \]

### Final Answer:
The correct relation is \( y = 2x \).