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=y
B. x=0.5y
C. x=0.4y
D. x=2.5y

Answer

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 heat released in each case.

### Step-by-step Solution:

1. **Understanding the Neutralization Reaction**:
- The neutralization reaction involves an acid reacting with a base to produce water and a salt, releasing heat in the process.
- The general reaction for HCl with NaOH is:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
- The reaction for 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. **Dissociation of Acids**:
- HCl dissociates completely in solution:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
This means 1 mole of HCl produces 1 mole of H⁺ ions.
- H₂SO₄ also dissociates completely, but it produces 2 moles of H⁺ ions:
\[ \text{H}_2\text{SO}_4 \rightarrow 2 \text{H}^+ + \text{SO}_4^{2-} \]

3. **Heat Released**:
- Let the heat released during the neutralization of 1 mole of HCl be \( x \) kJ.
- For H₂SO₄, since it produces 2 moles of H⁺ ions, the heat released will be double that of HCl:
\[ \text{Heat released for H}_2\text{SO}_4 = 2x \]
- We denote this heat as \( y \) kJ, thus:
\[ y = 2x \]

4. **Finding the Relation**:
- From the equation \( y = 2x \), we can express the relationship between \( x \) and \( y \):
\[ x = \frac{y}{2} \]
- Therefore, the correct relation is \( y = 2x \).

### Conclusion:
The correct relation among the options given is:
\[ y = 2x \]