For the reactions,
(i) `H_(2)(g)+Cl_(2)(g)rarr 2HCl(g)+ xKJ`
(ii) `H_(2)(g)+Cl_(2)(g)rarr 2HCl(l)+ yKJ`
Which one of the following statement is correct :

Options

A. x gt y
B. x lt y
C. x = y
D. More data required

Answer

To solve the problem, we need to analyze the two reactions given and determine the relationship between the enthalpy changes (X and Y) for the reactions.

### Step-by-Step Solution:

1. **Identify the Reactions**:
- Reaction (i): \( H_2(g) + Cl_2(g) \rightarrow 2HCl(g) + x \, \text{kJ} \)
- Reaction (ii): \( H_2(g) + Cl_2(g) \rightarrow 2HCl(l) + y \, \text{kJ} \)

2. **Understand the Nature of the Reactions**:
- In reaction (i), hydrogen and chlorine gases react to form gaseous hydrogen chloride (HCl) and release \( x \, \text{kJ} \) of energy.
- In reaction (ii), the same reactants form liquid hydrogen chloride (HCl) and release \( y \, \text{kJ} \) of energy.

3. **Reverse Reaction (ii)**:
- If we reverse reaction (ii), we get:
\[ 2HCl(l) \rightarrow H_2(g) + Cl_2(g) - y \, \text{kJ} \]
- This means that converting liquid HCl back to gaseous HCl requires energy, which is absorbed (hence the negative sign).

4. **Compare the Two Reactions**:
- Now, we can combine the two reactions:
- From reaction (i), we have:
\[ H_2(g) + Cl_2(g) \rightarrow 2HCl(g) + x \, \text{kJ} \]
- From the reversed reaction (ii):
\[ 2HCl(l) \rightarrow H_2(g) + Cl_2(g) - y \, \text{kJ} \]
- If we consider the conversion of \( 2HCl(g) \) to \( 2HCl(l) \), we can see that:
\[ 2HCl(g) \rightarrow 2HCl(l) \quad \text{(requires heat)} \]
- The enthalpy change for this conversion is the difference between the two reactions:
\[ x - (-y) = x + y \]

5. **Determine the Relationship**:
- The process of converting gas to liquid (condensation) releases heat, so it is exothermic. Therefore, the enthalpy change for converting gaseous HCl to liquid HCl should be positive.
- Thus, we can conclude that:
\[ x + y > 0 \quad \text{(since heat is released)} \]
- This implies that \( y \) must be greater than \( x \) because more energy is required to convert the gaseous HCl back to liquid HCl.

6. **Final Conclusion**:
- Therefore, the correct statement is:
\[ X < Y \]