Consider the following reactions:
(i) `H^(+)(aq)+OH^(-)(aq)rarrH_(2)O(l)` ,
`DeltaH=-X_(1)KJmol^(-1)`
(ii) `H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l),DeltaH=-X_(2)KJmol^(-1)`
(iii) `CO_(2)(g)+H_(2)(g)rarrCO(g)+H_(2)O(l)` ,
`DeltaH=-X_(3)KJmol^(-1)`
(iv) `C_(2)H_(2)(g)+(5)/(2)O_(2)(g)rarr2CO_(2)(g)+H_(2)O(l)` ,
`DeltaH=+X_(4)KJmol^(-1)`
Enthanlpy of formation of `H_(2)O(l)` is

Options

A. `-X_(2) KJ "mol"^(-1)`
B. `-X_(3) KJ "mol"^(-1)`
C. `+X_(4) KJ "mol"^(-1)`
D. `-X_(1) KJ "mol"^(-1)`

Explanation

To determine the enthalpy of formation of \( H_2O(l) \) from the given reactions, we need to analyze each reaction carefully and identify which one corresponds to the definition of enthalpy of formation.

### Step-by-Step Solution:

1. **Understanding Enthalpy of Formation**:
- The enthalpy of formation (\( \Delta H_f \)) is defined as the heat change that occurs when one mole of a compound is formed from its elements in their standard states.

2. **Analyzing the Reactions**:
- **Reaction (i)**:
\[ H^+(aq) + OH^-(aq) \rightarrow H_2O(l) \]
- This reaction represents the neutralization of an acid and a base, not the formation of water from its elements. Thus, it does not represent the enthalpy of formation.

- **Reaction (ii)**:
\[ H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l) \]
- This reaction shows the formation of water from its elements (hydrogen and oxygen). This is the correct representation of the enthalpy of formation of water. Therefore, \( \Delta H = -X_2 \) is the enthalpy of formation.

- **Reaction (iii)**:
\[ CO_2(g) + H_2(g) \rightarrow CO(g) + H_2O(l) \]
- This reaction involves the conversion of carbon dioxide and hydrogen into carbon monoxide and water. It does not represent the formation of water from its elements, so it is not the enthalpy of formation.

- **Reaction (iv)**:
\[ C_2H_2(g) + \frac{5}{2}O_2(g) \rightarrow 2CO_2(g) + H_2O(l) \]
- This reaction represents the combustion of acetylene (C2H2) and does not represent the formation of water from its elements. Hence, it is also not the enthalpy of formation.

3. **Conclusion**:
- The only reaction that represents the enthalpy of formation of \( H_2O(l) \) is Reaction (ii), where \( \Delta H = -X_2 \).

### Final Answer:
The enthalpy of formation of \( H_2O(l) \) is given by \( -X_2 \) KJ/mol.

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