Which of the following equation gives the values of heat of formation `(DeltaH_(f)^(@))`?

Options

A. C(diamond) ` + O_(2)(g) rarr CO_(2)(g)`
B. `(1)/(2) H_(2)(g) + (1)/(2)F_(2)(g) rarr HF (g)`
C. `N_(2)(g) + 3H_(2)(g) rarr 2NH_(3)(g)`
D. `H_(2)(g) + F_(2)(g) rarr 3HF(g)`

Explanation

To determine which equation gives the values of heat of formation (ΔH_f^(@)), we need to understand the definition of heat of formation. The heat of formation is defined as the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states.

### Step-by-Step Solution:

1. **Understand the Definition**:
- The heat of formation (ΔH_f^(@)) refers to the enthalpy change when one mole of a compound is formed from its elements in their standard states.

2. **Criteria for Heat of Formation**:
- The reaction must produce exactly one mole of the product.
- All reactants must be in their standard states.

3. **Evaluate Each Option**:
- **Option 1**: Carbon diamond (C_diamond) → This cannot be the heat of formation because carbon in its standard state is graphite (C_graphite), not diamond.
- **Option 2**: H2(g) + F2(g) → 2HF(g)
- This option produces 2 moles of HF, which does not satisfy the requirement of forming one mole of product. Hence, it cannot be the heat of formation.
- **Option 3**: 2H2(g) + O2(g) → 2H2O(l)
- This option also produces 2 moles of water (H2O), which again does not meet the one mole product requirement.
- **Option 4**: C(s, graphite) + O2(g) → CO2(g)
- This reaction produces one mole of CO2 from its elements in their standard states (C in graphite form and O2 as diatomic oxygen), fulfilling both criteria.

4. **Conclusion**:
- The correct equation that gives the values of heat of formation (ΔH_f^(@)) is **Option 4**: C(s, graphite) + O2(g) → CO2(g).