Which of the following reaction define `DeltaG_(f)^(@)` ?

Options

A. `C("diamond") + O_(2)(g) to CO_(2)(g)`
B. `1/2H_(2)(g) + 1/2F_(2)(g) to HF(g)`
C. `H_(4)P_(2)O_(7) + H_(2)O to 2H_(3)PO_(4)`
D. `SO_(2) (g) + 1/2O_(2)(g) to SO_(3)(g)`

Explanation

To determine which reaction defines the standard free energy of formation (ΔG_f^(@)), we need to understand the definition of ΔG_f^(@). The standard free energy of formation is the change in free energy when one mole of a substance is formed from its constituent elements in their standard states.

### Step-by-Step Solution:

1. **Understand the Definition**:
- The standard free energy of formation (ΔG_f^(@)) is the energy change when one mole of a compound is formed from its elements in their standard states.

2. **Identify Standard States of Elements**:
- Elements must be in their standard states for the reaction to qualify for ΔG_f^(@).
- For example:
- Hydrogen (H) is in gaseous form (H2).
- Oxygen (O) is in gaseous form (O2).
- Carbon is typically in the form of graphite.
- Phosphorus is commonly in the form of P4.
- Sulfur is often in the form of S8.

3. **Analyze Each Reaction**:
- **Option 1**: Formation of CO2 from Carbon and Oxygen.
- Carbon must be in the form of graphite (solid), and oxygen is in gaseous form. This option is incorrect because it does not specify graphite.

- **Option 2**: Formation of HF from Hydrogen and Fluorine.
- Hydrogen is in the form of H2 (gaseous), and Fluorine is in the form of F2 (gaseous). This option is correct as it meets the criteria for ΔG_f^(@).

- **Option 3**: Formation of H3PO4 from H2, P4, and O2.
- This reaction does not represent the formation from its constituent elements correctly, as it includes H4P2O7 and H2, which are not in their standard states. This option is incorrect.

- **Option 4**: Formation of SO3 from Sulfur and Oxygen.
- Sulfur is typically in the form of S8, and the reaction does not specify this. Therefore, this option is also incorrect.

4. **Conclusion**:
- The only reaction that correctly defines ΔG_f^(@) is **Option 2**, which is the formation of HF from its elements in their standard states.

### Final Answer:
The correct option that defines ΔG_f^(@) is **Option 2**: HF gas is formed from Hydrogen and Fluorine.