Which of the following reactions will define `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. `CO(g) + 1/2O_(2)(g) rarr CO_(2)(g)`

Explanation

To determine which of the given reactions defines the standard enthalpy of formation (ΔH_f^(@)), we need to understand the definition of standard enthalpy of formation. It is defined as the heat change that occurs when one mole of a compound is formed from its constituent elements in their standard states at 298 K and 1 atm pressure.

Let's analyze each option step by step:

### Step 1: Analyze Option 1
- **Reaction**: Formation of CO2 from carbon (diamond).
- **Elements**: Carbon (diamond) and oxygen (O2).
- **Analysis**: The standard state of carbon is graphite, not diamond. Since diamond is not the standard state of carbon, this reaction does not represent the standard enthalpy of formation.

### Step 2: Analyze Option 2
- **Reaction**: Formation of HF from H2 and F2.
- **Elements**: Hydrogen (H2) and fluorine (F2).
- **Analysis**: Both H2 and F2 are in their standard states (gases). The formation of one mole of HF from its constituent elements meets the criteria for standard enthalpy of formation. Therefore, this reaction correctly represents ΔH_f^(@).

### Step 3: Analyze Option 3
- **Reaction**: Formation of 2 moles of NH3.
- **Elements**: Nitrogen (N2) and hydrogen (H2).
- **Analysis**: The definition specifies the formation of one mole of a substance. Since this reaction forms 2 moles of NH3, it does not represent the standard enthalpy of formation.

### Step 4: Analyze Option 4
- **Reaction**: Formation of CO2 from carbon monoxide and oxygen.
- **Elements**: Carbon monoxide (CO) and oxygen (O2).
- **Analysis**: The reaction does not start from the constituent elements (graphite and O2) but rather from CO, which is a compound. Therefore, this reaction does not represent the standard enthalpy of formation for CO2.

### Conclusion
After analyzing all options, only **Option 2** represents the standard enthalpy of formation (ΔH_f^(@)).

### Summary of the Solution
- **Correct Option**: Option 2 (Formation of HF from H2 and F2).
- **Incorrect Options**: Options 1, 3, and 4.