Which of the reaction defines molar `DeltaH_(f)^(0)`?

Options

A. `CaO(s) + CO_(2)(g) rarr CaCO_(3)(s)`
B. `(1)/(2)Br_(2)(l) + (1)/(2)H_(2)(g) rarr HBr(g)`
C. `N_(2)(g) + 2H_(2)(g) + (3)/(2)O_(2)(g) rarr NH_(4)NO_(3)(s)`
D. `(1)/(2)I_(2)(s) + (1)/(2)H_(2)(g) rarr HI(g)`

Answer

To determine which reaction defines the molar standard heat of formation (ΔH_f^0), we need to understand the definition of standard heat of formation. The standard 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 standard heat of formation (ΔH_f^0) is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

2. **Identify Standard States**:
- Standard states refer to the physical states of the elements at 1 bar (or 1 atm) pressure and a specified temperature (usually 25°C or 298 K). For example, O2 is a gas, H2 is a gas, and Br2 is a liquid at these conditions.

3. **Analyze Each Reaction**:
- **Option 1**: Check if it forms one mole of product and if the reactants are in their standard states.
- **Option 2**: Check if it forms one mole of product and if the reactants are in their standard states.
- **Option 3**: Check if it forms one mole of product and if the reactants are in their standard states.
- **Option 4**: Check if it forms one mole of product and if the reactants are in their standard states.

4. **Evaluate Each Option**:
- **Option 1**: If the reactants are not in their standard states, this cannot define ΔH_f^0.
- **Option 2**: If it forms one mole of product and all reactants are in standard states, this is a valid reaction for ΔH_f^0.
- **Option 3**: If it also meets the criteria of forming one mole of product from elements in standard states, this is valid.
- **Option 4**: If it meets the criteria, it is also valid.

5. **Conclusion**:
- The options that correctly define the molar standard heat of formation (ΔH_f^0) are those that form one mole of product from elements in their standard states. Based on the analysis, the correct options are those that satisfy this condition.

### Final Answer:
- The reactions that define molar ΔH_f^0 are the ones where one mole of product is formed from elements in their standard states. Based on the analysis, options 2 and 3 are valid.