For which `Delta_(f)H^(Theta)` is zero?

Options

A. (a) `H`
B. (b) `H^(-)`
C. (c) `H^(+)`
D. (d) `H^(+)(aq)`

Answer

To solve the question "For which Δ_fH° is zero?", we need to analyze the concept of standard enthalpy of formation (Δ_fH°) and the conditions under which it is considered to be zero.

### Step-by-Step Solution:

1. **Understanding Standard Enthalpy of Formation (Δ_fH°)**:
- The standard enthalpy of formation (Δ_fH°) is defined as the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states.

2. **Standard State Definition**:
- The standard state of an element is its most stable form at standard conditions (1 atm pressure and 25°C or 298 K). For example, the standard state of oxygen is O₂ (g), and for hydrogen, it is H₂ (g).

3. **Δ_fH° for Elements in Standard State**:
- For any element in its standard state, the standard enthalpy of formation is defined to be zero. This is because there is no change in enthalpy when an element is formed from itself.

4. **Analyzing the Options**:
- **Option A: H** - This is a single atom of hydrogen and not in its standard state (which is H₂). Therefore, Δ_fH° is not zero.
- **Option B: H⁻** - This is a negative ion of hydrogen, which does not exist in its standard state. Hence, Δ_fH° is not zero.
- **Option C: H⁺** - This is a positive ion of hydrogen, but it is not in its elemental form. Therefore, Δ_fH° is not zero.
- **Option D: H⁺ (aqueous)** - The standard enthalpy of formation for H⁺ in aqueous solution is defined to be zero by convention. This is because it is the smallest ion and is used as a reference point.

5. **Conclusion**:
- Based on the analysis, the correct answer is **Option D: H⁺ (aqueous)**, as its standard enthalpy of formation is taken as zero by convention.

### Final Answer:
The correct option is **D: H⁺ (aqueous)**.