The `Delta_(r )H^@` (enthalpy of formation) is positive in :

Options

A. `O_(3)(g)`
B. `NO(g)`
C. `Hl(g)`
D. All of these

Explanation

To determine in which case the enthalpy of formation (ΔrH°) is positive, we need to analyze each option provided in the question. The enthalpy of formation is defined as the heat change that occurs when one mole of a compound is formed from its constituent elements in their standard states.

### Step-by-Step Solution:

1. **Understanding Enthalpy of Formation**:
- Enthalpy of formation (ΔrH°) is positive when energy is required to form a compound from its elements. This typically occurs when the product is less stable than the reactants.

2. **Analyzing Option 1: Ozone (O3)**:
- The formation of ozone from oxygen can be represented as:
\[ 3 O_2(g) \rightarrow 2 O_3(g) \]
- Ozone (O3) is less stable than diatomic oxygen (O2). Therefore, energy is required to convert O2 into O3, indicating that ΔrH° is positive for this reaction.

3. **Analyzing Option 2: Nitric Oxide (NO)**:
- The formation of nitric oxide can be represented as:
\[ N_2(g) + \frac{1}{2} O_2(g) \rightarrow NO(g) \]
- Nitric oxide is a highly reactive species and is less stable than its constituent elements (N2 and O2). Thus, energy is required for this formation, leading to a positive ΔrH°.

4. **Analyzing Option 3: Hydrogen Iodide (HI)**:
- The formation of hydrogen iodide can be represented as:
\[ \frac{1}{2} H_2(g) + \frac{1}{2} I_2(s) \rightarrow HI(g) \]
- Iodine (I2) must be sublimed from its solid state to gaseous state before it can react with hydrogen. This sublimation requires energy, indicating that ΔrH° is also positive for this reaction.

5. **Conclusion**:
- Since all three reactions (ozone, nitric oxide, and hydrogen iodide) require energy for their formation, the enthalpy of formation (ΔrH°) is positive in all these cases. Therefore, the correct answer is that ΔrH° is positive for options 1, 2, and 3.

### Final Answer:
The enthalpy of formation (ΔrH°) is positive for ozone (O3), nitric oxide (NO), and hydrogen iodide (HI).