`O(g) + 2e^(-) to O^(2-)(g) , DeltaH_(eg) = 744.7` kJ/mole . The positive value of `DeltaH_(eg)` is due to :

Options

A. energy is released to add on `1e^(-) " to " O^(-)`
B. energy is required to add on `1e^(-) " to " O^(-)`
C. energy is needed to add on `1e^(-) " to " O`
D. None of the above is correct

Explanation

To understand why the positive value of ΔH_(eg) = 744.7 kJ/mole for the reaction O(g) + 2e^(-) → O^(2-)(g), we need to analyze the concept of electron gain enthalpy and the processes involved in adding electrons to an oxygen atom.

### Step-by-Step Solution:

1. **Definition of Electron Gain Enthalpy (ΔH_(eg))**:
- Electron gain enthalpy is defined as the amount of energy released or absorbed when an electron is added to a neutral atom in the gas phase to form a negative ion.

2. **First Electron Gain Enthalpy**:
- When the first electron is added to a neutral oxygen atom (O), it forms O^(-). This process is exothermic, meaning it releases energy.
- The value for the first electron gain enthalpy of oxygen is approximately -41 kJ/mole. This negative value indicates that energy is released during this process.

3. **Second Electron Gain Enthalpy**:
- When a second electron is added to the O^(-) ion to form O^(2-), this process is endothermic. This means that energy must be supplied to overcome the repulsion between the negatively charged O^(-) ion and the incoming electron.
- The addition of the second electron requires energy input, which is why the second electron gain enthalpy is positive and significantly higher than the first.

4. **Overall Process**:
- The overall reaction involves adding two electrons to the neutral oxygen atom. The first electron adds energy release, while the second electron requires energy input.
- Therefore, the total energy change (ΔH_(eg)) for the addition of two electrons results in a positive value of 744.7 kJ/mole.

5. **Conclusion**:
- The positive value of ΔH_(eg) = 744.7 kJ/mole is primarily due to the energy required to add the second electron to the already negatively charged O^(-) ion, which experiences electron-electron repulsion.