The second electron gain enthalpies (in kJ `mol^(-1)`) of oxygen and sulphur respectively are:

Options

A. –780, +590
B. –590, +780
C. +590, +780
D. +780, +590

Explanation

To determine the second electron gain enthalpies of oxygen and sulfur, we need to understand the concept of electron gain enthalpy and how it varies between different elements.

### Step-by-Step Solution:

1. **Understanding Electron Gain Enthalpy**:
- Electron gain enthalpy is defined as the change in energy when an electron is added to a neutral atom to form a negative ion.
- The first electron gain enthalpy is usually negative because energy is released when an electron is added to a neutral atom.

2. **First Electron Gain for Oxygen and Sulfur**:
- When an electron is added to oxygen (O), it forms O⁻ (oxide ion).
- When another electron is added to O⁻, it forms O²⁻.
- For sulfur (S), adding an electron forms S⁻ (sulfide ion), and adding another electron forms S²⁻.

3. **Analyzing the Second Electron Gain Enthalpy**:
- The second electron gain enthalpy refers to the energy change when a second electron is added to the already negatively charged ion (O⁻ or S⁻).
- For oxygen, the addition of a second electron to O⁻ (to form O²⁻) experiences significant electron-electron repulsion due to the small size of the oxygen atom. This results in a positive electron gain enthalpy.
- For sulfur, the addition of a second electron to S⁻ (to form S²⁻) encounters less repulsion because sulfur is larger in size compared to oxygen. Thus, the second electron gain enthalpy for sulfur is less positive than that of oxygen.

4. **Values of Second Electron Gain Enthalpy**:
- The second electron gain enthalpy of oxygen (O) is approximately +780 kJ/mol.
- The second electron gain enthalpy of sulfur (S) is approximately +590 kJ/mol.

5. **Conclusion**:
- Therefore, the second electron gain enthalpies of oxygen and sulfur respectively are:
- Oxygen: +780 kJ/mol
- Sulfur: +590 kJ/mol

### Final Answer:
The second electron gain enthalpies of oxygen and sulfur are +780 kJ/mol and +590 kJ/mol, respectively.

---