Would you expect the second electron gain enthalpy of `S` as positive, more negative or less negative than the first? Justify your answer.

Answer

To determine whether the second electron gain enthalpy of sulfur (S) is positive, more negative, or less negative than the first, we need to analyze the process of adding electrons to sulfur and the associated energy changes.

### Step-by-Step Solution:

1. **Understanding Electron Gain Enthalpy**:
- Electron gain enthalpy is defined as the amount of energy released when an electron is added to a gaseous atom. A negative value indicates that energy is released, while a positive value indicates that energy is absorbed.

2. **First Electron Gain Enthalpy of Sulfur**:
- Sulfur (S) has the electronic configuration of [Ne] 3s² 3p⁴. When it gains one electron, it becomes S⁻ (sulfide ion). The process is energetically favorable because sulfur is close to achieving a stable octet configuration.
- The first electron gain enthalpy (ΔH₁) for sulfur is approximately -200 kJ/mol, indicating that energy is released when the first electron is added.

3. **Second Electron Gain Enthalpy of Sulfur**:
- When we try to add a second electron to the already negatively charged S⁻ ion, we are adding an electron to an anion. This process is less favorable due to the repulsion between the negatively charged electrons.
- The second electron gain enthalpy (ΔH₂) for sulfur is positive, approximately +590 kJ/mol. This indicates that energy is required to add the second electron, making the process unfavorable.

4. **Comparison of First and Second Electron Gain Enthalpy**:
- The first electron gain enthalpy is negative (favorable), while the second electron gain enthalpy is positive (unfavorable).
- Therefore, we can conclude that the second electron gain enthalpy of sulfur is **positive** and **much less negative** than the first electron gain enthalpy.

5. **Justification**:
- The reason for this difference is the increased electron-electron repulsion when adding a second electron to an already negatively charged ion. The additional electron experiences repulsion from the existing electron(s), making it energetically unfavorable to add.

### Conclusion:
The second electron gain enthalpy of sulfur is positive and significantly less negative than the first electron gain enthalpy due to the repulsion between electrons in the negatively charged ion.

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