Which of the following will have the most negative electron gain enthalpy and which the least negative? `P, S, Cl, F`. Explain your answer.

Options

A. `P, Cl`
B. `Cl, F`
C. `Cl, S`
D. `Cl, P`

Explanation

To determine which of the elements P (phosphorus), S (sulfur), Cl (chlorine), and F (fluorine) will have the most negative and least negative electron gain enthalpy, we will analyze the trends in electron gain enthalpy across the periodic table.

### Step-by-Step Solution:

1. **Understanding Electron Gain Enthalpy**:
- Electron gain enthalpy is defined as the energy change that occurs when an electron is added to a neutral atom in the gas phase. A more negative value indicates that energy is released when the electron is added, which means the atom has a stronger tendency to gain an electron.

2. **Periodic Trends**:
- **Across a Period**: As we move from left to right across a period, the electron gain enthalpy generally becomes more negative. This is because the effective nuclear charge increases, making it easier for the atom to attract additional electrons.
- **Down a Group**: As we move down a group, the electron gain enthalpy becomes less negative. This is due to the increased distance between the nucleus and the added electron, as well as increased electron shielding.

3. **Analyzing the Given Elements**:
- **Fluorine (F)**: Located in Group 17, Period 2. It has a high electron gain enthalpy due to its small size and high electronegativity.
- **Chlorine (Cl)**: Located in Group 17, Period 3. It has a slightly less negative electron gain enthalpy than fluorine because it is larger and has more electron shielding.
- **Sulfur (S)**: Located in Group 16, Period 3. It has a less negative electron gain enthalpy compared to chlorine and fluorine.
- **Phosphorus (P)**: Located in Group 15, Period 3. It has the least negative electron gain enthalpy among the four elements because it is further left in the periodic table and has a lower tendency to gain an electron.

4. **Conclusion**:
- The element with the **most negative electron gain enthalpy** is **Chlorine (Cl)**.
- The element with the **least negative electron gain enthalpy** is **Phosphorus (P)**.

### Final Answer:
- Most negative electron gain enthalpy: **Chlorine (Cl)**
- Least negative electron gain enthalpy: **Phosphorus (P)**