Sure, let's analyze the ionization energies provided to predict the formula of a compound formed when element "X" reacts with chlorine (Cl).
### Step-by-Step Solution:
1. Understanding Ionization Energies:
- Ionization energy is the amount of energy required to remove an electron from an atom.
- Successive ionization energies increase because it becomes harder to remove additional electrons from an increasingly positive ion.
2. Examining the Given Ionization Energies:
- The enthalpy values are:
- 1st Ionization Energy: 577 kJ/mol
- 2nd Ionization Energy: 1820 kJ/mol
- 3rd Ionization Energy: 2740 kJ/mol
- 4th Ionization Energy: 11600 kJ/mol
- 5th Ionization Energy: 14841 kJ/mol
3. Identifying significant jumps in ionization energies:
- From the 1st to the 2nd ionization, the increase is significant but manageable.
- The same pattern holds from the 2nd to the 3rd ionization energy.
- However, there is a large jump in energy from the 3rd ionization (2740 kJ/mol) to the 4th ionization (11600 kJ/mol).
- Similarly, the 5th ionization energy (14841 kJ/mol) is significantly higher than the 4th.
4. Implications of the Ionization Energy Jumps:
- The large increase between the 3rd and 4th ionization energies suggests that removing a fourth electron requires much more energy and is thus highly unfavorable.
- This indicates that the element X is likely to lose three electrons to achieve a more stable electronic configuration.
5. Forming Cations:
- Given the low relative energy up to the removal of the third electron, element X is likely to form a [tex]\( \text{X}^{3+} \)[/tex] cation, as it loses three electrons easily.
6. Combining with Chlorine:
- Chlorine forms [tex]\( \text{Cl}^- \)[/tex] ions (each chlorine atom gains one electron).
- To form a neutral compound, the charges must balance: one [tex]\( \text{X}^{3+} \)[/tex] ion requires three [tex]\( \text{Cl}^- \)[/tex] ions.
7. Predicting the Compound Formula:
- Therefore, the compound formed when X reacts with chlorine has the formula [tex]\( \text{XCl}_3 \)[/tex].
### Conclusion:
The formula of the compound formed when element X reacts with chlorine (Cl) is [tex]\( \mathbf{XCl_3} \)[/tex].
