LiF because of the lattice nrg is quite larger than hydration/solvation nrg and so with a highly electronegative element like F, the ∆H>0.Also the following halogens are just larger and more metallic in a sense and so LiF should have +ve enthalpy.

Positive Enthalpy of Solution

When a solute is dissolved in a solvent, energy is either released or absorbed. The enthalpy of solution is a measure of the energy change associated with the dissolution process. A positive enthalpy of solution indicates that energy is absorbed during the dissolution process.

Comparing the Compounds

To determine which of the compounds has a positive enthalpy of solution, we need to consider the strength of the intermolecular forces between the ions in the solid state. Generally, compounds with stronger intermolecular forces require more energy to break these forces and dissolve in a solvent, resulting in a positive enthalpy of solution.

Let's compare the compounds LiF, LiCl, LiBr, and LiI:

1. LiF (Lithium Fluoride)
Lithium fluoride is an ionic compound with a high lattice energy due to the strong electrostatic attraction between the lithium cations and fluoride anions. The small size of the ions and their high charge density contribute to the strong intermolecular forces. Therefore, it requires a significant amount of energy to break these forces and dissolve LiF in a solvent. Consequently, LiF is expected to have a positive enthalpy of solution.

2. LiCl (Lithium Chloride)
Lithium chloride is also an ionic compound, but its lattice energy is lower compared to LiF. This is because chloride ions are larger than fluoride ions, resulting in weaker intermolecular forces. Although LiCl still requires energy to dissolve, the energy needed is less compared to LiF. Thus, LiCl is likely to have a positive enthalpy of solution, but it may be smaller than that of LiF.

3. LiBr (Lithium Bromide)
Lithium bromide is another ionic compound, but the bromide ion is larger than the chloride ion. This leads to weaker intermolecular forces and a lower lattice energy. As a result, it requires less energy to dissolve LiBr compared to LiCl. Although LiBr still requires energy, it is less likely to have a positive enthalpy of solution compared to LiF and LiCl.

4. LiI (Lithium Iodide)
Lithium iodide is an ionic compound with the largest ions among the compounds considered. The larger size of iodide ions results in weaker intermolecular forces and a lower lattice energy. Consequently, less energy is required to dissolve LiI compared to LiBr, LiCl, and LiF. Therefore, LiI is less likely to have a positive enthalpy of solution compared to the other compounds. However, it is important to note that LiI may still have a small positive enthalpy of solution.

Conclusion

Based on the strength of intermolecular forces and lattice energies, it can be concluded that LiF and LiCl are more likely to have a positive enthalpy of solution compared to LiBr and LiI. However, the actual values of enthalpy of solution for each compound can vary depending on various factors such as temperature and concentration.