Which of the following statement is incorrect?

Let us analyze each statement:

Option A: "Low solubility of LiF in water is due to its small hydration enthalpy."

This statement is incorrect. LiF has low solubility in water despite having a very high hydration enthalpy (since both Li$$^+$$ and F$$^-$$ are small ions with high charge density). The actual reason for its low solubility is its very high lattice enthalpy, which exceeds the hydration enthalpy. So the statement incorrectly attributes the low solubility to small hydration enthalpy, when in fact LiF has a high hydration enthalpy — its lattice enthalpy is simply even higher.

Option B: "$$KO_2$$ is paramagnetic."

This is correct. Potassium superoxide ($$KO_2$$) contains the superoxide ion $$O_2^-$$, which has one unpaired electron, making it paramagnetic.

Option C: "Solution of sodium in liquid ammonia is conducting in nature."

This is correct. When sodium dissolves in liquid ammonia, it forms solvated electrons ($$Na^+$$ and $$e^-_{(amm)}$$), which are responsible for the electrical conductivity and the characteristic blue colour of the solution.

Option D: "Sodium metal has higher density than potassium metal."

This is correct. Sodium has a density of 0.97 g/cm$$^3$$ while potassium has a density of 0.86 g/cm$$^3$$. As we go down the alkali metal group, despite increasing atomic mass, the atomic volume increases more rapidly, causing potassium to have a lower density than sodium.

Therefore, the incorrect statement is Option A.