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(D) $I$. $LiF$ has a very high lattice enthalpy due to the small size of both $Li^+$ and $F^-$ ions,which makes it sparingly soluble in water. This is

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$I$,$III$ and $IV$

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(D) $I$. $LiF$ has a very high lattice enthalpy due to the small size of both $Li^+$ and $F^-$ ions,which makes it sparingly soluble in water. This is a correct statement.$II$. $LiBr$ is soluble in acetone due to its covalent character (Fajans' rule),which makes this statement incorrect as it claims it is not soluble.$III$. $LiCl$ is soluble in pyridine due to its covalent character,which makes this statement correct.$IV$. The melting point of alkali metal halides follows the order $MF > MCl > MBr > MI$ because the lattice energy decreases as the size of the halide ion increases. This is a correct statement.Therefore,statements $I$,$III$,and $IV$ are correct.

The correct statements are:
$I$. The low solubility of $LiF$ is due to its high lattice enthalpy.
$II$. $LiBr$ is soluble in acetone.
$III$. $LiCl$ is soluble in pyridine.
$IV$. The order of melting points of alkali metal halides is $MF > MCl > MBr > MI$.

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The correct statements are:$I$. The low solubility of $LiF$ is due to its high lattice enthalpy.$II$. $LiBr$ is soluble in acetone.$III$. $LiCl$ is soluble in pyridine.$IV$. The order of melting points of alkali metal halides is $MF > MCl > MBr > MI$.