Question

$Mg{\left(OH\right)}_2$ is soluble in ${NH}_{4}Cl$ but not in $NaCl$. If true write 1, else write 0.

Answer 1

$Mg(OH{)}_2+N{H}_{4}Cl\to N{H}_{4}OH$ weak base

The reaction with $N{H}_4^{+}$ reduces the amount of $O{H}^{-}$ ions, ie, they are 'consumed' from the equilibrium with magnesium hydroxide solid. So essentially, you are removing $O{H}^{-}$ ions from the expression.

This will cause the solid to dissolve more in order to produce more $O{H}^{-}$ ions to react with $N{H}_4^{+}$. The result of this is that the solid has become more soluble in the $N{H}_{4}Cl$ solution.