Question

Why is $I_2$ more soluble in $KI$ than in water?

Answer 1

Solubility follows law of "like" dissolves "like". Therefore, a non-polar molecule stays insoluble in polar solvent and solubilises into a non-polar solvent and vice-versa. Since $I_2$ is non-polar and $H_{2}O$ is polar, therefore they are immiscible. Upon addition of $KI$, $I_2$ forms $K{I}_3^{-}$ and becomes polar. Moreover, due to ion-dipole interaction between $K{I}_3^{-}$ anion and water the solubility increases.

$KI+I_2\rightleftharpoons K{I}_3$