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Which of the following compound will not dissolve in hot mixture of $NaOH$ and $H_2O$ ?
$Fe(OH)_3$
$Al(OH)_3$
$Cr(OH)_3$
$Zn(OH)_2$
Solution
Most hydroxide salts are insoluble. For example, the solubility of $Fe ^{+3}$ in basic solution is governed by the reaction shown in (eq 1), from which the corresponding equilibrium constant expression can be derived (eq 2). The equilibrium constant for the reaction $K _{s p}$ is $6.3 \times 10^{-38}$ which says that $Fe ( OH )_3$ is sparingly soluble under most conditions. Equation 3 says that the solubility of ferric ion rapidly decreases as the solution becomes more basic.
$Fe ( OH )_3 \rightleftharpoons Fe ^{+3}+3 OH ^{-}——(1)$
$K _{ sp }=\left[ Fe ^{+3}\right]\left[ OH ^{-}\right]^3—^{-(2)}$
$\text { Solubility }=\left[ Fe ^{+3}\right]=\frac{ K _{ sp }}{\left[ OH ^{-}\right]^3}——(3)$