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pH of a saturated solution of $Ca(OH)_2$ is 9. The solubility product ($K_{sp}$) of $Ca(OH)_2$ is:
Detailed Solution
$Ca(OH)_2\rightleftharpoons Ca^{2+}+2OH^-$
pH = 9, so pOH = 14 − 9 = 5 and $[OH^-]=10^{-5}\ M$
$[Ca^{2+}]=\frac{10^{-5}}{2}$
$K_{sp}=[Ca^{2+}][OH^-]^2=\frac{10^{-5}}{2}\times(10^{-5})^2=0.5\times10^{-15}$