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Imagine an unsaturated(No Ca(OH)2 (s) just Ca2+ (aq) and OH- (aq)) aqueous solution of Calcium Hydroxide.

Is the following equilibrium present in that solution and does the transparency of an unsaturated Calcium Hydroxide vanish after a while?

$$\ce{ Ca^2+_{(aq)} + 2OH- _{(aq)} <=> Ca(OH)2_{(s)}}$$

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    $\begingroup$ No and no (well, in real world the solution might get cloudy, but that's for entirely unrelated reasons). $\endgroup$ – Ivan Neretin Mar 24 '16 at 8:15
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Equilibria in solutions are given as solubility products, $K_{\text{sp}}$. Your reaction is:

$$\ce{Ca(OH)_2 <=> Ca^2+ + 2OH-}$$ for this, $K_{\text{sp}}=5.5\times 10^{-6}$ (from Wikipedia). What this means, is that in a saturated solution, at equilibrium, you will have: $$K_{\text{sp}}=[\ce{Ca^2+}] [\ce{OH-}]^2=5.5\times10^{-6}$$

However, for an unsaturated solution, you will have:

$$[\ce{Ca^2+}] [\ce{OH-}]^2 <K_{\text{sp}}$$

As mentioned the solution does get cloudy for different reasons, namely the formation of $\ce{CaCO3}$ by reaction with $\ce{CO2}$.

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