Recently I've been looking at this website, which says:
The $K_{\mathrm{sp}}$ of $\ce{Cr(OH)3}$ is $6.70 \times 10^{-31}$
Problem 1: What is the minimum $\mathrm{pH}$ at which $\ce{Cr(OH)3}$ will precipitate?
$$\ce{Cr(OH)3\rightleftharpoons {Cr^{3+}}+3OH-}$$ $$K_{\mathrm{\mathrm{sp}}}=[\ce{Cr^{3+}}][\ce{OH-}]^{3}$$ $$[\ce{Cr^{3+}}]=s$$ $$[\ce{OH^{-}}]=3s$$ Problem 2: What is the minimum $\mathrm{pH}$ at which $\ce{Cr(OH)3}$ will precipitate if the solution has $[\ce{Cr^{3+}}] = 0.0670~\mathrm{M}$? $$\ce{Cr(OH)3\rightleftharpoons {Cr^{3+}}+3OH-}$$ $$K_{\mathrm{sp}}=[\ce{Cr^{3+}}][\ce{OH-}]^{3}$$ $$6.70 \times 10^{-31}=[0.0670~\mathrm{M}][s^{3}]$$
I don't understand why the site wrote this:
Note that $3s$ is not necessary. In example one, $s$ was assigned to the chromium ion and we knew the hydroxide to be three times greater than that value. Here, the hydroxide is simply an unknown value and it is not expressed in terms of some other unknown value (as it was in Problem 1).
Can anyone tell me why?
Also is also used to other equilibrium constant equation? What did I miss?