In: Chemistry

At 22 °C an excess amount of a generic metal hydroxide M(OH)_{2} is mixed with pure water. The resulting equilibrium solution has a pH of 10.26. What is the K_{sp} of the salt at 22 °C?

\(\mathrm{M}(\mathrm{OH}) 2(\mathrm{~s})<->\mathrm{M}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq})\)

\(\mathrm{Ksp}=\left[\mathrm{M}^{2+}\right]\left[\mathrm{OH}^{-}\right]^{2}\)

1) Use the \(\mathrm{pH}\) to get the \(\mathrm{pOH}\)

\(14-10.26=3.74\)

2) Use the \(\mathrm{pOH}\) to get the \(\left[\mathrm{OH}^{-}\right]\)

\(\left[\mathrm{OH}^{-}\right]=10^{-} \mathrm{pOH}=10^{-3.74}=1.82 \times 10^{-4}\)

3) \(\left[\mathrm{M}^{2+}\right]\) is half the value of \(\left[\mathrm{OH}^{-}\right]\), therefore:

\(\left[\mathrm{M}^{2^{+}}\right]=1.82 \times 10^{-4}\) divided by \(2=9.10 \times 10^{-5}\)

4) Put values into Ksp expression

\(\mathrm{Ksp}=3.01 \times 10^{-12}\)

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