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