Answer :
Explanation:
Chemical reaction equation for [tex]Cr(OH)_{3}[/tex] is as follows.
[tex]Cr(OH)_{3} \rightarrow Cr^{3+} + 3OH^{-}[/tex]
As it is given that pH is 6. So, the concentration of hydrogen ions will be as follows.
pH = [tex]-log [H^{+}][/tex]
antilog (-6) = [tex][H^{+}][/tex]
[tex][H^{+}] = 10^{-6}[/tex]
and [tex][OH^{-}] = \frac{10^{-14}}{[H^{+}]}[/tex]
= [tex]\frac{10^{-14}}{10^{-6}}[/tex]
= [tex]10^{-8}[/tex]
Now, let us assume that the solubility is "s". Therefore,
[tex]Cr(OH)_{3} \rightarrow Cr^{3+} + 3OH^{-}[/tex]
s [tex]10^{-8}[/tex]
Therefore, calculate the value of [tex]K_{sp}[/tex] for this reaction as follows.
[tex]K_{sp} = [Cr^{3+}][10^{-8}]^{3}[/tex]
[tex]1.6 \times 10^{-30} = s \times (10^{-8})^{-30}[/tex]
s = [tex]1.6 \times 10^{-6} mol/L[/tex]
Thus, we can conclude that the molar solubility of [tex]Cr(OH)_{3}[/tex] is [tex]1.6 \times 10^{-6} mol/L[/tex].