Equilibrium Question 901

Question: A solution saturated in lime water has a pH of 12.4. Then the Ksp for $ Ca{{(OH)}_2} $ is:

Options:

A) $ 3.2\times {10^{-3}} $

B) $ 7.8\times {10^{-6}} $

C) $ 7.8\times {10^{-28}} $

D) $ 3.2\times {10^{-4}} $

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Answer:

Correct Answer: B

Solution:

$ pH=12.4 $

$ \Rightarrow $ $-\log ({H^{+}})=12.4,\Rightarrow $

$ \log [{H^{+}}]=13.6 $

$ Ca{{(\overset{+}{\mathop{OH}},)}_2}\rightarrow 2OH+C{a^{2+}} $

$ [{H^{+}}]=4\times {10^{-13}} $

$ [O{H^{-}}]=\frac{{10^{-14}}}{4\times 10}=\frac{1}{3}\times {10^{-1}}=2.5\times {10^{-2}} $

$ Ksp=[C{a^{2+}}][O{H^{-}}] $

$ [C{a^{2+}}]=\frac{1}{2}[O{H^{-}}] $

$ ( \frac{1}{8}\times {10^{-1}} ){{( \frac{1}{4}\times {10^{-1}} )}^{2}}=\frac{1}{8}\times \frac{1}{16}\times {10^{-3}} $

$ 7.8\times {10^{-6}} $



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