A) 1.66
B) 12.3424
C) 7.0
D) 14.0
Correct Answer: B
Solution :
\[Ca{{(OH)}_{2}}(s)\underset{s}{\mathop{C{{a}^{2+}}}}\,(aq.)+\underset{2s}{\mathop{2O{{H}^{-}}(aq.)}}\,\] \[{{K}_{sp}}=[C{{a}^{2+}}]{{[O{{H}^{-}}]}^{2}}\] \[=(s){{(2s)}^{2}}\] \[{{K}_{sp}}=4{{s}^{3}}\] \[5.5\times {{10}^{-6}}=4{{s}^{3}}\] \[S=\sqrt[3]{\frac{5.5\times {{10}^{-6}}}{4}}=1.1\times {{10}^{-2}}M\] \[\therefore \] \[[O{{H}^{-}}]=2s\] \[=2\times 1.1\times {{10}^{-2}}\] \[=2.2\times {{10}^{-2}}\] \[pOH=-[\log [O{{H}^{-}}]\] \[=-\log (2.2\times {{10}^{-2}})\] \[=2-0.3424\] \[=1.6576\] \[pH=14-pOH\] \[=14-1.6576\] \[=12.3424\]
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