A) \[2.6\times {{10}^{-9}}\]
B) \[4\times {{10}^{-8}}\]
C) \[8\times {{10}^{-12}}\]
D) \[3.2\times {{10}^{-11}}\]
Correct Answer: D
Solution :
Write reaction for dissociation of \[\text{Ca}{{\text{F}}_{\text{2}}}\]and then find relationship between \[{{\text{K}}_{\text{sp}}}\]and solubility. \[Ca{{F}_{2}}C{{a}^{2+}}+2{{F}^{-}}\] Given solubility of \[Ca{{F}_{2}}=2\times {{10}^{-4}}\,mol\,{{L}^{-1}}\] \[\therefore \] \[[C{{a}^{2+}}]=2\times {{10}^{-4}}\,mol\,{{L}^{-1}}\] \[[{{F}^{-}}]=2\times 2\times {{10}^{-4}}mol\,{{L}^{-1}}\] \[{{K}_{sp}}=[C{{a}^{2+}}]{{[{{F}^{-}}]}^{2}}\] \[=(2\,\times \,{{10}^{-4}}){{(2\times 2\times {{10}^{-4}})}^{2}}\] \[=32\times {{10}^{-12}}\] \[=3.2\times {{10}^{-11}}\]
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