A) \[2.0\times {{10}^{-6}}mol\,\,{{L}^{-1}}\]
B) \[1.0\times {{10}^{-5}}mol\,\,{{L}^{-1}}\]
C) \[1.0\times {{10}^{-6}}mol\,\,{{L}^{-1}}\]
D) \[1.0\times {{10}^{-7}}mol\,\,{{L}^{-1}}\]
Correct Answer: D
Solution :
Base \[BOH\] is dissociated as follows \[BOH{{B}^{+}}+O{{H}^{-}}\] So, the dissociation constant of base \[BOH\] \[{{K}_{b}}=\frac{[{{B}^{+}}][O{{H}^{-}}]}{[BOH]}\] ? (i) At equilibrium, \[[{{B}^{+}}]=[O{{H}^{-}}]\]\[\therefore \] \[{{K}_{b}}=\frac{{{[O{{H}^{-}}]}^{2}}}{[BOH]}\] Given that \[{{k}_{b}}=1.0\times {{10}^{-12}}\] and \[[BOH]=0.01\,\,M\] Thus, \[1.0\times {{10}^{-12}}=\frac{{{[O{{H}^{-}}]}^{2}}}{0.01}\] \[{{[O{{H}^{-}}]}^{2}}=1\times {{10}^{-14}}\] \[[O{{H}^{-}}]=1.0\times {{10}^{-7}}mol\,\,{{L}^{-1}}\]
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