A) \[1.0\times {{10}^{-10}}\]
B) \[1.0\times {{10}^{-14}}\]
C) \[1.0\times {{10}^{-16}}\]
D) \[1.0\times {{10}^{-8}}\]
Correct Answer: B
Solution :
[b] \[\underset{(1-\alpha )c}{\mathop{{{H}_{2}}O}}\,\rightleftharpoons \underset{\alpha c}{\mathop{{{H}^{+}}}}\,+\underset{\alpha c}{\mathop{O{{H}^{-}}}}\,\] \[\alpha =\frac{1.9\times {{10}^{-7}}}{100};\]Density of water =\[\frac{1.0g}{c{{m}^{2}}}\] \[\therefore c=\frac{1}{18}\times 1000=55.56moles/l\] \[\therefore [{{H}^{+}}]=55.56\times 1.9\times {{10}^{-9}}=1.055\times {{10}^{-7}}\] \[\therefore {{K}_{w}}=[{{H}^{+}}][O{{H}^{-}}]={{(1.055\times {{10}^{-7}})}^{2}}=1.0\times {{10}^{-14}}\]
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