Equilibrium Question 757
Question: The degree of dissociation of water at $ 25{}^\circ C $ is $ 1.9\times {10^{-7}} $ % and density is 1.0 g $ c{m^{-3}} $ . The ionic constant for water is
Options:
A) $ 1.0\times {10^{-10}} $
B) $ 1.0\times {10^{-14}} $
C) $ 1.0\times {10^{-16}} $
D) $ 1.0\times {10^{-8}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{(1-\alpha )c}{\mathop{H_2O}},\rightarrow \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}{cm^{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}} $
