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Given that the dissociation constant for water is  $ {k_w} = 1 \times {10^{ - 14}}mo{l^2}{L^{ - 1}} $ . The pH of a  $ 0.001M $  KOH solution is

A.  $ {10^{ - 11}} $ 

B.  $ {10^{ - 3}} $ 

C. 3

D. 11

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Last updated date: 18th Jun 2024
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Answer
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Hint: The degree of dissociation of water (or) ionic product of water can be written as,

 $ {k_w} = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right] $  It is known that in KOH solution, it contains  $ {K^ + } $ and  $ O{H^ - } $  ions.

It is also known that pH is the negative logarithm of the concentration of the  $ {H^ + } $  ion. Thus,  $ {H^ + } $  concentration can be determined by using the ionic product of water formula since the hydroxyl ion concentration of KOH is known.


Complete answer:

It is given that  $ \left[ {O{H^ - }} \right] = {10^{ - 3}}M $ , $ {k_w} = 1 \times {10^{ - 14}}mo{l^2}{L^{ - 1}} $ 

It is known that  $ {k_w} = \left[ {{H^ + }} \right]\left[ {O{H^ - }} \right] $ 

Thus,  $ {H^ + } $  can be determined as,

 $  \Rightarrow 1 \times {10^{ - 14}}mo{l^2}{L^{ - 1}} = \left[ {{H^ + }} \right]\left[ {{{10}^{ - 3}}M} \right] $ 

 $  \Rightarrow \left[ {{H^ + }} \right] = \dfrac{{1 \times {{10}^{ - 14}}mo{l^2}{L^{ - 1}}}}{{{{10}^{ - 3}}M}} $ 

 $  \Rightarrow \left[ {{H^ + }} \right] = {10^{ - 11}}M $ 

Thus, the concentration of  $ {H^ + } $  ion is obtained as  $ {10^{ - 11}}M $  and its pH is 11

The hydroxyl ion concentration  $ \left[ {O{H^ - }} \right] = {10^{ - 3}}M $  and its pH can be calculated by using the dissociation of water. We can find out the pH by the formula pH  $ = - \log [{H^ + }] $ .

It can be determined as,

 $ pH = - \log \left[ {{{10}^{ - 11}}} \right] $ 

 $ pH = - ( - 11)\log [10] $ 

 $ pH = 11 $ 


Hence, the correct option is D.


Note: But this answer is incorrect since KOH contains hydroxyl ions and pH is the negative logarithm of  $ {H^ + } $  ion. Thus,  $ \left[ {{H^ + }} \right] $  has to be calculated with the help of the ionic product of the water formula.

Generally in pH value,

 $ 1 - 7 $  indicates that the compound is acidic

7 indicates that the compound is neutral

 $ 7 - 14 $  Indicates that the compound is basic.

It is known that KOH is basic and its pH must be under  $ 7 - 14 $ . Hence, here we can rule out other options clearly.