Equilibrium Question 373

Question: At 25°C, the dissociation constant of a base BOH is $ 1.0\times {10^{-12}} $ . The concentration of Hydroxyl ions in 0.01 M aqueous solution of the base would be [CBSE PMT 2005]

Options:

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}} $

Show Answer

Answer:

Correct Answer: D

Solution:

$ BOH\rightarrow {B^{+}}+O{H^{-}} $

Initial C 0 0
At eq. C-Ca Ca Ca

$ K_{b}=\frac{C^{2}{{\alpha }^{2}}}{C(1-\alpha )}=C{{\alpha }^{2}} $ assuming $ \alpha «1 $ ; $ 1-\alpha \tilde{}1 $

$ {10^{-12}}={10^{-2}}\times {{\alpha }^{2}} $ ; $ {{\alpha }^{2}}={10^{-10}} $ ; $ \alpha ={10^{-5}} $

$ [O{H^{-}}]=C\alpha =.01\times {10^{-5}}={10^{-7}} $



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