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}} $
