At `25^(@)C`, the dissociation constant of a base. BOH is `1.0xx10^(-12)`. The concentration of hydroxyl ions in `0.01`M aqueous solution of the base would be

Options

A. `2.0 xx 10^(-6) mol L^(-1)`
B. `1.0 xx 10^(-5)mol L^(-1)`
C. `1.0 xx 10^(-6) mol L^(-1)`
D. `1.0 xx 10^(-7) mol L^(-1)`

Answer

D

Explanation

`BOH hArr B^(-) +OH^(-)`
`K_(b)=(Calpha .Calpha)/(C(1-alpha))=(Calpha^(2))/(1-alpha)=Calpha^(2)[:' 1-alpha=1]`
`alpha=sqrt((K_(b))/(C))=sqrt((1 xx 10^(-12))/(10^(-2))`
`=sqrt(10^(-10))=10^(-5)`
`[OH^(-)]=C alpha=10^(-2)=1 xx 10^(-7) mol L^(-1)`