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. `1.0xx10^(6)mol L^(-1)`
B. `1.0xx10^(-7)mol L^(-1)`
C. `2.0xx10^(-6)mol L^(-1)`
D. `1.0xx10^(-5)mol L^(-1)`

Explanation

`{:(,BOH(s)hArr,B^(+)(aq.),+OH^(-)(aq.)),("Initial conc.",C,0,0),("Equilibrium conc.",C-x,x,x):}`
According to the law of chemical equilibrium,
`K_(c)= (C_(B^(+))C_(OH^(+)))/(C_(BOH))`
`=(x.x)/(C-x)=(x^(2))/(C-x)`
Neglecting x relative to C (as equilibrium constant is very small), we have
`K_(c)=(c^(2))/(C )`
or `x= sqrt(K_(c).C)`
`=sqrt((10^(-12))(10^(-2)))`
`=10^(-7)mol L^(-1)`