The `pH` of `0.05M` aqueous solution of diethy`1` amine is `12.0` . Caluclate `K_(b)`.

Explanation

Diethyl amine is base and gives `OH^(-)` as,
`{:(,(C_(2)H_(5))_(2)NH+H_(2)Orarr,(C_(2)H_(5))_(2)NH_(2)^(+),+OH^(-)),("Intitial conc"., 1,0,0),("Equi. conc".,(1-alpha),alpha,alpha):}`
`:. [OH^(-)]=Calpha`
Where C is conc. Of base and `C= 0.05M`
`.: pH=12 :. pOH=2`
or `[OH^(-)]=10^(-2)M`
`:. Calpha=10^(-2)`
or `0.05xxalpha=10^(-2)`
`:. alpha=0.2` , `(.:C=0.05)`
Now for a base,
`K_(b)=(Calpha^(2))/((1-alpha))=(0.05xx(0.2)^(2))/((1-0.2))`
`=(0.05xx0.04)/(0.8)=2.5xx10^(-3)`
Note: Do not use `K_(b)=Calpha^(2)` since `alpha=0.2` and `1-alpha=0.8`