Find the concentration of hydroxide ion in a 0.25 M solution of trimethylamine, a weak base.
`(CH_(3))_(3)N+H_(2)OhArr(CH_(3))_(3)+OH^(-),K_(b)=7.4xx10^(-5)`

Explanation

Ionisation constant of weak base `K_(b)=7.4xx10^(-5)`
Suppose `alpha` is the degree of association of the base
At equilibrium [trimethyl amine]`=0.25(1-alpha)=0.25M`
`[(CH_(3))_(3)N^(+)H]=[OH^(-)]=0.25alpha`
`K_(b)=([(CH_(3))_(3)N^(+)H][OH^(-)])/([(CH_(3))_(3)N])=7.4xx10^(-5)`
`((0.25 alpha)(0.25alpha))/0.25=7.4xx10^(-5)`
`0.0625 alpha^(2)=1.85xx10^(-5)`
`alpha^(2)=(1.85xx10^(-5))/0.0625`
`=2.96xx10^(-4)`
`alpha=sqrt(2.96xx10^(-4))=1.726xx10^(-2)`
`[OH^(-)]=0.25 alpha=0.25xx1.726xx10^(-2)`
`=0.4315xx10^(-2)`
`pOH=-log[4.315xx10^(-3)]=2.365`
`pH=14-2.365=11.635`