Question #73661

May 10, 2015

For a weak acid, you can determine the value of the base dissociation constant, ${K}_{b}$, of its conjugate base by using the water dissociation constant, ${K}_{W}$.

Mathematically, the relationship that exists between ${K}_{a}$, ${K}_{b}$, and ${K}_{W}$ can be written like this

${K}_{W} = {K}_{a} \cdot {K}_{b} = {10}^{- 14}$

In the case of the hypobromite ion, $B r {O}^{-}$, the base dissociation constant will be

${K}_{b} = {10}^{- 14} / {K}_{a}$

${K}_{b} = {10}^{- 14} / \left(2.8 \cdot {10}^{- 9}\right) = \textcolor{g r e e n}{3.6 \cdot {10}^{- 6}}$

The same is tru for dimethylamine, ${\left(C {H}_{3}\right)}_{2} N H$, and its conjugate acid, the dimethylammonium ion, ${\left(C {H}_{3}\right)}_{2} N {H}_{2}^{+}$.

${K}_{a} = {10}^{- 14} / {K}_{b}$

${K}_{a} = {10}^{- 14} / \left(5.4 \cdot {10}^{- 4}\right) = \textcolor{g r e e n}{1.9 \cdot {10}^{- 11}}$