Write the chemical equation and the \(K_{b}\) expression for the reaction of each of the following bases with water: (a) dimethylamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} ;(\mathbf{b})\) carbonate ion, \(\mathrm{CO}_{3}^{2-} ;(\mathbf{c})\) formate ion, \(\mathrm{CHO}_{2}^{-} .\)

(a) Dimethylamine reacts with water: \((\mathrm{CH}_{3})_{2} \mathrm{NH} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow (\mathrm{CH}_{3})_{2} \mathrm{NH}_{2}^{+} + \mathrm{OH}^{-}\), with \(K_{b} = \frac{[ (\mathrm{CH}_{3})_{2} \mathrm{NH}_{2}^{+}] [\mathrm{OH}^{-}]}{[(\mathrm{CH}_{3})_{2} \mathrm{NH}]}\) (b) Carbonate ion reacts with water: \(\mathrm{CO}_{3}^{2-} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow \mathrm{HCO}_{3}^{-} + \mathrm{OH}^{-}\), with \(K_{b} = \frac{[\mathrm{HCO}_{3}^{-}] [\mathrm{OH}^{-}]}{[\mathrm{CO}_{3}^{2-}]}\) (c) Formate ion reacts with water: \(\mathrm{CHO}_{2}^{-} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow \mathrm{CHO}_{2}\mathrm{H} + \mathrm{OH}^{-}\), with \(K_{b} = \frac{[\mathrm{CHO}_{2}\mathrm{H}] [\mathrm{OH}^{-}]}{[\mathrm{CHO}_{2}^{-}]}\)