(Solved): Dimethylamine, \( \left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} \) is a weak base. (2 points for pa ...

Dimethylamine, \( \left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} \) is a weak base. (2 points for parts a-d, and 2 pts for parts \( e-h \) ) Write the proton transfer reaction that occurs when \( \left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} \) is added to water. Write an expression for \( \mathrm{K}_{\mathrm{b}} \) Identify the conjugate acid of \( \left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} \). Write the proton transfer reaction that occurs when the conjugate acid is added to water. Write an expression for \( \mathrm{K}_{\mathrm{a}} \). Use your expressions for \( K_{\mathrm{a}} \) and \( \mathrm{K}_{\mathrm{b}} \) to calculate their product. Simplify to show that \( \mathrm{K}_{\mathrm{a}} \mathrm{K}_{\mathrm{b}}=\mathrm{K}_{\mathrm{w}} \) If \( \left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} \) has \( \mathrm{K}_{\mathrm{b}}=3.6 \times 10^{-4} \), calculate \( \mathrm{K}_{\mathrm{a}} \) for its conjugate acid. Calculate \( \mathrm{pK}_{\mathrm{a}} \) and \( \mathrm{pK}_{\mathrm{b}} \). Do they add to \( 14 ? \)