If $K_{\mathrm{b}}$ for ammonia is $1.8 \times 10^{-5},$ calculate $K_{\mathrm{a}}$ for its conjugate acid, $\mathrm{NH}_{4}^{+}$. Note that $\mathrm{NH}_{3}$ is the conjugate acid of the amide ion, $\mathrm{NH}_{2}^{-}$. Can $K_{\mathrm{a}}$ and $K_{\mathrm{b}}$ for the $\mathrm{NH}_{3} \mid \mathrm{NH}_{2}^{-}$ pair be calculated from the preceding data and the value of $K_{\mathrm{w}} ?$