Why does $NH4^+$ react with NaOH to give $NH_3+H_2O$ and not $NH_4OH$

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    $\begingroup$ Because there is no $\ce{NH4OH}$, except as the separate solvated ions which are minor species in an aqueous ammonia solution. See this answer for the whole story. $\endgroup$ Nov 17 '19 at 14:32

$\ce{NH4+}$ is the weak acid and reacts with the strong base $\ce{OH-}$:

$$\ce{NH4+ + OH- <=>> NH3 + H2O}$$

by the same way as $\ce{HCN}$, an acid with similar acidity as $\ce{NH4+}$:

$$\ce{HCN + OH- <=>> CN- + H2O}$$


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