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Consider the reaction
$\ce{NH3 + H2O -> NH4+ + OH-}$
Here, $\ce{NH3}$ is a weak base, and thus $\ce{H2O}$ becomes a weak acid. Thus, shouldn't its conjugate be a strong acid? However, $\ce{NH4+}$ is a weak acid, instead of the strong conjugate acid it should be. Why is this?
Consider the $pK_b$ of the base $\ce{NH3}$ and the $pK_a$ of the acid $\ce{NH4+}$.
$pK_b$ = $4.8$
$pK_a$ = $9.2$
$\ce{NH3}$ is a stronger base than what $\ce{NH4+}$ is as an acid, being $4.8$ smaller than $9.2$: let's compare $pH$ for equal concentrations, say $0.1 M$.
For $\ce{NH3}$, you get $11.1$, while for $\ce{NH4+}$, you get $5.1$.
$11.1$ is about 100 times more "distant" from neutral $pH$ than $5.1$, if we move from the $pH$ scale to the concentration scale. That's what also stems from the comparison of the $pK$ values.
To simplify the problem, take the $pK_a$ for the acid/base couple, e.g. $\ce{NH4+/NH3}$, that is equal to $9.2$. If that value is larger than $7$, then, within that couple, the base will be stronger than its conjugated acid. The other way round, if $pK_a$ is lower than $7$.
