Strength of bases and acids
In the case of weak acids dissociating like strong ones when they are highly dilute, there is a limit to how far this can go.  If you were to try to measure acetic acid dissociation at $10^{-n}$ molar for $n=4,5,6,7,8,...$ at ambient temperature you would at first rise nicely towards $100$% as you might expect, but eventually level off at only about $99.4$%.
What stops you is the autoionization of water.  As you approach infinite dilution the hydrogen ion concentration approaches not zero but the autoionized value of $10^{-7}$ molar.  So the ratio of dissociated acid to undissociated acid levels off at $K_a/10^{-7}$.  Accordingly the limiting degree of dissociation is
$1/[1+(10^{-7}/K_a)]=K_a/(K_a+10^{-7})$
For acetic acid with $K_a\approx1.8×10^{-5}$ this limit is about $99.4$%, but for a much weaker acid such as a typical phenol or hydro-cyanic acid the dissociation is much lower even at extremely low concentrations.  When $K_a&lt;10^{-7}$ the limiting dissociation is less than $50$%; you need a stronger base than water to coax dissociation as a major reaction in aqueous solution.