Strong acid equilibrium So a teacher at school told me that strong acids do not create an equilibrium in general, while weak acids do (thats the difference, strong acids namely ionize completely). However, I lately stumbled upon a passage reporting that when experimenting with extreme pH, so extreme concentrations of acids, strange things start to occur and strong acids are not able to ionize completely, resulting in an equilibrium. I would explain this by the extreme concentration -> less water molecules in the vicinity of acid to react -> less chance to ionize.
But then I thought, are strong acids in fact not also creating an equilibrium, but because they react so strongly, they immediately release their proton. The conjugate bases are extremely weak, but they should be able to pick up a proton right? They simply become and acid, and release it immediately again. Please clarify this entire situation for me, thanks already.
Whether a substance is a strong or weak acid/base depends on the solvent it's in. For example, $\ce{HNO_3}$ is a strong acid in water. This is partly because $\ce{HNO_3}$ has a relatively high tendency to donate a proton (the conjugate base $\ce{NO^{-}_3}$ is quite stable and therefore has a low tendency to accept a proton back), and partly because water has a certain basic character, accepting protons to create $\ce{H3O+}$. However, the same $\ce{HNO_3}$ in pure liquid $\ce{H3CCOOH}$ (also known as glacial acetic acid) is actually a weak acid. This change in character is largely due to the fact that $\ce{H3CCOOH}$ is a much, much weaker base than water, forming the $\ce{H3CCOOH^+_2}$ ion with significantly more reluctance. Even though $\ce{HNO_3}$ can easily lose its proton, $\ce{H3CCOOH}$ is even moreso unwilling to accept it, and thus $\ce{HNO_3}$ becomes a weak acid. An amusing situation arises in pure liquid $\ce{H_2SO_4}$. Adding $\ce{HNO_3}$ there, we find that $\ce{HNO_3}$ actually behaves as a weak base. $\ce{H_2SO_4}$ itself also has a high tendency to donate protons, and of the two possible reaction products from protonation, $\ce{H_2NO^+_3}$ is somewhat more stable than $\ce{H_3SO^+_4}$.

Hence, acidity is dependent on the solvent, not only on the solute. A strong acid such as $\ce{HNO_3}$ in aqueous solution at high dilution is completely dissociated, as we expect of a strong acid. However, if more and more water is removed, then the solution starts to behave differently. Even though $\ce{HNO_3}$ has a strong tendency to protonate water, you can have a solution that contains more moles of $\ce{HNO_3}$ than water. Then it becomes obvious that not all $\ce{HNO_3}$ molecules are deprotonated. Practically all of the water left in the solution will be in the form of $\ce{H_3O^+}$, but there will be left over undissociated $\ce{HNO_3}$, so most of the excess stays undissociated, except for a small amount that undergoes self-protonation, generating a bit of $\ce{H_2NO^+_3}$.

All in all, in extremely concentrated solutions, even strong acids/bases will not show 100% dissociation, and saying that "strong acids completely ionize" is just a rule of thumb which shouldn't be taken too far.