acid base - A basic solution of HCl

So I had a test question the other day, and it essentially went as follows:

A student measures the concentration of a $\ce{HCl}$ solution to be $10^{-9}$M by using a pH meter. Is the meter wrong?

This means that the $\ce{HCl}$ solution has a pH of 9, which seems unreasonable, yet that is not what I said. I said that the meter is not wrong. My reasoning was that you could have an $\ce{HCl}$ solution so incredibly dilute that the pH would in fact be 9. Since molarity is defined as moles per liter, if you hold the moles constant and increase the volume of solution, you will eventually reach a very tiny molarity.

In essence what I was wondering was: Is my reasoning correct?

Is this solution considered basic?

Can this be generalized such that any originally acidic solution is considered basic at a low enough concentration, or a high enough dilution?

Answer

Unfortunately, your reasoning is wrong, because you forgot to take into account the acidity of water. While in most cases we can ignore the acidity of water as the hydrogen ion concentration contribution by $\ce{HCl}$ dominates, at an extremely low concentration of $\ce{HCl},$ water becomes the main $\ce{H+}$ contributor.

It is well known that water has a $\pu{10^{-7} M}$ concentration of hydrogen ions at $\ce{25^\circ C}.$ Therefore, water's effect on the acidity of the solution is significant when looking at solutions of $\pu{10^{-6} M}$ or lower concentrations of strong acids. For example, if there is $\pu{10^{-9} M } \ce{HCl,}$ then the total $\ce{H+}$ concentration would still nearly be $\pu{10^{-7} M}.$ Therefore, no matter how much you dilute the acid, it can never turn into a basic solution.