# Impossible pH For Aqueous Weak Acid Solution

An aqueous solution of $\ce{HCl}$ has a $\mathrm{pH}$ of $0.00$ if $[\ce{H+}] = 1.00 \; \mathrm{M}$. I tried to see if an aqueous solution of acetic acid could have a $\mathrm{pH}$ of $0.00$, given that its $K_a$ value is $1.8 \times 10^{-5}$. I tried finding the concentration $[\ce{H+}]$ of such a solution using

$K_a = \frac{[\ce{H+}][\ce{C_2H_3O_2^{-}}]}{[\ce{HC_2H_3O_2}]}$

and then using molar mass and density conversions to determine whether such an aqueous solution exists.

Does it make sense to say that such a solution does not exist if the number of moles of acetic acid in 1 liter of solution actually take up more than 1 liter of volume?

• See also superacids on Wikipedia for more context. – hBy2Py Feb 12 '16 at 19:02