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Fundamentals of Biochemistry: Student Companion: Life at the Molecular Level[1] states that,

The strongest acid that can stably exist in aqueous solutions is $\ce{H3O+}$.

This is restated in the Wikipedia entry about hydronium. In principle this makes sense for an acid $\ce{HA}$ that is stronger than hydronium since the forward direction in the following equation

$$\ce{HA + H2O -> H3O+ + A^-}$$

is favored. However, by adjusting the initial concentration of $\ce{HA}$, for a given $K_a$, I can ensure that the final concentration of the acid is high enough that it exists in solution in reasonable quantities.

What am I missing?

Reference:

[1]: Voet, D.; Pratt, C. W.; Voet, J. G. Fundamentals of Biochemistry: Student Companion: Life at the Molecular Level, 3rd ed.; John Wiley & Sons: Chichester, England, 2009.

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    $\begingroup$ Are you suggesting that concentration of a weak acid is a measure of acid strength? $\endgroup$
    – Ed V
    Jun 23 at 16:59
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    $\begingroup$ So what? Nitric acid is a strong acid and acetic acid is a weak acid. Put 1 mL of nitric acid in a liter of water and very few nitric acid molecules will be present: the acid is said to be leveled down to hydronium and nitrate. For the acetic acid, you can still have plenty of acetic acid molecules in solution: that is what it means to be a weak acid. So the book and wikipedia are correct. $\endgroup$
    – Ed V
    Jun 23 at 17:09
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    $\begingroup$ And if you have something like 99% pure nitric acid, then of course there are nitric acid molecules present: there is not enough water to yield hydroniums. But this is obvious and not what your book or wikipedia meant. $\endgroup$
    – Ed V
    Jun 23 at 17:12
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    $\begingroup$ @EdV Okay, I think I know where my confusion is coming from. I was assuming that acid strength is based on the K_a of an acid. So I was arguing I can have stable acids with K_a's higher than Hydronium's, or 1, that can exist in reasonable quantities in solution. But it looks like the textbook is defining a strong acid as anything that gives up almost all its protons in solution. In which case a strong acid by definition cannot exist in solution, and therefore the strongest acid that can is the hydronium ion. Did I get that right? $\endgroup$
    – Harry
    Jun 23 at 17:22
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    $\begingroup$ You can have acid dissociation constants much greater than one, e.g., nitric acid. So if you add it to water, with water in considerable excess, then it gets leveled: you get hydronium. But concentrated strong acid, like 90% nitric acid, obviously cannot be all leveled: there is not enough water to accomplish that. The textbook is just tacitly assuming the acid solution is not concentrated. $\endgroup$
    – Ed V
    Jun 23 at 17:28
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However, by adjusting the initial concentration of $\ce{HA}$, for a given $𝐾_𝑎$, I can ensure that the final concentration of the acid is high enough that it exists in solution in reasonable quantities.

What am I missing?

I think you are missing that an assumption of acid-base equilibria in water is that the $K_a$ values you are using tend to assume an infinite dilution in water. It's the background phase, and it is (at room temperature) 55 mol / L in concentration. If you did the calculation you suggest -- i.e. to find the amount of e.g. nitric acid you'd need to add to an aqueous solution in order to ensure that the final concentration of undissociated $\ce{HNO3}$ molecules is large -- you'll probably find that you need to add a large amount of acid, on the order of mols per liter or more.

At that point you arguably aren't even in water any more. Now maybe the real question is what's the pKa of water in a nitric acid solvent. In any case the whole $K_a$ value you've looked up for nitric acid at infinite dilution in water isn't going to apply.

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    $\begingroup$ That last paragraph is indeed pretty important. What's missing from this discussion is an analysis of the activity coefficient of the hydronium ions. In dilute strong acid solutions, all hydronium ions behave similarly as the activity coefficient is close to one. However, at high concentrations, this coefficient can deviate from 1 by several orders of magnitude depending on a multitude of parameters. Essentially, the same hydronium ion can become remarkably more acidic, "meeting" the acidity of any undissociated strong acid. $\endgroup$ Jun 23 at 22:04
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    $\begingroup$ This only goes so far though - sufficiently strong acids will overpower the acidity of even "strengthened" hydronium ions. These kinds of superstrong acids form isolable hydronium salts when mixed with water a 1:1 molar proportion. $\endgroup$ Jun 23 at 22:08

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