What's the Acid Ionization Constant of the Hydrogen Proton? What is the $\ce{K_{a}}$ value for $\ce{H^+}$. I understand that the hydrogen proton doesn't stick around in solution by itself for very long. Nonetheless, does it have a  $\ce{K_{a}}$ value? Can it have a  $\ce{K_{a}}$? I think it can have one but quantifying it might be hard. Its  $\ce{K_{a}}$ value I think would correspond to this reaction:

$\ce{H^+ + H_2O -&gt;H_3^+O}$

However this doesn't look like a conventional acid/base reaction; we don't have the conjugate base of $\ce{H^+}$ here, unless the definition of a conjugate base isn't what I think it is (acid missing one proton). 

So my questions are:

1) Does the above mentioned $\ce{K_{a}}$ value exist. 

2) Is my definition of a conjugate base too narrow?
The equillibrium between a proton plus water molecule and a hydronium ion is better considered using the concept of proton affinity.

\begin{aligned}
\ce{H^+(g) &amp;-&gt; H^+(aq)} \\
\Delta E &amp;= −1530~\mathrm{kJ/mol}
\end{aligned}

You could roughly convert to an equillibrium constant using

$$\Delta G = -RT \ln(K)$$