This is a great question. The quick response to your question is I tried to model it as an equilibrium, but it just doesn't work at the scales we're dealing with.
To give you a sense of why this has been so difficult, consider that a microworld has, on average, only 30-50 particles on the screen. What would a system look like that has [H3O+] = 1x10^-5 M vs. 1x10^-10 M? How many moles would a single hydronium or hydroxide ion stand for? Would this scale then work across all powers of 10 that are observed in acid/base solutions?
The current approach uses equilibrium position shifting that maps disparity in the instantaneous pK and the reference pKa (or pKb) to a sigmoid function. Dissolved particles are scaled down with a molar scale that is between 1e-3 and 1e-5 for most solutions (water molecules stay at a 1 particle on screen : 1 mol). However, the problem I have consistently found is that the concentration of [H3O+] and [OH-] in real solutions get many orders of magnitude smaller than the mol scale that I have to use for the rest of the particles on screen. So, when I calculate the product [H3O+][OH-] using instantaneous values from the microworld, I get either 0 or multiple orders of magnitude >> 1e-14. This presented a scenario where I either get no auto-ionization, or at maximum, only a single auto-ionization event would ever occur. This is not ideal, since pedagogically it would communicate to students that
- such this turnover is rare, when in fact it is happening constantly,
- and different strength acids/bases exhibit the same auto-ionization behavior
One possible fix to the scale problem is using a different molar scale for spectator ions vs. hydronium/hydroxide. However, I have hesitated to go this route because this creates incorrect stoichiometry when conjugate acids/bases react with these particles.
This is a capital "C" modeling challenge and one that we're still improving. Any suggestions are appreciated!
This post was modified 7 months ago 2 times by Dane DeSutter
Postdoctoral Research Associate