[Meter]

I will see various definitions in acid-base theory that either utilize hydronium, H₃O⁺, or protons, H⁺, for various definitions. That is, both pH = -log([H+]) and pH = H₃O⁺+]). And we will see equivalent definitions for acid dissociation constants and the like.

What is there fundamental difference here? To me it seems that the hydronium definition assumes that the acid is dissolved in water wheres the proton definition doesn't assume that. Is this correct? Then what is "most correct"?

[chenbeier]

More or less it is the same. H+ are protons, these are not existing alone. They associated to water H₂O and form H₃O⁺. For calculation of pH it doesn't matter.

[Borek]

pH is a property of water solutions, it doesn't work for non-aqueous solution (it is often generalized, but there is no merit to these generalizations). As chenbeier wrote in water there are no isolated H⁺. Actually even H₃O⁺ is a simplification, it is more like H(H₂O)_n⁺ with n typically quoted as being somewhere in a 2-5 range (this is not much different from every cation solvation).

[Meter]

pH is a property of water solutions, it doesn't work for non-aqueous solution (it is often generalized, but there is no merit to these generalizations). As chenbeier wrote in water there are no isolated H⁺. Actually even H₃O⁺ is a simplification, it is more like H(H₂O)_n⁺ with n typically quoted as being somewhere in a 2-5 range (this is not much different from every cation solvation).

So, strictly speaking, H⁺ concentration is just not as rigorous as using hydronium concentration?

[Borek]

So, strictly speaking, H⁺ concentration is just not as rigorous as using hydronium concentration?

Yes.