My prof told me that we can compare Lewis base strength based on electron donation to the $\ce{H+}$ proton - i.e sigma bond formation with the $\ce{H+}$ proton - and proceeded to conclude that $\ce{S^{2-}}$ is a weaker Lewis base than $\ce{O^{2-}}$, since the former is a weaker base than the latter. He then proceeded to generalize that the oxide ion is always a stronger Lewis base than the sulfide ion.
Is this a valid method of comparing the strength of Lewis bases? I have two issues:
Isn't Lewis acid/base strength quantified using kinetics, not thermodynamics? Don't stronger LAs react faster, and weaker LAs react slower?
Even if this comparison were valid, would the comparison still be valid outside of water solution?
Does this mean that this question is invalid? No medium is specified.
I think he knows what he's talking about. In explaining the much greater stability of silver sulfide ($K_{\mathrm{sp}} \approx 6 \cdot 10^{-51}$) vs. $\ce{Ag2O}$ ($K_{\mathrm{sp}} = 3.5 \cdot 10^{-16}$), he notes that charge density does not explain this disparity. In fact, charge density would imply that the oxide salt should be more stable.
For instance, although $\ce{O^2-}$ is a stronger B/L base than $\ce{S^2-}$, $\ce{S^2-}$ can be (and usually is) a stronger Lewis base than $\ce{O^2-}$ since S has a lower EN than O. Furthermore, recall that Lewis base strength depends on the Lewis acid with with the Lewis base interacts.
The text goes on to mention other factors such as having a metal cation with a surfeit of valence d electrons, and how that can populate the empty valence 3d orbitals of $\ce{S^2-}$. (S has 3d orbitals?)
This makes sense; a good nucleophile has less stabilized electrons - i.e. electrons that are further from the nucleus. It still seems that the questions posted above put B/L acidity ahead as the main deciding factor for sigma-donor strength.