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As far as I know, the absorption of $\text{SO}_2$ in water goes under physical absorption, meaning the sulfur dioxide bubbles are held in place by Van der Waals forces, in this case Keesom forces, since both water and sulfur dioxide molecules are dipoles. This table classifies the absorption of sulfur dioxide in water as physical absorption, taken from this site.

However, sulfur dioxide does create products (within an equilibrium) with water.

$$\ce{SO2 + H2O ⇌ HSO3^- + H3O+}$$

and

$$\ce{SO2 + OH- ⇌ HSO3^-}$$

Now, with chemical absorption, the absorbate is held within the absorbent due to interfacial chemical bonding. Could it be that these products don't aid with the absorption at all? Or, could it be that they aid with the absorption in conjunction with, but perhaps to a lesser degree than, the Keesom forces, thus making the absorption more physical than chemical? If so, is this perhaps the norm?

Or, is this absorption actually a chemical one?

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When you consider the dissolution of a gas like $\ce{SO3}$ , $\ce{CO2}$, $\ce{SO2}$ etc. there are three equilibria existing at the same time:

$$\ce{SO2(g)\overset{H2O}{<=>}SO2(aq)\overset{H2O}{<=>}H2SO3(aq)<=>H+(aq) +HSO3-(aq)}$$ The first equilibrium is the dissolution equilibrium of the gas, the second is the hydration equilibrium of the dissolved gas, and the third is the dissociation equilibrium of the acid.

The pKa associated with the first deprotonation of $\ce{H2SO3}$ is 1.81 from Wikipedia, so you can pretty much consider the last equilibrium as completely dissociated in dilute solutions.

You can consider $\ce{SO2(aq)}$ as the state where the $\ce{SO2}$ molecules are physically absorbed in the solution, the rest exist as $\ce{H+(aq)}$ and $\ce{HSO3-(aq)}$.

How much is physcially absorbed and how much is chemically dissociated would depend on the particular compound. Unfortunately, I cannot find any data on $\ce{SO2}$. However, in case of dissolving $\ce{CO2}$ in water, 99% exist as $\ce{CO2(aq)}$ i.e. the physically absorbed gas, and 1% as $\ce{H2CO3(aq)}$, $\ce{H+(aq)}$ and $\ce{CO3^2-(aq)}$. (reference)

So, the absorption of $\ce{SO2}$ is partly chemical and partly physical, but note that all of these reactions are reversible. Also keep in mind that the distinction between physical and chemical change is not clear-cut, and gets less and less useful the more you delve into chemistry.

The website you mention in the question gets a lot of other things wrong, for example, dissolution of $\ce{SO3}$ in water gets you sulfuric acid, which is quite stable and hygroscopic, so you would be hard pressed to reverse it, but the table lists it as physical absorption. Whereas chlorine does not dissolve that well in water, and you can drive it off by heating, but it's listed as a reversible chemical change. It doesn't make much sense to me, so I would advise you to get a more reliable source of information.

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