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My textbook says that $\ce{SO2}$ dissolving in water produces sulfurous acid, but that seems to be a chemical change. But $\ce{NaCl}$ dissolving in water is not a chemical change. Please explain.

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Your book is glossing over some details.

There are three things occurring when you dissolve non-metal oxides in water (e.g., SO2, CO2, NO2, etc.):

  1. The gas simply dissolves in the water. You are correct that this step is a physical change. How much dissolves depends on the partial pressure above the water and the Henry's law constant.
  2. Once dissolved in water, some of the non-metal oxide will react with water to form an acid (sulfuric/sulfurous acid, carbonic acid, nitric/nitrous acid, etc.) and this is the chemical change that your book is referring to. There will be an equilibrium constant that will dictate the relative concentration of dissolved gas to the corresponding acid that is formed.
  3. The acid (usually weak) will dissociate a little bit. Again, the exact amount of dissociation will depend on the equilibrium constant (Ka).

Using your example, we would have:

$\ce{SO2(g) <=> SO2(aq)}$

$\ce{SO2(aq) + H2O(l) <=> H2SO3(aq)}$

$\ce{H2SO3(aq) <=> HSO3^- (aq) + H+(aq)}$

Similar things happen when metal salts dissolve in water (although not $\ce{Na^+}$ or the other Group I and II metals). The metal cations will react with water and form a weak acid.

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$\ce{SO2}$ at normal pressure and temperature is a gas, and once dissolved follows an acid-base path. This is a chemical change.

NaCl is a salt and when immersed in water its crystal structure breaks and gives hydrated ions ($\ce{Na+}$ and $\ce{Cl-}$). This also is a chemical change.

The process of dissolution is always a chemical change because there is an interaction between solute and solvent (high or low interaction). Even when oil is in contact with water an equilibrium is established with partitioning coefficients and constants to describe the amounts of molecules inter-exchanged and rates.

What the textbook means to say is that in NaCl dissolution, no new molecules are generated. A specific chemical reaction (acid-base in this case) is taken place in dissolving the sulfur dioxide and generates a new molecule, sulphuric acid, but in both cases, there is a change in the chemical structure of solvent and solutes.

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