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Solids generally react only very slowly with each other, unless you put some energy into the system (e.g. by grinding them together) or the interface between them melts or liquefies somehow.

In the case of a frozen block of acid in contact with a piece of acid-reactive substance, there would likely be just enough melting or water vapour condensation at the surface to allow a reaction to occur -- this might in turn generate heat, that would keep the reaction going.

That would definitely depend on the type of material you are looking at. For example, aluminium is a solid and a Lewis-acid. But an unoxidized block of aluminium could possibly just react with it's surface-atoms and nothing would really happen. This is since the bulk of your material would not get in contact to react, and only miniscule amounts of atoms make up the surface of macroscopic bodies. If your surface-layer atoms would, however, dissolve or liquify, meaning your solid acid would break up or the resulting product would not block the surface, your acid could react completely and eat through something. If you were taking frozen glacial acidic acid and a block of sodium hydroxide for example, you'd form water during reaction, which can dissolve the acid, base and product. Also they'd attract water from the air. So your acid would be used up completely and would go through the sodium hydroxide with time.

So this question has a few levels I would like to touch on so you fully understand what is happening.

1. Acids are generally described and referred to in the way in which they react when dissolved in water. This means when they are in solution with water. Ex. Hydrochloric acid is hydrogen chloride gas (a colorless gas at room temp) dissolved in water

2. The solubility of solids in water trends downward with temperature while the solubility of gas actually trends opposite. Meaning the amount of the compound that is the acid that can be dissolved in water (the concentration of the acid) changes with temperature, especially if we are talking talking a room temp acid then freezing the water

3. Once water freezes you're no longer liquid and you begin forming a solid crystal structure (ice). At this point lots of gas would escape as it freezes and solids will fall out of solution (while some would be trapped in the solid ice).

So for your question, say you froze a cylinder of sulfuric acid and placed it on a steel table. It would begin melting at the interface between the ice and the table (table is very large and warmer than the ice, it also transfers heat between the atmosphere and the ice much faster than the air). This interface will be cold but liquid and will begin acting as an acid (and produce heat, melting more water) which would lead to corroding the table.

Now assuming we place the cylinder in a cold, atmosphere controlled box on an actively cooled table to prevent the ice from melting. it likely wouldn't be corrosive at all to the table but you'd have to see how the materials of the solid may interact with the base acid material when not dissolved in water

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