Question

Are solubilities of solids linear with temperature?

Answer 1

They don't have to be linear. Sometimes a solute is progressively easier to dissolve in a particular solvent as you add more solvent. It is like that for `"Na"_2"SO"_4` from `0^@"C"` to `32~34^@"C"`.

This is kind of a special case. If you compare it with this picture:

You can see that `"Na"_2"SO"_4` probably exists as `"Na"_2"SO"_4*10"H"_2"O"` (Mirabilite) from `0^@"C"` (at or below about `"0.3 mol/kg"`, or `"4.26 g/mL"`) until `32~34^@"C"`, and then at about `"50 g/100 mL"` in water (`"3.52 mol/kg"`), it starts following the solubility curve of Thenardite, an anhydrate.

So, you can also see that a solubility curve doesn't necessarily turn out to be linear or increasing. I haven't seen a curve that increases at a decreasing rate, but other than that, solubilities can decrease with increasing solvent, too, due to competing species.