Which procedure(s) will allow a student to differentiate between solid sodium sulfate and solid sodium sulfite?
Sodium sulfite and hydrochloric acid partially react to $\ce{SO2}$ which is gaseous and thus will form bubbles if not dissolved immediately.

When sodium sulfate is added to hydrochloric acid it will dissolve. The solution then contains sulphate and hydrogensulphate ions. No gaseous product will be formed.