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Residual entropy is essentially the disorder of a molecule, near absolute zero, that is the result of it's different possible microstates. Whenever a question is given on residual entropy it is usually asking you to measure entropy through the amount of microstates in a molecule(s). I believe that he mentioned it in class and that it is also in the homework, so there is a fair chance it will appear on the final.
Residual entropy is the entropy of a sample at T=0, due to positional disorder at that temperature. If it were to be on the final, I would think something along the lines of the book example, where we are asked to confirm whether or not the molecules in the crystal form are arranged randomly or not, or drawing conclusions from a given residual entropy.
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