Explain whether or not each of the following pairs of solvents might be useful as a solvent pair for recrystallization.

(a) ethanol-methanol
(b) hexane-cyclohexane
(c) acetone-ethanol
(d) water-ethanol
(e) water-cyclohexane

To work as a solvent pair, the two solvents must be miscible with each other. Therefore, e would not be a good pair. I will leave the others to you.

E would not be a good pair because one is polar and the other is nonpolar

So for B because they are both nonpolar would they be miscible?

Not necessarily. The polar/non-polar point makes them immiscible. B is miscible since both are non-polar.

Ah I see, so the rest A-D are all miscible since A, C, and D are both polar while B are both non-polar.

Yes, e is the only pair not miscible. One point I should make is that just because they are miscible doesn't make them a good pair for some recrystallizations. Some recrystallizations must be determined by experiment to see if there is a single solvent or a solvent pair that may work. Here is a site where that is amplified somewhat.

http://www.hartnell.edu/faculty/shovde/chem12a/lablecturehandouts/recrystallizationlecture.htm

An additional point is that a mixture of a pair of solvents that are too close in polarity may not be any better than a single solvent.

Another consideration on a larger scale where you will want to recover the solvent which is that this is much easier to do if a single solvent is used, or a pair that are easily separated.

Thank you very much for the responses. It has helped me alot!