To me, these questions sound a lot like homework questions. So I've decided to point you in the right direction rather than simply give the answers to the questions directly. Hopefully, this will clear up any confusion you have about the questions. Good luck.

1.Does propylene glycol dissociate in water?

Well, I think you need to know something specific about propylene glycol to answer this question, which makes it hard for me to answer for you.

It is much easier to first think about salt, that is NaCl. When you drop a chunk of sodium chloride in water, it will dissociate into ions. Why? Since the salt dissociates into ions which are oppositely charged and, hence, attractive, it might seem weird that dissociation will occur. After all, aren't the ions going to want to continue to stick together? However, there is also entropy to consider. In other words, there are many, many more configurations available for the ions to be dissociated in the water, and so some very large fraction of the ions will prefer to be in the water. In this case the entropy beats out the attraction between ions.

Remember that almost all of chemistry can be reduced to the competition between energy and entropy. Chemists have invented numbers to measure this competition for chemical reactions, namely equilibrium constants.

Presumably, the same sort of reasoning can be applied to propylene glycol. It's up to you to figure out the answer to your specific question, though.

2. Will a 1.0 m copper(II) sulfate solution have the same freezing-point depression as a 1.0 m copper(II) chloride solution? Why?

As I understand this question, the idea is that you have a solution of stuff which you freeze, and you have discovered that the freezing point of the solution is lower than that of water. To answer this question, you really need to understand why the freezing point of a solution will be lowered. The first thing to think about is: does this affect have anything to do with the interaction energy between the molecules in solution? If not, this effect must be entirely due to the entropy.

The only difference between your two solutions is that sulfate has been replaced with chloride. So, the question is, what effect does this have on the interaction energy between the dissociated particles in solution? What effect does this have on the entropy?

From this, you should be able to work out the answer.