Olga, you can use "about" and "of" almost interchangeably, although "about" is much more common. You can also use "at". Look at these examples: http://sentence.yourdictionary.com/apprehensive

Olga, Apprehensive has more than one meaning. I assume you are talking about apprehensive meaning “worried or anxious” or “fearful” and not apprehensive meaning “capable of apprehending”. Apprehensive “of” tends to have the meaning of “fearful’. This is the older of the two usages. -I am apprehensive of spiders. -I am apprehensive of what might happen. -I personally was somewhat apprehensive of my first jump. Apprehensive “about” tends to mean, “anxious”. This is the more modern usage. -I am apprehensive about the visit of my mother-in-law. -He's a bit apprehensive about living away from home. -Others are naturally apprehensive about navigating what are, for them, uncharted waters. Other prepositions are also less commonly used. Apprehensive “at” introduces the immediate cause or occasion of your emotions. -I was apprehensive at even the thought of spiders. (Not apprehensive at spiders) -Apprehensive at the prospect of the close intellectual scrutiny which the tutorial involves. -The meal was very well-received by my family, though they were a bit apprehensive at the appearance of the food Apprehensive “from’ introducing the source of emotion. -More than 15 years later, his heart aching and apprehensive from the news that the 31-year-old case had been reopened, Bobby brokenly told me the full story. Apprehensive “for” introducing the object for which you entertain the emotions. -I was apprehensive for the safety of the children on board the old ship.

A good solid question. You can use ABOUT and OF for most sentences. However, certain sentences are bound to have strict rules. "I am apprehensive OF the future" About would be wrong in this sentence.. I hope I've helped, even a little bit ;p