I know that we say that something is full of something, so why that doesn't apply to "rich of"? For instance:
The country is rich in oil.
The country is rich of oil
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As one commenter said, often there isn't much logic to which preposition sounds natural! However in this case, I would think about the meaning of the sentence without the prepositional phrase:
The country is full.
This seems to be lacking information. We are left asking, full of what?
The country is rich.
This is a complete thought; the country is generally wealthy. Now we could ask, in what areas is the country rich?
While this answer isn't based on a solid rule, I hope it's a helpful example of how to think through similar problems in the future!