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.

rather than

The country is rich of oil

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    There is often no logic to which preposition applies in a given situation. You just have to know them. – The Photon Jan 6 at 17:59
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    I’ve added an “is” to your second example to make it similar to the first. If that wasn’t your intention, you should edit your question to remove it. You can see the changes I made by clicking the “edited” link above. – ColleenV Jan 6 at 18:07
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    Offhand it's not easy to think of contexts where someone/something can be [ADJECTIVE] of [NOUN}. A couple that come to mind are A poor man is short of money and Monday's child is fair of face. There must be more, but I just can't come up with another right now (and even my second one there was a bit "dated", to say the least! :) – FumbleFingers Jan 6 at 18:18
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    My brother said it was "good of me" to help him. My aunt said I was "good for nothing". My father said I was "good at soccer". My grandma said I was "good in parts". – Weather Vane Jan 6 at 18:26
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    @FumbleFingersReinstateMonica empty of? :) (the streets are empty of people/rubbish) – Andrew Tobilko Jan 6 at 18:26

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!

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