Please help me! What's the difference 4 these two sentences?

[JangYong]

질문 있어요? 부탁해요!

Can someone please tell me what is the difference for these two sentences?

어디를 가기 몰라요

어디를 갈지 모르겠어요


And, please explain the grammatic errors (if any, that is)... Thank you very much...
감사합니다!

[yhenry]

어디를 가기 몰라요(X)

어디를 갈지 모르겠어요(O)

If you move the subject marker '를' to 갈 지, you can make it perfect.
어디 갈지(를) where to go 모르겠어요 don't know

어디를 가기 (where to go) is like a infinitive, or a basic form and is in need of conjugation in order to be used in a speech.
If it stands alone as a phrase, it is ok the way it is.

몰라요 and 모르겠어요 mean the same thing with the latter sounding more formal, and both are good in any situation.

[JangYong]

Thanks for your answer