"في ٱلْطّابِق اَلْأَوَّل مَطْبَخ."
Translation:There is a kitchen on the first floor.
you can use it. But to use it, you point out the "predicative" or what you are trying to bring attention to first: هناك مطبخ في الطابق الأول - in the same manner that English would use (there): there is a kitchen in the first floor.
So, the two sentences have the same meaning, it's just the word order and what you want to emphasize that changes by adding هناك
Edit: you can also say: هناك، في الطابق الأول، مطبخ
I think the commas here are important in ordering the speech and removing them might render the sentence unorganized.
What is the typical meaning of "first floor" in arabic speaking places? Like in the US where the first floor is at ground level? Or lile in Germany or latino countries where thr first floor means the first floor above the ground level (what we would call the second floor in the US)?
Not sure if there is a standard for this. Here for example people do use both ways (and yeah it might make some confusion). To what I see, though, the most common way is to call the base "the ground floor" and then "the first floor". I can't recall at any time I've seen an elevator here starting with (1) from the bottom, but they all start with (G); Just my observation. Below the ground is usually called Basement ("B" on elevator). Sooo... I think it depends on the country maybe or even the people you are dealing with ... each to whatever they think of!
Ground floor: الطابق الأرضي
Basement floor: السِّرْداب
I take that you are translating the Arabic sentence into English. Well, your English sentence actually translated into Arabic as في مطبخ الطابق الأول. Or if I want to rephrase your sentence into English as well, I would say in the kitchen which is in the first floor. This is, however, not exactly the sentence which is here in Arabic. The sentence here in Arabic actually tells an information that THERE IS some kitchen in the first floor, while your sentence TALKS ABOUT a kitchen which is in the first floor. In other words as well, the sentence here (English or Arabic) is a complete sentence with subject and predicative, but your sentence is a relative clause which is not complete (but it only describes a kitchen which is in the first floor, and not telling that there is a kitchen in the first floor).
The difference is in the logic. Hope this clears things :)