I have to add some make it Clear. You can leave out "Jo-Sa" because it is known as object for sure without special methods not because it isn't alive

You need to put words on right position to deliver information in a way you want in English. eg. Subeject + Verb + Object. On the other hand., Korean has special method to make you don't care about it. That is called 조사(Jo-Sa) which is poisioned right after noun. You can make noun Subject or Object no matter where you put. In Conclusion you hvae to study this Jo-sa with noun. It will help you study Korean better. Noun + 을/를 = Object / Noun + 은/는/이/가 = Subjcet 진정제가 주세요(not correct) 전정제를 주세요(Correct) -> 진정제 주세요(More casual) According to the explanation above. 진정제(를) 주세요 주세요, 진정제(를) Here you would woder why you can leave out "Jo-Sa". Even though it is a special word to make diferrence between S and O. Cause you already know sedative is not a one alive. I hope it is helpful

진정제좀 줘 or 진통제좀 주세요. Korean usually called '진통제'

Please give me Sedative/Tranquilizer. (?) = 진정제가 좀 주세요,

Are you trying to say "Please give me a sedative" or "Give me some sedatives"?