he wanted to find a seat to sit down还是sit on?

sit on
注意 to sit on (a seat ) 这个动宾关系那第一个句子还是用on吗he entered the lecture hall hoping to find a seat to sit 【on】he wanted to find a seat to sit【 on】那sit down 又在什么情况下用，麻烦举出一些例子以及解释，还有我想知道像这样的短语还有哪些？谢谢了Please sit downI have no pen to write withI have some friends to play withI have no paper to write onI have no house to live inI have nothing to worry about.......