I have 2 characters that I want to have a romantic tension with. The feelings are unrequited. Can I have it so that 1 chapter basically introduces and then ends the conflicting feelings or is this something that should be drawn out?
Drawn out, most likely. In special circumstances one chapter could be enough.
If you are introducing something like this, it shouldn't be "filler", it should have something to do with the story. It needs to have ramifications in the story, there must be some kind of consequences for this unrequited love.
Simple unrequited love may drive a character, but not once it gets resolved. Just like sexual tension can drive the story, but once it is resolved, the question of "Will They / Won't They" is answered and is no longer a reason to turn pages (or watch episodes, when that has happened on television shows).
If A is in love with B, and B turns down A definitively, then the question is what does A do about this? If A accepts that and moves on, then why was this all brought up in the first place?
If A resents it and grows to think B was unfair, and cruel, and evil, and deserves to die: Well, that's a driver for A, certainly, that can inform future chapters and cause a spot of trouble for B.
Or say A comes to terms and realizes the crush was more about the physical attributes of B, there was never any "love" of B as a person. So A matures after chapter 1. Then B realizes they have been making wrong choices in their life, and the real type of person they want is A, they should never have been so egotistical and self-centered to turn down A, and voila: B seeks out A, and finds A happily dating C.
Without consequences of some sort (learning, motives, regrets, etc), any romantic tension for the sake of filling a chapter is worthless. It wouldn't make a difference if it was drawn out or stuck in chapter 1 alone. These things have to go somewhere, and shape the story, or they don't belong in it.
As I stated in my comment, love is something that gradually develops, whether it is one sided or mutual, it takes time to develop. Some stories take a whole chapter just on the first meeting of 2 individuals, others sprinkle it throughout the story until it reaches an apex.
If you are introducing the feelings for the first time in a chapter, and then having them shut down in that chapter, there is nothing wrong with that persay. It depends on where YOU want the story to go. If this is an underlying theme where this guy does things for the one he cares about and it causes him to risk his life or what ever, then it should probably be drawn out.
If you want the audience to feel bad for the one who is unrequited, then you need to give the reader a chance to grow with the feelings too so that when the other person breaks their heart, the reader's heart is broken too.
Again it depends on your story, and the speed it is being paced at, however I would feel cheated if a love is introduced and then taken away within 1 chapter as a reader and would be given no time to really feel bad for the person who ultimately gets turned down. It would more be like "oh, dude got turned down by his first crush, oh well it happens."
As a side note... If your whole chapter is literally spent on this love and the growing feelings he has for the other character, and you are 20 pages deep into this chapter, sure you might be able to provide enough for a 1 chapter love affair that people could build a bond to. But again, it depends on the affect you want to create in the reader. If you want a deep emotion that is tied to importance, 1 chapter won't do it!
The times I have fallen hard, the feeling took more than a chapter in my life. I pined for those soul mates for years, and they were usually unrequited.
There are other times that I thought I was falling, but no, it was hormones. I could never really tell the difference on the front end.
If you want an emotion that comes on hard and then fades and resolves quickly, I suggest not love but extreme horniness, cured by something appalling.
Speaking as a reader, I find it frustrating when a romance is introduced and then just dropped. Like Chekhov's gun, don't leave it on the table if you aren't going to fire it, and don't set it up if you don't want to sustain it.
However, this doesn't mean that the characters have to actually get together. There's a lot of ways romantic tension can enrich a story beyond the obvious. Some possibilities are: A crush that turns into a friendship or other platonic relationship (Luke & Leia in Star Wars); a way to show the main character outgrowing an immature or unworkable attachment (Almost Famous); a object of affection that is revealed to be a terrible or deceitful match (Hans in Frozen); a placeholder for, or obstacle to a forthcoming real relationship (Rosaline in Romeo & Juliet, Viktor Krum in Harry Potter); a sustained unrequited or unconsummated love (the main characters in Remains of the Day).