To me there is many different plausible scenarios, that person may or may not be aware of the caused disturbance, that person may or may not agree to compromise and to make life easier for you. Finally, you may or may not be on the right side of management policies, that can lean on your side or your colleague side based on what's acceptable behavior on the workplace.
This is a lot of ifs that aren't covered by your question, so I'll answer generically but with the known limitation it may not cover your exact situation very well.
When a non-critical conflict happens in the workplace, and without knowing how cooperative my peer will be I tend to favor having a face to face meeting with that person before trying to escalate the matter. In several instances, I was taught escalating problems is fine when things are out of hand but if you happen to escalate too much problems or problems you could solve yourself you could also gain a mistrusting image toward your peers, by showing you prefer to "snitch" to the management than address the conflict yourself.
So, without knowing what is the exact policy of your workplace, I'll suppose you are asking for a favor here, and that your colleague has all latitude to ignore your requests.
When practicing NVC we are taught that one of the essential key for the other person to empathically connect with us, one of the key component in obtaining a favor, is that person understands our needs. So I would start right there, before even asking anything:
I need to concentrate
Then, without making any judgement, try to assess how the situation make you unsatisfied.
but when I don't wear headphones, noises from snacks disturb me.
You end up with making a positive action request. Usually, following the principle of persuasion (extracted from Dr. Robert Cialdini’s book, Influence), it's better to start by requesting something small.
Could you explain me why you eat snacks so often?
The script can be tweaked somewhat but the key philosophy of NVC is that both interlocutors exchange needs and connect empathically: so now you've explained your need, you invite them to share theirs.
Hopefully, you can then proceed to work out together a solution. It could be no-eat hours, changing type of food, putting the snacks in a bowl first and whatnot, it somewhat depends of what kind of things are relevant to that person and how defensive they behave.