Closest in meaning confusion
Acts the part of is an incorrect interpretation, because it indicates that you are about to tell us which part the NO2 will play.
What plays a role in indicates that NO2 is playing a role, but is not about to tell us which. It is less specific.
Take these examples:
Brad Pitt acts the part of Tyle Durden in Fight Club.
vs.
Dame Helen Mirren plays a role in the film The Queen.
In the first you are directly indicating which role Brad Pitt plays, where as in the second you are indicating that a role is played, but not which one.
You could change the verb play to act, and it would mean the same thing in a theatrical context - acts a role in - but this is not normally used in more general contexts.
Role can be used as a synonym for function, e.g.
The function of the bus driver is to drive the bus
or
The role of the bin man is to collect the rubbish
Serve and play can be used synonymously in some circumstances, in yours it depends what kind of imagery you want to use. Serving drawing the image of a servant, whereas playing evokes that of an actor.
So the phrase serves a function indicates that NO2 is doing something, but not what it is doing, much the same as plays a role. The main difference is that using serves has an implication of being under the control of someone, where as plays gives the NO2 a more autonomous image.
My reason was that since NO2 is a required substance in acid rain, its a part of it.
That reasoning would instead justify "acts as part of". As you wrote it, you suggest "NO2" performs a role in some sort of screenplay, pretending to be "the formation of acid rain".
Regardless, that wouldn't work here because NO2 isn't a part of the formation of acid rain, but a part of the acid rain itself.
The phrase "plays a role in" also suggests "some sort of screenplay", but here the "formation of acid rain" is our 'screenplay', metaphorically.
How can it be just a function when without it acid rain cannot happen?
A "function" absolutely can be essential to the entire process.