Hello,
I am working a beginner project with an Arduino Pro Mini and using it to generate tones, currently through a speaker. Is it possible for the Arduino to output the sound to 32 ohm headphones instead of the speaker? Through a 3.5mm jack.
Thanks! 
What happened when you tried it?
I expect that you'll get sound out of it. It won't be any worse or better than the speaker.
I am thinking I need a resistor from the Arduino pins to the jack? 125ohm is what I thought.
Sure, doesn't hurt to do that
The absolute maximum rated current from an I/O pin is 40mA. From Ohm's Law (R= V/I) that gives you a minimum resistance/impedance of 125 Ohms. So, you should add a resistor in series. A resistor will lower the volume but with headphones it will probably still blow your ears out...
If you are running both "ears" in parallel from a single I/O pin that's 16 Ohms, and your speaker is probably 4 or 8 Ohms. A 130 Ohm resistor (a standard 5% value) is "safe" no matter what.
Got it, thanks