elkniwcire32 ohm should be fine with a smartphone, and most headphones use the 3.5mm 1/8" jack. Ohms used to power the speaker don't relate to the connector.
If a headphone has a higher ohm rating, it will take more power(amps) to drive that headphone to an equal volume. The need for an amplifier arises when you have headphones around 80-100 ohms that need lots of power to get to higher volumes. For example, I have a pair of Beyer Bustom Studios that are 80 ohm. My Nexus 5X can only drive them to moderate volume, while my samsung s8+ can drive them to uncomfortable volume.
EDIT: The debate of whether a higher ohm rating = better quality sound is a whole other discussion. I personally believe driving a tube amp more by using higher ohm headphones produces a fuller sound with higher gains. When it comes to solid state (regular, non-tube) amps such as the ones in motherboards and smartphones, the sound quality is the same at high and low gain/volume.
elkniwcireThere are slight differences, but I'm very skeptical that most of us can detect them. Yes, they can be powered by a smartphone. I don't recall about the jack (mine is at my office, otherwise I'd look), but worse come to worse, you get an adaptor, which is super cheap. It's NOT a reason not get these.