LibreOffice's CPU/memory usage (on a Mac)

According to my understanding, usage of any single L.O. module, e.g., WRITER, requires all of L.O. to be run (at least that’s the case on a Mac).

The ‘System Requirements’ webpage mentions the amount of RAM that L.O. requires but nothing about CPU usage.

I use a Mac – not a recent one, with 2 GB RAM and a 1.83GHz processor. Since the browser I currently use, Google Chrome, is CPU- and RAM-intensive, I am wondering whether I will be able to run L.O. with the browser loaded without very slow performance in L.O. and/or the browser.

I’m also considering switching to TOR – should anyone be able to comment on how L.O. runs in tandem (CPU- and memory-wise) with that browser (instead of Chrome).