Its well known that Facebook on iOS is a battery hog. But a new update is supposed to fix all that. Facebook's Engineering Manager Ari Grant, wrote on a Facebook post:
"We found a few key issues and have identified additional improvements, some of which are in the version of the app that was released Friday"
The previous iterations of the Facebook app were caught in a CPU Spin which kept the processor engaged when using the app, moreover audio sessions were not closed properly.
The development team has fixed these issues, and the new update eats far less battery. You can download the update from the link below.