rant vs mouth off

rant is a noun but mouth off is not a noun.

Word	Noun	Adjective	Verb	Adverb
rant	Yes	No	Yes	No
mouth off	No	No	Yes	No

As verbs, rant and mouth off are synonyms defined as:

Other synonyms of rant include jabber, rabbit on, rave, spout.

rant (noun)	mouth off (noun)
pompous or pretentious talk or writing
a loud bombastic declamation expressed with strong emotion

rant (verb)	mouth off (verb)
talk in a noisy, excited, or declamatory manner	talk in a noisy, excited, or declamatory manner