responsibility has 4 distinct synonyms spread across 3 of its 3 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is irresponsibility.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the social force that binds you to the courses of action demanded by that force
“we must instill a sense of duty in our children”
the proper sphere or extent of your activities
“it was his province to take care of himself”
a form of trustworthiness; the trait of being answerable to someone for something or being responsible for one's conduct
“he holds a position of great responsibility”
Synonyms, antonyms and the broader and narrower relations for responsibility come from Princeton University’s WordNet. Full sources and licences.