To expiate is defined as to admit you did something that was a sin or something you feel guilty about.(verb)
When you feel guilty about a lie you told, and you come clean and ask for forgiveness, this is an example of a time when you expiate.
See expiate in Webster's New World College Dictionary
See expiate in American Heritage Dictionary 4
verb ex·pi·at·ed, ex·pi·at·ing, ex·pi·ates verb, transitive
Origin: Latin expiāre, expiāt-
Origin: : ex-, intensive pref.; see ex-
Origin: + piāre, to atone (from pius, devout).
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