Is adultery one of the oldest grounds for divorce?

Probably, yes. Traditionally adultery was the classic grounds for divorce. Adultery was considered the worst possible violation of marriage vows and proof of a marital breakdown. And because adultery does not just happen by accident, at least one of the two spouses had to be responsible for it.
Adultery was considered a grave moral failing worthy of harsh condemnation, which society reinforced with punitive financial punishment. And sometimes when a third party was named -- a co-respondent, who often was a paramour -- the whole town savored all the details of fallen people who had strayed from the straight and narrow. The just punishment of a roving husband and the vindication of a righteous wife made the divorce into a morality play. Sometimes, when the spouses were socially prominent, the details made for great gossip.