Hotel chain Sonesta will sell prized Key Biscayne acreage to an Argentine developer, ending its long, fruitless bid to build a luxury condo-hotel resort. Consultatio S.A. plans to pay $78 million and close by the end of September. Holliday Fenoglio Fowler’s office in Coral Gables handled the deal. Sonesta treasurer Boy Van Riel said the company would pay off its $56 million mortgage with the proceeds. Sonesta valued the land at $120 million four years ago, and had planned to build condos on the site of the Sonesta Beach Resort in a partnership with Boston developer Fortune International. It closed the resort in 2006, as the market collapsed.