Final answer:
Option (1), The Thomas Jefferson administration's purchase of the Louisiana Territory led to a dispute with Spain over the borders of the territory following its acquisition.
Step-by-step explanation:
The dispute over the borders of the Louisiana Territory following its purchase involved the nation of Spain. Despite Thomas Jefferson's initial hesitation due to the limited government he envisioned and the lack of constitutional provision for such a purchase, the acquisition of the territory doubled the size of the United States and granted control over New Orleans and the strategic Mississippi River.
The importance of New Orleans and the Mississippi to American commerce and the expansionist vision of an agrarian society was paramount, which outweighed Jefferson’s strict adherence to constitutional limitations. Eventually, this expansion led to the Adams-Onís Treaty which clarified the boundary between the U.S. and Spanish territories and legally secured Florida for the United States, although it did not resolve broader territorial claims.