Final answer:
Uruguay became an independent nation with the Treaty of Montevideo in 1828 after the Cisplatine War, which involved disputes over its territory between Brazil and Argentina.
Step-by-step explanation:
The country that became independent with the Treaty of Montevideo in 1828, at the end of the Cisplatine War, was Uruguay. After a series of battles between Brazil and Argentina over the territory known as the Eastern Band (Banda Oriental), Uruguay was finally established as a sovereign nation.
It was the efforts of figures like José Gervasio Artigas who championed autonomy for the region long before independence was achieved. The conflict eventually concluded with the intervention of the British Empire, which mediated negotiations leading to the Treaty of Montevideo that formally acknowledged Uruguay's independence.