Explain how nationalism threatened multi-ethnic empires like Austria-Hungary and the Ottoman Empire, and identify the Balkans as the "powder keg" that would help spark a wider war.
The same force that unified Italians and Germans into single nations threatened to tear apart empires built from many different peoples. After 1867, Austria-Hungary functioned as a "Dual Monarchy" -- one emperor ruling two officially equal halves -- but within its borders lived Germans, Hungarians (Magyars), Czechs, Poles, Slovaks, Croats, Serbs, Romanians, and more, many of whom increasingly wanted their own independent nation-states rather than a place inside someone else's empire. Nationalism, in other words, is not automatically a unifying force -- it unifies people who already share an identity, while threatening to fracture empires that govern many identities at once.
The Ottoman Empire faced an even sharper version of the same problem, so pronounced that European diplomats nicknamed it "the Sick Man of Europe." Greece had already won independence in 1830, and Serbia, Bulgaria, and Romania gained full independence over the following decades as Ottoman power receded from the Balkan Peninsula. Tension peaked in 1908, when Austria-Hungary formally annexed Bosnia-Herzegovina, a region with a large Serbian population -- infuriating Serbian nationalists who dreamed of uniting South Slavic peoples (a movement called Pan-Slavism) into one state, possibly including Bosnia. Layered ethnic rivalries, competing great-power interests, and the recent Balkan Wars of 1912-1913 left the region so volatile that historians still call it "the powder keg of Europe" -- and a single spark there was about to set off a fire that would consume the whole continent.
Mastery looks like: They can explain why nationalism unified some regions while threatening to fracture multi-ethnic empires, and identify the Balkans' key 19th-century flashpoints, including the 1908 Bosnia annexation.
Common stumbles: Assuming nationalism is always a unifying, positive force, without recognizing how the very same force could threaten empires that ruled over many different peoples at once.