Final answer:
The capital of South Dakota is Pierre, located on the Missouri River, and it is the second smallest state capital in the U.S. by population.
Step-by-step explanation:
The capital of South Dakota is Pierre. It is situated on the Missouri River and is indeed the second smallest state capital by population in the United States. Pierre's position on the river has historically been significant for transportation and trade, contributing to its status as the state capital. Despite its small size, Pierre serves as a political and administrative hub for South Dakota.