The capital of North Dakota is Bismarck, but it is not located on the Mississippi River. This is a frequent point of confusion because the Mississippi forms part of the eastern border of several Midwestern states.
The Missouri River joins the Mississippi near St. Louis, Missouri—about 700 miles southeast of Bismarck. Both rivers are part of the same vast watershed, but they are distinct waterways. Bismarck's historic role as a steamboat hub on the Missouri contributed to its early growth and selection as territorial (later state) capital.
If you're looking for a state capital on the Mississippi River, consider St. Paul (Minnesota), Baton Rouge (Louisiana), or Jackson (Mississippi).