This may be him...if it is him, he had a brother, Otto.
1880 Chicago, Cook County, IL census
Harmon Rhode, 31, labourer, born in Prussia, both parents born in Prussia. Agusta, 24, born in IL, both parents born in Prussia George, 6, born in IL Thedore, 2, born in IL Ella, 1, born in IL Otto, 24, brother, born in Prussia Henry Petervanderof, 22, boarder, labourer, born in IL, both parents born in Prussia.
Another possibility...The Teutonia landed in NY 6/6/1868, port of departure, Hamburg, Germany. Travelling together were Herman Rohde, 19; Theodor Rohde, 9; and Otto Rohde, 6