In 1920, at the age of twenty-one, Rossini entered Carnegie-Mellon University in Pittsburgh, and soon was awarded a full-time teaching scholarship. He graduated with a B.S. in chemical engineering in 1925, followed by an M.S. degree in science in physical chemistry in 1926.
As a result of reading Lewis and Randall's classical 1923 textbook Thermodynamics and the Free Energy of Chemical Substances he wrote to Gilbert N. Lewis and as a result he was offered a teaching fellowship at the University of California at Berkeley. Among his teachers were Gilbert Lewis and William Giauque. Rossini's doctoral dissertation on the heat capacities of strong electrolytes in aqueous solution was supervised by Merle Randall. His Ph.D. degree was awarded in 1928, after only 21 months of graduate work, even though he continued to serve as a teaching fellow throughout this entire period.
In 1932, Frederick Rossini, Edward W. Washburn, and Mikkel Frandsen authored “The Calorimetric Determination of the Intrinsic Energy of Gases as a Function of the Pressure.” This experiment resulted in the development of the Washburn Correction for bomb calorimetry, a decrease or correction of the results of a calorimetric procedure to normal states.
He served as dean of the Notre Dame College of Science from 1960 to 1967.