Arrhenius’s scientific career encompassed three distinct specialties within the broad fields of physics and chemistry: physical chemistry, cosmic physics, and the chemistry of immunology. Each phase of his career corresponds with a different institutional setting. His years (1884–90) as a doctoral and postdoctoral student pioneering the new physical chemistry were spent at the Institute of Physics of the Academy of Sciences in Stockholm and at foreign universities; his work in cosmic physics (1895–1900) was carried out at the Stockholms Högskola (now the University of Stockholm); and his studies in immunochemistry (1901–07) took place at the State Serum Institute in Copenhagen and the Nobel Institute for Physical Chemistry (established in 1905) in Stockholm.

Arrhenius’s main contribution to physical chemistry was his theory (1887) that electrolytes, certain substances that dissolve in water to yield a solution that conducts electricity, are separated, or dissociated, into electrically charged particles, or ions, even when there is no current flowing through the solution. This radically new way of approaching the study of electrolytes first met with opposition but gradually won adherents through the efforts of Arrhenius and Ostwald. The same simple but brilliant way of thinking that inspired the dissociation hypothesis led Arrhenius in 1889 to express the temperature dependence of the rate constants of chemical reactions through what is now known as the Arrhenius equation. Arrhenius’s work in immunochemistry, a term that gained currency through his book of that title published in 1907, was an attempt to study toxin-antitoxin reactions, principally diphtheria reactions, using the concepts and methods developed in physical chemistry. Together with Torvald Madsen, director of the State Serum Institute in Copenhagen, he carried out wide-ranging experimental studies of bacterial toxins as well as plant and animal poisons. The technical difficulties were too great, however, for Arrhenius to realize his aim of making immunology an exact science. Instead, it was his spirited attacks on the reigning theory in the field of immunity studies, the side-chain theory formulated by the German medical scientist Paul Ehrlich, that attracted attention. This, however, was of short duration, and Arrhenius gradually abandoned the field.