In later life, Arrhenius enjoyed using masses of data to discover mathematical relationships and laws. At age 8, he entered the local cathedral school, starting in the fifth grade, distinguishing himself in physics and mathematics, and graduating as the youngest and ablest student in 1876.

At the University of Uppsala, he was unsatisfied with the chief instructor of physics and the only faculty member who could have supervised him in chemistry, so he left to study at the Physical Institute of the Swedish Academy of Sciences in Stockholm under the physicist Erik Edlund in 1881. His work specialized on the conductivities of electrolytes. In 1884, based on this work, he submitted a 150-page dissertation on electrolytic conductivity to Uppsala for the doctorate. It did not impress the professors, and he received the lowest possible passing grade. Later this very work would earn him the Nobel Prize in Chemistry.

There were fifty-six theses put forth in the 1884 dissertation, and most would still be accepted today unchanged or with minor modifications. The most important idea in the dissertation was his explanation of the fact that neither pure salts nor pure water is a conductor, but solutions of salts in water are.

Arrhenius' explanation was that in forming a solution, the salt dissociates into charged particles (which Michael Faraday had given the name ions many years earlier). Faraday's belief had been that ions were produced in the process of electrolysis; Arrhenius proposed that, even in the absence of an electric current, solutions of salts contained ions. He thus proposed that chemical reactions in solution were reactions between ions. For weak electrolytes this is still believed the case, but modifications (by Peter J. W. Debye and Erich Hückel) were found necessary to account for the behavior of strong electrolytes.

The dissertation was not very impressive to the professors at Uppsala, but Arrhenius sent it to a number of scientists in Europe who were developing the new science of physical chemistry, such as Rudolf Clausius, Wilhelm Ostwald, and J. H. van 't Hoff. They were far more impressed, and Ostwald even came to Uppsala to persuade Arrhenius to join his research team. Arrhenius declined, however, as he preferred to stay in Sweden for a while (his father was very ill and would die in 1885) and had gotten an appointment at Uppsala.

Arrhenius next received a travel grant from the Swedish Academy of Sciences, which enabled him to study with Ostwald in Riga (now in Latvia), with Friedrich Kohlrausch in Würzburg, Germany, with Ludwig Boltzmann in Graz, Austria, and with van 't Hoff in Amsterdam.

In 1889 Arrhenius explained the fact that most reactions require added heat energy to proceed by formulating the concept of activation energy, an energy barrier that must be overcome before two molecules will react. The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the rate at which a reaction proceeds. In 1891 he became a lecturer at Stockholms Högskola (now Stockholm University), being promoted to professor of physics (with much opposition) in 1895, and rector in 1896.

He was married twice, to Sofia Rudbeck, (who bore him one son) from 1894 to 1896, and to Maria Johansson (who bore him two daughters and a son), from 1905 onward.

In 1901 Arrhenius was elected to the Swedish Academy of Sciences, against strong opposition. In 1903 he became the first Swede to be awarded the Nobel Prize in chemistry. In 1905, upon the founding of the Nobel Institute for Physical Research at Stockholm, he was appointed rector of the institute, the position where he remained until retirement in 1927.

Eventually, Arrhenius' theories became generally accepted and he turned to other scientific topics. In 1902 he began to investigate physiological problems in terms of chemical theory. He determined that reactions in living organisms and in the test tube followed the same laws. He also turned his attention to geology (the origin of ice ages), astronomy, cosmology, and astrophysics, accounting for the birth of the solar system by interstellar collision. He considered radiation pressure as accounting for comets, the solar corona, the aurora borealis, and zodiacal light.

He thought life might have been carried from planet to planet by the transport of spores, the theory now known as panspermia. He thought of the idea of a universal language, proposing a modification of the English language.

In an extension of his ionic theory Arrhenius proposed definitions for acids and bases. He believed that acids were substances which produce hydrogen ions in solution and that bases were substances which produce hydroxide ions in solution.

In his last years he wrote both textbooks and popular books, trying to emphasize the need for further work on the topics he discussed.

In September, 1927, he came down with an attack of acute intestinal catarrh, died on October 2, and was buried in Uppsala.

Svante Arrhenius developed a theory to explain the ice ages, and first formulated the idea that changes in the levels of carbon dioxide in the atmosphere could substantially alter the surface temperature through the greenhouse effect ("On the Influence of Carbonic Acid in the Air Upon the Temperature of the Ground", Philosophical Magazine 1896(41): 237-76). He was influenced by the work of others, including Joseph Fourier's argument that the earth's atmosphere acted like the glass of a hot-house. Arrhenius used the infrared observations of the moon by Frank Washington Very and Samuel Pierpont Langley at the Allegheny Observatory in Pittsburgh to calculate the absorption of CO2 and water vapour. Using the just published Stefan's law he formulated his greenhouse law. In it's original form, Arrhenius' greenhouse law reads as follows:

if the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression. Which is still valid in the simplified expression by Myhre et al(1998).

?°F = aln(C/C0)

Arrhenius' high absorption values for CO2, however, met criticism by Knut Ångström in 1900, who published the first modern infrared spectrum of CO2 with two absorption bands. Arrhenius replied strongly in 1901 (Annalen der Physik), dismissing the critique altogether. He touched the subject briefly in a technical book titled Lehrbuch der kosmischen Physik (1903). He later wrote Världarnas utveckling (1906), German translation: Das Werden der Welten (1907), English translation: Worlds in the Making (1908) directed at a general audience, where the suggested that the human emission of CO2 would be strong enough to prevent the world from entering a new ice age, and that a warmer earth would be needed to feed the rapidly increasing population. From that, the hot-house theory gained more attention. Nevertheless, until about 1960, most scientists dismissed the hot-house / greenhouse effect as implausible for the cause of ice ages as Milutin Milankovitch had presented a mechanism using orbital changes of the earth.

Arhenius estimated that a doubling of CO2 would cause a temperature rise of 5 degrees Celsius [1], recent values from IPCC place this value (the Climate sensitivity) at between 1.5 and 4.5 degrees. What is remarkable is that through a combination of skill and luck he came within a factor of two of the IPCC estimate. His calculations were important only in a qualitative way in showing that this was a significant effect. Arrhenius expected CO2 levels to rise at a rate given by emissions at his time. Since then, industrial carbon dioxide levels have risen at a much faster rate: Arrhenius expected CO2 doubling to take about 3000 years; it is now generally expected to take about a century.