Short answers, pulled from the story.
In 1896, Arrhenius was the first person to use physical chemistry principles to calculate how increases in atmospheric carbon dioxide would raise Earth's surface temperature through the greenhouse effect. He concluded that fossil fuel combustion was already producing enough CO2 to cause global warming. His formulation, now called Arrhenius's rule, is still used in a modified form today.
Arrhenius won the Nobel Prize in Chemistry in 1903 for his work on the dissociation of electrolytes, specifically his theory that salts dissolve into charged ions in solution even without an external electric current. This work was first presented in his 1884 doctoral dissertation, which initially received a near-failing grade from the committee at Uppsala.
The Arrhenius equation gives the quantitative relationship between the activation energy of a chemical reaction and the rate at which that reaction proceeds. Arrhenius formulated it in 1889 to explain why most chemical reactions require added heat energy before they will proceed.
Arrhenius viewed the warming he calculated as broadly beneficial. In his 1908 book Worlds in the Making, he argued that industrial CO2 emissions might prevent a new ice age and produce more equable climates that could support larger agricultural yields for a growing population. He did not frame the warming as a threat.
Arrhenius was a member of the Nobel Committee on Physics for the rest of his life after becoming involved in the Nobel Institutes around 1900, and he served as a de facto member of the Nobel Committee on Chemistry. He used his influence to arrange prizes for friends including Wilhelm Ostwald and Jacobus van 't Hoff, and to block prizes for scientists he considered rivals, among them Walther Nernst and Dmitri Mendeleev.
Svante Thunberg, the father of climate activist Greta Thunberg, was named after Arrhenius and is an ancestral cousin of his. The connection links Greta Thunberg by family to the scientist who first calculated the warming effect of CO2 emissions in 1896.