Question

What motivated arrhenius to calculate how changes in carbon dioxide might affect the climate?

Answer 1

Arrhenius was seeking to understand the causes of ice ages. 
He was the first to use basic principles of  physical chemistry to calculate estimates of the extent to which increases in atmosphere carbon dioxide increases Earth's surface temperature through the Arrhenius effect. Arrhenius's paper was the first to quantify the contribution of carbon dioxide to the greenhouse effect and to speculate whether variations in the atmospheric concentration of carbon dioxide have contributed to long-term variations in climate.