The calculation -- named the Cottrell equation for chemist Frederick Gardner Cottrell, who developed it in 1903 -- can help today's researchers understand the several reactions that carbon dioxide can take when electrochemistry is applied and pulsed on a lab bench.

The electrochemical reduction of carbon dioxide presents an opportunity to transform the gas from an environmental liability to a feedstock for chemical products or as a medium to store renewable electricity in the form of chemical bonds, as nature does.

Their work was published in the journalACS Catalysis.

"For carbon dioxide, the better we understand the reaction pathways, the better we can control the reaction -- which is what we want in the long term," said lead author Rileigh Casebolt DiDomenico, a chemical engineering doctoral student at Cornell under the supervision of Prof. Tobias Hanrath.

"If we have better control over the reaction, then we can make what we want, when we want to make it," DiDomenico said. "The Cottrell equation is the tool that helps us to get there."

The equation enables a researcher to identify and control experimental parameters to take carbon dioxide and convert it into useful carbon products like ethylene, ethane or ethanol.

Many researchers today use advanced computational methods to provide a detailed atomistic picture of processes at the catalyst surface, but these methods often involve several nuanced assumptions, which complicate direct comparison to experiments, said senior author Tobias Hanrath.

"The magnificence of this old equation is that there are very few assumptions," Hanrath said. "If you put in experimental data, you get a better sense of truth. It's an old classic. That's the part that I thought was beautiful."

DiDomenico said: "Because it is older, the Cottrell equation has been a forgotten technique. It's classic electrochemistry. Just bringing it back to the forefront of people's minds has been cool. And I think this equation will help other electrochemists to study their own systems."

The research was supported by the National Science Foundation, a Cornell Energy Systems Institute-Corning Graduate Fellowship and the Cornell Engineering Learning Initiative.