The timer started, and a middle school student named Tony Mack began his first chemistry experiment. As he weighed chemicals under a graduate student’s supervision, his father, James, a chemist at the University of Cincinnati, assembled glassware next to him, engrossed in his own experiment.

The two were racing to prepare a mix of stilbene molecules used to make dyes, but were employing different methods. For Dr. Mack, the ingredients simmered in a stirred solution in a heated flask. But for Tony, they were crushed with balls that tumbled and hit them as a machine called a ball mill shook them vigorously. Tony crossed the finish line while Dr. Mack was still two hours away, and did so with about 30 percent more stilbene.

“He was so happy he beat me,” Dr. Mack said, laughing.

Conducted at Dr. Mack’s laboratory in 2014, the race was designed to prove a point: that milling, or grinding chemicals together without a solvent, could outperform established methods and yet be safe and simple enough for an inexperienced eighth grader to do.