Graham was born in Glasgow, Scotland. At age 14 he attended Glasgow University and studied chemistry against his father's wishes, which were that he would become a clergyman rather than a scientist. His father cut off Graham's funding and Graham supported himself by teaching and writing. Upon his graduation from Edinburgh University at age 19, Graham took a teaching position at Mechanics Institute, where he became a professor in 1830. Graham's first scientific paper was on the movement of gas, a subject of great interest to him.

Graham spent the greater part of the 1820s studying the dissolution and diffusion of various gases through different mediums. He was intrigued by Johann Wolfgang Döbereiner 's observation that when a bottle of hydrogen with a crack in it was partially submerged in water, the water level rose. The bottle was losing hydrogen more quickly than it was gaining air. In his...