Born in Dundee, he was educated at the High School of Dundee, and though had passed the entrance examination for the University of Street Andrews at sixteen, he instead went for three years to the flax industry, entering the University of Edinburgh in 1882, graduating Bachelor of Science In 1885 and Doctor of Science in 1886.
He then spent three years in Germany, working with Ludwig Claisen, Adolf von Baeyer and Wilhelm Ostwald. Following a Doctor of Philosophy at the University of Leipzig in 1889, he returned to Britain, working in Edinburgh and University College, London, before being appointed professor of chemistry at the University of Dundee in 1894. In 1908 he returned to Edinburgh to succeed Alexander Crum Brown as professor
Walker"s main research interest was in physical chemistry.
He investigated methods of electrolysis in the synthesis of dicarboxylic acids, the dissociation constants of acids and bases, and measured molecular weights by freezing point depression. While he is personally credited with no truly major discoveries, his most important role was as a populariser of the new and controversial physical chemistry theories of Ostwald, van"t Hoff and Arrhenius in the English speaking world.
This he did through his 1890 translation of Ostwald"s Grundriss der allgemeinen Chemie (Outlines of General Chemistry), and his own textbook Introduction to Physical Chemistry (1899), which became a set text in many British universities.
Royal Society.