This brief thermodynamic analysis theoretically explores the performance of an electrolyser for various working reactions (WR). The electrolyser cell (EC) system is composed of an electrolyser and heat engines. The lowest electrical requirement for working reactions for electrolysis will have the highest possible Carnot temperature, T_{c ,} and ∆T∆^rS(T) values needed to minimize ΔG and maximize the amount of thermal that could be converted to chemical energy in an electrolyser. In addition, reactions with multiple products and few reactants create additional entropy, that is, many high entropy products coming from a few low entropy reactants, are optimal. A procedure using statistical mechanics was developed and employed to locate optimal WR’s focused on the values of Δ^rS^o, T_c, and the number of products and reactants. The research and development direction for electrolyser WR’s is discussed.