The unusual chemistry of sulfur is illustrated by the tendency for catenation. Sulfur forms a range of open and closed Sn species in the gas phase, which has led to speculation on the composition of sulfur vapours as a function of temperature and pressure for over a century. Unlike elemental gases such as O2 and N2, there is no widely accepted thermodynamic potential for sulfur. Here we combine a first-principles global structure search for the low energy clusters from S2 to S8 with a thermodynamic model for the mixed-allotrope system, including the Gibbs free energy for all gas-phase sulfur on an atomic basis. A strongly pressure- dependent transition from a mixture dominant in S2 to S8 is identified. A universal chemical potential function, μS(T,P), is proposed with wide utility in modelling sulfurisation processes including the formation of metal chalcogenide semiconductors.