  The unusual chemistry of sulfur is illustrated by the tendency for
catenation. Sulfur forms a range of open and closed S$_n$ 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 O$_2$ and N$_2$, there is no widely accepted thermodynamic potential
for sulfur. Here we combine a first-principles global structure search for the
low energy clusters from S$_2$ to S$_8$ 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 S$_2$ to S$_8$ is identified. A universal chemical
potential function, $\mu_{\mathrm{S}}(T,P)$, is proposed with wide utility in
modelling sulfurisation processes including the formation of metal chalcogenide
semiconductors.
