Evaporation of sulfuric acid from particles can be important in the atmospheres of Earth and Venus. However, the equilibrium constant for the dissociation of H₂SO₄ to bisulfate ions, which is the one of the fundamental parameters controlling the evaporation of sulfur particles, is not well constrained. In this study we explore the volatility of sulfate particles at very low relative humidity. We measured the evaporation of sulfur particles versus temperature and relative humidity in the CLOUD chamber at CERN. We modelled the observed sulfur particle shrinkage with the ADCHAM model. Based on our model results, we conclude that the sulfur particle shrinkage is mainly governed by H₂SO₄ and potentially to some extent by SO₃ evaporation. We found that the equilibrium constants for the dissociation of H₂SO₄ to HSO₄^-(K_H2SO4) and the dehydration of H₂SO₄ to SO₃ (^xK_SO3) are K_H2SO4 = 2-4 × 10⁹ mol kg^-1 and ^xK_SO3 ≥ 1.4 × 10¹⁰ at 288.8 ± 5 K.