The Mars Exploration Rover Opportunity identified the ferric sulphate mineral jarosite and possible relicts of gypsum at the Meridiani Planum landing site. On Earth, jarosite has been found to form in acid mine drainage environments, during the oxidation of sulphide minerals, and during alteration of volcanic rocks by acidic, sulphur-rich fluids near volcanic vents. Jarosite formation is thus thought to require a wet, oxidizing and acidic environment. But jarosite on Earth only persists over geologically relevant time periods in arid environments because it rapidly decomposes to produce ferric oxyhydroxides in more humid climates. Here we present equilibrium thermodynamic reaction-path simulations that constrain the range of possible conditions under which such aqueous alteration phases are likely to have formed on Mars. These calculations simulate the chemical weathering of basalt at relevant martian conditions. We conclude that the presence of jarosite combined with residual basalt at Meridiani Planum indicates that the alteration process did not proceed to completion, and that following jarosite formation, arid conditions must have prevailed.