Supersaturation occurs in many industrial applications promoting reactive crystallisation between the reactants to form solutes. These solutes accumulate during precipitation, leading to the formation of scales on the inner walls of the reactor and particularly around the stirrer, causing modifications in the hydrodynamics. This encrustation is responsible for process shutdowns in continuous crystallisation processes. Supersaturation control is essential for industrial processes aimed at controlling or inhibiting the formation of these solids. Knowledge of mineral solubility and chemical speciation is required to account for the composition of the complexes in the system in their various solid or aqueous forms. This speciation is obtained by considering the thermodynamic equilibrium constants of the dissociation/complexation reactions involved in the system, the pressure, and the activity coefficients of the chemical species in their molecular or electrolyte form. From these thermodynamic quantities and the state of the system, we can predict the direction of the reaction. This study highlights the risk of the lack of experimental information on equilibrium constants at high temperatures and moderate pressures. Our goal is to evaluate the accuracy of existing models classically used to predict the equilibrium constant in such very hard conditions encountered in hydrometallurgical processes. Furthermore, we demonstrate the influences of equilibrium constants estimation and activity coefficient models on the speciation of H₂SO₄–Al₂(SO₄)₃–MgSO₄ systems, forming hydronium alunite and kieserite in the laterite liquor of hydrometallurgical processes