Derivation of the stoichiometric coefficient of water (ν_w) to account for water uptake by atmospheric aerosols

Abstract. In this work we derive the effective stoichiometric coefficient of water (v_w), introduced by Metzger and Lelieveld, 2007 (ML07), from first principles. We give examples of the application of v_w in CPU efficient computations of the Deliquescence Relative Humidity (DRH) and the water uptake of atmospheric aerosols, being important parameters in atmospheric chemistry and climate modeling. We show that the application of v_w in a gas/liquid/solid aerosol equilibrium partitioning model (EQSAM3) leads to results that are in excellent agreement with those of widely used thermodynamic (reference) models (E-AIM and ISORROPIA2) for various single salt solutions (NaCl, NH₄NO₃, (NH₄)₂SO₄, NH₄HSO₄, NaHSO₄) and the corresponding mixed solutions (including (NH₄)₃H(SO₄)₂ and Na₃H(SO₄)₂), notwithstanding the distinct different theoretical and numerical concepts on which these models are based.