CORRELATIONS Reactive Gas Solubility in Water: An Empirical Relation Mohammed A. Islam,* ,† Mohammed A. Kalam, ‡ and Maksudur R. Khan † The Department of Chemical Technology and Polymer Science and The Department of Chemistry, Shahjalal University of Science and Technology, 3114 Sylhet, Bangladesh An empirical equation is proposed to describe the solubility vs pressure relation for some reactive gases. The systems under consideration are ammonia/water, sulfur dioxide/water, chlorine/water, and hydrogen chloride/water. It is assumed that the reactive gases are dissolved in water by two mechanisms: one described by Henry’s law and the other by a Langmuir type equation. Out of the four systems only hydrogen chloride showed no Henry’s type of sorption, and a threshold concentration term was added to validate the model. The proposed equation fits well to the solubility/pressure data from the literature. A possible variation in the values of the empirical coefficients with the change in the water chemistry (pH, ionic strength) is also discussed. Henry’s law states that the solubility of a gas in a liquid is proportional to its equilibrium partial pressure in the gaseous phase. 1-3 The linear relationship is valid only for very dilute solutions of nonreacting systems. At higher concentrations, the solubility vs equilibrium partial pressure relationship deviates so much from linearity that practically it cannot be used in precise analysis of industrial mass transfer processes. With the growth of environmental consciousness of the people, attention has been paid to the removal of pollutants from waste gases, and absorption method appears to be an effective one. Solubility vs pressure data are a prerequisite in the design and analysis of the perfor- mance of an absorber. So far as our knowledge goes, no mathematical relation is developed yet describing the solubility of a gas in a liquid over a wide concentration range. Such a relation is necessary in modeling of absorption processes and in developing analytical meth- ods for absorber and reactor designs. Once such a relation is established, it might easily be subjected to computer processing. In the present work, we have made an attempt to propose an empirical equation describing the solubility vs partial pressure relation over a wide range of concentration. For the development of the model, we have chosen four systems: ammonia/water, chlorine/ water, sulfur dioxide/water, and hydrogen chloride/ water. All of them react with water, partially ionize and change the pH of the medium. We drew the solubility vs partial vapor pressure curves based on the literature data. 2,4 The curves look like the deformational curve of a plastic body showing some viscous-elastic properties. 5 Having this similarity in mind, we present the solubility as a sum of two components. Such an approach is known in the literature as a dual sorption model, which was developed to account for the negative deviation of Henry’s law behavior exhibited by some gases in glassy polymers. 6-8 The dual sorption model postulates that two concurrent modes of sorption are operative in the dissolution of a gas in glassy polymers. Nonlinear sorption isotherms were decomposed into a linear part that accounts for normal dissolution and a nonlinear Langmuir-type curve that accounts for immobilization of penetrant molecules at fixed sites within the medium. It was assumed that glassy polymer network contains macrovoids capable of immobilizing a portion of the sorbed molecules by entrapment or by binding at high energy sites at the molecular periphery. 9-11 In the present model also, the total solubility is resolved into two components. The one follows Henry’s law for the dissolution of the nonreactive gases. The other is described by a saturation type curve. This component is related to the immobilization of the dissolved gaseous molecules by chemical reactions with water. It is found that a well-defined quantitative relation exists between these two components. It is also shown that by variation of the water chemistry (pH, ionic strength) the reactive gas absorption might be intensified. For the systems ammonia/water, chlorine/water, and sulfur dioxide/water, it was found that three empirical constants a, b, and x e completely describe the solubility vs partial pressure curve over a wide range of concen- tration. The coefficient a accounts for the Henry-type of sorption, and b and x e account for the sorption in form of the reaction products (including ionization products). For the system hydrogen chloride gas/water, a threshold concentration term x 0 appears at zero partial pressure, and the coefficient a characterizing the Henry-type of sorption completely disappears. Thus, three empirical constants x 0 , b, and x e describe the solubility vs partial pressure relation for a highly polar gas such as hydrogen chloride. It is concluded that the approach “resolution of the solubility into two components” might serve as a good base for a mathematical description of solubility † The Department of Chemical Technology and Polymer Science, Shahjalal University of Science and Technology, 3114 Sylhet, Bangladesh. ‡ The Department of Chemistry, Shahjalal University of Science and Technology, 3114 Sylhet, Bangladesh. 2627 Ind. Eng. Chem. Res. 2000, 39, 2627-2630 10.1021/ie990558j CCC: $19.00 © 2000 American Chemical Society Published on Web 06/14/2000