Evaluation of compressibility factor and mean ionic activity coefficient for aqueous electrolyte solutions with hard sphere equations of state in the MSA model and artificial neural network method

Abstract

In this study, twenty-five hard sphere equations of state (EOSs) were applied to evaluate the compressibility factor of fifty different single electrolyte solutions (Z1). Then by using two well-known mixing rules (Barrio Solana (BS) and Santos et al. (S)) the compressibility factor (Zm) was calculated for 1086 binary mixtures of electrolytes. The obtained results were compared with the simulation data and it was concluded that the Dehghani–Modarress (DM) EOS when applied along with the Santos et al. mixing rule has the highest accuracy (ARD%Z1DM=0.124 and ARD%ZmDM−S=0.466). Also, the mean ionic activity coefficients of a number of 1:1 electrolytes were calculated by applying the hard sphere EOSs with the mixing rules based on the mean spherical approximation (MSA) model where the concentration of cation was considered a function of electrolyte concentration. By comparing these results with reported experimental data it was found that the Ree–Hoover (RH) EOS with Santos et al. mixing rule predicts the mean ionic activity coefficients with the highest accuracy (ARD%γ(RH−S)=0.206). In continuation of this study the compressibility factor and mean ionic activity coefficient were recalculated by means of the artificial neural network (ANN) method. The optimum architectures of ANN models for predicting the compressibility factor of single and binary mixtures of electrolytes as well as the mean ionic activity coefficient of 1:1 electrolytes were respectively obtained as 2:4:1, 3:3:1 and 3:5:1. The calculated error in the results showed that the mathematical models of the ANN method predicted the abovementioned parameters with better accuracy in comparison with the EOSs and MSA models (ARD%Z1ANN=0.047, ARD%ZmANN=0.022 and ARD%γ(ANN)=0.014).