Prediction of Vapor-Liquid Equilibrium of Acid-Alcohol-Ester-Water Reactive Systems from First Principles Calculations

A chemical reaction of the system (such as esterification) of the vapor-liquid equilibrium data almost rely on experimental measurements. The experiment spend too much time and money, so we are effort to establish a theoretical model to provide reliable data of chemical reaction and vapor-liquid equilibrium data.　 The study have the two parts, the first part is to use first-principles calculations to calculate chemical reaction equilibrium constant, the second part is to use liquid model and state equation　with the equilibrium constants to calculate data of four components of vapor-liquid equilibrium with reaction. In this study, we use the density functional theory calculations to get the free energy of each component, and to calculate the equilibrium constant of chemical reactions. We test three kinds of functional (such as B3LYP, wB97X, wB97XD) and four kinds of basis set (such as 6-31g(d,p), 6-31+g(d,p), 6-311+g(d,p), 6-311+g(3d2f,2pd)). We compare the chemical reaction constants from calculated and experiments and found wB97X and wB97XD with 6-311+g(d,p) and 6-311+g(3d2f,2pd) are better results, and the reaction free energy probably in error 0.5 kcal/mol, less than chemical accuracy 1kcal/mol. In the phase and reaction equilibrium of the acid-alcohol-ester-water system, we use Hayden O''Connell state equation describes the fugacity coefficient of the components, then compare the two predictive activity coefficient models, including COSMO-SAC and functional group method modified-UNIFAC. We test ten kinds of four component system, the temperature range from 303.15 K to 404.687 K, pressure from the 3.2 kPa to 109.65 kPa, and 663 data points. It’s found that the performance of two liquid models have the advantages and disadvantages, and the best choice is using wB97XD/6-311+g(d,p) and HOC respectively with the case COSMO-SAC and modified-UNIFAC. The errors are pressure percentage 6.02% and 8.69%, temperature error 3.04 degrees and 4.82 degrees, vapor phase error of acid (2.83% and 1.97 %), alcohol (3.61% and 4.84%), esters(5.12% and 4.27%), and reaction extension(3.56% and 2.68%).