Analysis of Sensitivity of Equilibrium Constant to Reaction Conditions for Esterification of Fatty Acids with Alcohols Saeikh Z. Hassan and Madhu Vinjamur* Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India ABSTRACT: The equilibrium constant (K eq ) depends on temperature only, but reported measurements for esterification reactions show that it also depends on reactant concentration and amount of catalyst. In this work, analysis of sensitivity of K eq to errors in equilibrium composition of esterification reactions at different reaction conditions is presented. Rigorous error and Taguchi analyses showed that K eq is indeed a function of temperature only and not of molar ratio (MR) of the reactants and catalyst loading; reported dependency of K eq on reactants concentrations and catalyst loadings is due to errors in analysis of equilibrium composition. Sensitivity of K eq to these errors depends strongly on molar ratio (MR), and calculations show that K eq is least sensitive to error at 1.5 MR. However, phase separation of the reaction mixture is possible at 1.5 MR which can cause errors in measured equilibrium composition. K eq of esterification reactions should be obtained through kinetic data fitting to the rate model. For sulfuric acid-catalyzed esterification of oleic acid with methanol, a single K eq value for each reaction temperature is obtained through kinetics data fitting as 1.53 (±0.05), 1.67 (±0.04), and 1.91 (±0.06) at 313, 323, and 338 K, respectively. Equilibrium compositions are calculated reasonably well with these K eq values. 1. INTRODUCTION The basic criterion for a reaction to be at equilibrium is that the change in Gibbs free energy is zero (i.e., ΔG = 0) and thus, equilibrium constant (K eq ) is related to standard Gibbs free energy (ΔG 0 ) by the equation ΔG 0 = -RT ln K eq . 1 For liquid phase reactions, the thermodynamic K eq is dependent on temperature only and independent of pressure effect except for high pressures. 1,2 Temperature dependence of K eq is expressed by the van’t Hoff isochore assuming that the standard change in enthalpy (ΔH 0 ) is constant for a small range of temperatures. 2 For esterification reactions, determination of K eq from ΔG 0 has large uncertainty and nonreliability because standard Gibbs energy of formation (G f 0 ) for each reacting component is high, and the difference between the free energies of the products and reactants (i.e., ΔG 0 ) is small. Hence, small errors in measured G f 0 results in large deviations in K eq . 3 Many researchers prefer to determine K eq at different temperatures from experimental data at equilibrium or from fitting kinetics data to a reaction rate model. Thermodynamic K eq , when estimated from thermodynamic properties of reacting components, depends on temperature only but the experimental values of K eq are reported to depend also on the composition of the reaction mixture and on the amount of catalyst. 4-7 Homogeneous catalysts HCl, HClO 4 , HNO 3 , and H 2 SO 4 , each affect K eq differently in similar reaction mixtures, and an increase in K eq with catalyst concentration is found. 6 K eq at 298 K varied from 1.91 to 4.58 over the range of reaction compositions studied using acid-ion-exchange resin. 6 The equilibrium constant of the esterification of ethanol with acetic acid varied between 2.47 and 4.74, and the dependency on the molar ratio of the reactants is reported. 8 Othmer and Rao 9 showed that catalyst concentration and reaction temperature have no significant influence on the equilibrium constant of sulfuric acid-catalyzed esterification of oleic acid with butanol. There was no significant influence of temperature because of the low endothermicity of the reaction. However, the equilibrium constant decreased with an increase in molar ratio (alcohol to fatty acid) as reported by Othmer and Rao 9 and Lee et al. 10 Usually, concentration-based K eq (assuming ideal solution) is considered to depend on many factors, whereas activity-based K eq is considered to depend on temperature only. However, Pereira et al. 11 reported the variation in activity-based K eq of esterification of lactic acid with ethanol from 3.813 to 4.637 for the same reaction temperature 323.15 K with di fferent concentrations of initial reactants and catalyst. Pereira et al. 11 attributed this variation in K eq to experimental errors as well as deficiencies in the thermodynamic models used to calculate the activity coefficients. Therefore, in order to minimize the error in equilibrium compositions, Pereira et al. 11 have estimated a unique K eq for each temperature by applying an iterative procedure and using the experimentally measured equilibrium compositions. The estimated K eq have been applied successfully in estimation of equilibrium compositions. From the foregoing, it can be asked if experimentally determined K eq depends on reaction conditions other than temperature or the reported dependency on the conditions is due to some other reasons such as error in composition analysis. The accuracy in analysis is always a matter of concern in experimental study and use of even high precision analytical tools for quantitative measurements of reacting agents is prone to errors. Martin 12 discussed for reactions type R ↔ P and R + S ↔ P that show how error in terminal absorbance (using spectropho- tometer) can cause an inconsistency of calculated K eq . Yalcinyuva et al. 13 and Jong et al. 14 reported the phase splitting behavior in esterification of myristic acid with isopropyl alcohol and n-propanol. Since phase splitting causes difficulty in Received: July 15, 2012 Revised: October 21, 2012 Accepted: December 19, 2012 Published: December 19, 2012 Article pubs.acs.org/IECR © 2012 American Chemical Society 1205 dx.doi.org/10.1021/ie301881g | Ind. Eng. Chem. Res. 2013, 52, 1205-1215