366 JOURNAL OF COSMETIC SCIENCE EXPERIMENTAL DESIGN AND BOX–BEHNKEN MODELING The response surface methodology is used to determine the mathematical relationship between the dependent variable (response) and the independent variables and to opti- mize the response variable affected by the various process parameters. This method also describes the effect of single or multiple combinations of independent variables on the process response (57). The Box–Behnken experimental design of response surface methodology was applied to estimate the conversion of AA (%) and reaction parameters. For this purpose, the Design-Expert® Software Version 7 Trial (Stat-Ease, Inc., USA) was used in which the experimental studies will be performed for the esterification reaction of AA with BA. In the study, the effect of three process parameters on acid conversion (%) was investigated to determine the catalyst activity of ILs. Box–Behnken experimental design was made with three levels and three factors. A total of 17 experiments were designed, including five center points. Three parameters affecting the esterification reaction, acid/alcohol mole ratio (x 1 ), IL mole ratio (x 2 ), and time (x 3 ), were determined as the process parameters in the system, and these parameters were cho- sen as independent variables. Variable levels and coded values were shown in Table I. The conversion of AA (%) was selected as the dependent variable (58). The response surface function of the parameters that affect the process is expressed as follows (59) (Eq. 8): ε ) (x = ….,x + Y f x , , k 1 2 (8) where Y is the dependent variable or response, x i is the independent variable, f is the function of response, and ε is the experimental error. The second-order polynomial equation (Eq. 9) represents the response surface method as shown in the following (60): ∑ ∑β ∑∑β β β ε = + + + + = =1 =1 =2 Y x x x x i k i i i k ii i i k-1 j k ij i j 0 1 2 (9) where β 0 is the constant regression coefficient, β i , β ii , β ij are the interaction coefficients, and k is the factor number. The statistical analysis of the experimental data was carried out with the Design-Expert program. Analysis of variance (ANOVA) was used to explain the effect of variables on the mathematical model obtained in the selected study range. Table I Variable Levels and Coded Values in the Experimental Design Range and level Independent variable Symbol –1 0 1 Acid/alcohol molar ratio x 1 1.0 1.5 2 IL molar ratio x 2 0.25 0.50 0.75 Reaction time (h) x 3 4 6 8

367 SYNTHESIS OF BENZYL ACETATE RESULTS AND DISCUSSION Time, temperature, catalyst ratio, and acid/alcohol mole ratio parameters were investi- gated in detail for the esterification experiments. Besides, the experimental design of the studies was conducted to determine the effects of the interactions of the variables in the system used separately and on each other. The effect of the presence and type of ILs used as catalysts in esterification reactions on acid conversion was investigated. For this purpose, firstly, esterification of AA and BA without catalyst was carried out according to the experimental procedure described. The obtained results of the conversion of AA (%) were presented in Figure 1. The rate of catalyst-free esterification reaction is prolonged under atmospheric conditions. The reaction rate depends on the rate of catalysis of the carboxylic acid itself. For a faster reaction, a catalyst is added to the reaction medium to serve as a proton donor to the car- boxylic acid (61). For this purpose, ILs consisting of [EMIM]+, [OMIM]+, and [DEIM]+ cationic groups and [HSO 4 ]−, [BF 4 ]−, and [NTf 2 ]− anionic groups were used as catalysts. EFFECT OF EXPERIMENTAL VARIABLES For industrial esterification reactions, the kinetic study of the conversion is of great importance for process design and economy. In order to investigate the esterification reaction, kinetics of AA with BA catalyzed by [EMIM] [HSO 4 ], experiments were done with AA:BA:[EMIM] [HSO 4 ] molar ratio of 1:1:0.5 at 110°C. While only 39.59% of AA was converted to benzyl acetate at the end of 1 h, this conversion increased to 85.3% at the end of 8 h, and the system came to equilibrium at the end of this period. The effect of time on acid conversion (%) was shown in Figure 2. It can be seen that the conversion of AA will not change after this time. For this reason, 4, 6, and 8 h, which are the critical stages of the conversion, were chosen as the reaction time in the optimization experiments performed in the later stages of the study. Generally, in esterification reactions, high temperature increases the reaction rate and acid conversion (62). Therefore, three different temperatures were selected to find the 2 1.5 1 0 20 40 60 80 100 4 6 8 Reaction time (h) Figure 1. Conversion of acid (%) for acetic acid and benzyl alcohol esterification without catalyst at 110°C. Conversion of acid (%)