Optimization and kinetic study of methyl laurate synthesis using ionic liquid [Hnmp]HSO4 as a catalyst

Methyl laurate was synthesized from lauric acid (LA) and methanol via an esterification reaction using ionic liquids (ILs) as catalysts. The efficiencies of three different catalysts, 1-methylimidazole hydrogen sulfate ([Hmim]HSO4), 1-methyl-2-pyrrolidonium hydrogen sulfate ([Hnmp]HSO4) and H2SO4, were compared. The effect of the methanol/LA molar ratio, reaction temperature, reaction time and catalyst dosage on the esterification rate of LA was investigated by single-factor experiments. Based on the single-factor experiments, the esterification of LA and methanol was optimized using response surface methodology. The results showed that the most effective catalyst was the IL [Hnmp]HSO4. The optimal conditions were as follows: [Hnmp]HSO4 dosage of 5.23%, methanol/LA molar ratio of 7.68 : 1, reaction time of 2.27 h and reaction temperature of 70°C. Under these conditions, the LA conversion of the esterification reached 98.58%. A kinetic study indicated that the esterification was a second-order reaction with an activation energy and a frequency factor of 68.45 kJ mol−1 and 1.9189 × 109 min−1, respectively. The catalytic activity of [Hnmp]HSO4 remained high after five cycles.

) and H 2 SO 4 , were compared. The effect of the methanol/LA molar ratio, reaction temperature, reaction time and catalyst dosage on the esterification rate of LA was investigated by singlefactor experiments. Based on the single-factor experiments, the esterification of LA and methanol was optimized using response surface methodology. The results showed that the most effective catalyst was the IL [Hnmp]HSO 4 . The optimal conditions were as follows: [Hnmp]HSO 4 dosage of 5.23%, methanol/LA molar ratio of 7.68 : 1, reaction time of 2.27 h and reaction temperature of 708C. Under these conditions, the LA conversion of the esterification reached 98.58%. A kinetic study indicated that the esterification was a second-order reaction with an activation energy and a frequency factor of 68.45 kJ mol 21 and 1.9189 Â 10 9 min 21 , respectively. The catalytic activity of [Hnmp]HSO 4 remained high after five cycles.
Guaranteed reagent-grade IL [Hmim]HSO 4 was purchased from Shanghai Chengjie Chemical Co., Ltd 3A molecular sieves were purchased from Guangzhou Chemical Reagent Factory. Deionized water was prepared in our laboratory. All reagents were obtained from commercial sources and used without further purification.

Preparation of Brønsted acidic IL [Hnmp]HSO 4
In the absence of solvent, 1-methyl-2-pyrrolidone was added to a 250 ml round-bottom flask. Then, a stoichiometric amount of concentrated sulfuric acid (98%) was added dropwise at 08C, and the mixture was stirred for 1 h at 08C and then stirred for 24 h at room temperature [25]. The Brønsted acidic IL [Hnmp]HSO 4 was washed repeatedly with ethyl acetate to remove non-ionic residues and dried under vacuum.

Catalytic testing and measurement of the reaction extension
Weighed amounts of LA, methanol and IL were added to a three-necked round-bottom flask equipped with a reflux condenser, a water separator and a magnetic stirring apparatus. The esterification reaction was typically carried out for a certain amount of time at the desired temperature with vigorous stirring. Then, the reaction mixture became biphasic, and the upper phase, which was mainly the desired methyl laurate, could be isolated simply by decantation; the lower phase, the viscous IL, could be reused after the water in the IL was removed. The product was directly measured by KOH-EtOH titration, and the acid value (AV) was calculated.
AVs were analysed according to AOCS Cd 3d-63 and AOCS Ca 5a-40 [26], which were used to evaluate the rate of esterification (RE). The AV (mg KOH g 21 ) of biodiesel was determined as follows: where C is the concentration of KOH solution (mol l 21 ); V 1 and V 2 are the volumes of KOH solution consumed for the titrating sample and blank test (ml), respectively; M is the weight of the sample (g); and 56.11 is the molar mass of potassium hydroxide (g mol 21 ). RE was defined as follows: where X 0 and X are the initial and equilibrium AVs of biodiesel, respectively. The initial AV (X 0 ) of LA is 280.2 + 2.0 mg KOH g 21 . 3) as follows:

Comparison of different catalysts
where x i is the independent variable coded value, X i is the independent variable real value, X 0 is the independent variable real value at the centre point and DX i is (variable at high level 2 variable at low level)/2. The independent variables and their levels and real values are presented in table 1.
The second-order model equation given by RSM was used to predict the optimum value and analyse the interaction between the variables and the yield of biodiesel, which was the response of the experimental design. The quadratic equation model was described according to the following equation: where Y is the response variable, X i is the coded level of the independent variables and the terms b 0 , b i , b ii and b ij are the regression coefficient, the linear terms, the squared terms for variable i and the interaction terms between variables i and j, respectively. X i , X ii and X ij represent the linear, quadratic and interactive terms of the coded independent variables, respectively. k is the total number of variables and is optimized in the present experiment. e is a random error. The polynomial equation visualized the relationship between the response and experimental levels of each factor and determined the optimum conditions by response surface and contour plots. The coefficient of determination (R 2 ) could be used to evaluate the accuracy and general ability of the second-order multiple regression models. The significance of the regression coefficient was checked with the value of F-test. Design-Expert software (V. 8.0.6, Stat-Ease. Inc., USA) was used to analyse the data, perform analysis of variance (ANOVA) and estimate the regression equation.

Kinetics of the esterification process
Acid esterification involves a reversible reaction between a fatty acid and a primary alcohol in the presence of an acid catalyst [29]: The general reaction rate equation is represented as follows: where C A , C B , C R and C S represent the concentrations of LA, methanol, methyl laurate and water, respectively. k 1 and k 2 are the forward and reverse reaction rate constants, respectively. a, b, r and s are the reaction orders with respect to A, B, R and S, respectively [29]. In this work, excess methanol is used to drive the reaction towards the product side. When the methanol to LA molar ratio is sufficiently high, the concentration of methanol is considered constant. Thus, this esterification can be approximately described by as an irreversible reaction. Based on the abovementioned assumptions, the IL catalysed esterification could be simplified by a pseudo-homogeneous equation with a as the reaction order as follows: The conversion of LA is assumed to be X at t ¼ 0; hence, the concentration of the reactants can be expressed as C A ¼ C A0 (1 2 X ), where C A0 is the initial concentration of LA. Equation (2.6) can be expressed as follows: Based on the abovementioned hypothesis, this esterification is a second-order reaction, so we can establish the reaction order a ¼ 2. Equation (2.7) can be expressed using an integral transformation as follows: where k and X are the reaction rate constant and the reaction conversion, respectively. They can be determined by plotting 1/((1 2 X)C A0 ) against t. In this kinetic study, the experiments were carried out under the optimal conditions with respect to a reaction time interval of 30 min (30, 60, 90, 120, 150 and 180 min) and four different temperatures (60, 65, 70 and 758C). All the experiments were repeated three times. The Arrhenius equation, which expresses the temperature dependence of the reaction rate, was used to determine the activation energy and frequency factor of the esterification process: where A is the pre-exponential factor, min 21 ; E is the activation energy, J mol 21 ; R is the gas constant (8.314 J mol 21 K 21 ); and T is the absolute temperature, K. By using the integral transformation of equation (2.9), it becomes: In a plot of lnk versus 1/T, the slope and the intercept of the regression line equal 2E/R and lnA, respectively. The activation energy and pre-exponential factor are then calculated from those values.

Recycling experiment for [Hnmp]HSO 4
The IL was recycled after withdrawing the lower layer from the separating funnel. The lower phase was a mixture of the IL, water and unreacted methanol. The water and excess methanol were removed from the mixture by rotary evaporation, and then the IL catalyst [Hnmp]HSO 4 was further washed with ethyl acetate to remove the organic ester, followed by vacuum drying for 5 h at 808C. The IL catalyst obtained was used in the next cycle.

Effect of three different catalysts on the lauric acid conversion
The efficiency of [Hnmp]HSO 4 was studied by comparison with other catalysts, such as 1-methylimidazole hydrogen sulfate salt ([Hmim]HSO 4 ) and concentrated sulfuric acid (H 2 SO 4 ). According to the literature reports [9,25,29,30], imidazolium salts are the most widely investigated ILs and have been applied in many fields [9].
[Hmim]HSO 4 is a Brønsted acid IL composed of 1-methylimidazole and concentrated sulfuric acid, and H 2 SO 4 is the most commonly used acid catalyst [29]. IL [Hnmp]HSO 4 has several advantages: (i) the preparation of [Hnmp]HSO 4 is very easy, and the cost is low [25,30]. (ii) The IL [Hnmp]HSO 4 showed good catalytic performance for the esterification of acetic acid with n-butanol. The esterification procedure could be carried out at mild temperatures, and the esters produced could be isolated conveniently in high yields and purity [25]. Therefore, the use of [Hnmp]HSO 4 will reduce production costs. The reaction without catalyst was also carried out to evaluate the conversion gain provided by the catalyst over the non-catalytic reaction performance.
rsos.royalsocietypublishing.org R. Soc. open sci. 5: 180672 As shown in figure 1, the LA conversion was only 3.25% without using a catalyst. In other words, the chemical reaction takes place very slowly in the absence of a catalyst. Three different catalysts were used separately in the esterification reaction. H 2 SO 4 had the best catalytic effect, with an LA conversion of 98.23%. The catalytic efficiency of [Hnmp]HSO 4 was close to that of the conventional catalyst H 2 SO 4 . The worst catalytic efficiency was shown by [Hmim]HSO 4 , for which the LA conversion was only 62.83%. However, H 2 SO 4 has some disadvantages, such as strong corrosivity, non-recyclability and environmental pollution. The use of [Hnmp]HSO 4 could overcome these drawbacks.
The performance of various catalysts in the esterification of LA is summarized in table 2, where the response is reported as the LA conversion. Clearly, the IL used in this study exhibited lower catalytic activity in the esterification of LA than some solid catalysts, i.e. ferric alginate [31] and CePW 12 O 40 [32]. But, the conversion was better than that achieved using montmorillonite K10 [33], MMT-NO 3 [34] and SO 2À 4 =SnO 2 -SiO 2 [35]. In this study, the IL [Hnmp]HSO 4 showed some advantages in our case. First, it showed higher conversion rates than the IL [Hmim]HSO 4 . Second, the use of 1-methyl-2-pyrrolidone as a source of cations is more economical than that of 1-methylimidazole and 1-methylpyrrolidine [30]. In addition, the recycling of [Hnmp]HSO 4 was very easy. Taking all factors into consideration, [Hnmp]HSO 4 was selected for further research.

Single-factor experiments
The effect of the [Hnmp]HSO 4 dosage, methanol/LA molar ratio, reaction temperature and reaction time on the LA conversion was analysed and is shown in figure 2. The effect of different catalyst dosages on  LA conversion was studied first. To find the optimum value of the amount of catalyst, the other three variables were fixed. According to the value in the literature [25], the temperature was set to 1008C.
To make the reaction go to completion, the reaction time was set to 4 h, and the molar ratio of methanol to acid was set to 3 : 1. Generally, the catalyst dosage should influence the reaction rate and the LA conversion. In this work, a succession of experiments were carried out using different dosages of [Hnmp]HSO 4 . As shown in figure 2, initially, the rate of the esterification reaction sharply increased with increasing [Hnmp]HSO 4 dosage, reaching 95.85% LA conversion at a 5% dosage; however, there was no significant improvement beyond 5%. Considering the preparation cost, 5% was chosen as the optimum catalyst dosage. Subsequently, the effect of different molar ratios on LA conversion was studied. The other three variables were also fixed. An excess of the reactant methanol is necessary for the esterification of LA because it can increase the rate of methanolysis. The molar ratio of methanol to LA varied from 1 : 1 to 9 : 1, and the conversions obtained are shown in figure 2. The greater the amount of methanol added, the higher the conversion of LA to methyl laurate obtained in the same reaction time. The LA conversion rapidly increased with molar ratio up to 6 : 1 and decreased thereafter. The highest conversion of LA achieved was 96.87% with a methanol to LA molar ratio of 6 : 1 in 4 h. Further increases in this molar ratio did not result in an increase in the conversion, which could be because of the excess methanol, which diluted the concentration of hydrogen ions in the reaction mixture. This result was in good agreement with the literature reported previously [36]. As a result, 6 : 1 was considered the optimum molar ratio of the reactants for this reaction.
Then, the effect of different temperatures on LA conversion was studied. Similarly, the other three variables were fixed. As shown in figure 2, the LA conversion slightly increased when the temperature was increased from 55 to 708C. The highest LA conversion of 97.11% was obtained at 708C. However, an increase in temperature from 70 to 1008C reduced LA conversion. Then, the conversion slightly changes with the temperature from 100 to 1158C. This could be because the increasing temperature increased the rate of methanol evaporation, which ultimately influenced the esterification reaction [37].  4 ] are stable at temperatures in this experiment. Furthermore, studies on pyrrolidinium-based ILs are limited and need further investigation. Therefore, to reduce the energy use of the process, 708C was selected as the optimum reaction temperature. Finally, the effect of different reaction times on LA conversion was studied. The effect of reaction time on LA conversion is shown in figure 2. The LA conversion increased noticeably up to 97.41% with increasing reaction time and remained stable thereafter. This could be because the methanolysis reaction approached equilibrium after 2 h, which explains the reason that the conversion of LA did not increase when the reaction time was prolonged further.
The LA conversion rate in this study is not significantly different from that in our previous study without removing water during esterification [23]. This may be because the esters produced during the reaction are not soluble in ILs and because ILs have strong water absorbability; i.e. they can absorb the water generated by the esterification reaction [40]. In addition, the reaction temperature was only 708C in our present study. The steam cannot escape into the water separator, and the esterification reaction can remain only near the equilibrium conversion rate.

Regression equations and analysis of variance
Factorial experimental design has been extensively used for optimization because it reduces the number of cumbersome experiments, which in turn minimizes the consumption of the laboratory prepared catalyst. Furthermore, ANOVA methods are effective in the analysis of variables. The independent variables and their levels for the Box -Behnken design are given in table 1. To verify the models, 17 sets of experiment were required, and the obtained response values are shown in table 3. Table 3 shows that there was no observable difference between actual values and predicted values. Based on the data in table 3 and the quadratic equation model in equation (2.4), the relationship between the yield of biodiesel and the process variables was expressed by the following equation: Y ¼ 95:43 þ 3:27X 1 þ 8:62X 2 þ 4:32X 3 À 1:55X 1 X 2 À 0:29X 1 X 3 À 1:63X 2 X 3 À 12:31X 2 1 À 7:16X 2 2 À 6:34X 2 3 , ð3:1Þ where X 1 , X 2 and X 3 are the coded values of the test variables amount of catalyst, methanol/LA molar ratio and reaction time, respectively, whereas Y is the response of LA conversion. In the equation, the terms X 1 , X 2 and X 3 had a synergistic effect on the response value due to the positive sign in front of those terms, while other terms had a negative sign. As shown in table 4, statistical analysis based on ANOVA was used to estimate whether the quadratic model and model terms were significant or not by p-value. At the 1% level, the model F-value of 95.40, which was much greater than the tabular F-value (3.70), implied that the model was significant. The coefficient of determination (R 2 ) of the model was 0.9919, which meant that the polynomial model was accurate and at least 99.19% of the variability in the data could be explained by the model. The value of the adjusted determination coefficient ðR 2 adj ¼ 0:9815Þ was found to be high enough to support the high significance of the model. The adequate precision of 28.266, a measure of the signalto-noise ratio, was much greater than 4, indicating adequate model discrimination. Furthermore, the relatively low value of the coefficient of variation (CV ¼ 0.90%) demonstrated that the model had good precision and that the experiments carried out were reliable. Hence, this model was extremely significant, and the p-value of the lack of fit was 0.935, which was greater than 0.10, indicating that this model was reasonable. From these statistical tests, it was found that the model was adequate for predicting the LA conversion in the range of the variables studied.   The influence of each independent factor on the models was tested by analysing the variance at its level. According to table 4, the analysis of these parameters with the p-value indicated that the X 1 , X 2 , X 3 , X 2 1 , X 2 2 and X 2 3 terms had significant effects on the LA conversion. The three-dimensional response plots and contour plots of the amount of catalyst, methanol/acid molar ratio and reaction time are presented in figures 3 and 4, respectively. The three-dimensional surfaces are a graphical illustration of the regression equation. Each contour curve represented the combinations of two test variables while maintaining the other one at a level of zero.
The variations of LA conversion with the amount of catalyst and methanol/acid molar ratio are shown in figures 3a and 4a. The conversion varied with the amount of catalyst and methanol/acid molar ratio. The variation with different amounts of catalyst was obvious. The LA conversion first increased gradually to the peak value at a low amount of catalyst and then decreased with increasing  The effect of the interaction of the two variables was also not significant with a symmetrical mound shape. The LA conversion was good at moderate reaction times and low amounts of catalyst.
Based on the comprehensive analysis of the response surface, we found that the interaction effects of [Hnmp]HSO 4 dosage, methanol/acid molar ratio and reaction time were not significant parameters affecting the conversion of LA. According to the Box-Behnken design, the optimal conditions were as follows: [Hnmp]HSO 4 dosage of 5.23%, methanol/LA molar ratio of 7.68 : 1 and reaction time of 2.27 h. The model predicted that the LA conversion could reach 98.58%.

Verification of the regression model
According to the discussion above, it is possible to obtain a high LA conversion by searching for the optimum conditions. Hence, to test and verify these operations, a [Hnmp]HSO 4 dosage of 5.23%, a methanol/LA molar ratio of 7.68 : 1, a reaction time of 2.27 h and a reaction temperature of 708C were used. The LA conversion reached 98.35%, which confirmed that this model was reasonable.

Kinetics model
In this work, the esterification reactions were carried out under the optimized conditions, and the conversion of LA at different times and temperatures is shown in figure 5.
The experiments were performed at four different temperatures to investigate the conversion of LA with respect to reaction time. Figure 5 shows the comparison of LA conversion at 60, 65, 70 and 758C. When using 5.23 wt% of [Hnmp]HSO 4 in LA and a 7.68 : 1 methanol to LA molar ratio, the conversion of LA was found to increase with the reaction time. Clearly, the LA conversion rate was remarkably fast in the initial 120 min and then slowed up gradually from 120 min to 180 min. The conversions at 120 min for the reactions conducted at 608C, 658C, 708C and 758C were 89.00%, 90.91%, 94.77% and 95.98%, respectively. On the other hand, the LA conversion rate increased considerably with an increase in reaction temperature from 608C to 758C and reached the maximum conversion at 758C. This could be because the methanolysis reaction approached equilibrium after 120 min, which explained why the conversion of LA did not increase when the reaction time was prolonged further. Based on the theory of Le Châtelier's principle, for endothermic reactions, the equilibrium shifts to the right as the temperature increases [42]. Therefore, the reaction temperature shows a positive effect on the conversion of LA. Figure 6 indicates that the relations of 1/((1 2 X )C A0 ) with time at different temperatures were straight lines, which implied that the kinetic equation of equation (2.8) for this esterification is correct. Figure 6 depicts the plots of 1/((1 2 X )C A0 ) against t, where the slopes are equal to the reaction rate constants at four temperatures. The reaction rate constants are 0.0378, 0.0.0437, 0.0775 and 0.1022 g mol 21 min 21 , corresponding to 60, 65, 70 and 758C, respectively. The rate constants increase with the increase in temperature from 608C to 758C. This is because the reaction is endothermic and the forward reaction accelerates as the temperature increases.   The influence of the temperature on the reaction rate was determined by fitting k to equation (2.10). Figure 7 shows the plot of lnk versus 1/T. The regression line was found to be linear with a high regression coefficient of 0.9516. From the slope and the intercept, the activation energy and the frequency factor are calculated to be 68.45 kJ mol 21 and 1.9189 Â 10 9 min 21 , respectively. The relation between the equation and reaction rate constant and the temperature is described as follows:   recycles, the data shown in figure 8 indicate that there is little decrease in catalytic activity. The esterification rate of LA was still above 95%, which was in accordance with the literature [23]

Conclusion
This study indicated that IL [Hnmp]HSO 4 is an effective catalyst for methyl laurate synthesis. The esterification procedure could be carried out at mild temperature, and the esters produced could be isolated conveniently. Response surface tests indicated that the optimal conditions were as follows: [Hnmp]HSO 4 dosage of 5.23%, methanol/LA molar ratio of 7.68 : 1, reaction time of 2.27 h at 708C; under these conditions, the LA conversion reached 98.35%. Moreover, a simple kinetic model was proposed, and the kinetic parameters were estimated by regression analysis. The activation energy and the frequency factor were determined to be 68.45 kJ mol 21 and 1.9198 Â 10 9 min 21 , respectively. Notably, the catalytic activity of [Hnmp]HSO 4 was still high after five cycles. Therefore, the process could become a viable alternative to the conventional process due to the uniqueness of the IL [Hnmp]HSO 4 as a green catalyst, and could provide reference for the scale-up esterification of LA.