Adsorption and Kinetic Parameters for Synthesis of Methyl Nonanoate

Oct 2, 2012 - Energy Research Centre, Panjab University, Chandigarh, India ... Activation energy and pre-exponential factor of the reaction were found...
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Adsorption and Kinetic Parameters for Synthesis of Methyl Nonanoate over Heterogeneous Catalysts Mamta Sharma,† Ravinder Kumar Wanchoo,†,‡ and Amrit Pal Toor‡,* †

Energy Research Centre, Panjab University, Chandigarh, India University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh, India

‡

ABSTRACT: Methyl nonanoate was synthesized in a batch reactor by esterification of nonanoic acid with methanol catalyzed by the cation exchange resins, Dowex 50Wx2, Amberlyst 35, and Amberlyst 15. The effect of various parameters such as speed of agitation, catalyst loading, molar ratio, and reaction temperature on degree of conversion has been reported. The conversion of nonanoic acid to methyl nonanoate was found to increase with an increase in temperature in the range of 303.15−333.15 K and the increase was appreciable with an excess use of methanol in the reaction mixture. Nonideality of the liquid phase was taken into account by using activities instead of concentration. The activity coefficients were calculated using the UNIFAC group contribution method. The possible mechanism of reaction was mathematically treated using theories of the Eley−Rideal model based on inhibition by water and methanol on the Amberlyst 15. The reaction rate constants and the adsorption coefficients for methanol and water were determined from the experimental data established at three different temperatures for the effect of initial concentration of acid and alcohol. The kinetics reported in this study was obtained under conditions free of both external and internal mass transfer resistance. Activation energy and pre-exponential factor of the reaction were found to be 47.6 kJ mol−1 and 3.2 × 104 L2 g−1 mol−1 h−1, respectively. over heterogeneous catalyst, Amberlyst 36, has been reported,12 where it was concluded that the magnitude of adsorption strengths follows the order of water > methanol > acetic acid > methyl acetate and that the ER and the LHHW model determine the kinetic parameters equally well. The investigation of the kinetics for the esterification reaction on the basis of experimental data obtained in the batch reactor has been widely reported in the literature. Despite many reports on the esterification with heterogeneous catalysts, however, a few kinetic studies consider the effect of adsorption, desorption, reaction, and diffusion in the heterogeneous system, unlikely to homogeneous catalytic system. Therefore, the reaction mechanisms and rate expressions are more complex than those in the case of the homogeneous system. Typical and widely used kinetic models in heterogeneous catalytic systems are the pseudo-homogeneous (PH) model,13−15 Langmuir−Hinshelwood (LH) model, and Eley− Rideal (ER) model.16−18 The PH model is similar to the power law model for homogeneous reactions where adsorption and desorption of all components are negligible. The LH model represents the rate-determining step being the reaction of both the reactants (e.g., acid and alcohol in the esterification reaction) adsorbed on the catalyst surface, whereas the ER model indicates that the rate-determining step is the reaction between one reactant adsorbed on the catalyst surface and its counterpart reactant in the bulk region. Sanz et al.19 carried out the kinetic study for the esterification of lactic acid with methanol over Amberlyst 15, where the kinetic behavior of heterogeneous

1. INTRODUCTION Esterification of carboxylic acids with alcohols represents wellknown liquid-phase reactions of considerable industrial interest due to the importance of organic ester products. 1−10 Esterification reactions can proceed with or without a catalyst but in the absence of a catalyst, the reaction is, however, extremely slow, since its rate depends on the autoprotolysis of the carboxylic acid. Therefore, esterification is carried out in the presence of an acid catalyst, which acts as a proton donor to the carboxylic acid. For this reason, both homogeneous and heterogeneous catalysts have been used to accelerate the reaction rate. While the mineral acids can be given as the example of the homogeneous catalyst, a cation-exchange resin in the acid form can serve as a heterogeneous catalyst. Despite a strong catalytic effect, the use of homogeneous catalysts such as sulfuric acid suffers from drawbacks, such as the existence of side reactions, equipment corrosion, and having to deal with acid-containing waste.8−10 The replacement of homogeneous catalysts by heterogeneous catalysts is gaining importance because heterogeneous catalysts have good physical and chemical properties, show no corrosion, and have high selectivity and thermal stability.8 Many heterogeneous catalysts reported in literature for the esterification reaction includes ion exchange resins, H-ZSM5, niobic acids, hetropolyacids, and zeolites-T membrane.8,9 The effects of many ion exchange resins were investigated in esterification reactions. For example; The esterification of acrylic acid with propylene glycol10 was investigated in the presence of Amberlyst 15. Miller et al11 studied the kinetics of mixed succinic acid/acetic acid with Amberlyst 70 ion-exchange resin as catalyst and investigated batch isothermal reactions at different ethanol/ acid molar ratios (1:1−27:1), temperatures (343−393 K) and catalyst loadings (1.0−9.3 wt % of solution). Meanwhile, the research on the esterification of acetic acid with methyl alcohol © 2012 American Chemical Society

Received: Revised: Accepted: Published: 14367

June 22, 2012 October 1, 2012 October 2, 2012 October 2, 2012 dx.doi.org/10.1021/ie301661n | Ind. Eng. Chem. Res. 2012, 51, 14367−14375

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Scheme 1. A Systematic Reaction Scheme for Esterification of Nonanoic Acid with Methanol

Table 1. Physiochemical Characteristics of Catalysta

Dowex50 Wx2b Amberlyst 15 (wet)c Amberlyst 35 (wet)c

matrix type

ionic form

total exchange capacity (a)meq/mL (wet)

cross-linkage (%DVB)

max.Operating temp (K)

surface area (m2 g−1)

Styrene DVB Styrene DVB Styrene DVB

H+

0.6

78

423

6.940

H+

1.9

20

393

H+

1.9

20

423

particle size (mm)

total pore vol (mL/g)

average pore diameter (A)

0.4 − 1.0

1.48 × 10−2

85.34

45

0.600−0.850

0.40

300

45

0.700−0.950

0.35

300

a Note: Figures are approximate, and vary somewhat with manufacturers. bDow Chemical Co., Michigan. cRohm and Hass Co., Washington Square, Philadelphia, PA.

ratio on degree of conversion. (iii) development of a kinetic model, based on assumption of strong resin water affinity, and the nonideality of the system.

esterification and the correlation of experimental data with the PH, LH, and ER models were investigated. The behavior of liquid mixtures in the liquid phase reactions may deviate markedly from that of the ideal solution. The activity coefficients were used in the model to account for the nonideal mixing behavior of the bulk liquid phase, and the activity coefficients were predicted using the UNIFAC group contribution method.20−22 Nonanoic acid can be esterified with alcohols such as methanol, ethanol, and propanol. A systematic reaction scheme for esterification of nonanoic acid with methanol is given in Scheme 1 The ester of nonanoic acid with methanol, namely, methyl nonanoate finds wide industrial application. It is used as plasticizers and lubricating oils. It is used in modifying alkyd resins to prevent discolour and to keep flexibility and resistance to aging since saturated nonanoic acid will not be oxidized. It is known that C8−C12 straight and saturated chain fatty acids esters are capable of removing the waxy cuticle of the broadleaf or weed, causing the tissue death. Methyl nonanoate is used as an active ingredient of environment friendly herbicides and as a chemical intermediate for synthetic flavours, cosmetics, pharmaceuticals and corrosion inhibitors. The present work is directed toward understanding the chemistry of the reaction and obtaining a suitable rate expression and checking its validity under different experimental conditions. To the best of our knowledge no information is available in the open literature describing the kinetics of nonanoic esterification with methanol in the presence of ion-exchange resin catalysts. Appendino et al.23 have carried out the chemo-selective esterification of nonanoic acid with vannilic alcohol in order to prepare the esters of phenolic acids with the use of vannilic nonanoate esters. Otherwise, most of the literature shows that esterification of nonanoic acids is carried out with the help of biocatalysts, a specific type of enzymes, that is, lipase, etc. In the case of biocatalysts esterification the rate of conversion is very slow as it takes 2 to 3 days to reach the equilibrium.24−27 The kinetics of ion-exchange resin-catalyzed esterification, with nonanoic acid and methanol as reactants to produce methyl nonanoate, is reported in the present work. The study includes (i) the use of Amberlyst 15, Amberlyst 35, and Dowex 50WX2 containing sulfonic acid groups, as an heterogeneous catalyst due to their high catalytic activity. (ii) study of the effect of temperature, catalyst loading, and reactant

2. EXPERIMENTAL SECTION 2.1. Materials. Nonanoic acid (purity >99.5), methanol (purity >99), and 1,4-dioxane were purchased from Merck and used without further purification. The purity of all chemicals was checked by gas chromatography. Heterogeneous catalysts Amberlyst 15 (wet) and Amberlyst 35 (wet) were obtained from Rohm and Hass, and Dowex 50Wx2 was obtained from Dow Ltd. The catalyst was initially washed with distilled water four to five times and was dried at ambient conditions for 4−5 h. Further the catalyst was washed by dipping in 0.1 N hydrochloric acid solutions for half an hour. This solution was then filtered to separate the catalyst and dried at atmospheric conditions for about 48 h. The characteristics of the catalysts used in the present work are listed in Table 1. 2.2. Apparatus and Procedure. The batch experiments were carried out in a 500 mL double jacketed three necked glass reactor equipped with a reflux condenser in the temperature range of 303 to 333 K. The reaction temperature was maintained using a thermostatic water bath (Julabo F20). The temperature was maintained within an accuracy of ±0.1 °C. The reaction mixture was continuously stirred with an overhead stirrer fitted with a motor and a speed regulator. The nonanoic acid and the catalyst were first charged into the reactor through a peephole on the lid and heated to the desired temperature. Then methanol at the same temperature was fed into the reactor. The time at which the methanol was added was considered as zero time or the starting point of the reaction. Samples of 1 mL were taken every 15 min for the first hour, and 30 min for the next 2−6 h for analysis. The reaction parameters are given in Table 2. All experiments were performed at least three times in order to ensure reproducible results. Experimental setup is shown in Figure 1. 2.3. Analysis. For kinetic measurements, samples were taken periodically, and the amount of nonanoic acid was determined by titration with a standard sodium hydroxide solution of normality 0.5 using phenolphthalein as an indicator. Parallel tests indicated that the average error of the titration method was less than 2%. The samples were also analyzed by a gas chromatograph (Nucon 5765) equipped with a fused silica capillary column 30 m × 0.25 14368

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Table 2. Reaction Parameters sample no.

temperature (K)

1

303 to 333

2

333

3

333

molar ratio 1:10 (acid to alcohol) 1:10 (acid to alcohol) 1:1 to 1:20 (acid to alcohol)

catalyst loading

RPM

65.87 g/L (8% w/v)

500

32.93 g/L to 81.20 g/L (4% to 11%) 65.87 g/L (8% w/v)

500 500

mm i.d. × 0.25 μm film thickness, flame ionization detector and a thermal conductivity detector by matching the retention time of the reaction product to the retention time of methyl nonanoate. Nitrogen with a purity of 99.99% was used as the carrier gas.

Figure 2. Fractional conversion vs time for different catalysts: (○) Amberlyst 15, (■) Dowex 50WX2, (▲) Amberlyst 35, (×) without catalyst, (●) H2SO4. Catalyst loading for all reactions, 9%; RPM, 500; molar ratio, 1:10; temperature, 333.15 K.

3. RESULT AND DISCUSSION A parametric study was carried out to establish the optimum parameters for this reaction. The parameters included: type of catalysts, molar ratio of nonanoic acid to methanol, catalyst loading and reaction temperature. The presence or absence of mass transfer effect was established by carrying out experiments at different rpm and different particle size of the catalyst. 3.1. Comparison of Homogeneous and Heterogeneous Catalysts. Batch experiments on homogeneous (sulfuric acid) and heterogeneous (Amberlyst 15, Amberlyst 35, Dowex 50Wx2) catalysts were conducted for the esterification of nonanoic acid with methanol at 333 K temperature, for 9% catalyst loading and 1:10 (acid/alcohol) molar ratio. The observed conversion for each catalyst is shown in Figure 2. From Figure 2 it is observed that 86% conversion is achieved in 30 min using H2SO4 as catalyst because it releases two times higher H+ ions. Because of the disadvantages of H2SO4, the use of ion exchange resins as catalyst is preferred over mineral acid. Experiments were carried out using three heterogeneous catalysts (Amberlyst 15, Amberlyst 35, and Dowex 50 WX2) at 333 K using 9% (w/v) at 500 rpm. From Figure 2 it is observed

that Amberlyst 15 and Dowex 50 WX2 yield nearly same conversion of nonanoic acid at a reaction time of 360 min in comparison to Amberlyst 35. Keeping in view the higher cost of Dowex 50WX2 in comparison to Amberlyst 15, in all subsequent experiments Amberlyst 15 was used as a catalyst. 3.2. Effect of External Mass Transfer. To determine the optimum agitation speed, four runs were carried out at stirrer speed of 300, 500, 600, and 800 rpm using acid to alcohol molar ratio of 1:10, temperature of 333.15 K, Amberlyst 15 as catalyst with catalyst loading of 8%, for each run. As shown in Figure 3 there was a slight increase in maximum percentage conversion for each run when the stirrer speed was increased from 300 to 500 rpm but above 500 rpm the differences in maximum percentage conversion for each run can be considered to be negligible. This indicates the absence of external mass transfer limitations above 500 rpm. Therefore, all experiments were conducted at 500 rpm so as to neglect the effect of external mass transfer and to avoid the breakage of catalyst at higher rpm. 3.3. Influence of Internal Mass Transfer. To access the activation sites inside the catalyst particle, the reactants have to

Figure 1. Experimental setup. 14369

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Figure 3. Plot of percentage maximum conversion for each run up to 360 min vs RPM (revolutions per minute) at 333.15 K, 1:10 molar ratio, and catalyst loading of 8% (w/v).

Figure 4. Fractional conversion vs time (min) for different particle sizes at 333.15 K, 1:10 molar ratio, and catalyst loading of 8% (w/v), (□) 600−850 μm, (◆) 250−300 μm.

diffuse into the particle, be adsorbed and react; then the products have to be desorbed and diffuse out of the particle. Setting up a model to describe the internal mass transfer effect is not the focus of this work. Instead, the major interest is to study the macroscopic reaction kinetics using the catalyst in its commercially available form. Nevertheless, the influence of the internal mass transfer within the catalyst particle can be discussed qualitatively as follows. To evaluate the effect of internal diffusion on the cation-exchange resins by using the Weisz−Prater criteria21 eq 1 was used. ϕ=

r o2k 9De

Figure 5. Fractional conversion vs time for different catalyst loading: (◆) 4%, () 5%, (▲) 6%, (×) 7%, (■) 8%, (●) 9%, (+) 10%; molar ratio, 1:10; temperature, 333.15 K; RPM, 500.

(1)

where ro and De denote the radius of catalyst particle and the effective diffusion coefficient, respectively; k is the reaction rate constant, and φ is the Thiele modulus. If the calculated value of φ is less than 1, the internal diffusion could be neglected. The effective diffusion coefficient was defined as follows: εD De = A (2) τ where DA is the liquid phase diffusion coefficient, τ is the particle tortuosity, and ε is the porosity. For most resin catalysts, the values of ε/τ are between 0.25 and 0.50.28 For the present work the value of ε/τ for Amberlyst 15 was taken as 0.50.13 The liquid phase diffusion coefficient DA was evaluated using the Wilke− Chang equation.21 The liquid phase diffusion coefficient DA of nonanoic acid in methanol thus obtained was 1.063 × 10−5 cm2/ s. Using the Weisz-pourier criteria, the value of φ was estimated as 2.66 × 10−6 and the value of effectiveness factor η was found to be ∼1; hence, no pore diffusion limitation was detected. The hypothesis is further supported by the observed fractional conversion for two different sizes of catalyst particles as shown in Figure 4. 3.4. Effect of Catalyst Loading. Experiments were carried out at 4% (32.93 g/L) to 11% (81.20 g/L) (weight of the catalyst/total volume of the mixture) at a temperature 333.15 K, molar ratio 1:10 (acid/alcohol) and stirrer speed of 500 rpm. The conversion of nonanoic acid as a function of time with different catalyst loadings is shown in Figure 5. As it can be seen from this Figure, with increasing catalyst loading the conversion of nonanoic acid increases due to the increase in the total number of available active catalytic sites for the reaction. From Figure 6 it is evident that the percent conversion of nonanoic acid to methyl nonanoate becomes almost constant as the catalyst loading is increased after 8% (65.87 g/L). The optimum catalyst loading was taken as 8% (65.87 g/L).

Figure 6. Plot of percentage maximum conversion obtained for each catalyst loading up to 360 min vs catalyst amount: molar ratio, 1:10; temperature, 333.15 K; RPM, 500.

3.5. Effect of Temperature. To investigate the effect of temperature on the esterification rate constant, the reactions were carried out in the temperature range of 303.15 to 333.15 K while keeping the molar ratio of acid to alcohol at 1:10 and catalyst loading of 8% (w/v). The ester conversion was found to increase with an increase in reaction temperature. Increasing the temperature is apparently favorable for the acceleration of the forward reaction. The observed value of fractional conversion at 360 min is about four times higher for the experiments at 333.15 K than the one for experiments at 303.15 K as shown in Figure 7. 3.6. Effect of Feed Molar Ratio. Esterification of nonanoic acid with methanol is an equilibrium limited chemical reaction and the position of equilibrium controls the amount of ester formed: the esterification reaction is generally slowed down by the reversible reaction so use of an excess of methanol drives the equilibrium toward the formation of an ester and enhances the forward reaction. The molar ratio of methanol to nonanoic acid was varied from 1:1 to 20:1 at a reaction temperature 333.15 K, 14370

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reactants. A general kinetic expression for all the three models is written as − ri =

kwcat(CAC B − (C EC W /Ke)) (1 + KACA + KBC B + KEC E + KW C W )n

(3)

where ri is the reaction rate in terms of concentration of i component, A, B, E, and W are nonanoic acid, methanol, methyl nonanoat, and water, respectively; K is the adsorption constant and Ke is equilibrium reaction rate constant; k is the rate constant and wcat is the weight of catalyst in g/L, with n = 0 for the PH model, 1 for the ER model, and 2 for the LHHW model. Reactions over heterogeneous catalysts are more complex than a normal elementary reaction mechanism and are not so easily reducible to a simple pseudohomogeneous model. Hence when modeling the reaction for a liquid system where the mixture is nonideal, the correction must be made to the concentration to indicate the departure from the ideal case. The nonideality spawns from differences in interactions between the molecules, as well as size and shape of differences in the molecules participating in the liquid mixture. Nonideality of the mixture needs to be approximated in the rate equation. Generally the rate eq 3 is then written in the form activity of each component (ai = γixi = γi(Ci/Ct)),29 ai is activity of each component, γi is activity coefficient, xi is mole fraction of each component, ci is concentration of each component, and ct is total concentration of reaction mixture which is kept constant. First the concentration needs to be written in terms of activity. Hence eq 3 becomes:

Figure 7. Fractional conversion vs time at different reaction temperature: (◆) 303.15 K, (■) 318.15K, (▲) 323.15K, (×) 328.15K, (●) 333.15; molar ratio, 1:10; catalyst loading, 8%; RPM, 500.

8% (w/v) catalyst loading, and stirrer speed of 500 rpm. Acid conversion increases with the increase in the amount of methanol under otherwise similar conditions as is evident from Figure 8. Beyond 1:10 there is not a significant effect on the conversion of acid and it is almost independent of mole ratio as evident from Figure 9.

− ri =

k f wcat(aA,aB − (aEaW /Ke)) (1 + KAaA + KBaB + KEaE + KW aW )n

(4)

where kf = (kCt )/(γAγB) is a forward reaction rate constant. Activities of the chemical compounds used in this study were calculated using the UNIFAC group contribution method (Table 3). The UNIFAC group contribution method allows 2

Figure 8. Fractional conversion vs time for different molar ratio: (■) 1:20, (▲)1:15, (+) 1:10, (●) 1:5, (×) 1:1; temperature, 333.15 K; catalyst loading, 8%; RPM, 500.

Table 3. UNIFAC Activity Coefficients Parameters for a System component

concentration, Ci, (mol/L)

activity coefficient, γ

nonanoic acid methanol methyl nonanoate water

1.72 1.64 0 0

1.01 1.26 0.82 3.52

the prediction of liquid phase activity coefficients γ as a function of temperature and composition. The activity coefficient is expresses as the sum of a combinatorial part (C) and a residual part (R).30 The values can be derived from the quantities that have been tabulated by Fredenslund.31−33 The relative van der Waals volume (ri) and surface area (qi) values of molecule i can be calculated from the known van der Waals properties Rk and Qk of the structural groups k. 4.1. Prediction of Rate and Adsorption Constants. Experiments were carried out in the presence of Amberlyst 15 catalyst at three different temperatures 321, 326, and 333 K using 1,4-dioxane as solvent. Influence of external or internal diffusion was neglected on the basis of studies on mass transfer in sections 3.2 and 3.3. An initial rate of reaction (rAo) defined up to conversion of 10% was observed using different concentrations of nonanoic acid, methanol, and water. The concentrations were expressed in terms of activities so as to account the nonideal behavior of the reaction mixtures. As seen in Figure 10, that initial

Figure 9. Plot of percentage maximum conversion obtained for each molar ratio up to 360 min vs molar ratio at temperature of 333.15 K, RPM of 500, and catalyst loading of 8%.

4. KINETIC MODELING The esterification reaction catalyzed by heterogeneous catalysts can be described using different kinetic models such as PH, LHHW, and ER, etc. based on different approaches. Although the PH model does not take into account the adsorption effect of species in the reactant medium, the LHHW and ER models both include the adsorption effects of species in the reactant medium. The basic assumption of the LHHW model is that all reactants are adsorbed on the catalyst surface. The ER model assumes that the reaction takes place between adsorbed and nonadsorbed 14371

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protonated form. This hypothesis is justified by the high methanol molar excess used in most of the experimental runs (molar ratio of methanol/nonanoic acid, >10:1) by considering that, initially, water is not present in the reacting medium. Methanol will be preferably adsorbed with respect to acid. (ii) All the components (acid, water, and methyl ester) undergo a protonic exchange equilibrium with the protonated methanol adsorbed onto the active sites. (iii) The reactive event occurs through an Eley−Rideal mechanism between a protonated acid and the methanol coming from the liquid phase absorbed inside the resin particles. The stoichiometry and corresponding reaction rate expression is in the form of the Eley−Rideal model with the surface reaction as the rate determining step; after excluding the adsorption effects of nonanoic acid and methyl nonanoate eq 4 can be written as

Figure 10. Initial rate of reaction (−rAo) vs activity of acid (aAo) at three different temperatures: (◊) 333 K, (■) 326 K, (▲) 321 K; catalyst loading, 8% (w/v); RPM, 500.

reaction rate is a linear function of initial activity of acid. Figure 11, shows that the initial reaction rate, increases with increasing

−ri =

k f wcat (aA aB − (aEaW /Ke)) 1 + KBaB + KW aW

(5)

where kf is the forward reaction rate constant in mol·L/(g min) and is given as ki = Kio exp (−Ei/(RT)), wcat is weight of catalyst in g/L and Ke is the esterification reaction equilibrium constant based on activity catalyzed by Amberlyst 15. In eq 5, activity rather than concentration is used in the rate expression, because it results in improvement in the predictions of the models fitted against the measured kinetic data. Using eq 5, the initial reaction rate, with no product present, can be defined as −rAo = Figure 11. Initial rate of reaction (−rAo) vs activity of alcohol (aBo) at three different temperatures: (◆) 333 K, (■) 326 K, (▲)321 K, catalyst loading, 8% (w/v); RPM, 500.

(k f wcataB, o) (1 + KBaB,o)

aA,o

(6)

Rearranging eq 6 as aA,oaB,o

alcohol activity whereas at high alcohol activity, the rate is essentially independent of the alcohol activity, hence we can conclude that the initial reaction rate is a nonlinear function of initial activity of methanol. Figure 12 shows that the initial rate is

−rAo

=

⎛ K ⎞ 1 + ⎜ B ⎟aB,o k f wcat ⎝ k f wcat ⎠

(7)

A plot of (aA,oaB,o)/−rAo versus aB,o results in a straight line with the slope KB/(kfwcat) and intercept 1/(kfwcat) as shown in Figure 13.

Figure 12. Initial rate of reaction (−rAo) vs activity of water (awo) at three different temperatures: (◆) 333 K, (■) 326 K, (▲)321 K; molar ratio, 1:10 acid/alcohol; catalyst loading, 8% (w/v); RPM, 500.

Figure 13. (aA,oaB,o)/−rAo versus aB,o at three different temperatures: (◆) 333 K, (■) 326 K, (▲)321 K; catalyst loading, 8% (w/v); RPM, 500.

a nonlinear function of activity of water and decreases with an increase in the activity of water, hence confirming the inhibiting effect of the water concentration as the reaction proceeds. From Figures 10 to 12 we conclude that the adsorption effect of nonanoic acid can be neglected as it is a linear function of activity, but a significant adsorption effect of methanol and water is present. The adsorption of solvent (dioxane) and ester were reported to be negligible in the literature.2,19,35 This analysis demonstrates the Eley−Rideal model based on these hypotheses: (i) All the active sites of the resin are occupied and, in particular, the major part of them is occupied by the methanol in a

To evaluate the inhibiting effect of activity of water, eq 5, with no ester being present initially, can be written as −rAo =

(k f wcataA,oaB,o) (1 + KBaB,o + KW aW,o)

(8)

from which the following equation can be obtained: aA,oaB,o −rAo 14372

=

1 + KBaB,o k f wcat

⎛ K ⎞ + ⎜ W ⎟aW,o ⎝ k f wcat ⎠

(9)

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A plot of (aA,oaB,o)/−rAo versus aw,o results in a straight line with the slope of KW/(kfwcat) and intercept (1 + KBaB,o)/(kfwcat) as shown in Figure 14.

Figure 16. Plot of ln KB, ln KW vs 1/T for catalyst loading of 8% (w/v) and RPM of 500.

Figure 14. (aA,oaB,o)/−rAo versus aw,o for alcohol at three different temperatures: (◆) 333 K, (■) 326 K, (▲) 321 K; catalyst loading, 8% w/v; RPM, 500.

From Figures 13 and 14 the slopes and intercept of the linear equation were obtained and the corresponding rate constant and adsorption parameters were calculated by the method of averages (Alime et al.2), the values of which are tabulated at different temperatures in Table 4.

321 326 333

kf (L2/(mol·g·h)) −4

5.4 × 10 6.9 × 10−4 1.02 × 10−3

Kalcohol (L/mol)

KWater (L/mol)

0.53 0.40 0.25

2.68 1.90 1.18

4.2. Temperature Dependency. The effect of temperature on the rate of reaction was studied by conducting the reactions at different temperatures from 321 to 333 K under the conditions of catalyst loading of 8% (w/v) and RPM of 500. The temperature dependency of the rate constant is expressed by the Arrhenius law: ki = kioexp(−Ei / RT )

(11)

⎡ 6670.2 ⎤ KB (L/mol) = exp⎢ − 21.39⎥ ⎣ T ⎦

(12)

⎡ 7304 ⎤ KW (L/mol) = exp⎢ − 21.76⎥ ⎣ T ⎦

(13)

4.3. Chemical Equilibrium Constant. In principle, the chemical equilibrium constant can be determined either by the thermodynamic data (the enthalpies and free energies of formation of all components, ΔHf and ΔGf) or by long-time experiments. However, the estimation based on the thermodynamic data is usually much less reliable because a small deviation in ΔHf and ΔGf can lead to a relatively large error in the reaction enthalpy ΔHr and the reaction free energy ΔGr, and thus the equilibrium constant Ke.33 Moreover, for the considered reaction system, the necessary thermodynamic data of methyl nonanoate are not available; therefore, the equilibrium constant is determined experimentally. The equilibrium constant in terms of activity coefficients can be calculated from the following equation:

Table 4. Kinetics and Adsorption Parameters temp (K)

⎡ 5689.2 ⎤ k f (L2/(g dry resin) mol h) = exp⎢10.39 − ⎥ ⎣ T ⎦

Ke = KeCKeγ

(14)

where KeC is the constant based on concentration, Keγ is constant based on activity coefficients, and constant KC was computed using the equilibrium concentrations of the individual components of the reaction mixture. The temperature dependence of Ke can be found by the plot of ln Ke versus reciprocal temperature (1/T) as shown in Figure 17.

(10)

Where i = f, B, and W, Ei is activation energy, and koi is the frequency factor. From eq 10, a plot of ln kf, ln KB and ln KW versus 1/T, gives a straight line with the slope of (E/R), as shown in Figures 15 and 16. The activation energy was found to be 47.5 kJ mol−1 in the presence of Amberlyst 15 ion-exchange resin. By applying the Arrhenius equation to the values of slope and intercepts of graphs 15 and 16 the temperature dependency of the constants can be correlated by the following equations:

⎡ −10.861 ⎤ ln Ke = ⎢ + 33.77⎥ ⎣ T ⎦

(15)

4.4. Reaction Enthalpy, Entropy, and Free Energy. If a constant reaction enthalpy is assumed within the operating temperature range, the reaction enthalpy ΔHr and entropy ΔSr

Figure 15. Plot of ln kf vs 1/T for catalyst loading of 8% (w/v) and RPM of 500.

Figure 17. ln Ke vs 1/T for catalyst loading of 8% (w/v) and RPM of 500. 14373

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coefficients reasonably well. On the basis of an adsorption study, the Eley−Rideal (ER) was developed to interpret the obtained kinetic data. Besides proving the adequacy of the model tried, error values obtained also proved the success of the UNIFAC model in predicting the activity coefficients of the components present in the system. The activation energy and preexponential factor for the forward reaction were found to be 47.6 kJ·mol−1 and 3.2 × 104 L2 g−1 mol−1 h−1, respectively, for the ER model catalyzed by Amberlyst 15.

can be estimated by setting the experimental value of eq 15 in to eq 16: ⎡ −ΔHr ΔSr ⎤ ln Ke = ⎢ + ⎥ ⎣ RT R ⎦

(16)

The reaction enthalpy ΔHr and reaction entropy ΔSr are found to be 90 J·mol−1 and 280.805 J K−1 mol−1, respectively. Furthermore, the liquid phase reaction free energy change can be calculate to be ΔGr = ΔHr − TΔSr = −93418.18 J·mol−1 4.5. Model Prediction. The observed reaction rate for the esterification of nonanoic acid with methanol was compared with the proposed Eley−Rideal model (eq 5) using the rate consants described by eqs 11−13 over the whole range of predicted parameters (given in Table 2). And experimental data was calculated by this equation −rA,experimental =

ΔC ΔX = CA Δt Δt

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support received from UGC (Government of India) vide Project No. F.No.37-295/ 2009 (S.R.).

(17)

The parity between the experimental and calculated value is given in Figure 18. The model eq 5 represents the data reasonably well within ±15%.

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Figure 18. Fitting calculated to experimental data over Amberlyst 15 as catalyst in the catalyst range of 4% (w/v) to 11% (w/v), molar ratio 1:1 to 1:20, and temperature 303−333 K; RPM, 500.

5. CONCLUSION For the esterification of nonanoic acid with methanol, cation exchange resins as catalysts were investigated. The catalytic activity of three heterogeneous catalysts, Amberlyst 15, Amberlyst 35, and Dowex50WX2, was tested at temperatures of 333.15 K, catalyst loading of 9% (w/v), and 1:10 molar ratio (acid/alcohol). Amberlyst 15 was found to be the most costeffective catalyst in this study. A stirrer speed of ≥500 rpm was found to be effective in eliminating external diffusion limitations. Hence, the effect of catalyst loading, temperature, and acid to alcohol molar ratio on reaction kinetics was determined at 500 rpm. At 500 rpm, internal diffusion limitations were assessed by the Weisz Prater criterion and found to be absent. For all the reactions, increasing the acid to alcohol molar ratio increases conversions of the acid, and this enhancement in kinetics is more pronounced when the molar ratio is raised from 1 to 10 than when it is raised from 1 to 1. Under the conditions studied, the increase in the catalyst loading is found to increase the percent conversion of nonanoic acid. The adsorption effect of nonanoic acid was found to be negligible, but the effect of methanol and water is included in the study. Nonideal behavior of the liquid mixture is taken into account, and the UNIFAC group contribution method was found to predict component activity

NOTATIONS a = activity A = nonanoic acid B = methanol E = methyl nonanoate W = water EA = activation energy (kJ·mol−1) ko = preexponential factor (mol L·g−1 min−1) kf = forward reaction rate constant, (mol·L·g−1 min−1) wcat = weight of catalyst, g·L−1 T = absolute temperature, K t = time, min C = concentration γ = activity coefficient ΔGr = reaction free energy change, J/mol vk = number of structural groups of kind k in a molecule of component i qi = relative van der Waals surface area of compound i ri = relative van der Waals volume of compound i Qk = relative van der Waals surface area of subgroup k ΔHr = reaction enthalpy ΔSr = reaction entropy ln = natural logarithm (base e) !k = group activity coefficient of subgroup k R = 8.314 J/mol/K γC = combinatorial part of the activity coefficient of component i γR = residual part of the activity coefficient of component i amk = interaction parameters

Abbreviations

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ER = Eley−Rideal LHHW = Langmuir−Hinshelwood Haugen−Watson PH = pseudohomogeneous RPM = revolutions per minute UNIFAC = universal quasichemical functional group activity coefficients

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