3044
Ind. Eng. Chem. Res. 1996, 35, 3044-3054
Solvent Effects in the Carbonylation of Methanol D. A. Nguyen and T. Sridhar* Department of Chemical Engineering, Monash University, Clayton, 3168 Australia
The kinetics of the carbonylation of methanol to methyl formate in the presence of sodium methoxide is reported in this paper. It is found that the presence of an inert nonpolar solvent has a significant effect on the rate of the reaction. The composition of the solvent is found to have a significant effect on the forward and reverse rate constants. This is also accompanied by a decrease in the activation energy of the reaction. These effects are consistent with the Scatchard equation which relates the rate constant to the dielectric constant of the reaction medium. 1. Introduction Methanol is an important chemical raw material and is produced at an annual rate of more than 20 million tons, and the annual demand of methanol is expected to reach 25.4 million tons in 1996 (Crocco, 1994). About 85% of the methanol produced worldwide is used in the chemical industry as a solvent or for chemical syntheses. Presently, methanol is mainly produced from synthesis gas (CO, CO2, and H2) in a gas-phase reaction over copper-based catalysts such as Cu/ZnO/Al2O3 or Cu/ ZnO/Cr2O3 at temperatures ranging from 200 to 270 °C and pressures from 50 to 100 bar. One of the major disadvantages of conventional reactors has been the low per pass conversion (around 3040%; Berty et al., 1990) that is obtained. This is due to the reversible nature of the reaction and the high temperatures required to give reasonable rates. Two avenues of overcoming this problem have received attention recently. One is to sequester or remove the methanol as it is formed, and the other is to seek more active catalysts which permit operation at lower temperature. Both these methods are the subject of continuing research. Of the methods relying on a lower reaction temperature for improving methanol yields, we cite the development of the Brookhaven process (Sapienza et al., 1984) and the Sintef process (Onsager, 1984). The Brookhaven process relies on using a complex reducing agent, which is derived from NaH, NaOR (R ) C1-6 alkyl), and M(OAc)2 (M ) Ni, Pd, or Co). The process conditions are a temperature of 100 °C and a pressure of 51 atm. The Sintef process is based on a two-stage process first proposed by Christiansen (1919) which suggested that methanol could be produced by the carbonylation of methanol to methyl formate followed by the hydrogenolysis of methyl formate to 2 mol of methanol. In the Sintef process, the methanol reactor may be operated at temperatures ranging from 70 to 150 °C, a pressure in the range of 5-60 bar, and compositions of the synthesis gas as a molar ratio of hydrogen to carbon monoxide ranging from 8 to 1. The reaction may be carried out continuously using the known reactor types, and the products, which are mainly methanol and methyl formate as a byproduct, may be removed from the reactor in the form of gases or in liquid form. With copper chromite catalyst and sodium methoxide in pure methanol, the Sintef process could achieve a very high production rate of methanol at temperatures as low as 90 °C and a pressure of 35 bar with a selectivity to methanol of 61%. Onsager (1984) also S0888-5885(95)00755-X CCC: $12.00
showed that with addition of a nonpolar solvent, which has a dielectric constant lower than that of methanol (e.g., cyclohexane, decalin, 1,4-dioxane, p-xylene, n-butyl stearate, and toluene), the rate could be doubled and the reaction selectivity to methanol increases to 96%. The effect of a nonpolar solvent on such reactions obviously merits a detailed study and is the subject of this paper. The primary aim of this paper is to clarify the mechanism of the Sintef process by studying the carbonylation reaction and to clarify the effect of a nonpolar solvent by examining the thermodynamic properties of the solvent and its effect on the rate of reaction. The carbonylation of methanol to methyl formate in liquid phase can be represented as follows:
CH3OHliq. + COgas ) HCOOCH3 liq.
(1)
The carbonylation of an alcohol to the corresponding formate in liquid phase with an alkali-metal alkoxide has been studied since the early 1940s by Christiansen and Gjaldbaek (1942). The alcohols used in their study were methanol and ethanol, and they showed that the rate constant was higher in ethanol than in methanol. They also found the rate constant increased when the reaction mixture contained dioxane. Gjaldbaek (1948) extended the above study to include propyl and butyl alcohols with sodium methoxide as the catalyst except for tert-butyl alcohol where potassium tert-butoxide was used as the catalyst. The kinetic data were reported for the alcohols including methanol and ethanol, and the reaction rate was found to increase with the length of the alkyl group and the degree of substitution close to the hydroxyl group. Tonner et al. (1983) also came to the same conclusion when they studied the carbonylation of a number of alcohols in liquid phase. The increase in the electron density by any substituent group increases the reaction rate. They also suggested that the catalyst activity increases with decreasing ionization potential of the alkali metals, and hence the carbonylation rate is the slowest with lithium alkoxide and fastest with potassium alkoxide. Recently, Liu et al. (1988) studied the carbonylation of methanol with potassium methoxide as the catalyst in a range of temperatures from 60 to 100 °C and pressures from 25 to 65 bar. Both the forward and reverse rate constants were reported; they also reported the data on the equilibrium constant based on the concentration of the reactants but did not report on the thermodynamic equilibrium constant. The equilibrium © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 3045
conversion of methanol was reported by Couteau and Ramioulle (Aguilo and Horlenko, 1980) at temperatures of 80 and 100 °C and various pressures. 2. Experimental Techniques The experimental measurements were carried out in a 1 L stainless steel autoclave. A glandless permanent magnet stirrer with a maximum speed of 3000 rpm is used to mix the reactor contents. The reactor has facilities for sampling the gas and liquid phases and can be rapidly pressurized by a piston pump. The reactor was cleaned, dried, and loaded with a sodium methoxide solution in pure methanol or a methanol/toluene mixture (approximately 500 mL at 20 °C). It was then flushed with argon to remove oxygen, and then the stirrer and heater were turned on. The reactor reaches thermal equilibrium in about 3 h. The reactor pressure is noted, and the heated reactor is then pressurized with carbon monoxide using a pressure vessel containing carbon monoxide at about 100 bar. A piston pump is used to charge the pressure vessel from bottle gas. The stirrer was switched off during this process to minimize any reaction. The experiment was commenced by stirring the liquid mixture. A stirrer speed of 900 rpm was used because at this stirrer speed the mass-transfer resistance between the gas phase and the liquid phase was found to be negligible and the fact that the experiments which were carried out at two stirrer speeds (900 and 1500 rpm) gave identical reaction rates. The consumption of carbon monoxide due to reaction caused a decrease in the reactor pressure, and this was recorded until at equilibrium no further decrease in pressure is evident. Liquid samples were taken at the end of the experiment. A GC equipped with a flame ionization detector (FID) along with a 6 ft length, 1/4 in. glass column packed with Porapak Q 80/100 mesh was used for the analysis of methanol, methyl formate, and toluene. The gases were analyzed using a GC with a thermal conductivity detector packed with HayeSep A. Two different lengths of this column were used. The longer one (approximately 11 m) was used to separate argon, nitrogen, oxygen, and carbon monoxide, and the column was placed in an ice bucket. The shorter column (approximately 4 m) was used to detect methane and carbon dioxide (if there are any of these gases) in the gas phase. The same column but with a different column temperature program was also used to detect dimethyl ether in the liquid phase. Sodium methoxide and the total sodium content in the liquid sample were determined by titration with benzoic and hydrochloric acids with thymol blue as the indicator. Methanol (analar grade) used was supplied by Ajax Chemicals with 99.7% purity and a moisture content of less than 0.1% by weight; toluene (supplied by Mallinckrodt Australia Pty. Ltd.) has a purity of 99.9% and a moisture content of less than 0.01%. Sodium methoxide catalyst was purchased from Aldrich Chemical Co., Inc., as a methanol solution which contains 25% by weight of sodium methoxide. As methanol and toluene contain a small amount of water which turns sodium methoxide to sodium hydroxide, the actual concentration of sodium methoxide needs to be known before it is loaded into reactor. The determination of sodium methoxide relies on first converting all the sodium hydroxide to sodium formate (using methyl formate) and the sodium meth-
oxide to sodium benzoate (using benzoic acid). The total sodium salts are determined by titration with hydrochloric acid. By conducting two measurements with the same amount of methyl formate but differing the mass of the sample, any water present in the added methyl formate can also be accounted for. The reactor pressure was monitored by using a pressure gauge. The pressure gauge, which was supplied by VDO Australia, had a maximum reading of 60 bar; it was calibrated with a dead weight tester, and its accuracy is (0.1 bar. 3. Estimation of Physicochemical Data 3.1. Dielectric Constant. Experimental data on dielectric constants of methanol (Nicolas et al., 1980) and toluene (Singh et al., 1986) are available at various temperatures. Franck and Deul (1978) have shown that the dielectric constant of methanol increases by about 2% for an increase of 100 bar in pressure. Hence, the dielectric constant can be assumed to be independent of pressure. The dielectric constant of a substance can be related to its refractive index, molar volume, and the structure parameter G by using the significant structure theory (Hobbs et al., 1966; Eyring et al., 1967; Jhon and Eyring, 1968) as follows:
)
(
)(
)
v - vs n2 + 2 n2 n4 6πNA µ2 vs + + G+ 2 2 v kT v 3v 3
2
(2)
where is the dielectric constant of a liquid, µ is the dipole moment (D), NA is Avogadro’s number, k is Boltzmann’s constant, T is the absolute temperature (K), v is the saturated liquid molar volume (cm3/mol), and vs is the solid molar volume (cm3/mol). The refractive index, n, can be estimated using the empirical Eykman equation (Riddick and Bunger, 1970), and the structure parameter G for methanol and toluene was evaluated from eq 2 using the available data on their dielectric constants (Jhon et al., 1967; Singh et al., 1986). The only data on the dielectric constant for methyl formate seem to be those given by Weast (1988) at a single temperature of 293.15 K. The structure parameter G calculated using this value is 0.3203. Lack of any other data forces us to assume that G is independent of temperature. In any case, the dielectric constant of methyl formate is not a significant contributor to mixture properties because it is present in very small quantities. The dielectric constant for mixtures of liquids can be estimated from pure component values as proposed by Jhon and Eyring (1968). 3.2. Solubility. Using the theory of regular solutions, Prausnitz and Shair (1961) proposed that, when a gas at a partial pressure of 1 atm dissolves into a nonreacting liquid B at a temperature lower than the liquid critical temperature, it is first condensed into a hypothetical liquid which then dissolves into liquid B. For low gas solubility, they developed the following equation:
(δ - δA)2 -ln xA ) ln fAL (1 atm) + vAL RT
(3)
where xA is the mole fraction of gas A in the liquid at
3046 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
atmospheric pressure, fAL (in atm), vAL (in cm3/mol), and δA (in cal0.5/cm1.5) are the fugacity, molar volume, and solubility parameter of the hypothetical liquid A, respectively, and δ is the solubility parameter of liquid B and can be estimated from its molar heat of vaporization, ∆Hv, and molar volume as:
δ)
[
]
(∆Hv - RT)2 v
0.5
(4)
Values of vAL, fAL, and δA of the hypothetical liquid A are obtained by using the known solubility data of A in various solvents using eq 3. Then the solubility of A in other solvents can be approximately estimated from the solvent property with eq 3. Using literature data, the solubilities of carbon monoxide in methanol (Dake and Chaudhari, 1985) and toluene (Field et al., 1974) were found to depend on temperature as in eqs 5 and 6, respectively, where the partial pressure of carbon monoxide is in bar. To
ln(PCO/xCO)m ) 6.7003 + 367.03/T
(5)
ln(PCO/xCO)t ) 6.6383 + 150.15/T
(6)
estimate the solubility of carbon monoxide in a methanol/ toluene mixture, the molar volume and fugacity of hypothetical liquid carbon monoxide have to be known. A least-squares method was used to estimate the properties of hypothetical liquid carbon monoxide by fitting eq 3 with solubility data of carbon monoxide in methanol, toluene, and a number of other solvents from the literature, such as ethanol (Dake and Chaudhari, 1985), cyclohexane (Wilhelm and Battino, 1973), and methylcyclohexane (Field et al., 1974). δCO was taken as 3.13 cal0.5 cm-1.5 from Prausnitz and Shair (1961). The molar volume of hypothetical liquid carbon monoxide was found to be independent of temperature and had a value of 20.47 cm3/mol, and the fugacity, fCOL in atm, depended on temperature as follows:
ln fCOL (atm) ) 7.9679 - 593.5/T
(7)
For solubility parameters greater than 9.1 cal0.5 cm-1.5, a correction as proposed by Lencoff (1977) was necessary. Hildebrand et al. (1970) proposed an expression for calculating the solubility of a gas in a binary mixture from gas solubility in pure solvent and its solubility parameter as:
ln xAM ) $1 ln xA1 + $2 ln xA2 - vALβ12$1$2 (8) where xAM and xAi are the mole fractions of a gas in liquid mixture and pure solvent, respectively, $i is the volume fraction of solvent i in a mixture and estimated as in eq 9, and β12 is obtained from the solvent solubility parameters as in eq 10. Thus, the solubility of carbon
$i )
xivi x1v1 + x2v2
(9)
(δ1 - δ2)2 RT
(10)
β12 )
monoxide in any mixed solvent can therefore be calculated using eqs 8-10.
3.3. Activity Coefficient. The activity coefficients of methanol and methyl formate in methanol/methyl formate mixtures have been studied by Polak and Lu (1972) at atmospheric pressure and a temperature of 298.15 K. Kozub et al. (1962) studied the system at isothermal (303.15 K) as well as isobaric (1 atm vapor pressure) conditions and showed that the activity coefficients of methanol and methyl formate could be well represented by eqs 11 and 12, respectively. The activity
log γm )
157.64 (1 - xm)2 T
(11)
157.64 2 xm T
(12)
log γf )
coefficients of methanol and methyl formate calculated from these equations are in agreement with the data of Polak and Lu (1972). For the liquid mixtures, which contain toluene, the UNIFAC method, which was originally developed by Fredenslund et al. (1975), was used to estimate the activity coefficients. The activity coefficients in liquid mixtures are related to interaction between structural groups. This method gives a good prediction of the activity coefficients of nonelectrolyte systems in the temperature range 2-127 °C. The predicted activity coefficients for mixtures of methanol/methyl formate and methanol/toluene compare well with the experimental data of Kozub et al. (1962) and Nagata (1988). The expressions proposed by Kozub et al. (1962) and the UNIFAC method both gave a good prediction of the activity coefficient of the methanol/methyl formate system, but the former was used due to its simplicity and the latter was used for systems containing toluene. 4. Results and Discussion It was assumed that the pressure drop was only due to the consumption of carbon monoxide by the carbonylation of methanol. Such an assumption is consistent with the presence of carbon monoxide, argon, methanol, and methyl formate in the gas phase at the end of a run. Some typical pressure-time curves are shown in Figure 1. From a pressure-time curve the reaction rate and the equilibrium constant could be obtained. 4.1. Reaction Equilibrium. When a reaction has reached equilibrium, the equilibrium constant satisfies the following relationship:
ln K ) ∆G°/RT
(13)
where ∆G° is the standard Gibbs free energy of the reaction at temperature T. The van’t Hoff equation relates the equilibrium constant K to temperature:
d(ln K)/dT ) ∆H°T/RT
(14)
where ∆H°T is the heat of reaction at temperature T. The standard Gibbs free energy and heat of reaction can be calculated from the Gibbs free energy of formation and heat of formation of carbon monoxide, methanol, and methyl formate (Dean, 1973). The heat capacities of liquids methanol and methyl formate were obtained using the group contribution method (Reid et al., 1977), and the heat capacities of carbon monoxide, hydrogen, and vapor methanol are available in Reid et
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 3047
Figure 1. Some typical pressure-time curves of the carbonylation at various catalyst loadings (mol/L) and temperatures for a pure methanol system.
al. (1977). Hence, the carbonylation’s equilibrium constant can be expressed as a function of T:
5689 ln K ) -100.96 + + 15.77 ln T - 3.56 × T 10-2T + 1.04 × 10-5T2 + 1.27 × 10-10T3 (15) The equilibrium constant of the carbonylation reaction can also be defined as:
K ) af/amfCO
(16)
where af and am are the activities of methyl formate and methanol, respectively, and fCO is the fugicity of carbon monoxide in the gas phase. The activity is related to the mole fraction (xi) and the activity coefficient (γi). For gaseous mixtures at moderately high pressures and temperatures, the solution of gases is generally ideal; hence, the fugacity of carbon monoxide in the gas phase is the same as that of pure gas CO. The fugacity coefficient of pure CO gas is close to unity for pressures as high as 50 atm and temperatures as low as 343.15 K (Perry and Chilton, 1973). Equation 16 can be written as:
K ) 1.01325γfxf/γmxmPCO
(17)
An equilibrium constant based on the concentration of the constituents can also be defined as:
KC ) Cf/CmPCO
(18)
where Cm and Cf are the concentrations of methanol and methyl formate at equilibrium conditions, respectively. As the mole fraction ratio of methyl formate to methanol is the same as the molar concentration ratio, the equilibrium constant K is related to KC.
K ) 1.01325KC(γf/γm)
(19)
Equation 19 indicates that the equilibrium constant based on concentration is not a constant; it varies with
Figure 2. Effect of temperature on K (eq 15) and KC for a pure methanol system.
the activity coefficients of methyl formate and methanol, but for systems in which the concentration of methyl formate ranges from 0.5 to 1.5 mol/L, the ratio γf /γm is nearly constant. As the concentration of sodium as sodium methoxide in the solution at equilibrium was approximately 1% by weight or smaller, its effect on the activity coefficients of the solvents was assumed to be negligible. For the pure methanol system with a methyl formate concentration of less than 1.5 mol/L, it was found that the concentration-based equilibrium constant of the carbonylation reaction depends on temperature (Figure 2) in the range of temperatures from 70 to 118 °C as:
ln KC ) -13.881 + 3294.5/T
(20)
The values of KC found were approximately 25% lower than that of Liu et al. (1988). This is possibly due to the fact that the concentrations of methyl formate at equilibrium in their work were greater than 3 mol/L, while in the present study its concentration was approximately 1 mol/L. According to eqs 11 and 12, the activity coefficient ratio, γf /γm, in Liu et al.’s work would be lower than that of this study; hence, from eq 19 the KC value of Liu et al. (1988) would be expected to be larger. It has been shown that the value of KC depends on the activity coefficient ratio, and this in turn depends on the equilibrium concentration of methyl formate. With eqs 11 and 12, the ratio of activity coefficients for methyl formate and methanol can be obtained. Hence, the dependence of KC on the equilibrium concentration of methyl formate can be calculated using eq 19 and is shown in Figure 3 at 355.15 K. When Cf is approximately 5 mol/L, the value of KC is approximately the same as that obtained by Liu et al. (1988), who did not specify the concentration of methyl formate when presenting their equation for the concentration-based equilibrium constant.
3048 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
Figure 3. Dependence of KC on methyl formate concentration for a pure methanol system at a temperature of 355.15 K.
Figure 5. Activity coefficients of methyl formate and toluene in methyl formate/toluene mixtures at a temperature of 355.15 K, UNIFAC method.
Figure 4. Activity coefficients of methanol and toluene in methanol/toluene mixtures at a temperature of 355.15 K, UNIFAC method.
Figure 6. Dependence of KC on the volume percentage of toluene at a temperature of 355.15 K.
As toluene is added into the reaction solution, the degree of solvation of methanol by toluene is different from that of methyl formate. The intermolecular interaction between methanol and toluene is not the same as that between methyl formate and toluene. The difference can be indicated by the activity coefficients, which were obtained by the UNIFAC method, of methanol and toluene in a methanol/toluene mixture and of methyl formate and toluene in a methyl formate/toluene mixture, as shown in Figures 4 and 5, respectively. As the concentration of toluene in the reaction solution increases, the activity coefficient ratio, γm/γf, will also
increase. Hence, according to eq 19, the equilibrium constant KC will increase as well, and this was verified by the experimental data shown in Figure 6. Table 1 shows the values of the concentration-based equilibrium constants at different temperatures and various volume percentages of toluene in the reaction solution. By using eqs 11 and 12 for the binary methanol/ methyl formate and the UNIFAC method for the mixtures containing toluene, the activity coefficients of methanol, methyl formate, and toluene were calculated;
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 3049 Table 1. Values of KC at Various Temperatures and Toluene Contents toluene (% v/v) 0 30 60 80 90
343.15
355.15
0.0138
0.010 05 0.014 25 0.022 33 0.040 47 0.066 69
0.0325 0.0566 0.0947
T (K) 363.15
370.15
391.15
0.008 38
0.006 61
0.004 30
0.018 20 0.029 95 0.051 41
0.015 18 0.025 72 0.037 33
0.008 44 0.015 45 0.021 44
Table 2. Comparison of Experimental and Calculated Equilibrium Constants at Various Temperatures and Volume Percentages of Toluene toluene (% v/v) 0 30 60 80 90 K (average) K (eq 15)
343.15
355.15
0.0364
0.0264 0.0270 0.0259 0.0264 0.0254 0.0262 0.0258
0.0368 0.0347 0.0344 0.0356 0.0369
T (K) 363.15
370.15
391.15
0.0207
0.0165
0.0105
0.0204 0.0198 0.0193 0.0201 0.0206
0.0180 0.0172 0.0159 0.0169 0.0170
0.0102 0.0110 0.0101 0.0105 0.0100
Table 3. Values of K Calculated from Couteau and Ramioulle’s Data and from Equation 15 at Various Temperatures and Pressures P (bar) T (K)
19.614
39.288
58.842
78.456
K (eq 15)
353.15 373.15
0.0287 0.0166
0.0235 0.0135
0.0237 0.0140
0.0379 0.0148
0.0273 0.0157
then the equilibrium constant K was obtained from eq 19. The result is tabulated in Table 2 which shows a very good agreement between the values of K from experimental data and thermodynamic data (eq 15). The prediction from eq 15 was further tested using the data presented by Couteau and Ramioulle (Aguilo and Horlenko, 1980). These data were reported as the equilibrium conversion of methanol. The equilibrium constants calculated from their data are compared with eq 15 in Table 3. 4.2. Kinetics. In the initial stages of the reaction only a small amount of methyl formate is formed and the change in methanol concentration was negligible. Under these conditions the reverse reaction is negligible. The partial pressure of carbon monoxide was calculated as the difference between the reactor pressure and the pressure just before carbon monoxide was introduced into the reactor. Previous researchers (Christiansen and Gjaldbaek, 1942; Tonner et al., 1983; Liu et al., 1988) have shown that the carbonylation reaction is first order in carbon monoxide. During the initial stages of the reaction, a plot of ln PCO versus time results in a straight line as shown in Figure 7. From the slope and intercept, an initial carbonylation rate could be obtained. It was found that the reaction rate is a first-order reaction with respect to the partial pressure of CO as shown in Figure 8. Such a conclusion confirms the results obtained by Liu et al. (1988). The reaction order with respect to the concentration of sodium methoxide is shown in Figure 9. Again, the reaction is found to be first order with respect to the sodium methoxide concentration. For the reaction order with respect to the methanol concentration, the order of unity is employed by previous researchers (Tonner et al., 1983; Liu et al., 1988), whereas the reverse reaction order with respect to the concentrations of sodium methoxide and methyl formate is taken as unity, as suggested by Liu et al. (1988). Hence, the
Figure 7. Plot of ln PCO against time for the data shown in Figure 1.
Figure 8. Plot of the initial carbonylation rate versus CO partial pressure at a temperature of 355.15 K and a catalyst loading of 0.136 mol/L for a pure methanol system.
carbonylation rate, r (mol of CH3OH/L‚min), can be expressed as:
r ) k1CcatCmPCO - k-1CcatCf
(21)
where k1 (L/mol‚min‚bar) and k-1 (L/mol‚min) are the forward and reverse rate constants, respectively, and Ccat is the concentration of the sodium methoxide catalyst. From the initial rate technique, the forward rate constant can be obtained. The reverse rate constant can be calculated from the condition of equilibrium which
3050 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
Eyring and by Evans and Polanyi (Laidler and King, 1983). The theory is based on the assumption that first the reactants, A and B, form an activated complex, [AB]q, which then decomposes to the end products, C and D, as follows:
A + B ) [AB]q ) C + D
(23)
With other assumptions the theory suggested that the rate constant of reaction (23) is proportional to the quasi-equilibrium constant of the reaction A + B to [AB]q, which in turn depends on ∆Gq, the Gibbs energy of the reaction A + B to [AB]q. Hence, from statistical calculations (Reichardt, 1988) the specific rate constant k of the elementary reaction is given as:
k)
Figure 9. Plot of the ratio, r/PCO, at the initial conditions against catalyst loading at a temperature of 355.15 K for a pure methanol system.
(
)
∆Gq RT exp NAh RT
(24)
If the reaction (23) is carried out in different solvents, the reactants and the activated complex will be solvated to a different extent by these solvents. This may result in a difference in ∆Gq of the reaction and hence the rate constant. According to Entelis and Tiger (1973), the rate constant k of the reaction (23) in a particular solvent can be related to the rate constant k0 of this reaction in a standard solvent or in the gas phase as:
ln k ) ln k0 -
(
)
1 ∆GA;solv ∆GB;solv ∆Gq;solv + RT RT RT RT
(25)
where ∆Gi;solv is the free solvation energy released by solvent change and is defined as the difference between free energies of component i in two different solvents. Because of the complicated interactions between solutes and solvents, the prediction of solvent effects on reaction rates, and the correlation of these effects with intrinsic solvent properties, is very difficult. However, depending on the type of reaction, many authors have tried to correlate rate constant k, or Gibbs free energies of a reaction with solvent properties such as dielectric constant , refractive index n, etc. Christiansen and Gjalbaek (1942) proposed that the carbonylation of methanol in the liquid phase is a result of a reaction between molecule methanol and carbonyl ion (CH3OC-dO), which in turn is produced from carbon monoxide reacting with methoxide ion as follows: C
Figure 10. Dependence of the forward rate constant on volume percentage of toluene at a temperature of 355.15 K.
yields eq 22. The effect of a nonpolar solvent was
KC ) k1/k-1 ) Cf/CmPCO
(22)
investigated by conducting the reaction with varying concentrations of toluene. As the volume fraction of toluene in the reaction solution increased, the forward rate constant was found to increase and this is shown in Figure 10. The change of the rate constant may be explained qualitatively by the transition-state theory, which was developed almost simultaneously in 1935 by
O + CH3O–: = CH3OC–:
(26)
O CH3OC–: + CH3OH = HCOCH3 + CH3O–: O
(27)
O
Scatchard (1932) used Bronsted’s theory to investigate a number of reactions in a dilute solution for both ionic and molecular reactants, that is, for a simple reaction between an A ion of charge ZAe with a neutral molecule B (ZBe ) 0). By assuming that at a great distance from the A ion its effect would vanish, the activity of the molecule B was equal to its concentration at infinite distance, C∼, and the activity coefficient of B was the ratio of C∼ over the average concentration of B. Ac-
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 3051
Figure 11. Dependence of the forward rate constant on the medium’s dielectric constant at a temperature of 355.15 K.
cording to the Debye theory, the concentration of B, CB,d, at a distance d from the ion A was given by:
CB,d ) C∼ exp(-D4/d4)
(28)
where D is related to the standard state dielectric constant, *
D4 )
e2ZA2ZB
(29)
128π302RT*
where
λB ) (* - )/CB
(30)
and e is the elementary charge, ZA is the valance, 0 is the permittivity of vacuum, and is the dielectric constant of the reaction solution. Using the Debye theory, Scatchard (1932) proposed the expression that described the effect of the medium dielectric constant on the rate constant as:
ln k ) ln k∼ +
e2ZA2vB 2
4
32π 0RTd
(31)
where k∼ is the rate constant in a medium with a dielectric constant of infinite magnitude, R is the gas constant in J‚mol-1‚K-1, and vB is the molar volume of B in m3/mol. Equation 31 is limited to the case of a uniform dielectric constant and so applies to changes from one pure solvent to another. A plot of ln k versus the reciprocal of the dielectric constant predicts a straight line, and the distance, d, can be obtained from the slope. Despite the limitations of eq 31, a plot of the natural logarithm of the forward rate constant of the carbonylation gave a straight line in the region of relatively low concentrations of methanol as shown in Figure 11, and
Figure 12. Dependence of the reverse rate constant on the medium’s dielectric constant at a temperature of 355.15 K.
from the slope the distance, d, of 3.53 × 10-10 m was obtained for the temperature of 355.15 K. The reverse reaction is, also, between an ion, CH3O-, and a neutral molecule, HCOOCH3. The concentration of methyl formate studied was small, resulting in a linear relationship between ln k-1 and 1/ for the whole range of dielectric constant studied, as would be expected, and this is shown in Figure 12. The distance between ion CH3O- and methyl formate was approximately 4.74 × 10-10 m at 355.15 K, and k-1 at infinite dielectric constant was approximately 0.071 L/mol‚min. From these properties we are able to predict the carbonylation rate in any medium whose dielectric constant is known. Equation 5 shows that the solubility of carbon monoxide will increase with temperature; however, this increase that is only 8% for temperatures changing from 343.15 to 370.15 K is insignificant compared with the increase in the reaction rate. The effect of temperature on the rate constant can be examined by using the Arrhenius equation.
k1 ) A exp(-Ea/RT)
(32)
where Ea is the activation energy (J/mol), and A is the preexponential factor. The experimental data are shown in Figure 13. The activation energy and preexponential factor obtained from Figure 13 are tabulated in Table 4 for various toluene volume fractions. Using values of the activation energy and preexponential factor, the forward rate constant k1 could be estimated for any reaction medium with known dielectric constant. Christiansen and Gjaldbaek (1942) studied the carbonylation of methanol to methyl formate in the dioxane-methanol mixture (50% by volume), which has a dielectric constant of 11.2 (Papanastasiou and Ziogas, 1993). They reported a forward rate constant of 5.5 × 10-4 L/(mol‚ min‚bar), whereas the estimated value from eq 32 was 3.0 × 10-4 L/(mol‚min‚bar). Figures 14 and 15 show the effect of temperature on the forward and reverse rate constants at various
3052 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
Figure 13. Dependence of the forward rate constant on temperature at various volume percentages of toluene in the reaction solution.
Figure 15. Dependence of the reverse rate constant on the medium’s dielectric constant at various temperatures. Table 5. Distances between Carbonyl Ion and Methanol, and Methoxide Ion and Methyl Formate at Various Temperatures T (K) d1 × 1010 (m) d-1 × 1010 (m)
343.15
355.15
363.15
370.15
3.50 4.55
3.53 4.74
3.58 4.78
3.58 4.80
between ion methoxide and methyl formate, d-1, were obtained and are shown in Table 5. For the reaction with a small amount of methyl formate produced, that is, where the dielectric constant of the medium is nearly constant, the carbonylation rate can be expressed as in eq 33 for a pure methanol system.
(
)
9887.6 CcatCmPCO - 1.086 × T 13182.1 CcatCf (33) 1015 exp T
r ) 1.017 × 109 exp -
(
Figure 14. Dependence of the forward rate constant on the medium’s dielectric constant at various temperatures. Table 4. Values of Ea/R and ln A at Various Volume Percentages of Toluene toluene (% v/v) Ea/R ln A
(K-1)
0
60
80
90
9887.6 20.74
8825 18.96
8135 17.91
7545.7 17.20
dielectric constants. In each case the linear relationship predicted by eq 31 is observed for a low concentration of reactants. From the slopes and with eq 31 the distances between carbonyl ion and methanol, d1, and
)
The carbonylation rates calculated from eq 33 are about double that reported by Tonner et al. (1983), although the solubility of carbon monoxide in methanol used in this study is about the same as that reported by Tonner et al. (1983). The slower reaction rate obtained by them may be due to the trace of water in their reactant solutions, causing lower sodium methoxide concentration, however, the trace of water, only will cause a significant effect when a total sodium concentration of less than 0.1 mol/L is used and in their work the sodium methoxide concentrations ranged from 0.3 to 1 mol/L. However, the values obtained from eq 33 are comparable to those reported by Christiansen and Gjaldbaek (1942) and shown in Table 6. A similar discrepancy exists between the data of Tonner et al. (1983) and Liu et al. (1988) when potassium ethoxide and methoxide are used as catalysts. The carbonylation was very selective to methyl formate, but small amounts of sodium formate may be
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 3053 Table 6. Comparison of the Carbonylation Rates at Sodium Methoxide and Carbon Monoxide Concentrations of 0.1 mol/L 103r (mol/L‚min) researcher
50 °C
60 °C
70 °C
Tonner et al. (1983) Christiansen and Gjaldbaek (1942) this work
0.787 1.397 1.323
1.743 3.548 3.204
3.336 8.533 7.368
produced by the reaction between sodium methoxide and methyl formate as follows:
NaOCH3 + HCOOCH3 ) CH3OCH3 + HCOONa (34) Dimethyl ether was not detected; the sodium formate can also be formed by the following reactions due to traces of water in the reaction solution.
NaOCH3 + H2O ) NaOH + CH3OH NaOH + HCOOCH3 ) CH3OH + HCOONa
(35) (36)
The amount (in moles) of sodium formate was found to be approximately the same as the amount of sodium hydroxide at the beginning of an experiment. It was also found that the amount of sodium methoxide and the total sodium remained unchanged from the beginning to the end of an experiment. 5. Conclusions Kinetic rate equations for the liquid phase carbonylation of methanol have been developed, and the effect of a nonpolar solvent on the rate constants has been explained by the transition-state theory and correlated well with the medium’s dielectric constant. The equilibrium constant determined from thermodynamic calculations is consistent with the experimental data. This paper shows how the dielectric constant of the medium can be exploited to obtain improvements in rate and conversion. Acknowledgment The authors are pleased to join their colleagues in felicitating Professor Ruckenstein. During his tenure at Buffalo, Professor Tam Sridhar had the privilege of collaborating with Professor Ruckenstein. The authors express their appreciation to Prof. F. Lawson for his comment on the reaction equilibrium, to Dr. M. Wadsley for his suggestion to use the UNIFAC method for calculating the activity coefficients of individual components in a mixture, and to Dr. I. R. McKinnon for useful discussions on the dielectric constant. We appreciate the financial support from MGS and GDS. Notation (L‚mol-1‚min-1‚bar-1)
A ) preexponential factor af ) activity of methyl formate am ) activity of methanol C∼ ) concentration of species B at infinite distance Ccat ) concentration of sodium methoxide in liquid solution (mol/L) CB ) concentration of species B CB,d ) concentration of species B at a distance d from an A ion Cf ) concentration of methyl formate (mol/L) Cm ) concentration of methanol (mol/L) D ) defined in eq 29
d ) distance between A ion and molecule B d-1 ) distance between methoxide ion and methyl formate (m) d1 ) distance between carbonyl ion and methanol (m) e ) elementary charge (C) En ) activation energy of the forward carbonylation (J/mol)fAL ) fugacity of hypothetical liquid A (atm) fCO ) fugacity of carbon monoxide gas (atm) fCOL ) fugacity of hypothetical liquid carbon monoxide (atm) K ) equilibrium constant of liquid phase carbonylation of methanol k ) rate constant k∼ ) rate constant in a medium with a dielectric constant of infinite magnitude k0 ) rate constant in a standard solvent or in the gas phase k-1 ) reverse rate constant of the carbonylation (L‚mol-1‚min-1) k1 ) forward rate constant of the carbonylation (L‚mol-1‚min-1‚bar-1) KC ) equilibrium constant based on the concentration (bar-1) P ) total pressure (bar) PCO ) partial pressure of carbon monoxide (bar) R ) gas constant r ) carbonylation rate (mol‚L-1‚min-1) T ) absolute temperature (K) v ) liquid molar volume (cm3/mol) vAL ) molar volume of hypothetical liquid A (cm3/mol) vB ) molar volume of B in eq 31 (m3/mol) xA, xAi ) mole fraction of gas A in pure liquid xAM ) mole fraction of gas A in a liquid mixture xCO ) mole fraction of carbon monoxide in liquid xf ) mole fraction of methyl formate xm ) mole fraction of methanol Greek Symbols β12 ) defined in eq 10 δ ) solubility parameter of liquid (cal0.5 cm-1.5) δA ) solubility parameter of hypothetical liquid A (cal0.5 cm-1.5) ∆Gq ) Gibbs energy of the reaction A + B to [AB]q ∆G° ) standard Gibbs free energy (J/mol) ∆Gi;solv ) free solvation energy (component i) released by solvent change ∆H°T ) standard heat of reaction at temperature T (J/mol) ∆Hv ) molar heat vaporization (cal/mol) ) dielectric constant * ) standard-state dielectric constant 0 ) permittivity of vacuum (C2‚N-1‚m-2) γf ) activity coefficient of methyl formate γm ) activity coefficient of methanol γt ) activity coefficient of toluene λB ) defined in eq 30 $i ) volume fraction of liquid i in a mixture of eq 9
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Received for review December 15, 1995 Revised manuscript received May 31, 1996 Accepted June 6, 1996X IE950755S
X Abstract published in Advance ACS Abstracts, August 15, 1996.
