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May 31, 2007 - A study of adsorption of thiophenic sulfur compounds, thiophene (T), benzothiopnene (BT), and dibenzothiophene (DBT), in normal alkane ...
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Ind. Eng. Chem. Res. 2007, 46, 4874-4882

Heats of Adsorption from Liquid Solutions and from Pure Vapor Phase: Adsorption of Thiophenic Compounds on NaY and 13X Zeolites Liping Ma†,‡ and Ralph T. Yang*,† Department of Chemical Engineering, UniVersity of Michigan, Ann Arbor, Michigan 48109, and Faculty of EnVironmental Science and Engineering, Kunming UniVersity of Science and Technology, Kunming, Yunnan, People’s Republic of China 650093

A study of adsorption of thiophenic sulfur compounds, thiophene (T), benzothiopnene (BT), and dibenzothiophene (DBT), in normal alkane solvents (n-octane and hexadecane) on NaY and 13X zeolites was performed. Adsorption isotherms of pure-component n-octane, hexadecane, and T from the vapor phase were also measured. Analysis of the heats of adsorption (including differential and integral heats) calculated by using the Clausius-Clapeyron equation were in agreement with the results obtained by Ng et al. using flow calorimetry for the same systems. The simple theory estimating the relationship between the heat of adsorption from liquid solution and that from the vapor phase proposed in our previous work was tested using the experimental data. The enthalpies of solvation for T-octane and T-hexadecane were also used to validate the simple theory. The theoretical predictions were in close agreement with experiments. The simple theory is easy to use and can explain and provide insight into adsorption from liquid solution. 1. Introduction As a result of worldwide environmental mandates, ultradeep desulfurization of transportation fuels (gasoline, diesel, and jet fuels) has become an important and active research subject worldwide in the last 10 years.1-5 Selective adsorption is of particular interest because adsorption can be performed at ambient temperature and pressure and the content of sulfur in fuels can be reduced to very low levels compared with the hydrodesulfurization process by which the fuel quality would be subsequently altered.6 Various types of adsorbents such as mixed metal oxides, active carbon, clays, zeolites, and some novel mesoporous materials have been studied.7-12 In our previous studies, we have developed a class of sorbents that rely on π-complexation for selective adsorption of organic sulfur molecules from liquid fuels.13-17 These sorbents were prepared by using several ion-exchange techniques to introduce d-block metal cations into zeolites, including Ag+, Cu+, Ni2+, and Zn2+. These ion exchanged zeolites are capable of producing fuels with a total sulfur concentration less than 1 ppmw. In particular, the Cu(I)-Y zeolite (vapor-phase ion exchanged, VPIE) exhibits the highest sulfur selectivity and capacity.1,13,17 A recent report showed that Pd-based sorbents have higher sulfur capacities than Cu(I)-Y.18 In addition, we have shown that activated carbon used as a guard bed can improve the adsorptive performance of Cu(I)-Y.13,16 The equilibrium isotherm and heat of adsorption are the critical design variables in estimating the performance of an adsorptive separation process. The shape of an isotherm provides significant information on the adsorption process. It indicates the nature and strengths of sorbate-sorbent and sorbate-solvent interactions and also the degree of energetic heterogeneity of the solid surfaces, which provide useful information for the design of adsorbents. In our previous studies,19 vapor-phase adsorption isotherms were studied to understand the interactions * Corresponding author. Tel.: 734-936-0771. Fax: 734-764-7453. E-mail: [email protected]. † University of Michigan. ‡ Kunming University of Science and Technology.

between benzene/thiophene (T) and various sorbents, including Ag-Y, Cu-Y, Na-Y, H-USY, Na-ZSM-5, activated carbon, and modified activated alumina. Ng et al.20-22 studied the adsorption of thiophenic compounds in normal alkane solvents on NaY zeolite using flow calorimetry and thermogravimetric analysis. More recently, we have carried out a systematic study23 on the adsorption isotherms and heats of adsorption of T type sulfur compounds [i.e., T, benzothiophene (BT), dibenzothiophene (DBT), and methyl substituted benzothiophenes] on Cu(I)-Y (VPIE) and PdCl2/AC sorbents from the liquid phase in octane solvent. We have also reported the vapor-phase adsorption isotherms of pure-component n-octane and T on these sorbents. By considering the influence of solute-solvent interaction on the adsorption, a simple theory was proposed for estimating the relationship between the heats of adsorption from liquid solution and that from vapor phase. The experimental results were in fair agreement with the theory for adsorption of thiophenic sulfur compounds on Cu(I)Y and PdCl/AC.23 In this work, the heats of adsorption of thiophenic sulfur from solutions on NaY and 13X zeolites were obtained from the temperature dependence of isotherms and were compared with that from calorimetric measurements reported by Ng et al.20-22 Our simple theory for the relationship between heats of adsorption from the vapor phase and that from liquid solution was further tested using the results of Ng et al.20-22 and the results of this work. The simple theory should be useful for the design of adsorption from liquid solutions based pure compound vapor-phase data. 2. Experimental Section 2.1. Preparation of Sorbents. Zeolites NaY (Si/Al ) 2.4) and 13X (Si/Al ) 1.2), in powder form, were obtained from Strem Chemicals and Sigmal Aldrich, respectively. They were chosen as the sorbents in this study because they were used in the study of Ng et al.,20-22 whose results were used to test our simple theory. The zeolites were dried at 400 °C in helium for 6 h before use. 2.2. Characterization of Sorbents. The BET surface areas, pore volumes, and the median pore widths of the sorbent

10.1021/ie070336i CCC: $37.00 © 2007 American Chemical Society Published on Web 05/31/2007

Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007 4875 Table 1. Surface Areas and Pore Volumes of Sorbents sample NaY 13X

SBET (m2‚g-1)

Vmax (cm3‚g-1)

Vmic (cm3‚g-1)

568 621

0.373 0.332

0.304 0.298

samples were measured by physical adsorption of N2 at 77 K using Micromeritics ASAP 2010. The results are shown in Table 1. T, BT, DBT, n-octane, and hexadecane (>99%) were purchased from Sigma-Aldrich and were used without further purification. 2.3. Adsorption Procedure. Adsorption isotherms were measured by a batch method. Binary solutions containing n-octane or hexadecane and a sulfur compound of different concentrations (ranging from 1 to 400 ppmw-S) were used. The solution (3 cm3) and the sorbent (30-50 mg), after in situ activation pretreatment, were mixed in a tubular vial (10 cm3 volume) equipped with a magnetic stirrer. The vial was then sealed and placed in a thermostated bath with stirring for a desired equilibrium time at 20 °C and 50 °C. In each case, a control vial with the same amount of solution but without any adsorbent was also placed in the same bath. The liquid phase was filtered with Whatman Grade 1 filter paper after equilibrium. The adsorbate concentrations in the filtrate were determined by a gas chromatograph which is described below, and the amount of sulfur removed was calculated by comparing the sulfur content in the solution with that in the control vial. Pure-component, vapor-phase isotherms for n-octane, hexadecane, and thiophene were measured at 90 °C, 120 °C, and 160 °C using standard gravimetric methods. A Shimadzu TGA50 automatic recording microbalance was employed. Helium (prepurified grade, Metro welding, 99.995%) was used as the carrier gas and was first passed through two consecutive gaswash bottles (to ensure saturation), which contained octane (Aldrich, >99%), hexadecane (Aldrich, >99%), or thiophene (Aldrich, >99%). After the concentration had been diluted to the desired value by blending with additional helium, the mixture was directed into the microbalance. The differential enthalpy of adsorption ∆Had values were calculated using the Clausius-Clapeyron equation from vaporphase isotherms at different temperatures:

∆Had ) - RT2

(∂ ∂Tln p)

q

(1)

where q is the adsorbed amount (mmol-S/g-sorbent), p is the partial pressure of the sorbate, T is the adsorption temperature (K), and R is the gas constant. ∆Had is negative because adsorption is exothermic. Isosteric heats of adsorption qst are the absolute values of ∆Had. For liquid-solid adsorption the Clausius-Clapeyron equation should be

(∂ ∂Tln C)

∆had ) -RT2

q

(2)

where C is the equilibrium concentration of sulfur compound at temperature T. 2.4. Gas Chromatograph Analysis and Calorimetric Procedure. All of the samples collected during the isotherm measurements were analyzed using a Shimadzu GC-17A v3 unit equipped with an EC-5 capillary column and a flame photometric detector. More details on the GC sulfur analysis can be found elsewhere.13,14 Heats of solution of thiophene in octane and hexadecane were measured using a calorimetric method. The apparatus and the procedure reported by Saluja et al.24 were followed. The calorimeter was immersed in a water bath at 25 °C. Liquid

Figure 1. Adsorption isotherms of thiophenic sulfur compounds (T ) thiophene, BT ) benzothiophene, DBT ) dibenzothiophene) in hexadecane on NaY: 4, T (20 °C); ], T (50 °C); 2, BT (20 °C); 9, BT (50 °C); ×, DBT (20 °C); [, DBT (50 °C); solid and dashed lines are fitted with the Langmuir-Freundlich model.

Figure 2. Adsorption isotherms of thiophenic sulfur compounds in hexadecane on 13X: 4, T (20 °C); [, T (50 °C); 2, BT (20 °C); b, BT (50 °C); 0, DBT (20 °C); ×, DBT (50 °C); solid and dashed lines are fitted with the Langmuir-Freundlich model.

samples were introduced into 100 mL of solvent with 3, 5, or 7 mL syringes into the calorimeters. Calibration for each determination was accomplished using KCl as a standard and measuring the heat of solution in water. The standard deviation from the mean of five determinations was 7%. 3. Results and Discussion 3.1. Adsorption Isotherms. The rates of adsorption from all binary solutions were fairly rapid.23 In all cases, 7 h was adequate for reaching equilibrium. The adsorption isotherms were measured in the low concentration range of sulfur (0-400 ppmw-S) for simulating the sulfur contained in commercial fuels1 and for understanding the heterogeneous character of the sorbents. The equilibrium isotherms for the adsorption of thiophenic sulfur compounds from binary solutions in hexadecane on the NaY and 13X zeolites are shown in Figures 1 and 2. The equilibrium data was fitted to the Langmuir-Freundlich single solute isotherm,19 which has the form

q)

kQmC1/n 1 + kC1/n

(3)

where Qm is its maximum adsorption capacity, k is the Langmuir-type constant, and the exponent n indicates the

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Table 2. Parameters for the Langmuir-Frenudlich Isotherm for Adsorption of Sulfur Compounds from Binary Solution solution NaYa

T BT DBT

13Xa

T BT DBT

NaYb

T

13Xb

T

temperature (°C)

Qm (mmol‚g-1)

k

n

20 50 20 50 20 50 20 50 20 50 20 50 20 50 20 50

19.12 12.47 2.286 1.756 1.602 1.466 38.44 32.24 3.263 3.243 2.153 1.724 2.324 1.25 2.42 1.601

4.13 × 10-9 1.17 × 10-8 0.0194 0.0157 0.0889 0.0421 3.08 × 10-17 3.66 × 10-8 0.0165 0.0068 0.1838 0.2172 1.8 × 10-4 0.6 × 10-4 0.00245 0.00022

0.323 0.349 1.072 1.123 1.161 1.016 0.476 0.425 1.173 1.127 5.411 5.244 0.736 0.649 1.204 0.774

a The solution is sulfur compound in hexadecane. b The solution is sulfur compound in n-octane.

heterogeneity of the site energies. The use of this equation for (1/n) greater than 1 may be referred to as the “Hill Equation”.25 The fitting range was from 0 to 400 ppmw-S per gram of sorbent. The fitted parameters for the Langmuir-Freundlich equation are given in Tables 2 and 3. From Figure 1, it is interesting to note that at a low concentration of thiophene sulfur compounds, a systematic increase in adsorption capacity was observed with an increase in the size of the sulfur molecule. On the contrary, the adsorption capacity had an opposite relationship with the size of the sulfur molecule when the concentration was higher than about 150 ppmw-S. This aspect was also pointed out by Ng and co-workers in discussion of their calorimetric results on heats of adsorption from solutions.20 On the one hand, NaY zeolite has a large pore volume, giving a high sorbate capacity, which follows the pore filling mechanism.26 At low concentrations of sulfur compounds, each sulfur molecule is assumed to rest preferentially at a position at which its energy potential within the pore would be minimum and forms a monolayer of adsorbate molecules. In this range, the larger molecular size sulfur compound has a higher adsorption capacity because of the stronger electrostatic interactions between adsorbate molecule with the cationic charges of NaY. With the increase in concentration of sulfur compounds, for the smaller molecular-size thiophene, adsorbate-adsorbate interaction commences, leading to cluster formation and eventually pore filling in the micropores, which leads to the sharply increasing adsorption capacity for thiophene at high concentrations. In the same higher concentration range, the larger molecules of BT and DBT cannot fill further in the micropore cavities, as shown by the low adsorption capacities in this range. The recent work of Yang et al. on using mesoporous silicas with large pore sizes for selective adsorption of thiophene sulfur compounds showed promising results.27,28 On the other hand, the interactions of the adsorbate molecule with the cation charges and the framework oxygen atoms also affect the adsorption phenomena. Laborde-Boutet and his co-workers29 proposed that the main interaction between the adsorbates and NaY zeolite occurs on SII surroundings and that the hydrogen atoms of the adsorbates can also interact with the framework oxygen atoms of the D6R window surrounding the SII site. Figure 2 shows the adsorption isotherms of T, BT, and DBT in hexadecane on 13X. It can be seen that at low concentrations of sulfur compounds, the adsorption capacity of 13X for BT is higher than T and DBT. At still higher concentrations, the loadings of BT and DBT approach saturation gradually, while

the adsorbed amount of T continues to increase with the increase in concentration. This phenomenon is the same as that on NaY because both of them have the similar cavity structure. In the 13X zeolite there are two sites, type II and type III, which contain sodium ions of six- and fourfold oxygen coordination, respectively, at which it is possible for sulfur compounds to adsorb. To understand the effect of solvent on the adsorption of sulfur compounds, the adsorption isotherms of T in octane and hexadecane solvents were measured on NaY and 13X and are shown in Figure 3. At concentrations less than 150 ppmw, slightly more T is adsorbed on 13X from octane solvent than from hexadecane, whereas there is essentially no difference for NaY between the two solvents. With the increase in sulfur concentration, there is clearly a higher adsorption capacity for T from hexadecane than from octane. This result seems to suggest that at very low concentrations of sulfur, the difference of adsorption capacity for T may come from the difference in the chain lengths of the alkane solvents and the pore volume of sorbents. With the increasing in the concentration of T, the strong electrostatic interactions between T molecule with the cationic charges and adsorbate-adsorbate interaction increase, just as in the analysis in Figure 1, which leads to the high adsorption amount for T. And it seems that the adsorption of alkane solvent with the longer chain (hexadecane) on zeolites is easily displaced by the sulfur compounds which show the higher adsorption capacities in hexadecane than in octane on both sorbents. This will be further explained with the results on adsorption of the two solvents from vapor phase as shown below. 3.2. Heats of Adsorption from Binary Liquid Solutions. In Figures 1 and 2, the equilibrium isotherms of thiophenic sulfur compounds on NaY and 13X at 20 °C and 50 °C are shown. The data were fitted by the Langmuir-Freundlich eq 3, and the fitting parameters are included in Table 2. Heats of adsorption are calculated using the Clausius-Clapeyron (CC) equation (eq 2) from isotherms at two different temperatures and are summarized in Table 4. The Clausius-Clapeyron equation (C-C equation) was formulated for phase transition between two phases of matter and has been used widely in calculation for isosteric heats of adsorption.30-32 There are two methods to calculate the isosteric heat of adsorption by the C-C equation (eq 1 or eq 2). One is the graphical method by the C-C equation:

qst ∂ ln p )R ∂(1/T)

(4)

By plotting ln(p) or ln(c) versus 1/T for a given adsorbed amount q, qst could be obtained from the slope of the plot. The other is the integrated method. By integrating eq 1 for two isotherm temperatures, qst is expressed as

qst ) R

(

)()

T1T2 p2 ln T2 - T1 p1

(5)

Here, c (as in eq 2) is used to replace p in eq 5 for calculating the heat of adsorption in the liquid phase. The net isosteric heats obtained by these two methods have been compared by Mulet et al. for gas adsorption,33,34 and no significant difference was found. It is important to keep in mind that the derivation of eq 4 or eq 5 has the simplifying assumptions that the gas or liguid is assumed to be an ideal gas or liquid and the isotherms must be measured at closely spaced temperature intervals; therefore, the isosteric heat is assumed to be constant. In this work,

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Figure 3. Comparing adsorption isotherms of T in n-octane and in hexadecane on NaY and 13X at 20 °C. a: Concentration of T ) 0-400 ppmw-S. b: Concentration of T ) 0-200ppmw-S. b, T + hexadecane on 13X; *, T + octane on 13X; 4, T + octane on NaY; ], T + hexadecane on NaY; solid and dashed lines are fitted with the Langmuir-Freundlich model. Table 3. Parameters for the Langmuir-Frenudlich Isotherm for Pure-Component Vapor-phase Adsortpion sorbate NaY

T

n-octane hexadecane 13X

T n-octane hexadecane

Table 4. Integral Enthalpy of Adsorption (kJ/mol) for Adsorption from Binary Solution and from Vapor Phasea,b

temperature (°C)

Qm (mmol‚g-1)

k

n

90 120 160 180 120 160 90 120 120 160 120 160 90 120

3.151 3.078 3.183 3.697 1.74 1.51 1.215 0.793 3.665 3.549 1.158 1.126 0.40 0.363

2455.1 1085.4 474.72 1073.5 614.67 334.10 5.35e19 1.62e31 40.08 91.33 39081 66442 4.46 × 1018 2.03 × 1018

1.204 1.086 1.009 0.779 1.105 1.116 0.282 0.167 2.041 1.493 0.543 0.481 0.314 0.302

adsorption measurements are carried out at low concentrations for liquid phase or low partial pressures for vapor phase, and it is reasonable to assume that the gas and liquid are ideal. Ranke and Joseph35 used isosteric methods to determinate adsorption energies and kinetic parameters. They showed that the isosteric heat of adsorption qst may be expressed as

∆h˜ average (this work; -kJ/mol)

∆H (Ng et al.;20,21-kJ/mol)

sorbent

T

BT

DBT

T

BT

DBT

NaY (in hexadecane) NaY (in octane) 13X (in hexadecane) 13X (in octane)

20.21 19.30 16.08 27.94

20.85

19.08

20.97

22.59 22.4

18.82 21.8

25.58

13.89

∆h˜ average (this work; -kJ/mol) vapor

phasec

NaY 13X

T

octane

hexadecane

60.8 66.59

28.15 17.76

48.32 36.45

a The liquid solution is sulfur compound in hexadecane or n-octane. b T ) thiophene, BT ) benzothiophene, DBT ) dibenzothiophene. c Vapor phase adsorption is for pure component adsorption.

Table 5. Hildebrand Solubility Parameters of T Sulfur Compounds δ (cal/cm3)1/2

Ta

BTb

DBTb

n-octanec

10.1

12.5

12.3

7.6

a

hexadecanec 8.2 b

(6)

Calculated from heat of vaporization, from ref 43. Calculated by δ ) (D∑G)/M, where D (density), M (molecular weight), and molar attraction constant G of phenylene and -CH3 are from ref 43. G of T was from a. c From ref 43.

where Ed and Ea are the activation energies for desorption and adsorption, respectively. Thus, the determination of qst from C-C equation is independent of the kinetics. Another method of measuring the isosteric heat is calorimetry. The working equation depend upon the design of the apparatus for an isothermal calorimeter is36

Figure 4 shows the isosteric heats of adsorption as functions of amount adsorbed on NaY, calculated by using eq 5, for sulfur compounds from hexadecane solutions. The integral heats of adsorption, ∆h˜ calculated with eq 8 below, are also shown on the figure (i.e., the positive quantity of integral enthalpy of adsorption).

qst ) Ed - Ea

-qst )

Q + Vt∆p ∆nm

(7)

where Q is the heat registered for an incremental dose of gas ∆nm introduced at the temperature of the calorimeter cell and Vt is the dead space in the sample cell. The Vt∆p term in eq 7 is small compared to Q. Many researches have carried out comparisons of adsorption heat from isosteric and calorimetric methods for gas adsorption on zeolites and activated carbon.36-39 From these results, a good agreement between measured and calculated isosteric heats from the C-C equation was observed. To our knowledge, comparisons between the heats of adsorption from liquid phase using the C-C equation and by calorimetric method are rare.

∆h˜ )

∫0q∆had dq

1 q

(8)

It is interesting to note that all the isosteric heats of adsorption had the tendency of increasing with the loading and the integral heats for all thiophenic sulfur compounds remained nearly constant. This result coincided with the results on sorbents such as ion-exchanged zeolites and activated carbon which also had heterogeneous sites.36,40 The heat of adsorption results measured directly by using calorimetry by Ng et al., which are integral heats, on the same sorbent for T sulfur compounds are also listed in Table 4. A good agreement is seen between our work and that of Ng et al.,20-22 which indicates there is no significant difference in heats

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Figure 4. Heats of adsorption of thiophenic sulfur compounds on NaY as a function of adsorbed amount. 9, Differential heat of adsorption; O, integral heat of adsorption.

Figure 5. Adsorption isotherms of vapor-phase n-octane on NaY and 13X at different temperatures. 2, NaY (120 °C); 9, NaY (160 °C); 0, 13X (120 °C); O, 13X (160 °C); solid and dashed lines are fitted with the LangmuirFreundlich model.

Figure 6. Adsorption isotherms of vapor-phase hexadecane on NaY and 13X at different temperatures. 2, NaY (90 °C); [, NaY (120 °C); 0, 13X (90 °C); O, 13X (120 °C); solid and dashed lines are fitted with the Langmuir-Freundlich model.

of adsorption between that calculated by the C-C equation and that measured directly by calorimetry for adsorption from dilute liquid phase. 3.3. Heats of Adsorption from Vapor Phase. To understand the roles played by the solvent-sorbent interaction and sorbatesolvent interaction in the adsorption from binary liquid solutions, pure-component isotherms for vapors of T, n-octane, and hexadecane were measured at different temperatures using a standard gravimetric method. The results are shown in Figures 5-7. Only T was used because the other sulfur compounds are solid at room temperature, and the measurements of adsorption from vapor phase for such low volatile compounds are extremely difficult. By comparing Figure 5 with Figure 6, it can be seen that NaY has a higher adsorption capacity than 13X zeolite for both n-octane and hexadecane, which was due to the larger micropore volume and pore width of NaY (Table 1). In comparing the isotherms of these two molecules, in both zeolites, the shorter molecule, n-octane, can more easily fill in the supercages and leads to a high adsorption capacity for octane than for hexadecane (in mol/g). For adsorption of T, Figure 7 shows that the amount adsorbed was still increasing at a partial

pressure of 0.06 atm and that the saturated amounts were much greater than that of n-octane and hexadecane. Also, 13X zeolite seemed to show a slightly higher adsorption capacity than NaY. Though NaY and 13X have the same faujasite structure and the same cation, the large difference in the Si/Al ratio led to many differences in the adsorption sites in their interactions with T molecules. It should be noted that the adsorbed amounts for T and the two solvents on NaY and 13X mainly took place in Henry’s law region at low partial pressures, as the energy of adsorption of a monolayer of adsorbate molecules on a clean sorbent surface was the highest and that, on subsequently adsorbed layers of adsorbate molecules, the adsorption energy dropped to nearly a constant lower value.26 This was especially true for the adsorption of hexadecane, because of its long chain that it could not further fill in the pores with further increase in partial pressure. Figure 8 shows the data for T on NaY plotted in ln(p) versus (1/T), and the isosteric heats of adsorption were calculated from the slopes by using eq 4. The integral heats of adsorption are also included in Table 4. This result (60.8 kJ/mol on NaY for T) is in good agreement with the theoretical result given by Ju

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Figure 7. Adsorption isotherms of T in vapor phase on different sorbents at 120 °C. 2, NaY (120 °C); b, NaY (160 °C); ], 13X (120 °C); *, 13X (160 °C); solid and dashed lines are fitted with the Langmuir-Freundlich model.

almost always measured by pure-component adsorption from vapor phase. Pure-component vapor phase adsorption can be predicted once the sorbate-sorbent interaction potentials are known. Adsorption from the binary liquid solution is much more complex than that from the gas phase. Sircar and his co-workers42-45 have carried out many studies to analyze the relationship between heat of adsorption in liquid and their vapors using direct calorimetric measurements based on thermodynamic analysis. A simple theory for understanding the relationship between purecomponent adsorption from vapor phase and adsorption from liquid solution using solute-solvent interaction theory was proposed by us recently.23 The heat of adsorption in pure component vapor phase can give the Henry’s constant. Adsorption of a solute (i.e., sorbate) from a binary solution depends on sorbate-sorbent, sorbate-solvent, sorbate-sorbate, and solvent-solvent interactions. In the process of a solute molecule to be adsorbed on the site of a sorbent, it needs to overcome the energy of interactions between solvent-solvent and solventsolute and the energy used to displace the solvent molecules which initially hold the adsorption site. Usually a lower exothermal heat is measured as the overall heat of adsorption from a liquid solution. The basic equation of this simple theory previously proposed23 is as follows:

∆h˜ ) ∆H ˜ - hi - βHs

Figure 8. Isosteric heat of vapor-phase adsorption of T on NaY plotted as ln(p) versus (1/T) at different loadings (mmol-S/g).

et al. using Monte Carlo simulation.41 Figure 9 shows the change of the isosteric heats and the integral enthalpy of adsorption ∆h˜ with loading for T on NaY and 13X. It is clear that qst calculated with eq 1 was sensitive to the amount adsorbed, and the value of the integral heat ∆H ˜ was less dependent on or rather independent of the amount adsorbed. For small uptakes, the isosteric heat of adsorption generally decreased rather strongly with the amount adsorbed, indicating strong site heterogeneity. The opposite was true for adsorption from liquid solutions. Comparing with Figure 4, heat of adsorption on NaY in liquid solution increased with the increase of loading, and all of the isosteric heats declined and eventually approached saturation. This indicates that the process of adsorption in liquid solution is strongly affected by the solvent. When the solid is immersed in a liquid, the adsorption sites are held by solvent molecules first. With the increase in loading, more solvent molecules are displaced by adsorbate molecules. For adsorption in the vapor phase, no solvent effects are present. 3.4. Relationship between Adsorption from Vapor Phase and from Liquid Solution. Heat of adsorption provides the basic information for the adsorption process, which is also important in design for practical applications. Adsorption bond energies can now be calculated for both physical adsorption (by Monte Carlo simulation) and chemisorption (by ab initio molecular orbital theory), and these energies are approximately equal to the heats of adsorption.26 The heats of adsorption are

(9)

where ∆h˜ is the integral enthalpy of adsorption of solute from liquid solution according to eq 8; ∆H ˜ is integral enthalpy of adsorption for pure solute component in vapor-phase adsorption; hi is the heat of immersion of solid sorbent in the solvent; Hs is the energy for dissociating solute molecule from solution; and β is the fractional constant, accounting for remaining interactions between the adsorbed molecule with the solvent. The heat of immersion (i.e., molar immersion heat, hi) is related to the integral enthalpy of adsorption of solvent from the vapor phase (∆H ˜ ) by38,44

hi ) -∆H ˜ + ∆HL

(10)

where ∆HL is the heat of liquefaction; the negative quantity of ∆HL is the heat of vaporization of solvent Hvap. For hexadecane, it is 64.39 kJ/mol, and for n-octane, it is 38.54 kJ/mol.46 One of the tools for the investigation of solute-solvent intermolecular interaction is the study of transfer of the solute molecules from the ideal gas phase to the solvent at infinite dilution. This transfer is referred to as solvation, while solution means the transfer to the same state but from the standard state of the solute at a given temperature. The enthalpy of solvation can be represented as a sum of the enthalpy of solute-solvent interactions and the change in solvent-solvent interactions. The standard molar enthalpies of these processes are expressed by a simple equation:

∆Hsolv(A f S) ) ∆Hsoln(A f S) - ∆Hvap(A)

(11)

where A denotes solute and S denotes solvent, ∆Hsoln(A f S) is the enthalpy of solution for solute A, and ∆Hvap(A) is the standard molar vaporization enthalpy of the solute. Many studies have been performed by Fuchs et al.47,48 on the determination of enthalpies of interaction of polar and nonpolar solutes with polar or nonpolar solvents, and many organic compounds have been tested. Solomonov et al.49 have developed methods for extracting the enthalpy of specific

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Figure 9. Heats of adsorption of T on NaY and 13X from vapor phase as a function of adsorbed amount. 9, Differential heat of adsorption; O, integral heat of adsorption.

solute-solvent interaction based on the basic relationship above (eq 11). Jesus et al.50 determined the enthalpies of solutesolvent interactions of erythritol and L-threitol in aqueous solution from solvation based on the enthalpies of solution and sublimation. To our knowledge, there is no solvation data published in the literature on the T sulfur compounds in hexadecane or n-octane solvent. The enthalpy of solvation contains not only the enthalpy of cavity formation in the solvent but also the enthalpy of solute-solvent interactions. Therefore it can be used directly in eq 9 to replace the last term βHs. On the other hand, cohesive energy density (CED or c) can reflect the cavity formation energy of solvent molecules.51 According to the CED and Hildebrand solubility parameter theory, the last term in eq 9 can be expressed as follows which were explained in detail in ref 23:

βHs )

-βδ122V12l

(12)

where V is the molar volume, δ is the Hildebrand solubility parameter, V12l ) x(Vl1V2l), δ12 ) x(δ1δ2), subscript 1 represents the solute (sulfur molecule), 2 represents the solvent, and the fractional parameter β corrects for the partial dissociation of the solute molecule from the solvent upon adsorption. The minus sign means this part of the enthalpy in the energy balance of eq 9 is the opposite quantity that is used to break up the solvent-solvent and solvent-sorbate interactions. The Hildebrand solubility parameter δ of T can be calculated from its molar enthalpy of vaporization.46 The values of δ in eq 12 for the other sulfur compounds can be estimated using Small’s molar attraction constants combined with the T molar attraction constant.52,53 The results are given in Table 5. To compare the results for assessing the relationship between the heats of adsorption from pure-component vapor phase adsorption and the heat of adsorption from binary liquid solutions calculated using solvation and eq 12, the heat of solution of T in hexadecane and octane were measured by using calorimetry. Only T was used because the other sulfur compounds are solid at room temperature. There is lacking of data

Table 6. Enthalpies of Solution and Solvation of T in n-Octane and Hexadecane at 25 °C ∆Hvap (kJ/mol)

∆Hsoln (octane) (kJ/mol)

∆Hsoln (hexadecane) (kJ/mol)

∆Hsolv (octane) (kJ/mol)

∆Hsolv (hexadecane) (kJ/mol)

36.56

3.96

4.56

-32.6

-32.0

T

Table 7. Prediction for Heat of Adsorption from Vapor Phase Using Equation 9 Based on That from Binary Liquid Solution Using Equation 11 and Equation 12a,b -∆H ˜ (kJ/mol) sorbent

adsorbate

-∆H ˜ (kJ/mol) (in octane)

-∆H ˜ (kJ/mol) (in hexadecane)

expt

eq 11

eq 12

eq 11

eq 12

NaY

T

60.8

62.29

68.28

13X

BT DBT T

66.59

81.32

66.33 59.70c 87.54d 98.37d 85.36 76.82c

82.26 65.81c 105.54 118.04 89.70 71.76c 121.83 124.42

BT DBT

75.72

a T ) thiophene, BT ) benzothiophene, DBT ) dibenzothiophene. b β in eq 9 take as 1.0, i.e., no correction for cavity formation energy. c β in eq 9 take as 0.9 for adsorption in octane and 0.8 for adsorption in hexadecane for correction cavity formation energy. d Heat of adsorption of liquid phase from Ng et al.21

of their enthalpies of sublimation or lattice energies which are to be estimated. The calorimetric procedure described in the literature was followed.48 The results are summarized in Table 6. On the basis of the above simple analysis, the relationship between the heats of adsorption from pure-component vapor phase adsorption and the heats of adsorption from binary liquid solutions (in hexadecane and n-octane) were calculated using eq 9, eq 11, and eq 12 and are summarized in Table 7. The heats of adsorption from the gas phase are predicted by using eq 9, based on the heat of adsorption from binary solutions using eq 11 and eq 12. From these results it is noted that when β ) 1, meaning no correction for the cavity formation energy, the predictions by using eq 9 for T adsorption on NaY from both eq 11 and eq 12 are quite reasonable, for both solutions in n-octane and hexadecane. The average errors of the predicted

Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007 4881

heats of adsorption for T from the vapor phase are 2.5% and 12% using eq 11 (heat of solvation) in octane and hexadecane, respectively, and the errors are 9% and 35% using eq 12 for solutions in octane and hexadecane, respectively. The predicted vapor-phase heats of adsorption calculated by eq 11 and eq 12 are greater than calculated from experiments, and the average errors from eq 12 are larger than from eq 11, which indicates that the use of enthalpy of solvation can reasonably predict the solute-solvent interactions and that the correction parameter β is needed. From the experiments, for adsorption on 13X, the errors are greater from the solution in n-octane than that in hexadecane when predicted with the heat of adsorption. The predicted heats of adsorption for pure-component vapor-phase adsorption follows the order T < BT < DBT for both sorbents. This is similar to that obtained from the prediction on Cu(I)Y and PdCl2/AC.23 In Table 7, if we take β ) 0.9 for T in octane and 0.8 for T in hexadecane, for both NaY and 13X, the predicted results for heats of adsorption have less errors when compared with experiments. This result indicates that when thiophenic sulfur compounds were adsorbed from the liquid solution, breakage of only parts of the cavity formation interactions is required, and this energy differs for different solvents and different sorbents. It seems that the solvent with a longer chain has a larger enthalpy of cavity formation, and more correction is needed because breaking of only part of such interactions is required for solute adsorption. 4. Conclusion Adsorption isotherms for thiophenic sulfur compounds in binary solutions, in hexadecane or n-octane, were measured for two different sorbents (NaY and 13X zeolites). The adsorption selectivity increased in the order of T < BT < DBT at low sulfur concentration on both NaY and 13X. However, in the high concentration range, the adsorption-selectivity order became: DBT < BT < T for both zeolites. The heats of adsorption (including differential and integral heats) calculated by using the Clausius-Clapeyron equation based on isotherms at different temperature were in agreement with the results given by Ng et al.20-22 using flow calorimetry for the same system. To test the simple theory proposed by us previously,23 the heats of adsorption calculated from the Clausius-Clapeyron equation using our data were in close agreement with the direct measurements of Ng et al.20,21 using calorimetry. The enthalpy of solvation of both T in n-octane and T in hexadecane were also used to validate the simple theory proposed by us previously. The predicted results were in close agreement with experiments. Although the enthalpy of solvation can provide accurate information on the solute-solvent intermolecular interactions, it is difficult to obtain by simulation. Our simple theory can provide insight into the mechanism of adsorption from liquid solutions, and it is simple to use. The results showed that the order of the predicted heats of adsorption for purecomponent sulfur compounds on both sorbents was in agreement with the order obtained from ab initio molecular orbital theory that we performed previously, that is, T < BT < DBT. The correction parameter β was affected by both the solvent and the sorbent for adsorption of the same sulfur compound. The alkane solvent with longer chain required a smaller correction parameter β. The results are useful for designing and selecting sorbents for desulfurization of different fuels (gasoline, diesel, and jet fuel). Further study is needed to understand the dependence of β on different solvents.

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ReceiVed for reView March 5, 2007 ReVised manuscript receiVed April 17, 2007 Accepted April 18, 2007 IE070336I