Rates of Reaction of Wyodak Rawhide Coal Hydroxyl Groups with

The rates of coal swelling in the base solutions were measured independently. The following observations were made for Wyodak Rawhide coal: (1) NaOH a...
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VOLUME 15, NUMBER 4

JULY/AUGUST 2001

© Copyright 2001 American Chemical Society

Articles Rates of Reaction of Wyodak Rawhide Coal Hydroxyl Groups with Tetra-alkylammonium Hydroxides and Rates of the Concomitant Swelling J. W. Larsen*,† and J. Jones University of Tennessee, Department of Chemistry, Knoxville, Tennessee 37916

G. B. Brons, J. J. Isaacs, and R. Liotta Corporate Research-Science Laboratories, Exxon Research and Engineering Company, Linden, New Jersey 07036 Received August 27, 2000

Reaction rates of coals are often limited by the mass transfer rates of reagents into coals. The reaction of tetralkylammonium hydroxides with coals giving coal polyanions is much more rapid than any other derivatization of coal’s hydroxyl groups. A calorimetric technique for measuring these rates was developed. The rates of coal swelling in the base solutions were measured independently. The following observations were made for Wyodak Rawhide coal: (1) NaOH and KOH do not rapidly diffuse into coals, (2) R4N+Br- does not swell coals, (3) R4N+OH- reacts rapidly with coals, the rate of heat liberation being first order and independent of the size of R in methanol and slightly dependent on the size of R in water, and (4) R4N+OH- swells coals, the swelling rate being proportional to xt, independent of R, and slower than the rate of heat liberation. The neutralization of the hydroxyls and the swelling of the coal are kinetically independent, although the former provides the driving force for the latter. The hydroxyl’s reaction is diffusion controlled and the slow step may be (1) diffusion of the hydroxyl anion or (2) the desolvation of the basic anion as it enters the hydrophobic coal, or (3) self-diffusion of coal molecular segments. The R4N+ ions can penetrate the coal because they are poorly solvated in water and methanol making desolvation easy and because they interact favorably with aromatic structures. The swelling rate-determining step appears to be the diffusion of the coal macromolecular segments through and past each other and is dominated by coal-coal interactions.

Introduction Both the thermodynamics and kinetics of coal solvent swelling have been the subject of numerous investigations. Thermodynamic studies have been aimed at * Corresponding author. † Present address: Department of Chemistry, Lehigh University, Bethlehem, PA 18015.

understanding coal macromolecular structure and its interactions with solvents. A good review is available.1 Whenever a coal reacts chemically, diffusion into, out of, or within the coal is involved. For this reason as well as to probe coal structure, diffusion rates of solvents into coals have been extensively studied. Noticeably absent (1) Suuberg, E. M.; Otake, Y.; Langner, M. J.; Leung, K. T.; Milosavljevic, I. Energy Fuels 1994, 8, 1247-1262.

10.1021/ef000193b CCC: $20.00 © 2001 American Chemical Society Published on Web 06/28/2001

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from the coal literature are studies of diffusion coupled with reaction. This paper addresses that topic. Our goal is to understand the factors which control rates of diffusion through coals in the hope that this will enable us to design reagents which can diffuse into the solid more rapidly. Diffusion rates of organic liquids into coals have been studied most often by following the extent of coal swelling vs time. This has been done using apparatus as simple as glass tubes2-5 and as complex as video microscopes.6 Dilatometers have been used.7-9 Direct observations of organic liquids in coals have been made using NMR imaging techniques.10-12 Changes in particle size have been measured.13,14 The data analysis developed by Ritger and Peppas has been almost universally used.15 Both Fickian and Case II diffusion have been observed.6,15 With Case II diffusion, there is a sharp solvent front moving through the coal and the rate-limiting process is the coal macromolecular system rearranging and swelling to accept the solvent.10,12,15 When the diffusion is Fickian, there is a swelling-liquid concentration gradient within the coal and the activated diffusion of the solvent is rate determining.15 Diffusion rates are known to be sensitive to the size of the diffusing molecule13,16 and to the identity of the coal.3,17 Diffusion rates are temperature dependent and activation energies between 31 kJ/mol and 70 kJ/mol have been observed for pyridine in various coals.3 Swelling rates for individual macerals have been measured.14 They show no regular pattern and do not correlate with equilibrium swelling ratios. Coals are anisotropically strained so the initial swelling of a whole coal is anisotropic, greater perpendicular to the bedding plane than parallel to it.18,19 Rates of extraction from coals have also been measured and are diffusion controlled with low activation energies.20 Only a few quantitative studies of the interdependence of reagent diffusion and reaction have been published. The early mostly qualitative work has been reviewed.21 The reaction of maleic anhydride with coals (2) Otake, Y.; Suuberg, E. M. Fuel 1989, 68, 1609. (3) Otake, Y.; Suuberg, E. M. Energy Fuels 1997, 11, 1155-1164, and references therein. (4) Peppas, N.; Lucht, L. M. Chem. Eng. Commun. 1986, 43, 301. (5) Larsen, J. W.; Lee, D. Fuel 1983, 62, 1351-1354. (6) Gao, H.; Nomura, M.; Murata, S.; Artok, L. Energy Fuels 1999, 13, 518-528. (7) Hall, P. J.; Thomas, K. M.; Marsh, H. Fuel 1992, 71, 1271-1275. (8) Aida, T.; Squires, T. G. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1985, 30 (1), 95-101. (9) Nadaji, F. E.; Thomas, K. M. Fuel 1995, 74, 842-845. (10) Cody, G. D., Jr.; Botto, R. E. Energy Fuels 1993, 7, 561562. (11) Cody, G. D., Jr.; Botto, R. E. Macromolecules 1994, 27, 26072614. (12) Hou, L.; Cody, G. D., Jr.; French D. C.; Botto, R. E.; Hatcher, P. G. Energy Fuels 1995, 9, 84-89. (13) Turpin, M.; Rand, B.; Ellis, B. Fuel 1996, 75, 107-113. (14) Nadaji, F. E.; Thomas, K. M. Fuel 1995, 74, 842-845. (15) Ritger, P. L.; Peppas, N. A. Fuel 1987, 66, 1379. (16) Aida, T.; Fuku, K.; Yoshihara, M.; Maeshima, T.; Squires, T. G. Energy Fuels 1991, 5, 79-83. (17) Peppas, N. A.; Lucht, L. M. Chem. Eng. Commun. 1985, 37, 333. (18) Cody, G. D., Jr.; Larsen, J. W.; Siskin, M. Energy Fuels 1988, 2, 340-344. (19) Larsen, J. W.; Flowers, R. A., II; Hall, P. J.; Carlson, G. Energy Fuels 1997, 11, 998. (20) Yoshi, T.; Yoshimura, F. Fuel 1969, 48, 229-235. (21) Larsen, J. W.; Green, T. K.; Choudhury, P.; Kuemmerle, E. W. In Coal Structure; Gorbaty, M. L., Ouchi, K., Eds.; Adv. in Chem. 1981, 192, 277. Am. Chem. Society: Washington, DC, and references therein.

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(presumably a Diels-Alder reaction22) was studied in a series of solvents and the rate was measured as a function of the extent of coal swelling.5 Activation energies were only a few kcal/mol confirming that the reaction was diffusion limited. The rate is independent of the extent of coal swelling. This is surprising. As coal swelling increases it becomes less glassy, more rubbery, and free volume increases. All of these factors should work together to increase diffusion rates. But the maleic anhydride reaction rates are not affected suggesting that it is not translational diffusion of the maleic anhydride that is rate limiting, despite the xt dependence and very low activation energy. The conversion of coals to solubles using tetralin and t-butyltetralin as hydrogen donors has been studied to determine the effect of reduced diffusion rate (accessibility) on coal conversion.23 At the high reaction temperatures used (>325 °C), the increased molecular size and branching had no effect. Relevant to this study is a comparison of the reaction rates of the hydroxyl groups in coals with similar hydroxyl groups in molecules in solution.20 Not unexpectedly, hydroxyls in solid coal always react more slowly than their solution counterparts, sometimes by factors of thousands, presumably because mass transport of the reagents into the coals is slow. A pair of reactions have been reported in which the diffusion of the reagents through the coal was very rapid.24-26 These are of great interest because of this rapid mass transport. If the factors responsible can be discovered, it may be possible to increase diffusion rates for other coal reactions. The reactions are the conversion of coals to polyanions by reaction of hydroxyl groups with tetra-alkylammonium hydroxides and the alkylation of these polyanions with agents such as methyl iodide.24-26 Earlier work showed that the oxygen alkylation of the polyanions of Illinois No. 6 and Rawhide coals with alkyl iodides was not mass transport limited.26 The alkyl halide’s diffusion to the anions in the coal is faster than its reaction with those anions. This is a remarkable observation. In addition, a thirtyminute exposure of these coals to the tetra-alkylammonium hydroxide base in aqueous THF at room temperature was sufficient to convert all of the coal hydroxyls to their anionic forms. This is by far the most rapid reaction of these hydroxyls yet reported. Because the diffusion of the tetra-alkylammonium hydroxides into coal is so rapid, we embarked on a more detailed study of the process, beginning with its kinetics. There is one published study of the reaction rates of Illinois No. 6 coal with tetra-alkylammonium and metal hydroxides.27 The coal behaves as a polyelectrolyte and is so treated. Illinois No. 6 coal was studied under somewhat different conditions than those used in this work and its behavior is somewhat different in the two sets of conditions. A detailed comparison of the results is contained in the Discussion section. Using methanol solvent and several tetra-alkylammonium hydroxides (22) Larsen, J. W.; Quay, D. M.; Roberts, J. E. Energy Fuels 1998, 12, 856-863. (23) Larsen, J. W.; Amui, J. Energy Fuels 1994, 8, 513-514. (24) Liotta, R. Fuel 1979, 58, 724. (25) Liotta, R.; Rose, K. D.; Hippo, E. J. Org. Chem. 1981, 46, 277283. (26) Liotta, R.; Brons, G. J. Am. Chem. Soc. 1981, 103, 1735. (27) Matturro, M. G.; Liotta, R.; Isaacs, J. J. J. Org. Chem. 1985, 50, 5560-5566.

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[R4N+OH-], the swelling rates previously observed are Fickian and depend on the size of the tetra-alkylammonium ion.27 The equilibrium swelling value for the coal is also caton size dependent. The extent of neutralization of the coal’s acidic groups decreases as the tetraalkylammonium ion size increases. As expected for a polyelectrolyte, the observed kinetics and thermodynamics depend on the ionic strength of the base solutions used. Results Reaction of the Hydroxyl Groups. This study began with measurements of the rates of neutralization of weakly acidic hydroxyl groups in coals with strong tetra-alkylammonium hydroxide bases. The reaction immediately liberates heat, and this heat production was followed over time. The rates were measured calorimetrically using a simple solution calorimeter of the original Arnett design.28 The use of twin solution calorimeters for kinetic measurements is well developed29 and procedures similar to those published by Meites29 were used. About 500 mg of powdered coal was injected into 180 mL of a rapidly stirred 1.0 M ammonium hydroxide solution and the heat evolved was followed until the baseline returned to normal in about twenty minutes. If a phenol or carboxylic acid was injected instead of coal, the heat liberation was effectively instantaneous. The reaction rates observed are very convenient for calorimetric study, and heat evolution is one of the few available good probes of this system because the reactions are occurring in a nontransparent solid. Except where noted, six injections of coal were made into each base, so that the rates and heats expressed are the average of six individual, separate determinations. The first task is to establish the rate law followed. The reactions of phenolic and carboxylic hydroxyl groups with strong bases in solution are instantaneous on the calorimeter’s time scale. The reactions of coals take minutes to complete, establishing that they are mass transport limited. The reaction of these hydroxyl groups held in a solid matrix is similar to reactions occurring in ion-exchange resins, in the polystyrene bead during peptide synthesis by the Merrifield technique,30 and in polymer-supported phase transfer catalysis.31 Mass transport in ion-exchange resins has been extensively studied and is complex.32 Our purpose is to find a convenient mathematical expression for the rate of heat evolution to shed some light on the nature of the processes involved, to enable us to express our results succinctly, and to allow the easy comparison of different systems. Figure 1 shows a plot of the recorder pen displacement in mm (q), equivalent to the heat evolved, versus xt in seconds for Rawhide Wyodak coal in methanol (28) Arnett, E. M.; Bentrude, W. G.; Burke, J. J.; Duggleby, P. McC. J. Am. Chem. Soc. 1965, 87, 1541-1553. (29) Meites, T.; Meites, L.; Jaitly, J. N. J. Phys. Chem. 1969, 73, 3801-3809; Ahlberg, P. Chem. Scripta 1975, 8, 50; Frankvoort, W.; Dammers, W. R. Thermochim. Acta 1975, 11, 5-16. (30) Sarin, V. K.; Kent, S. B. H.; Merrifield, R. B. J. Am. Chem. Soc. 1980, 102, 5463-5470. (31) Tomoi, M.; Ford, W. T. J. Am. Chem. Soc. 1980, 102, 71407141. (32) Helferich, F. Ion Exchange; McGraw-Hill Book Company: New York, 1962.

Figure 1. Dependence of the heat evolved (q) from rawhide coal in (CH3)4N+OH- (1.0 M) in methanol at 25 °C on the square root of time (t).

Figure 2. First-order kinetic plot of the heat evolved (q) from rawhide coal in (CH3)4N+OH- (1.0 M) in methanol at 25 °C.

solvent containing tetra-methylammonium hydroxide. If simple Fickian diffusion were the rate-determining step, this plot would be a straight line. It is straight for the first 22 min, but then curves. A plot of log q versus t is shown in Figure 2 and is a good straight line for more of the reaction duration. It deviates only near the end of the reaction when errors due to calorimeter instability will be most important. This reaction can be treated phenomenologically as a first-order reaction. Examination of the same coal with other ammonium hydroxide bases, and other solvents, gives the same results as did a brief study of Illinois No. 6 coal. The heat evolved and the observed first-order rate constants are shown in Tables 1 and 2. Swelling. When the coal is contacted with a tetraalkylammonium hydroxide, it swells. There are undoubtedly two factors responsible for the swelling. The coal is converted to a polyanion by the base and the electrostatic repulsion between the anions (5 per hundred carbon atoms with Illinois No. 6 and 8 per hundred carbon atoms with Rawhide coal)25 causes the coal

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Table 1. Heats (∆H) and Rates (k) of Ionization of Rawhide Coal in (1.0 M) Tetra-alkylammonium Hydroxide (R4N+OH-) Solutions at 25 °C R

solvent

∆H(cal/g)

k x 103(s-1)

H H Me Et n-Pr n-Bu Me Meb Etc n-Bub n-Hexd

H2O H2O H2O H2O H2O H2O H3COH H3COH H3COH H3COH H3COH

-5.32 ( 1.21a -5.18 ( 0.88 -10.4 ( 2.0 -8.22 ( 0.49 -6.76 ( 0.82 -2.43 ( 0.32 -20.7 ( 1.0 -22.7 ( 2.0 -18.2 ( 0.9 -11.9 ( 1.3 -10.2 ( 0.6

1.99 ( 0.57 1.90 ( 0.54 2.19 ( 0.55 2.25 ( 0.28 2.03 ( 0.49 2.52 ( 0.23 1.01 ( 0.13 1.07 ( 0.14 1.18 ( 0.08 1.25 ( 0.l4 1.12 ( 0.09

a Except where noted all results are the average of at least 6 replicate determinations. Errors are standard deviations at the 95% confidence level. b 4 data points. c 5 data points in two runs. d Solution was 0.5 M in base.

Table 2. Heats (∆H) and Rates (k) of Ionization of Illinois No. 6 Coal in (1.0 M) Tetra-alkylammonium Hydroxide (R4N+OH-) Solution at 25 °C R

solvent

∆H(cal/g)

k x 103(s-1)

Me Et

H3COH H3COH

-14.0 ( 1.7a -13.9 ( 2.2

0.83 ( 0.13 0.92 ( 0.14

a

Average of 4 points. Errors shown are standard deviations at the 95% confidence level.

macromolecular network to expand. The tetra-alkylammonium counterions diffuse into the coal and the coal must expand to contain them. Thus, the reaction between the hydroxyl groups and the ammonium hydroxide should be accompanied by swelling of the coal. The swelling was measured by a straightforward technique. The coal was introduced into a glass tube containing the base solution and the height of the coal column measured. The tube was shaken and the height, increasing as the coal swells, was measured at known time intervals. This simple swelling technique has been shown to give the same results as more elaborate gravimetric techniques when used with coal and pure solvents. Again, the first task is to establish the rate law followed by the swelling. Figure 3 shows a plot of the volume change (∆V in mL) of the coal versus xt and Figure 4 shows a plot of log ∆V versus t. Only the plot of ∆V versus xt is a straight line, consistent with simple Fickian diffusion as the rate-determining step. All of the swelling data reported here follow the same rate law, one which is different from the rate law followed by the neutralization reactions. Tables 3 and 4 contain the rates of swelling of whole Illinois No. 6 and Rawhide coals in ammonium hydroxide bases. Similar data are shown for the same coals after extraction with pyridine in Tables 5and 6. The pyridine extraction does not have a large effect on the swelling rate. It is clear that the swelling is slower than the neutralization’s reaction and follows a different rate law. Discussion Two processes are occurring: neutralization of the hydroxyl groups and swelling of the coal structure. The first question to be addressed is the relationship between these two processes. The four situations shown in Scheme 1 must be considered.

Figure 3. Time dependence of the volume change ∆V, mL/g) of Illinois No. 6 coal in methanolic n-Bu4N+OH- (2.0 M).

Figure 4. First-order kinetic plot of the volume change (∆V, mL/g) of Illinois No. 6 coal in methanolic n-Bu4N+OH(2.0 M). Table 3. Rates of Swelling of Whole Illinois No. 6 Coal in Methanolic Tetra-alkylammonium Hydroxide (R4N+OH-) Solutions at Room Temperature R

base concentration

slopea

intercepta

r2

no. of points

Me n-Bu n-Bu n-Bu

1.0 0.5 1.0 2.0

0.28 0.21 0.20 0.086

2.34 2.15 2.15 2.25

0.93 0.99 0.99 0.99

6 7 8 12

a Of a plot of coal volume (V) versus xt; linear least squares regression analysis.

In the first case, the swelling and neutralization are simultaneous, coupled, and inseparable. The second case has the coal swelling first, followed by diffusion of the

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Table 4. Rates of Swelling of Whole Rawhide Coal in Tetra-alkylammonium Hydroxide (R4N+OH-) Solutions (1.0 M) at Room Temperature R

solvent

slopea

intercepta

r2

no. of points

Me n-Pr n-Bu n-Bu n-Bu n-Hex

CH3OH CH3OH CH3OH H2O THF CH3OH

0.12 0.31 0.21 0.44 0.27 0.22

3.61 3.09 3.25 2.87 3.07 2.10

0.97 0.97 0.90 0.98 0.93 0.99

5 6 7 6 6 7

a Of a plot of coal volume (V) versus xt; linear least squares regression analysis.

Table 5. Rates of Swelling of Pyridine-Extracted Illinois No. 6 Coal in Tetra-alkylammonium Hydroxide (R4N+OH-) Solutions (0.714 M) at Room Temperature R

solvent

slopea

intercepta

r2

no. of points

Me Et n-Pr n-Bu n-Hex Me Et n-Pr n-Bu n-Hex n-Oct n-Bu

H2O H2O H2O H2O H2O CH3OH CH3OH CH3OH CH3OH CH3OH CH3OH THF

0.09 0.04 0.02 0.011 0.009 0.16 0.21 0.24 0.16 0.26 0.17 0.52

2.9 2.0 1.9 1.9 2.0 3.4 3.4 3.5 3.7 2.8 2.5 3.7

0.92 0.96 0.99 0.98 0.98 0.96 0.88 0.86 0.74 0.91 0.95 0.91

5 8 11 13 15 4 4 5 7 7 9 4

a Of a plot of coal volume V(mL/g) versus xt; linear least squares regression analysis.

base anion and neutralization. In the third case, the neutralization of the hydroxyl group occurs first, followed by swelling. Finally, the last possibility is simultaneous, independent processes. We believe the last case is the one which is occurring. Two additional experimental observations are relevant: (1) the coals are not swollen by, nor do they react rapidly with solutions of NaOH or KOH, and (2) solutions of n-Bu4N+Br- do not swell coals. Case 1 is ruled out by the observations that the rates of swelling and neutralization are very different and the processes follow different rate laws. The rate of neutralization is faster than the rate of swelling, so reaction cannot follow swelling. This rules out Case 2. Case 3 is ruled out by the observation that swelling and neutralization occur simultaneously, but that swelling continues and follows an unchanged rate law after the reaction is over. The

Table 6. Rates of Swelling of Pyridine-Extracted Rawhide Coal in Tetra-alkylammonium Hydroxide (R4N+OH- Solutions (0.714 M) at Room Temperature R

solvent

slopea

intercept2

r2

no. of points

Me Et n-Pr n-Bu n-Hex Me Et n-Pr n-Bu n-Hex n-Oct n-Bu

H2O H 2O H 2O H 2O H 2O CH30H CH30H CH30H CH30H CH30H CH30H THF

little swelling observed little swelling observed 0.11 0.14 0.05 0.17 0.19 0.16 0.14 0.19 0.13 0.21

5.0 4.2 3.0 3.9 4.2 4.1 4.2 3.3 3.2 3.8

0.54 0.68 0.99 0.90 0.95 0.75 0.92 0.95 0.93 0.57

4 7 7 4 4 5 7 7 8 5

a Of a plot of coal volume, V(mL/g) versus xt; linear least squares analysis.

kinetics of the two processes are independent of each other. The neutralization reaction kinetics are independent of the extent of swelling. No matter how swollen the coal is, the neutralization follows the same rate law. One consequence of this case is that the extent of swelling can have no effect on the rate of diffusion of the basic anion. This was previously observed for maleic anhydride-coal reactions.5 The Diels-Alder reaction of maleic anhydride with Illinois No. 6 and Bruceton coals has been studied,5 and diffusion of the maleic anhydride has been established as the rate-determining step. It was shown that the degree of swelling of the coal from a factor of 1.05 to ∼1.8, had no effect on the diffusion rate of maleic anhydride. During the neutralization reaction, the swelling of each particle of coal must be nonuniform and changing because swelling is slower than neutralization and continuous during the reaction. Mid-way through neutralization, the center of the particle will be less swollen than the outer portions. Each of the two processes can now be considered in more detail beginning with the neutralization reaction. The neutralization of the coal’s hydroxyl groups was followed calorimetrically and obeys first-order kinetics to nearly complete reaction. The deviations occur near the end of the reaction, where errors due to calorimeter insensitivity and thermal drift will be largest. In following the rate by measuring heat evolution, we assume that the average heat liberated per hydroxyl group reacting is independent of the extent of reaction. This assumption is troublesome. As the coal becomes more ionized, more highly charged, the thermodynamics of

Scheme 1

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Energy & Fuels, Vol. 15, No. 4, 2001

the neutralization reaction will change due to changes in electrostatic repulsive interactions. Diffusion processes in porous polyelectrolyte solids such as coal are very complex, and no detailed mathematical analysis of the data will be offered. It has been reported that the heat liberated on immersion of coals in water also follows a first-order rate law.33 The rate of water adsorption on 40-60 mesh Illinois No. 6 is about twice the rate of the Illinois No. 6 hydroxyl group’s reaction with the ammonium hydroxide bases. Some conclusions about the nature of the diffusion are possible. For the tetra-alkylammonium hydroxides, the rate constants are independent of the size of the alkyl groups. This is most surprising and means that the diffusion of the ammonium ion is not the ratedetermining step. The rate-determining step must be diffusion of the base anion or self-diffusion of the coal as it expands. The role of the tetra-alkyl groups is mysterious. They are necessary for the reaction to occur rapidly, as shown by the fact that sodium or potassium hydroxide does not react rapidly, yet it is not involved in the rate-determining step. To preserve electrical neutrality, it is necessary for the cations to diffuse into the coal. If it cannot, the reaction will be terminated quickly as the coal particle becomes increasingly negatively charged and electrostatically repels anion bases. We speculate that the alkylammonium ions are mobile within coals due to their ability to interact favorably with aromatic structures.34 Also, extensive desolvation before penetration of the coal is not necessary for the poorly solvated tetra-alkylammonium ions as it would be for the strongly solvated Na+ and K+. It is assumed that the solid coal provides an environment like a slightly polar organic liquid and is hydrophobic. We do not know whether ions will move with some surrounding stabilizing solvent molecules or will require complete desolvation of the ions before they can diffuse into the coal. It is possible that the movement of the anion through the coal is independent of the cation and is the slow step, explaining the observed independence of the diffusion rate on alkylammonium ion. It seems likely that anion and cation motion will be coupled, due to their electrostatic interactions. The anion diffusion must precede cation diffusion and be rate determining. The cation follows behind, lured forward by electrostatic attraction. There are three possibilities for the rate-determining step in anion diffusion. They are translational motion of the anion (Fickian), segmental motion of the coal (Case II), or desolvation of the anion. Because the neutralization thermodynamics will change as the charge density in the coal particle changes, we are not willing to use these calorimetric rates to distinguish between Fickian and Case II diffusion. Our data analysis assumes the same amount of heat is liberated every time a hydroxyl reacts but we expect the heat to decrease as the coal charge density increases. Anion desolvation may be the rate-determining step. Small molecules move through coals much faster than large molecules.35 It may be necessary to remove some of the solvent surrounding the anion to permit diffusion. There (33) Fuller, E. L., Jr. J. Colloid Interface Sci. 1980, 75, 577. (34) Hardy, J. W.; Williams, E. M.; Lipkin, E.; Rosen, J. M.; Roizen, M. F.; Buchin, P. J.; Taylor, E. G.; Taylor, C. L.; March, R. E. Can. J. Chem. 1973, 51, 2161-2165.

Larsen et al.

is precedence for desolvation as the rate-determining step.1 This desolvation also would not involve the cation and so is consistent with our observation that the rate is independent of cation size. Although we cannot establish the rate-determining step for anion diffusion, its independence of ammonium cation size is an important observation and is most helpful in designing ionic reagents that must penetrate coals. The remaining possibility is that self-diffusion of the coal is the rate determining step. This is consistent with our data. We turn now to the swelling phenomenon. Except in one system (pyridine-extracted Illinois No. 6 solvent watersTable 5), the rate of swelling is essentially independent of the tetra-alkylammonium ion and follows xt (the Fickian diffusion law). The independence of ammonium ion size is consistent with the ratedetermining step being the expansive movement of the coal macromolecular structure; that is diffusion of coal through coal. This expansion is obviously necessary for swelling, will be independent of the cation size, and might well depend on xt. The slow step cannot be diffusion of the ammonium ions, since this would depend on the size of the ion. It is surprising that the swelling rate remains independent of the ammonium ion even for very large ions. It seems that once the coal structure has relaxed and become rubbery, even large molecules or ions can diffuse easily. If this is so and if the neutralization rate-determining step is also coal structure changes, the two structure changes must be different because the rates are different. The independence on cation size and Fickian time dependence are consistent with solvent diffusion into the coal being rate determining. In this picture, reaction of the coal’s hydroxyl groups is followed by solvation and swelling with cation diffusion following after solvent and expansion of the coal. We cannot distinguish between this possibility and rate-determining coal structure changes. The heat generated by the reactions of the bases and the coals is reported in Tables 1 and 2. A quantitative interpretation is not possible. The heat of reaction of m-cresol in aqueous solution with 0.4 M Me4N+OH- is -7.80 kcal/mol, and this can be used to calculate the heat which should be evolved when coals react with Me4N+OH- if the coal anions are subject to small substituent effects and if they are solvated the same as in the m-cresolate ion in water. Solvation within the coal should be poor, so the value observed should be less than that calculated based on the heat of reaction of m-cresol and the phenolic hydroxyl population of these coals. This is observed. As the cation size increases, the heat evolved decreases, consistent with reduced ionic interactions as previously postulated.27 A comparison of our results with those published by Matturro et al. is instructive.27 They measured the rate and swelling of pyridine-extracted Illinois No. 6 coal with tetra-alkylammonium hydroxides in methanol and in water and measured the extent of neutralization of the coal at equilibrium. They mostly used 0.25 M base solutions while we use 1.0 M solutions. Concentration is known to have a significant effect on polyelectrolyte behavior.32 Both studies report that swelling follows (35) Larsen, J. W.; Hall, P.; Wernett, P. C. Energy Fuels 1995, 9, 324-330.

Reaction of Wyodak Rawhide Coal Hydroxyl Groups

xt. Matturro et al. report a cation size dependence on swelling rates in methanol where we see none. They observed that swelling with Me4N+ was 3.5 times faster than swelling with tetra-n-octyl salts. This is a small difference; about 0.5 kcal/mol in activation energy. Diffusion rates of hydrocarbons in glassy Illinois No. 6 coal vary as the (hydrocarbon radius)23.35 This extraordinary sensitivity to size is common for diffusion through glassy polymers.36 The observed size dependence of diffusion rates in Illinois No. 6 coal would lead to a diffusion rate difference of 106 fold between tetra-methyl and tetra-octyl. We do observe a size dependence of swelling rate in water: a factor of 10 between tetramethyl and tetra-n-hexyl. Apparently, the sensitivity of the swelling rate to cation size is small and dependent on solvent and ion concentration. Matturro et al. measured the extent and rate of neutralization of the coal. As expected, all acid sites never reacted. Half-lives for this process in their system range from about 15 min. to 50 min. Because we were able to follow the reactions for only about 20 min until the slow rate of heat release and calorimeter thermal drift conspired to end our ability to follow the reaction, we probably were not following the neutralization to completion. Our rates must therefore be treated as initial rates. Conclusions Mass transport of tetra-alkylammonium hydroxides into and through coals is very rapid, and the ratedetermining steps are not diffusion of the bulky ammonium ions. It is possible to achieve very rapid rates of mass transfer in coals, rates faster than many common organic reactions. Some cation structural fea(36) Berens, A. R.; Hopfenberg, H. B. J. Membr. Sci. 1982, 10, 283303.

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tures necessary for rapid diffusion are clear: easy desolvation and favorable interactions with aromatic structures. Introducing these features into ionic reagents may increase their diffusion rates and make possible rapid, mild condition reactions of coals. Having established that rapid diffusion is possible, and having obtained a little insight into the factors involved, there is no reason to accept as inevitable the current diffusion limitations on coal reactions. An attempt to understand the diffusion processes better and to use this understanding to remove this factor as a strong limitation in coal chemistry clearly is warranted. Experimental Section Calorimetric Rate Studies. A simple twin solution calorimeter of the early Arnett design was used. The base solution, 180 mL, was placed in the calorimeter vessel and samples 0.5 to 1.0 g of -200 mesh powdered coal were accurately weighed into 5 cm3 plastic syringes whose tips had been cut off and which were plugged with silicone rubber gc septa. After hanging in the solution long enough to reach thermal equilibrium, usually ca. 20 min, the contents of a single syringe were introduced into the rapidly stirred solution. The temperature change was followed until a stable baseline was reached. The reaction was always monitored for at least 20 min. The data workup followed Meites’ procedures.29 Swelling Rates. About 1.0 g of coal (-200 mesh) and 10.0 millimoles of base in 14 mL of the appropriate solvent (0.714 or 1.0 M) were placed in a 15 mL graduated centrifuge tube. The tubes were shaken, then spun at 2500 rpm for 10 min to cause the coal to settle. The height of the coal column was read, the time recorded, and shaking resumed. Al rates were measured at room temperature.

Acknowledgment. The work performed at the University of Tennessee was supported by Exxon Research and Engineering Company to whom we are grateful. EF000193B