J. Phys. Chem. 1981, 85,3225-3230
3225
Composition of Clathrate Gas Hydrates of CHCIF2, CC13F, C12, C103F, H2S, and SF6 George H. Cadyt Department of Chemistry, UniversW of Washington, Seattle, Washington 98 195 (Received: April 28, 198 1)
A procedure has been developed for the quantitative synthesis of a gas hydrate by slow condensation of a known weight of water vapor upon a cold surface of known temperature in the presence of the gas at constant pressure. From the weight of water and weight of hydrate produced, the hydration number of the gas is calculated. At 0 “C, the structure I1 hydrates of CC13F and SF6have hydration numbers of 17.0 within in the experimental limits while the structure I hydrates of CHClF2and C103Fhave hydration numbers very close to 7.67. Hydration numbers for C12and H2S are variable and depend upon the temperature and gas pressure. Since some of the observed hydration numbers differ appreciablyfrom those predicted by a theory of long standing, additional gases are being studied.
Introduction Gas hydrates are solid solutions in which the guest molecules are trapped through clathration within cavities in forms of ice. Each of the solids, with the possible exception of bromine hydrate, may be classed as being of either structure I or structure II.’-” While these structures are well-known, the determination of the composition of the solid hydrates remains a problem. The author became interested in the problem in 1976-77 when he worked with perchloryl fluoride, C103F, and found an attractive procedure for quantitative synthesis, worthy of further studyS6 A part of this study is now being reported. In principle, the method is simple. A known weight of water vapor is condensed slowly upon a cold surface at constant temperature in the presence of the guest gas held at a constant pressure high enough to cause the condensate to be the solid hydrate of the gas. Under these conditions, the solid which forms has a fixed composition. From the weight of water and the weight of hydrate produced, one learns the composition. In practice the method is complex. It is also not completely new. CeccottP used the process in principle to determine the composition of propane hydrate; however, it is likely that his complex procedure produced a large experimental error. In his method liquid water was removed by flooding with mercury. This would have left an unremoved film of water in the apparatus. With the technique to be described below, the method consumes the whole sample of liquid water and gives compositions which are probably accurate to within about 1%. A major experimental problem in the method is the determination of the weight of hydrate. After the formation of hydrate is complete, the vessel containing the solid also contains a substantial amount of unreacted gas and a trace of water vapor. It is necessary either to remove the gas phase before weighing the solid or to learn the weight of the gas phase or the weight of gas released when the hydrate is allowed to decompose. For all but one of the hydrates studied in this research, the first of these alternatives has been preferred. For the hydrate of CC13F the procedure involved determination of the weight of the gas phase. It is of interest to compare the experimental results with predictions made by the theory of van der Waals and I am delighted to have a place in this publication honoring Joel H. Hildebrand a t the time of his 100th birthday. He was my inspiring thesis professor over half a century ago and gave me a love for experimental chemistry which continues today. As a truly exceptional teacher he has always set an excellent and challenging example for his students. Thank you, Joel.
Plateeuw’ and extended by Davidsona8 Extensive reviews of the literature about clathrate hydrates have been made by other~.~-lOThe author has found the review of Davidson to be particularly helpful and has been much interested in papers from the following groups: (1)Davidson and others at the National Research Council of Canada; (2) Barrer and others at Imperial College, London; (3) Kobayashi and others a t Rice University; (4) Stupin and others at the Leningrad Technological Institute; ( 5 ) Byk and Fomina a t the Institute for Synthetic Alcohols and Organic Products, Moscow. Experimental Section Gases used in this study were high grade commercial chemicals. No evidence for poor quality was found except that the hydrogen sulfide contained a small proportion of an easily removed gas which was noncondensible at -196 “C. Each of the gases was subjected to a simple distillation and the middle portion of the distillate was used. Figure 1 represents the glass reactor for quantitative synthesis of hydrates. Usually two reactors were used simultaneously to permit comparison of results, Fischer-Porter quick opening valves having Teflon stems were used. The reactors could be attached, in vertical positions, to a vacuum line which allowed manipulations involved in the procedure. All weighings were made with much care after waiting for the observed weight to remain constant for about 30 min or more. A counterpoise of correct volume was always used and the ground joint and Teflon stem valve were jacketed with aluminum shields, because these parts retained electrical charge. Halocarbon or Kel-F stopcock lubricant was used on ground joints in the system. The author believes his errors in weighing were not greater than 0.0003 g. Pressures were measured to about 0.01 atm with a Bourdon tube gage calibrated against a mercury manometer from 0 to 2 atm pressure. (1)W. F. Claussen, J. Chem. Phys., 19,1425 (1951). (2) H.R.Miiller and M. v. Stackelberg, Naturwissenchaften, 39,20 (1952). (3) M. v. Stackelberg and H. R. Miiller, 2.Elektrochem., 68,25(1954). (4)L.Pauling and R. E. Marsh, h o c . Natl. Acad. Sci. U.S.A.,38,112 (1952). (5)G.H.Cady, J. Fluorine Chem., 11,225(1978). (6)P. J. Ceccotti, 2nd. Eng. Chem., Fundam., 5 , 106 (1966). (7)J. H.van der Waals and J. C. Plateeuw, Aduan. Chem. Phys., 2, l(1959). (8)D. W. Davidson in “Water: A ComprehensiveTreatise”, Vol. 2,F. Franks, Ed., Plenum Press, New York, 1976,Chapter 3. (9)D. W. Davidson and 3. A. Ripmeester, J. Glaciol., 21, No.85,33 (1978). (10)S.Sh. Byk and V. I. Fomina, Russ. Chem. Reu., 37 (19,469(1968), in English.
0022-365418112085-3225$01.25/0 @ 1981 American Chemical Society
3226
The Journal of Physical Chemistry, Vol. 85, No. 22, 1981
/Ill
ICE
Il 1
WATER EVAPORATES
Figure 1. Cross-sectional view of reactor. The vessel is double walled like a Dewar flask. A Teflon stem valve is attached at the rim.
Procedure About 0.2 g of water was added to the reactor. The vessel was evacuated to remove air, and the weight of water was determined. The reactor was attached to the vacuum line and the gas to be studied was added to give a pressure close to that to be used in the experiment. The valve of the reactor was closed. By cooling the bottom 1cm with liquid Nzall water was condensed in the bottom tip of the reactor and was later caused to remain there by keeping the tip chilled with liquid nitrogen or dry ice. A series of steps was now carried out to cause nucleation of the hydrate to occur as soon as water vapor began to condense on the surface of the cold finger. First, a cylindrical cloth bag of proper size containing pulverized solid carbon dioxide was inserted and allowed to remain in the cold finger. Second, the cooling agent was removed from the bottom tip of the reactor, and this partion was allowed to warm for a short time until it reached a temperature of 0 "C or slightly below. The first bit of water to distill condensed on the cold finger at a temperature well below 0 "C. The bag of dry ice was then removed from the cold finger, and ice plus a little water was added in its place. A cylindrical jacket of Styrofoam was used as thermal insulation around the bulb of the reactor except for the bottom 2 cm. Water at a nearly constant temperature somewhere within the range 30-40 "C was used to warm the bottom 1 cm of the reactor. A convenient temperature was about 37 "C. This allowed the whole 0.2-g portion of water to transfer to the cold finger within 4-5 h. Immediately after installing the bath of warm water, the valve of the reactor was opened so that the pressure of gas could be held constant within a 0.02-atm range by adding gas from time to time from a reservoir. While this pressure was held constant, the temperature in the cold finger was also held constant by adding ice and removing melt water at intervals. In some experiments the bath in the cold finger was a partially frozen aqueous solution of KC1 having the eutectic composition and temperature, The solution was kept
Cady
partially frozen (at -10.7 "C) by adding portions of solid carbon dioxide to a small test tube immersed in the solution. In other experiments, a eutectic mixture of NaCl in water was used to give a temperature of -21.1 "C. After the liquid water had entirely evaporated from the bottom of the reactor, the solid hydrate was present as a layer of crystalline material on the bottom 3 cm of the cold finger. At this stage in the procedure, the reactor contained both the solid hydrate and a gaseous phase. To obtain the weight of the solid only, one of the following two methods was used. (1)Glass bulbs of about 100-mL volume suitable for measuring gas density were attached to the vacuum line. Both they and the reactor(s) were cooled to 0 "C by ice up to the level of their valves. Gas was admitted to the bulbs up to the pressure of gas in the reactor($; then the gas pressures in the bulbs and reactor(s) were equalized and the valves were closed. Reactor(s) and gas density bulbs were weighed at room temperature, and from the measured gas density the weight of gas in each reactor was calculated. A problem here was that the measured density was for dry gas, while the gas in the reactor contained water vapor at an unknown pressure less than 4.5 mmHg. This introduced a small uncertainty in the measured composition of the hydrate. The data given in Table I for CC13F were obtained by using this method. For each sample, two hydration numbers are given. The uncorrected value is that obtained by assuming the gas in the reactor to have the density of dry gas. The corrected value assumes water vapor to be present at 4.5 mm pressure. The true experimental hydration number should be between the two values. (2) The refrigerant in the cold finger was removed and was immediately replaced by pulverized solid carbon dioxide. The exterior of the bulb of the reactor was then cooled by solid carbon dioxide. At this temperature (-78 "C) the decomposition pressures of the hydrates in this study were low, and the compositions remained as they were at 0 "C (or -10.7 or -21.1 "C). Gas was then removed r8ther slowly from the reactor until the pressure fell and remained well below the vapor pressure of this substance at -78 "C but above the decomposition pressure of the hydrate at -78 "C. At this stage, gas remained at a few centimeters pressure in the reactor. The valve of the reactor was opened wide for about 7 s to allow the remaining gas to escape freely to the evacuated line. The valve of the reactor was closed and the reactor was warmed to room temperature, cleaned, and weighed. This was the preferred procedure and was used to obtain the data presented below except for CCl,F, which was not conveniently volatile at -78 "C. With only three weighings and no calculated corrections the weight of water and the weight of solid hydrate were obtained. When methods 1 and 2 were compared for samples which should have had identical compositions, the agreement was good. For the gases used in this work the compositions of the solids at -78 "C remained as they had been at 0 "C and in the brief period of full dynamic vacuum the extent of decomposition of the hydrate was negligible. As a safety precaution and because of problems with valves and ground joints, pressures in excess of 3.5 atm were not used. Several types of apparatus and procedures were tested and many data not presented here were obtained. The preferred method was that just described and the data to be presented below resulted from its use. Results The compositions given in Table I are stated as hydration numbers. The hydration number, n,is the molar ratio
The Journal of Physical Chemistty, Vol. 85, No. 22, 1981 3227
Quantitative Synthesis of Gas Hydrates
TABLE I: Hydration Numbers f o r t h e Various C o m p o u n d s Studied
n
2.07 17.10
2.07 17.09
3.02 17.05
SF, a t 0 " C 3.02 16.97
P, atm n ( n o t cor) n (cor)
0.37 17.14 16.98
0.37 17.10 16.95
0.37 17.24 17.09
CC1,F a t 0 O C 0.38 0.38 17.05 17.06 16.91 16.93
P, a t m n
1.55 7.70
1.55 7.71
2.01 7.65
Cl0,F at 0 C 2.01 3.02 7.68 7.55
P, a t m n
1.33 7.71
1.33 7.66
CHClF, (Runs in April 1980) 2.1 2.1 3.02 3.02 7.61 7.65 7.61 7.56
P,a t m
1.51 7.75
1.51 7.75
CHClF, a t 0 " C (Runs in March 1981) 1.70 1.70 1.80 1.80 3.02 7.62 7.66 7.68 7.66 7.65
0.50 7.67
0.50 7.66
0.50 7.67
CHClF, a t -21.1 1.70 0.50 7.70 7.62
P, a t m
1.62 5.99
1.62 5.96
2.87 5.85
2.87 5.86
P, a t m n
0.46 7.28 3.08 6.22
0.48 7.38 3.08 6.22
1.00 6.94 3.35 6.19
C1, a t 0 " C 1.01 6.96 7.04 3.35 6.20
P, a t m
0.48 7.01
0.48 7.04
1.00 6.59
C1, a t -10.7 " C 1.55 2.50 6.29 6.04
2.50 6.05
P, a t m n
0.20 7.24
0.20 7.16
0.20 7.17
C1, a t -21.1 C 0.49 0.49 6.67 6.73
1.00 6.24
P, a t m
n
P, atm
n
3.02 7.66 3.0a 7.56 3.02 7.65
C 1.70 7.66
2.05 7.63
2.05 7.64
2.05 7.57
2.87 5.84
3.41 5.81
3.41 5.79
3.44 5.86
3.44 5.86
1.01 6.99
1.01 6.92
1.55 6.62
1.55 6.66
2.04 6.48
2.04 6.45
1.01 6.26
1.01 6.36
1.52 6.05
1.52 6.10
1.55 6.02
H,S a t 0 " C
P,a t m n
2.87 5.85
1.00
TABLE 11: Hydration Number of Chlorine A t or Near 0 'C
n
ref
date
n
ref
date
12, 7, 4 8 6 7
Faraday" Maumen6' Rooze boom' Villard' de ForcrandI5
1823 1883 1884 1884 1902
6 6 7.27 7.05a
BouzatI6 Anwar-Ullah I ' Allen' Wilms e t al. '
1923 1932 1959 1970
10
a A t the quadruple point.
of water to gas in the solid hydrate. Each value in the tables was calculated as follows: g of water
n = g of gas
X
X mol w t of gas mol wt of water
(1)
The numbers are given to the nearest 0.01 unit. They are not accurate within this precision but the size of the number in the second decimal place has some significance. It was not uncommon to find differences as much as 0.1 unit or even more, but in such cases there usually was an understandable reason for error (failure in nucleation, etc.). These obviously erroneous data are not given. Discussion The dzta for chlorine hydrate in Table I show clearly that the composition is highly dependent upon temperature and pressure. This dependence may account in part for the wide variety of hydration numbers reported in the past. It must also be true, however, that experimental error is largely responsible. Hydration numbers for chlorine which have been reported previously are given in Table II.11-19 Some of these data were obtained by
quantitatiive analysis or synthesis. Others were obtained by measurement of physical properties. Other previously reported hydration numbers are as follows: (1)for SF6, n = 17.02,2017.03 for D20;21(2) for CCI3F,n = 16.6;22(3) for CC12F2,n = 15.6,2216.0 for D20;% (4) for C103F,n = ~ 7 . 7 5(5) ; ~for H2S, n = 6.06;24(6) for CHClF2,n = 8.3 for H20,238.5 for D20;2312.6 for H20.22 It has been pointed out by Stupin et that the value n = 12.6 for CHClF2 given in ref 22 must be erroneous. (11) M. Faraday, Quat. J. Sci. Lit. Arts, 15, 71 (1823). (12) E. Maumeng, Bull. SOC.Chim. Paris, 39, 397 (1883). (13) H.Roozeboom, Recl. Trau. Chim., 3, 71 (1884). (14) M. Villard, Comptes Rendus, 119, 370 (1894). (15) R. de Forcrand, Comptes Rendus, 134, 835, 991 (1902). (16) A. Bouzat and L. Azinieres, Comptes Rendus, 177, 1444 (1923). (17) S. Anwar-Ullah, J. Chem. SOC.,1172 (1932). (18) K. Allen, J. Chem. SOC.,4131 (1959). (19) D. A. Wilms and A. A. van Haute, Proc. Znt. Symp. Fresh Water Sea, 3, 117 (1970). (20) I. D. Sortland and D. B. Robinson, Can. J. Chem. Eng., 42, 38 (1964). (21) D. Yu. Stupin, V. N. Tezikov, A. Seleznev, and V. V. Durkheev, Izu. Vyssh. Uchebn. Zaued., Khim. Khim. Tekhnol., 21, 979 (1978). (22) T. A. Wittstruck, W. S. Brey, Jr., A. M. Buswell, and W. H. Rodebush, J . Chem. Eng. Data, 6 , 343 (1961). (23) D. Yu. Stupin, V. N. Tezikov, and A. P. Seleznev, Zh. Prikl. Khim., 51, No. 3, 589 (1978).
3228
The Journal of Physical Chemistry, Vol. 85, No. 22, 1981
This opinion is correct. The pressure vs. temperature data in ref 22 correspond to a value of AH for the reaction CHClF2 + nHzO CHClF2(g)+ nH20(l)of about 19 kcal mol-' of CHCIFz rather than 25 kcal given in ref 22. The value of n corresponding to the data of ref 22 is about 8 rather than 12.6. The method used to obtain most of the old hydration numbers given above was first employed by de Forcrand.15 In this method the equilibrium pressure of gas in the system, gas plus hydrate plus ice or liquid solution, is measured from a temperature a few degrees above 0 "C to a few degrees below the quadruple point near 0 "C. A graph of In P vs. 1/T then gives a value of AH for the reaction M(HzO), -+ M(g) + nHzO (1) and a value of AH for the reaction M(H,O), --* M(g) + nH2O(s) When one divides the difference between these values of AH by the molar heat of fusion of ice, the value of n at the quadruple point is obtained. Hydration numbers found by this method are not precise, because the values of AH are not precise. A number such as 17.02 given above for SF6 is misleading. The experiment only justifies the conclusion that n is approximately 17. An example which illustrates results obtained by this method is a study of the hydrate of CF31in which Stupin and Tevikov2smade P vs. T measurements of good quality. For H20their data correspond to the formula CF31.16.6Hz0. For D20, the formula appears to be CF31.17.9D20. It is highly probable that the correct hydration numbers are very close to 17.0 in both cases. One of the difficulties in quantitative synthesis is to cause the whole of a sample of water to react with gas. The last bit of water becomes shielded from contact with gas and does not react. Various methods have been used to try to obtain complete reaction. Galloway et al.26produced the hydrates of methane and ethane from water and gas in a rotating ball-mill operating for many hours. Their values for the hydration numbers of these gases are probably the best which have been obtained. Barrer and Edge27formed the hydrates of the noble gases A, Kr, and Xe by reaction of gas with ice crystals in a vessel containing small steel balls. Vigorous shaking allowed most of the ice, but not all, to react. In spite of this problem, the extent of absorption of noble gas in the small cavities of chloroform hydrate was shown to follow the Langmuir isotherm as predicted by the theory of van der Waals and Platee~w.~ The author has performed many experiments using a ball-mill-type of reactor made from a 25-mL glass flask containing glass spheres of about 7 mm diameter. This reactor was rotated about its long axis at approximately 70-100 rpm while the bulb of the flask was cooled by ice. The flask contained 0.1-0.5 g of water and sufficient gas to convert all of the water to hydrate. In these experiments the hydrate was formed by crystallization from solution. Usually nucleation was caused by stopping the rotation for a few seconds and pressing a piece of solid carbon dioxide against the bulb. Crystallization then occurred rapidly and at a rate controlled largely by the rate of dissolving of gas in water. As the remaining amount of -+
(24)A. E. Korvezee and F. E. C. Scheffer, Red. Truv. Chim. Pays-Bus, SO, 256 (1931). (25) D. Yu. Stupin and V. N. Tezikov, Zh. PrikE. Khim., 49, 2337
(1976).
(26) T.J. Galloway, W. Ruska, P. S. Chappelear, and R. Kobayashi, Ind. Eng. Chem., Fundum., 9,237 (1970). (27)R. M.Barrer and A. V. J. Edge, Proc. R.SOC.London, Ser. A, 300, l(1967).
Cady
water became small, the rate of absorption of gas kept decreasing until it became very small. Even after many hours, however it appeared that a trace of liquid remained. As a result, the observed hydration numbers were in error by being to high. For example, hydration numbers such as 17.25, 17.38, and 17.24 were found for SF,. All of the hydrates were soft solids which collected as plastic masses on the spheres and wall of the reactor. Eventually this method was abandoned. One reason for abandoning was that the solid which formed would have a composition corresponding to equilibrium with a liquid solution of lower concentration than that of a solution saturated with gas at the pressure in the flask. Subsequent absorption of gas to raise its concentration in the solid is a very slow process. It is desirable that the procedure used to study the relationship between pressure of gas and composition of solid hydrate be one in which the solid, as it forms, has the equilibrium composition. This is accomplished by forming the solid directly from the gaseous phase. The procedure of Barrer and Edge2' should have been satisfactory in this respect. Formation of hydrate must have involved transfer of water as vapor from ice to hydrate. Ceccotti's6 procedure was also good in this respect. It appears, however, that the procedure of Barrer and Edge left unreacted ice in the system while the procedure of Ceccotti left liquid water. In the present study all of the water was converted to hydrate except for the trace (perhaps up to about 0.0001 g) which remained as water vapor. A defect in the present procedure was that the temperature at the surface of the forming hydrate must have been a little higher than the temperature of the refrigerant in the cold finger. Therefore, the composition of the solid must have corresponded to a somewhat higher temperature than that given in the table. Another possible experimental error was related to nucleation. In the distillation procedure, it was necessary that solid be formed throughout the distillation, even from the very beginning. It was the experience of the author that he needed to run the distillation at a pressure somewhat above the decomposition pressure of the hydrate. This may have been due to the temperature problem just mentioned or to the difficulty of nucleation. The system behaved as if a driving force was needed to help form the hydrate. When the cold finger was held at -10.7 or -21.1 "C, nucleation was not as much a problem as at 0 "C. It was usually not neccessary to precool the finger with solid carbon dioxide. On one occasion when the hydrate of CH3I was formed on the cold finger in one reactor at -21.1 "C, the solid which formed in the other reactor contained almost no CH31. It must have been ice. In runs at 0 "C without the step of precooling with solid carbon dioxide, it was frequently found that liquid water, rather than solid hydrate, condensed on the cold finger. Usually the layer of hydrate which formed on the cold finger was approximately uniform in thickness. At times, however, there were rather long crystals which extended like whiskers away from the surface, The temperature at the whisker tips must have been well above that in the bath of refrigerant. The tendency for growth of whiskers seemed to increase as the temperature of the refrigerant was lowered. Crystals of an unsatisfactory quality were also obtained when a sufficient amount of gas was present to allow liquified gas to form on the cold finger. The hydrate formed as a spongy mass which fell away from the cold finger. All of the experimental errors mentioned in the last three paragraphs give hydration numbers larger than the correct values. Still another possible error of this type,
Quantitative Synthesis of Gas Hydrates
which was looked for but not observed, was fog formation. A detailed study has not been made to learn the relationship between distillation rate and observed composition of the hydrate. In general, however, it was found that the temperature of the warm bath used to heat the bottom of the reactor could be within the range 25-40 “C without having much, if any, influence upon the composition of the hydrate. At times, hydration numbers were found which must have been smaller than the correct values. In such cases the error usually was either in weighing or in the incomplete removal of uncombined gas.
Experiment vs. Theory Through X-ray cry~tallographyl~ it has been shown that the unit cell of a structure I hydrate contains 46 water molecules arranged in such a way that six “large” cavities and two “small” cavities are present. If the guest molecules of ‘‘gas” are small enough to occupy both types of cavities, the lowest theoretically possible hydation number is 46/8 = 5.75. If the guest molecules are too large to occupy “small” cavities but small enough to occupy “large” cavities, the lowest theoretically possible hydration number is 46/6 = 7.67. The unit cell for a structure I1 hydrate contains 136 water molecules arranged to form 16 “small” cavities like those in structure I and 8 “large” cavities somewhat larger than the “large” cavities in structure I. The lowest theoretically possible hydration number for a gas having molecules too large for structure I but small enough to occupy the type of “large” cavities of structure I1 is 136/8 = 17.0. van der Waals and Plateeuw’ have considered gas hydrates to be solid solutions and through a sophisticated theoretical treatment have arrived at equations which may be compared with the experimental results of the present study. One equation says, for constant temperature, that the extent of occupancy, 8, of a set of cavities by guest molecules is given by the Langmuir isotherm 8 = K P / ( l + KP) (2) in which P is the pressure of the gas and K is a constant. In the discussion which follows, d1 is the fraction of occupancy of “small” cavities, fl2 is the fraction for “large” cavities in structure I, and d3 is the fraction of occupancy of “extra large” cavities in a structure I1 hydrate. K1 and K2 are the constants which correspond to 8, and 02. Other equations relate to the least degree of occupancy which can stabilize the lattice of water molecules present in the hydrate. For each system involving a gas hydrate there is a quadruple point which, because of dissolved gas in the liquid phase, is a little below 0 “C. It is convenient to compare systems at this point, because the chemical potentials of water are the same in all four phases and because the hydrate compositions given by the method of de Forcrand are those at the quadruple points. Compositions found in the present study at 0 “C should be very close to those which would be obtained at the quadruple point temperature. For a structure I1 hydrate in which only the “extra large” cavities may be occupied, the following equation results from the van der Waals t h e ~ r y : ~
pwo is the chemical potential per mole of water in the empty structure I1 lattice and pw(h)is the chemical potential of water in the hydrate. If these values are at the quadruple point, O3 is the extent of occupancy of the “extra
The Journal of Physical Chemistv, Vol. 85,No. 22, 1987 3229
large” cavities required to stabilize the structure at that temperature. By considering the various experimental composition data, all widely scattered and all of doubtful precision, Davidson8 has concluded for structure I1 hydrates that n is probably 17.01 f 0.31 and that ApW probably lies between 125 and 265 cal mol-l at the quadruple point near 0 “C. The corresponding range for O3 is 0.980-0.99975 and for the hvdration number. 17.34-17.0004. While the data for SFn and CCLF in Table I do not include values at the quidruple points, they permit one to conclude by extrapolation that the hydration numbers of SF6 and CFC1, at the quadruple points (0 “C, 0.80 atm; -0.1 “C, 0.08 atm, respectively) are below 17.10 and are probably close to 17.00. Although these hydrates may actually be solid solutions and nonstoichiometric in composition they are for practical purposes stoichiometric crystalline solids, M.17Hz0. A hydration number of 17.10 at the quadruple point results from O3 = 0.994 and corresponds to A h = 163 cal mol-l. The observed compositions of hydrates of SF6 and CC13F are in agreement with Davidson’s opinion that Apw is closer to 265 than to 125 cal mol-l. For structure I hydrates in which only the “large” cavities may be occupied by guest moleculFs, the theoretical equation corresponding to (3) is
If both “large” and “small” cavities are occupied by guest molecules, the equation is
The hydration number, n, of the guest molecules in a structure I hydrate is related to O1 and O2 by the equation n = 46/(6& + 24) (6) because the unit cell contains 46 water molecules and 6 “large” cavities and 2 “small” cavities. The data for C l o g at 0 “C and CHCIFz at 0 and -21.1 “C in Table I indicate that molecules of CHCIFz or C103F may occupy only the “large” cavities. Molecules of Clz or H2Smay occupy both types of cavities. By considering the various experimental values of hydration numbers for structure I hydrates which have been reported in the past, Davidson* has decided that /.two p,(h) at the quadruple point near 0 “C is about 265 cal mol-l. When this value is substituted into eq 4, one finds the corresponding values of e2 and n to be respectively 0.976 and 7.853. It is of interest to compare the latter number with the experimental values of hydration numbers of C103F and CHClF2given in Table I and shown in Figure 2. These data indicate strongly that the hydration numbers are very close to 7.67 over the range of pressures studied. In Figure 2 a line has been drawn showing the theoretical pressure vs. composition relationship for CHCIFz calculated from eq 4 and 6 with Apw = 265 cal mol-l. Theory and experiment do not agree well in this case. The extent of occupancy of “large” cavities appears to be greater than is predicted by theory. Experimentaldata for hydrates of chlorine and hydrogen sulfide also are shown in Figure 2. Lines shown in the figure represent theoretical behavior at 0 OC calculated in the following way: (1)From the experimental data for 0 “C, values were estimated for the hydration numbers of Clz and HzS at their known quadruple point pressures: for Clz, n = -7.47
3230
J. Phys. Chem. lQ81,85,3230-3237
-r
0
e
P 0 0 I
I
7.8 7.67
I
I
-1
1
I
X
I
1
7.4 7.2 7.0 6.8 6.6 6.4 6.2 6.0 HYDRATION NUMBER
Flgure 2. Relatlonshlp between composltion and pressure of hydrates of C103F, CHCIF,, CI,, and H2S.
5
gas for
at 0.316 atm; for H2S, n = 6.12 at 0.918 atm. (2) For each gas it was assumed that eq 5 was obeyed and that Ahw = 265 cal mol-l. (3) A simultaneous equation for chlorine was n = 7.47 = 46/(619~+ 2&) and for H2S, n = 6.12 = 46/(602 + (4) These pairs of simultaneous equations were solved to obtain and 4 for each gas at its quadruple point pressure. (5) These values were then substituted into eq 2 to obtain values for K 2 and K1 for each gas. (6) It was then possible to use eq 2 to calculate and 61 at various pressures and to obtain corresponding values
of n by use of eq 6. The lines drawn in Figure 2 pass through these calculated values of n. When considering the quality of agreement between theory and experiment for C12 and H2S, one should not take into account the location of the line. That is arbitrarily established in step 1of the calculation. The item to consider is the slope and shape of the curve, because this is determined through use of theoretical eq 2 and 5. In slope and shape, there is qualitative but not quantitative agreement in the case of chlorine. For H2S it appears that the agreement is nearly quantitative within the limits of experimental precision and that 61 and 62 are substantially equal. The assumed value of Ahwplays a part in the shape of the theoretical curves. A value higher than 265 cal molw1 would make the curves rise more steeply with pressure and agree less well with experiment for C12 and H2S but better for CHClF2and C103F. A value lower than 265 cal mol-I would improve the situation for Clz and H2S but make it worse for CHClF2 and C103F. The lowest value of Ab,,, which can give a hydration number of 6.12 (that estimated for H2S) at the quadruple point is 265 cal mol-l. It is, of course, possible that the theory is strictly correct and that the experimental compositions for hydrates of C103F, CHC1F2,and C12 are systematically in error. The author feels, however, that the experimental data given here are close to correct. He is continuing to work with other systems and hopes that the added information will be helpful. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for the partial support of this research. The author thanks D. W. Davidson for his interest and helpful advice.
Solubility of Gases in Liquids. 13. High-Precision Determination of Henry's Constants for Methane and Ethane in Liquid Water at 275 to 328 K Tlmothy R. Rettlch, Y. Paul Hands,+ Rubin Battino,' and Emmerlch Wllhelmt Departmen?of Chemistry, Wright State University, Dayion, Ohio 45435 (Received: April 30, 198 1; In Final Form: June 26, 198 1)
A high-precision apparatus of the Benson-Krause type has been used to measure the solubilitiesof methane and ethane in pure liquid water in the pressure range 50-100 kPa and temperature range 275-328 K. From these data, Henry's constant Hz,l is derived. Its temperature dependence is accounted for by both a ClarkeGlew-type fitting equation, and a power series in 1/T. The imprecision of our measurements is characterized by average deviations of Hz,l from these smoothing equations of ca. &0.06% for H20 + CHI, and ca. f0.08% for HzO + CzHG.From the temperature variation of H2,1, partial molar quantities pertaining to the solution process, Le., standard changes in enthalpy, entropy, and heat capacity, have been obtained. In addition, several thermodynamic quantities used in discussing hydrophobic interaction are presented.
Introduction In recent years there has been a resurgence of interest in the solubility of gases in liquids in general,l-s and in liquid water in particular?Sa The need for high-precision experimental data on very dilute aqueous solutions can be 'Division of Chemistry, The National Research Council of Canada, Ottawa, Canada KIA OR6. *Visiting Associate Professor of Chemistry from Institut fur Physikalische Chemie, Universitat Wien, Wahringerstrasse 42,A1090 Wien, Austria.
traced to research activities in a variety of areas.12p26-2e Measurements covering sufficiently large ranges of tem(1) R. Battino and H. L. Clever, Chern. Reu., 66, 395 (1966). (2) E. Wilhelm and R. Battino, Chern. Rev., 73, 1 (1973).
(3) H.L. Clever and R. Battino in "Weissberger: Techniques of Chemistry", Vol. 8, Part 1,M.R.J. Dack, Ed., Wiley-Interscience, New York, 1975, p 379. (4) R. A. Pierotti, Chern. Reu., 76, 717 (1976). (5)W. Gerrard, "Solubility of Gases in Liquids. A Graphic Approach", Plenum Press, New York, 1976. (6) E. Wilhelm, Fortschr. Verfahrenstechn.,Abt. A, 16, 21 (1977). (7) S. Goldman, Acc. Chem. Res., 12, 409 (1979).
0022-3654/81/2085-3230$01.25/0 0 1981 American Chemical Soclety
