J. Phys. Chem. iW3, 87, 4437-4441
adsorption (coordination or solvation) energy of the cation with adsorbed molecules. In zeolites AIOzhas an effective negative charge. Site SI has the largest s u m of electrostatic contributions from this. Therefore, if there are no adsorbed molecules, site SI is the most preferred site for the cations. However, since adsorbed molecules cannot occupy site SI, it has the lowest adsorption energy. In contrast, site SIV near the center of the supercage has the lowest electrostatic energy and the highest adsorption energy because the free space around site SIV can allow the cation to be fully coordinated by adsorbed molecules. Upon ion exchange with C U ~ + ( H ~ O Cu2+ ) ~ ,loses half of its coordinated water molecules and is trapped in site SII*. Through this process the Cu2+gains more electrostatic energy than it loses adsorption energy. When the adsorbed molecules are removed thermally, Cu2+goes into the hexagonal prism to maximize the electrostatic energy. Upon rehydration, most of the alkali cations are hydrated. The migration of Cu2+from the hexagonal prism to the site SII* is normally accompanied by the migration of an alkali cation to SI. If the alkali cation is hydrated it must lose its coordinated water before going into SI, so the total energy for transferring Cu2+out of the hexagonal prism increases with increasing adsorption (hydration) energy of the hydrated alkali cation. The hydration energy is 27% higher for Na+ with a smaller ionic radius than for K+. In the postulated model this difference is apparently sufficient so that, upon
4457
rehydration, Cu2+in CuNa-Y stays in the hexagonal prism, while in CuK-Y, Cu2+migrates from the hexagonal prism to site SII* and K+ replaces Cu2+in the hexagonal prism. In addition to hydration energy the diffusion of the hydrated alkali cations through the 6-rings is probably relevant. The diffusion coefficients are difficult to predict but it is interesting that in water the mobility of K+is 50% greater than that of Na+. If relevant to zeolites, this is in the correct direction to contribute to the preferential Cu2+ locations found. Since Cu2+ in CuNa-Y does not migrate into site SI directly upon ion exchange as is the case in CuNa-X,’* it is concluded that some activation energy is necessary for Cu2+migration from the supercage to the hexagonal prism. The electrostatic energy of site SI in the hexagonal prism is greater in X zeolites than in Y zeolites because of the lower Si/Al ratio in X zeolites. Within this model this additional energy is sufficient to overcome the activation energy so that Cu2+in CuNa-Y can migrate directly into site SI during ion exchange.
Acknowledgment. This work was supported by the National Science Foundation and the Robert A. Welch Foundation. We thank M. Narayana for his critical comments. Equipment support from the University of Houston Energy Laboratory is greatly appreciated. Registry No. Cu, 7440-50-8; HzO, 7732-18-5.
Composltlon of Clathrate Gas Hydrates of H2S, Xe, SO,, CI,, CH,CI, CH,Br, CHCIF,, CCI2F2,and C3Hs George H. Cady Depertment of Cbmbm, UnherSny of Washlngfon, Siwttk, Washington 98195 (Received: December 9, 1982)
Compositions of the clathrate hydrates of gases have been determined at 0 “C by quantitative synthesis at various constant pressures. Within the limits of experimental accuracy, the hydration numbers of CC12F2and C3H8are 17.0. Hydration numbers of H2S,Xe, SOz, CH3Cl,and (probably) CH3Br and CHCIFzdecrease as the pressure increases in quantitative agreement with predictions of the statistical theory of van der Waals and others, as applied to structure I hydrates. For chlorine there is qualitative but not quantitative agreement. Hydrogen sulfide moleculeti appear to occupy equally the two sizes of cavities in structure I solid. With increasing molecular size in the order, Xe, SOz, Clz, CH3Cl,CH3Br,CHC1F2,the tendency to occupy the smaller type of cavity becomes less in comparison to the tendency to occupy the larger type. However, even the largest of these molecules apparently occupies some of the smaller sites.
In an earlier paper the author described a procedure for the quantitative synthesis of a clathrate gas hydrate by slow condensation of a hewn weight of water vapor upon a cold surface at constant temperature in the presence of the gas a t constant pressure.’ The influence of pressure and temperature upon the composition of several hydrates was reported and the experimental results were compared with those predicted by the statistical theory of van der Waals and others.2-5 In some cases agreement was good; in others, however, it appeared that agreement might not (1) G. H. Cady, J. Phys. Chem., 86, 3225 (1981). (2) J. H. van der Waals, Tram. Faraday Soc., 52,184 (1956). (3) R. M. Barrer and W. L. Stuart,R o c . R. Soc. London,Ser. A, 243, 172 (1957). (4) J. H. van der Waals and J. C. Plateeuw, Adu. Chem. Phys., 2, 1 (1959). (5) D. W. Davidaon in ‘Water: A Comprehensive Treatise”,Vol2, F. Franks Ed., Plenum Press, New York, 1976, Chapter 3. 0022-3654/83/2087-4437$01.50/0
be good. Additional experimental information of the type which was needed is ?ow presented.
Experimental Section Some of the new data were obtained with the procedure described previously.’ In this method a weighed sample of water (usually about 0.2 g) distilled from the bottom of a reactor containing the gas a t constant pressure and condensed upon the surface of a cold finger, usually at 0 OC. The hydrate was then weighed and the hydration number, n, was calculated from eq 1. A somewhat difg of water X mol wt of gas n= (1) g of combined gas X mol w t of water ferent procedure was used to obtain some of the new data. Weighings of the new reactor shown in Figure 1were made without the plastic cup in place. About 0.2-0.5 g of water 0 1983 American Chemical Society
4438
The Journal of Physical Chemistry, Vol. 87, No. 22, 1983
Cady
TABLE I: Hydration Numbers, n, at 0 "C for Gases Studied at Various Ressures CCLF, 1.00 1.00 2.70 2.10 '3.&00 3.00 P,atm 1.00 1.00 n 17.09 11.05 11.03 17.03 16.96 16.96 16.90 11.12
P,atm
CJ-4
n
3.46 17.01
3.46 17.26
4.22 16.83
4.22 16.89
P,atm n
1.77 6.39
2.00 6.31
2.00 6.33
2.25 6.24
2.25 6.24
2.65 6.16
P,atm n
0.49 6.98
0.49 7.00
0.69 6.81
0.69 6.82
1.00 6.59
1.00 6.51
P,atm n
0.95 6.65
0.95 6.68
3.55 6.16
3.55 6.21
P,atm n
0.68 7.56
0.68 7.51
1.00 7.42
1.00 7.46
2.44 I.06
CH,C1 2.44 7.06
P,atm n P,atm n
0.39 7.11 0.65 I . 61
0.39 7.73 0.84 7.63
0.43 1.69 0.84 7.67
0.43 7.16 0.84 1.62
0.43 1.68 0.84 7.61
CH,Br 0.49 0.49 7.70 1.72 0.84 0.84 7.64 7.61
0.53 I. I1 0.81 1.62
0.53 1.69 0.81 7.62
P,atm
1.17 7.77
1.17 7.79
1.35 7.75
1.35 7.72
2.00 7.69
CHClF, 2.00 2.bo 7.17 1.71
2.00 7.71
3.46 7.68
Xe
n
2.65 6.18
so2
1.51 6.39
3.00 6.13
3.00 6.14
1.51 6.40
c1,
was introduced and weighed. The plastic cup was then set in place as shown in Figure 1. The plastic to glass joint was made water tight with paste. The reactor was then attached to a vacuum line. Gas was added to give the desired pressure for the run. The valve was then closed, and all of the water and gas was caused to condense in the bottom of the reactor by chilling with liquid nitrogen. Nucleation to start formation of hydrate was then accomplished by chilling the upper part of the reactor with solid carbon dioxide in a cloth bag while the bottom part warmed until the frozen water started to melt. The cloth bag containing solid carbon dioxide was then removed, and ice plus water was added to fill the plastic cup. During a run, the pressure in the reactor was held constant by frequently adding gas. The refrigerant in the plastic cup was held a t 0 "C by adding ice from time to time, and the water in the reactor was encouraged to distill by holding the bottom 1 cm of the reactor at about 25-30 "C. The whole of the sample of water distilled within about 3-4 h, and the hydrate formed as a crystalline deposit of approximately uniform thickness over nearly all of the colder inner surface of the reactor. The unreacted gas was then removed from the reactor in the manner previously describedl and the vessel was weighed. When good nucleation occurred, both methods gave the same results within limits of experimental accuracy. In runs involving gas pressure more than about 1.4times the decomposition pressure of the hydrate, nucleation usually was good and reaulta were reproducible. At pressures lower than this it was common to have incomplete conversion of water to hydrate and to obtain erroneously high apparent hydration numbers. The gases were commercial products of high purity. With the exception of xenon, each substance was distilled, and the middle portion was used in the experiments. Results Table I gives observed hydration numbers obtained at various pressures when the cold zone of the apparatus was chilled by ice and water. It is believed that the new data
3.46 7.61
4.18 7.69
4.18 7.66
4.22 1.10
4.22 1.66
Flgus 1. Croas-sectlonalvkw of reactor. The vessel is a Pyrex glass cylinder whlch may be pushed through a snug hole In the polyethylene cup. Paste is used to make a water-tlght plastic to glass seal. All weighings of the reactor are made with the cup removed.
given here for Cl, and CHClF, are somewhat more accurate than those given previous1y.l A correction was made for the amount of gas dissolved in the Teflon valve stem. Similar corrections were made, when necessary, when measuring the other hydration numbers given in Table I. This correction usually was made by subtracting the increase in weight of the valve stem during a run, from the total weight of gas remaining of the reactor at the end of the run. The gain in weight of the stem was normally not more than 0.0003 g. A t times, it was as large as 0.001 g.
Composition of Clathrate Gas Hydrates
In the hydration numbers in Table I the second decimal place has some significance but probably is not accurate.
*
The Journal of phvsical Chemistry, Vol. 87, No. 22, 1983 4489
Discussion Structure 11 Hydrates. A structure I1 hydrates has a unit cell containing 136 water molecules arranged to give eight “large” (16-dedral) and sixteen “small” (12-hedral) cavities. Hydrates of this type are formed by gases of molecular diamters within the range, approximately 5.6-6.7 Such molecules are so much larger than the “small” cavities that they have not been expected to occupy any of the “small” sites. While many values covering a wide range have been reported for hydration numbers of gases in structure I1 hydrates, there is now good reason to feel that these hydrates are nearly stoichiometric with hydration numbers ranging from slightly over 17.00 at the decomposition pressure down almost to 17.000 at higher p r e ~ u r e s .The ~ author has reported experimental values very close to 17.00 for CC13F and SF6. When the author measured the hydration number of CClZFz,he at first found values ranging from about 16.6 to 16.8, with an indication that increasing pressure caused decreasing hydration number. It was then found that the Teflon valve stem increased in weight by an amount up to about 0.001 g during a run, because the gas dissolved in the Teflon valve stem. When a correction for this increase was made, hydration numbers near 17.0 were found. Values previously reported for CClzFzare 15.6,7 16.0 for Dz0.8 Nucleation of propane hydrate occurred with difficulty. Since the decomposition pressure is rather high (1.74 atm at about 0 OC9) it was not safe to use glass reactors at pressures much above twice the decomposition pressure. Several experimental determinations gave values much above 17.0. Finally, by using the pressures shown in Table I the results given there were obtained. The number is near 17.0 and probably is not less than this. Nucleation was started by using solid carbon dioxide in the usual manner. Nucleation of propane hydrate was found by Ceccotti’o to be difficult. He used gas pressure in excess of 3 atm. and reported that solid Ag I aided in the nucleation process. He found the hydration number to be 19.7. This high value could have been caused by having some liquid water present with the crystals of hydrate. In the present research, attempts were made to aid nucleation by having a little Ag I present on the inner wall of the reactor. If it made a difference, the author did not observe it. Other values which have been reported for propane are 17.959 and 17.9.’’ Structure I Hydrates. The unit cell of a structure I hydrate contains 46 water molecules. There are six “large” (14-hedral) and two “small” (12-hedral) cavities available for occupancy by gas molecules.6 Complete filling of the eight cavities would give a hydration number of 5.75, while complete filling of the “large” but none of the “small” cavities would give a hydration number of 72/3. Data for (6)M. V. Stackelberg and H. R. MUer, 2.Elektrochem.,58,25(1964). ( 7 ) T. A. Wittatruck, W. S. Brey, Jr., A. M. Buswell, and W. H. Rodebush, J. Chem. Eng. Data, 6,343 (1961). (8)D. Yu. Stupin, V. N. Tezikov, and A. P. Seleznev, Zh. Prikl.Khim., 51, No. 3,589 (1978). (9)W. M. Deaton and E. M. Frost, ‘Gas Hydratea and Their Relation to the Operation of Natural Gas Pipe Lines”,U.S. Department of Interior, Bureau of Mines, Washington, DC, 1946,Monograph No. 8. (10)P.J. Ceccoti, Ind. Eng. Chem., Fundam., 5, 106 (1966). (11) A. J. Barduhn, H. E. Towlson, end Y. C. Hu, Am. Inst. Chem. Eng. J., 8, 176 (1962).
I
24
l
1
l
70
1
6.6
Hydration number
1
1
82
5.8
Flgure 2. Pressure vs. composition relationships for structure I gas hydrates at 0 ‘C. Dots represent experimental data. Lines are based in part upon statistical theory.
CHCIFzand C103F given in the previous paper’ indicated these substances to have hydration numbers of 72/3within the limits of experimental accuracy. Increasing gas pressure had little influence upon the value. There was an indication in the data, however, that a small decrease occurred in hydration number with an increase in pressure. Since theory predicts such a d e c r e a ~ e , ~the - ~author has made several new determinations of the hydration number of CHCIFz at 0 O C and various pressures. The new data in Table I confirm the decrease. They also indicate that a similar small decrease occurs for CH3Br, which has hydration numbers near 72/3. The new data for chlorine given in Table I involve a small correction for gas dissolved in the valve stem. They confirm the old data’ which were not corrected. The following hydration numbers have previously been reported (1)H a , 6.06;12 (2) Xe, 5.9E~6.25,’~ 7.61: (3) SOz, 6.0,15 6.1;14 (4) CH3C1, 8.2;6*’6(5) CH3Br, 7.89,’’ 8.0;14(6) CHCIFz, 8.3,8 7.6L7 Several other values (old) have been reported for HzS and SOz. Figure 2 shows the data for structure I hydrates given in Table I. The experimental values for Clz and HzS from the previous paper’ also are shown. Lines in the f i i e are based upon theory. The basis for drawing these lines will now be stated. Experiment us. Theory. The statistical theoryz4 says that the fraction of occupancy, 8, of a set of cavities in a hydrate is given by the Langmuir isotherm
o=-
KP 1+KP
in which P is the partial pressure of the gas and K is a constant. For the “small” set of cavities in a structure I (12)A. E.Korvezee and F. E. C. Scheffer, Recl. 7”. Chim. Pays-Bas, 50, 256 (1931). (13)R. M. Barrer and A V. J. Edge, R o c . R. SOC.London, Ser. A, 300, l(1967). (14)M. V. Stackelberg, Naturwissenschaften, 36,359 (1949). (15)G. Tammann and G. J. R. Krige, 2.Anorg. Chem., 146, - Allgem. 179 (1925). (16)D.N.Glew and E. A. Moelwyn-Huges, Discuss. Faraday SOC.,15, 150 (1953).
4440
The Journal of fhyskal Chemisw, Vol. 87, No. 22, 1983
Cady
TABLE 11: Langmuir Constants for Structure I Hydrates at 0 "C gas
HZS
Xe
SO, C1Z CH,C1 CH,Br CHCIF, a
Estimated when
Po,atm
ref
na
elb
ezb
0.955 1.46 0.323 0.320 0.386 0.241 0.870
12 13 15 18,17
6.119 6.478 7.240 7.503 7.717 7.829 7.839
0.940 0.651 0.255 0.140 0.052 0.0090 0.0050
0.940 0.9664 0.9739 0.9751 0.9759 0.9763 0.9763
P = Po.
d
11 7
Calculated when P = Po.
Langmuir constants.
Kl 16.42 1.28 1.08 0.518 0.146 0.039 0.0058
KZC 16.42 19.78 118 125 107 175 47.7
This work.
hydrate we have 81 and K 1 and for the "large" set 8 2 and K 2 Relationships are as follows:
If pure unoccupied structure I solid could exist, its chemical potential, k0, would be higher than that of ordinary ice. Davidson6has concluded that the difference is about 265 cal per mol of water. A& = pwo- p,(ice) = -265 cal mol-l
The theory says that this difference is related to 8 2 by A& = 265 = - RT[
(7) 81
6 2 In (1 - 8 2 ) + - In (1 - 8 J ] 46 46
and (8)
which leads to 3 In (1 - 82) + In (1 - 81) = -11.236
(9)
In eq 8 and 9 the values of 81 and 8 2 are those which cause the chemical potential of water in the hydrate at 0 "C to be equal to the chemical potential of water in ice or liquid water at 0 "C. Different seta of values of 81 and 8 2 satisfy eq 9. Each hydrate has ita own set of values and a corresponding hydration number, n, given by 46 =- 23 n= 682 281 382 81
+
+
If n were to be measured experimentally at 0 "C when the pressure of gas is that existing at equilibrium with a mixture of ice and hydrate, it would be possible to obtain 82 and 81 by using eq 9 and 10 as a pair of simultaneous equations. These values of el and e2 could then be used in eq 5 and 6 to evaluate Kl and K 2 Theoretical hydration numbers could then be calculated for the gas over a range of equilibrium pressure, and these could be compared with experimentally observed hydration numbers. An unsolved problem in this plan is that no procedure is known to determine directly an accurate experimental value of the hydration number in a hydrate existing a t equilibrium with gas and ice. Furthermore, theory does not accurately predict n for these conditions. In the pressent research, values of n were measured at 0 "C and a t various pressures. The data were then used to esstimate the hydration number of the hydrate existing in equilibrium with gas and ice a t 0 "C. (Such an equi-
Hydration number
Figure 3. Pressure vs. compositlon relationships for structure I gas hydrates at 0 "C. Pressure is ghren as the ratio, P l P o. Experimental polnts for Cl$,Br are not shown. Unes are based in part upon statistical theory. The theoretical behavior of different gas hydrates havlng the same composbn at Po Is [dentical up to thelr limiting values of P l P o.
librium cannot in fact exist for a gas which is soluble in liquid water.) The estimated value for the pressure for this condition was obtained from literature giving P vs. T data for the gas-hydrate-ice equilibrium. This relationship is commonly called the HIG line. A graph of In P vs. 1 / T was extended from lower temperatures to give the pressure a t T = 273.15 K. In Table 11, this presssure is called Po and is given in atmospheres. The partial pressure of gas was then taken to be (Po- vapor pressure of ice at 0 "C). An estimated value of n at Po was then chosen so that the calculated theoretical hydration number at a pressure of 3P0was the same as that found experimentally. For xenon, the agreement was at 2P,. Table I1 gives (1)the estimated values of n, at Po;(2) the values of 81 and O2 calculated from the estimated n, and simultaneous eq 9 and 10; and (3) Kl and K 2 calculated from eq 5 and 6. In Figure 2 the experimental values of n from Table I are plotted vs. pressure in atmospheres. The lines in the figure are the theoretical relationships obtained from the valuess of K 1 and K2 in Table I1 and from the use of eq 3, 4, and 10. The pressure at the lower end of a line corresponds to Po for the gas. The upper end, if there is one, is at the pressure equal to the vapor pressure of the liquid form of the substance at 0 "C. Figure 3 is like Figure 2 except that the unib of pressure are PIP, rather than P. This type of graph shows CH3Br to be almost identical in behavior to CHClF2except for the value of Po. In Figure 3, the experimental points for CH3Br have not been shown, because they would be confused with the points of CHC1F2.
J. Phys. Chem. 1003, 8 7 , 4441-4446
The agreement between theory and experiment is very good for the gases H2S, Xe, SO2,and CH3C1. For CHClF2 and CH3Br there is little change of composition with pressure. Theory predicts little change. Because of the size of possible experimental error, one cannot say that the data clearly are in agreement with theory. They certainly are not in disagreement, and it appears likely that they agree. The data suggest strongly that molecules of CHClF2 and CH3Br occupy some of the “small” cavities. Such a situation would probably require distortion of the lattice, because these molecules are much larger than the “small” cavities. In Figure 3 the line drawn farthest to the left shows the theoretical relationship for a structure I hydrate having no “small” cavities occupied by guest molecules. Relative positions of the lines in Figure 3 correspond to increasing molecular diameter of gases in the order H2S, Xe, SO2, C12, CH,Cl, CH3Br, CHClF,. For C12 there is only qualitative agreement between theory and experiment. The amount of gas found in the hydrate increases more rapidly with pressure than is expected by theory. The author thinks that this difference is real and not caused by experimental error. The ratio of occupancy, 01/02, for xenon at Po is 0.651/0.9664 = 0.67. This may be compared with a ratio of 0.77 found by Ripmeester and Davidsonlg through the (17)H.Roomboom, Rec. Trau. Chim., 4,65 (1885). (18)D. A. Wilms and A. A. van Haute, h o c . Znt. Symp. Fresh Water Sea, 3, 117 (1970). (19)J. A. Ripmeester and D. W. Davidson, Bull. Mag. Reaon., 2,139 (1980).
4441
use of NMR for Xe-nH20formed at 275 K under a pressure of 1.5 atm. While the theory is good, it alone is not a sufficient device for accurately calculating the composition of a structure I gas hydrate at 0 OC over a range of pressures. One must also know the composition at one (preferably more) pressure, and he must know Po. The experimental data for the hydrate of hydrogen sulfide indicate that A k 0 is probably not less than 265 cal mol-l. If it were less, the hydration number at Po in all structure I hydrates at Po and 0 “C would be greater than 6.119. The number for H2S is close to 6.12. This makes it probable that Apwo is 265 cal mol-’ or more. For a structure I hydrate having zero occupancy of “small” sites, the value of n a t Po is 7.852, if A h o is 265 cal mol-’. For higher values of A k 0 the corresponding values of n at Po are (1) Apwo= 275, n = 7.827; (2) Apwo = 285, n = 7.806. The experimental data for CHClF2 and CH3Br indicate that Apwo probably is not more than 285 cal mol-’. If Apwois found to have a value different from 265 cal mol-’, it will follow that the numbers given in columns 4-8 in Table 11 are incorrect and will need to be changed to correspond to the correct value of Apwo. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for the partial support of thisresearch. The author thanksD. W. Davidson and Riki Kobayashi for their interest and helpful advice. Registry No. CClzF2,75-71-8;C3H8,74-98-6;Xe, 7440-63-3; SOz, 7446-09-5;Clz,7782-50-5; CH3Cl,74-87-3;CH3Br,74-83-9; CHClFZ, 75-45-6; HZS, 7783-06-4;HzO, 7732-18-5.
Quantum Yield Determinations for Sub-Nanosecond-Lived Excited States and Photoproducts. Applications to Inorganic Complexes and Photosynthetic Models Michael A. Bergkamp,+Chi-Kwong Chang,t and Thomas L. Netrelet Department of Chemistry, Brookhaven National Laboratmy, Upton, New York 11973, and Depertment of Chemistry, Michigan State Universl&, East Lansing, Michigan 48824 (Received: January 21, 1983)
This paper presents a procedure for determining the quantum yields of nonluminescent excited states and photoproducts with subnanosecond lifetimes. We describe both a procedure for calibrating the intensity of the photoexcitation pulse (einstein cm-2pulse-’) and a numerical calculation of percent excitation for an optically dense sample. Particular attention is paid to the case for which a large fraction of starting material is transformed into photoproduct, a common occurrence in picosecond absorption spectroscopy. As motivating applications, we determined the quantum yields of (1)the lowest energy ligand-field excited state of Fe(phen)32+(phen = 1,lO-phenanthroline)and (2) the 200-ps-lived electron-transfer (ET) photoproduct (Mg+-Hp) in a diporphyrin model of photosystem I1 (PSII) to be 1.00 f 0.05 and 0.9 f 0.1, respectively. In both cases the observed photoproducts are formed from the decay of ultrashort-lived, initial excited states (T < 10 ps).
it undergoes an ultrafast electron transfer (ET) from its lowest excited ‘(?r,?r*) state in
