3.398
DENNISR. HAFEMANN AND STANLEY L. MILLER
The Deuteriohydrates of Cyclopropane1 by Dennis R. Hafemann2and Stanley L. Miller Department of Chemistry, Universz'ty of Californta, San Diego, La Jolla, California 92037 (ReceZved October 2 , 1 9 6 8 )
The thermochemical constants of the two clathrate deuteriohydrates of the cyclopropane-D20 system have been determined by pressure vs. temperature measurements. The deuteriohydrate formulas are C3He.7.8D20 and C~H6.17.2D20,corresponding to the structure I 12-A and structure I1 17-,&hydrates, respectively, Below O", the deuteriohydrate dissociation pressures are higher than the hydrate dissociation pressures, but above 0" the deuteriohydrate dissociation pressures are lower than the hydrate dissociation pressures. The structure I deuteriohydrate is less dense than liquid D20, but the structure I hydrate is more dense than liquid HZO. An explanation is offered for this anomaly. A comparison of the free energies of empty clathrate lattice formation from HzO and D2O ice shows that the deuteriohydrate lattice is only slightly more unstable than the hydrate lattice. Although the dissociation pressure and structures of many gas hydrates have been measured, the similar compounds with DzO have been neglected except for the early measurements of Godchot, et u Z . , ~ on krypton and xenon. The stabilities of the deuteriohydrates should provide some insight into the stability of deuterium bonds in the crystalline forms and in the liquid. Cyclopropane is an attractive gas with which to measure the deuteriohydrate stabilities because both the 12- and 17-A cubic clathrates occur in its phase diagrama4 We have measured the phase diagram of cyclopropane and D20 and find it to be similar to that of CaHa and HzO. The dissociation pressures are higher for DzO ice than for H20 ice, and the dissociation pressures are lower for liquid DzO than for liquid H2O.
Experimental Section The experimental technique was the same as described previou~ly.~The DzO was obtained from Liquid Carbonic, and its purity was >99.5%. The finely ground D20ice was prepared by grinding with a mortar and pestle on a day of very low humidity. Density measurements indicated that less than 0.5% H20contaminated the DzOduring this grinding process. The triple point of D20 was taken as 3.82'. The vapor pressures of D20were taken from Kirshenbaum.6
Results There are four segments in the dissociation pressure curve of cyclopropane deuteriohydrate which are similar to the cyclopropane hydrate. These are shown in Figure 1, and the data are given in Table I. Deuteriohydrate I is stable below -23", but it was possible t o measure the dissociation pressure of the metastable deuteriohydrate up to - 10". This was done by forming deuteriohydrate I below -23" and raising the temperature quickly. The rate of reversion to stable deuteriohydrate I1 was low enough to permit accurate The Journal of Physical Chemislrg
,
measurement of the metastable deuteriohydrate I dissociation pressure. The dissociation pressure is given by 1OgPmm
=
8.2419 - 1511.10/T
+ 9.969 X lO-4T
in the range -63 to -10". This includes the metastable points. The designation dJg refers to the deuteriohydrate I-ice-gas dissociation pressure curve. The symbols dz, 11, and la refer to deuteriohydrate 11, liquid D20,and liquid cyclopropane, respectively. The fugacity corrections were estimated from the second virial coefficients as bef01-e.~ The fugacity is given by log fmm
= 8.4283
- 1591.31/T f 5.654 X 10-4T
Deuteriohydrate I1 is stable between -23.31 and +5.52". It was possible to measure one metastable deuteriohydrate I1 dissociation pressure below -23". The dissociation pressure and fugacity for points below the triple point of D20 (3.82")are given by the equations log P,,
=
10.1087 - 1727.76/T - 3.965 X lO-?f' (d2Ig)
logf,,
=
10.4541
(3)
- 1768.42/T - 4.705 X lO-*T
(d2Ig) (4) The dissociation pressure of this deuteriohydrate above 3.82" is given by log P,,
=
28.9231 - 7240.50/T
(d211g)
(5)
(1) This work was supported by Grant GM 11906 from the National Institutes of Health. (2) Department of Physiology, University of California, Los Angeles, Calif. 90024. (3) M. Godchot, G . Cauquil, and R. Galas, Compt. Rend., 202. 759 (1936). (4) D. R. Hafemann and 5. L. Miller, J. P h y s . Chem., 7 3 , 1392 (1969). ( 5 ) I. Kfrshenbaum, "Physical Properties and Analysis of Heavy Water," McGraw-Hill Book Go., Inc., New York, N. Y., 1951.
1399
THE DEUTERIOHYDRATES OF CYCLOPROPANE The corrections to obtain the fugacity at unit water activity ( f')were calculated as before.'^^ The f / P was obtained from the virial coefficients, and the solubility of cyclopropane was assumed to be the same in DzO as in HzO. Since the solubility of cyclopropane in water is low, no substantial error in the fugacity should result from this approximation. The corrected fugacity is given by log f'mm
=
28.3165
- 7075.55/T
(d211g)
(6)
Deuteriohydrate I becomes stable again from 5.52 to 18.34'. The dissociation pressure and corrected fugacity are given by the equations log P m m = -17.8700
+ 756.61/T + 6.4936 X 10-2T (dlllg)
logf'mrn
=
10.1976
- 3122.15/T + 1.4120 X
(7)
10-'T
(dJ1g)
(8)
Table I: Dissociation Pressures of Cyclopropane Deuteriohydrate. The Metastable Points are Labeled (m). T,OC
-63.36 -60.09 -53.07 -49.64 -36.78 -35.81 -35.74 -34.34 -32.10 -31.83 -29.98 -27.90 -20.05 -19.98 -15.04 -14.94 -10.13 -10.07 -29.87 -19.94 -15.02 .-14.95 10.03 -9.96 -5.15 -5.08 -4.95 -0.14 $0.02 +3.96 4.31 4.62 4.95 5.95 6.74 7.94 8.95 10.25 18.34
--
Pcans,m m
~ ' c ~ Hmm ~ ,
Deuteriohydrate
9.22 11.99 20.9 27.3 67.7 72.3 72.6 79.8 91.8 93.3 105.4 120.9 194.6 195.1 258.7 260.7 337.6 339.4 110.1 190.8 247.8 248.0 314.2 316.8 396.2 396.6 401.3 501.9 500.8 622.9 672.0 719.1 771.5 919.1 1021.1 1192.4 1349.3 1591.7 4509
9.21 11.98 20.9 27.3 67.5 72.1 72.4 79.6 91.5 93.0 105.1 120.5 193.4 193.9 256.7 258.7 334.8 336.1 109.6 189.6 246.0 246.2 311.4 313.9 391.9 392.3 396.9 495.4 494.3 606.9 653.6 698.4 748.0 893.2 989.7 1150.5 1296.8 1520.0 4005
I I I I I I I I I I I I I(m) I(m) I(m) I(m) I(m) 1 (m) 11 (4 I1 I1 I1 I1 I1 I1 I1 I1 I1 I1 I1 I1 I1 I1
I I I I I I
Figure 1. Dissociation presure curve for cyclopropane deuteriohydrate: 0,selected data points; ,. quadrupole points; -, stable deuteriohydrate dissociation pressure curve and cyclopropane vapor pressure curve; * *, metastable deuteriohydrate dissociation pressure curves; --, stable cyclopropane hydrate dissociation pressure curve. All metastable data points are omitted.
-
The Quadruple Points. There are four stable and two metastable quadrupole points in the cyclopropane deuteriohydrate phase diagram. These were calculated from the appropriate pairs of dissociation pressure equations. The pressures and temperatures are given in Table 11. The Enthalpies of Dissociation. The enthalpies of dissociation of the hydrates to an ideal gas were calculated from the equation d lnf/d(l/T) = - A H / R . The AH values for the different segments of the dissociation pressure curve at 3.82" are given in Table 111. The ACp values are also included, as well as the AH values for cyclopropane hydraten4 The Deuteriohydrate Formulas. The number of moles of DzO per mole of cyclopropane was calculated by the equation n=
AH1 - AH8 AHt
(9)
where the subscripts f, 1, and s refer to the heat of fusion of DzO and the enthalpies of dissociation to liquid DzO and to solid DzO, respectively. These heats of dissociation are for the quadrupole point at 3.82". The heat of (6) D. N. Glew, Can. J . Chem., 38, 208 (1960).
Volume YSS Number 6 May 1889
1400
DENNISR. HAFEMANN AND STANLEY L. MILLER
Table 11: The Quadrupole Points Phases
did& dzIlig dlIllg (metastable) didzlig d1~112g d21112g (metastable)
T, OC
Po,ns, mm
-23.31 +3.78 3.76 5.52 18.34 12.58
159.4 595.2 698.5 872.6 4509 3825
fusion of DzO was taken as 1515 cal/mol.6 This equation gives n = 7.76 f 0.05 (deuteriohydrate I)
n
=
17.18 f 0.12 (deuteriohydrate 11)
The stated errors refer only to the deviations of the experimental points from the calculated equations. The Deuteriohydrate Structures. The formula for deuteriohydrate 11, C3H6* 17.2D20, is the same as that for hydrate 11, CsHe- 17.0H20,4and can be assigned the hydrate structure I1 as given by Claussen and by Stackelberg and Muller.7 The X-ray powder pattern was not obtained for deuteriohydrate I, but the structure is very likely the same as that of hydrate I. The formulas CaHe-7.8D20and C3He.8.0H20are very close. This would correspond to almost complete occupancy of the tetrakaidecahedra of the structure I 12-A cubic hydrate, but with no CaH6 in the pentagonal dodecahedra. The formula for the bromine hydrate tetragonal structure8 would be C3R6~8.60H20.There is insufficient water in the observed hydrate I formula to be consistent with the bromine hydrate tetragonal structure unless some of the smaller pentagonal dodecahedra are occupied by cyclopropane. The Clathrate Densities. The densities of the hydrates and deuteriohydrates were not measured directly, but both of the structure I1 clathrates were observed to float. The calculated density for the structure I1 hydrate is 0.9418 assuming a 17.0-A lattice and full occupancy of the large cavities by cyclopropane. The calculated density for the deuteriohydrate is 1.0342 with the same assumptions. For comparison, at 7Othe densities of HzO and DzO are 0.99993 and 1.10583, respe~tively.~ The structure I hydrate was observed to sink in H20,
Table 111: Thermochemical Constants at 3.82" Expressed as Calories per Mole of Cyclopropane Equilibrium phases
dik dzk dalig dilig ~~~
~~
7,479 f 20 6,439 f 30 32,370 f 500 19,240 f 70 ~
The Journal of Physical Chemistry
AC*
AHna
+ 1 . 4 f 3.0 -12 f 4
7,405 6,424 29,200 19,060
...
$36 f 10
but the structure I deuteriohydrate floated in liquid D2O. This observation can be accounted for on the following basis. Taking the cell constant as 12.11 A, the density of the empty clatharate lattice would be 0.7747 for HzO and 0.8613 for DzO. Assuming full occupancy of the tetrakaidecahedra, the cyclopropane makes the same density contribution of 0.2360 in both cases giving a total density of 1.0107 for the hydrate and 1.0973 for the deuteriohydrate. The hydrate has a density 0.0108 greater than the liquid, while the deuteriohydrate has a density 0.0085 less than the liquid.1° The density observations also place limits on the cell constant. Assuming full occupancy of the tetrakaidecahedra, the cell constant must be less than 12.15A or the hydrate will float, and greater than 12.08A or the deuteriohydrate will sink. The calculated cell constant would be reduced if the per cent occupancy were less than 100%. Assuming the density of the hydrate to be 1.0107, the occupancy would be 93% (CaHe*8.25H20) for a cell constant of 12.04 A; less than 93% occupancy would give a cell constant inconsistent with the X-ray data. The density of cyclopropane hydrate I is inconsistent with a structure like that of tetragonal bromine hydrate.8 This hydrate would have a density of 0.9467 assuming full occupancy of the tetrakaidecahedra and pent& kaidecahedra.
Discussion The phase diagram of cyclopropane deuteriohydrate is very similar to that of cyclopropane hydrate. The formation of the clathrate with DzO ice requires a slightly higher (-18%) pressure of C3Hs than with HzO ice. The opposite is true for clathrate formation from liquid DzO and HzO. This reversal of stability is due to the 3.82" difference in the melting points. Between 0 and 3.82" the deuteriohydrate dissociation pressure increases by 20%, but the dissociation pressure of the hydrate increases by 80%, the difference being the much larger AH of clathrate formation with liquid HzO than with DzO or HzO ice. For this reason the lower dissociation pressure with DzO (1) than with H2O (1) need not be attributed to a greater degree of association in liquid DzO than in liquid HzO. The only deuteriohydrates studied previously are those of krypton and xenon from liquid Dz0.3 The reported dissociation pressures of the krypton deuteriohydrate are about 5% higher than the hydrate data of (7) W. F. Claussen, J . Chem. Phys., 19, 259, 662 (1951); M. V. Btackelberg and H. R . Mtiller. 2. Elektrochem., 58, 25 (1954);T. Mak and R . K . McMullan, J . Chem. Phys., 42, 2732 (1965). (8) K . W. Allen and G. A. Jeffrey, J . Chem. Phys., 38, 2304 (1963). (9) F. Steckel and S. Szapiro, Trans. Faraday Soc.. 59, 331 (1963). (10) The molar volume of D z O hexagonal ice is larger than Hz0 ice by a factor of 1.001. If the molar volumes of the hydrates are in the same ratio, this density calculation would no$ be substantially afiered.
THE DEUTERIOHYDRATES OF CYCLOPROPANE
1401
de ForCrand11a and Braun.11" The xenon deuteriohydrate dissociation pressures are about 5% greater than the hydrate data of de Forcrand, but 18% less than the data of Braun. Our measurements of the dissociation pressures at - 12.00" of xenon deuteriohydrate and hydrate are 726 and 672 mm, respectively, a ratio of 1.08. This extrapolates to PD~o/PH~o = 0.82 at 4". In the case of CH3F, P D ~ O / P H = ~1.06 O at -24.9". The heats of formation of the deuteriohydrates are the same as those of the hydrates within the experimental error, with the exception of the d211g. The errors of the d211g and hzllg equilibria may be greater than estimated because of the short temperature interval available for measurement. The hydrate formulas are nearly equal in the two systems, 7.8 and 17.2 for D2O and 8.0 and 17.0 for H20, which are the same within the experimental error. These formulas correspond to 98% occupancy for the deuteriohydrate tetrakaidecahedra and 96% occupancy for the hydrate. However, these data are not sufficiently accurate to make a meaningful calculation of the free energy of empty clathrate lattice formation from the formula12 Y
In (1 - y)
=Y
In (1
+ CjE) = -Ap/RT
(10)
where Y is 3/23 for structure I clathrates and 1/17 for structure I1 clathrates, C is the binding constant for the large cavities, and Ap is the free energy of formation of empty clathrate lattice from ice. The dissociation pressure data are sufficiently accurate to calculate the difference in Ap for the formation of the empty deuteriohydrate lattice and the empty hydrate lattice. We assume that the binding constant is the same in the deuteriohydrate cavities as in the hydrate cavities. Taking A p ~ ~ o=' 300 cal/mol of water18 and the fugacity at 0" for the hydrate, C1 is calculated to be 0.131 rnm-'. Using the same value of C1 and the fugacity of the deuteriohydrate at 0", A p ~ ~ obecomes ' " 190 cal/mol of 306 cal/mol of DzO. Taking A p ~ ~ o = HzO for the structure I1 hydrate,13 Cz is calulated to be 0.820 mm-', and A ~ D ~ O = I I 192 cal/mol of D20at 0". Similar small differences are obtained using other reasonable values12bof A,UH~OIand A / L H ~ O ~It~ .can be
concluded that the empty deuteriohydrate lattices are only slightly more unstable with respect to D2O ice than the empty hydrate lattices are with respect to HzOice. These small differences in the free energy of formation of the empty hydrate lattice can account for the nearly equal solubility of gases in H2O and DzO within the framework of an iceberg solubility model. Comparative data are limited,l4but argon is 15% more soluble in D 2 0 and I2is 17% less eoluble in D20. Molecules of intermediate size have intermediate solubility ratios. The solution of the gas in water would be described by
n water -+ iceberg iceberg
+ gas --+
iceberg-gas
Assuming that the binding constant of gases is the same in both H 2 0 and DzO icebergs, then the cyclopropane clathrate data would predict a slightly smaller solubility in D2O. The hydrate dissociation fugacity is greater with DzO (9.3% for structure I hydrate and 6.5% for structure I1 at 0") because of the slightly greater Ap of formation of the empty hydrate lattice from ice, and a greater Ap would also be expected for the iceberg. On the other hand, the increase in temperature from 0 to 4" increases A ~ H more ~ o than A p ~ ~ oThese . two factors are closely balanced and the solubilities are nearly equal. Small differences in Ap result in large changes in solubility; a decrease in Ap of 2.2 cal/mol of H2O in a tetrakaidecahedral iceberg would increase the solubility by 10%. The lower solubility of large gas molecules in ~ oslightly larger than A ~ H ~ o DzO suggests that A ~ D is for tetrakaidecahedral and hexakaidecahedral icebergs, but A ~ D ~
