J . Phys. Chem. 1987, 91, 5998-6002
5998
which is twice as large as that from experiment. Since missing factors in our treatment (discussed below) will probably further increase rather than decrease the simulated rate, the implication is that the electron-transfer mechanism may involve at least partial alignment of the heme planes. However, heme plane alignment is not a necessary prerequisite to obtaining a complex with a sufficiently small heme edge separation. Interestingly, the requirement of C20-A separation between heme edges may be met through basically two surfaces of the C Y P protein rather than from a single complexation state. Further examination of the conformational data generated by this simulation will be presented in a future paper. Not only is the detailed potential energy map around the C Y P protein rationally consistent with the successful approach vectors for reaction observed in the simulation, but the association rate in the absence of electrostatic forces is exceedingly slow, indicating the critical necessity of the particular charge arrangement on C Y P and CYTC. In future studies it will be possible to determine the rate effect of mutations at critical positions on the protein surfaces. The present model is vastly more realistic than the previous model employed, consisting of 3-charge spheres with axially symmetric reactive patches. However, additional improvements must be made to optimize the treatment within the context of BD simulation methodology, particularly (i) inclusion of the rotation
of the larger protein (requiring an additional storage grid of forces surrounding the CYTC protein), (ii) inclusion of hydrodynamic interactions based on the irregular geometry of the proteins,50(iii) inclusion of a low dielectric treatment inside the smaller protein CYTC, and (iv) inclusion of the capability of mobile charged surface side chains to dynamically adjust their positions during protein-protein docking.49 Such improvements are under consideration for future studies on this and related systems.
Acknowledgment. This work has been made possible by Grants DK01403 and GM34248 from the National Institutes of Health and by support from the donors of the Petroleum Research Fund, administered by the American Chemical Society. We express thanks to Wilfred van Gunsteren and BIOMOS for the commercially available GROMOS package, to Profs. Dabney WhiteDixon, Barry Honig, Stu Allison, Russell Bacquet, and Andy McCammon for helpful input, and to Alan Luton, Christine Northrup, Cynthia Miller, and Michael Parker for graphics assistance and secretarial support. S.H.N is the recipient of an NIH Research Career Development Award. Registry No. CYTC, 9007-43-6; CYP,9029-53-2; heme, 14875-96-8. (50) Garcia de la Torre, J.; Jimenez, A,; Friere, J. Macromolecules 1982, 1 5 , 148.
Thermochemlstry of Inorganic Solids. 6. The Enthalpies of Formation of Crystalline Hydrates, Ammoniates, and Alcoholates, and Some Observations on Heats of Dilution Mohamed W. M. Hisham and Sidney W. Benson* Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park mc- 1661, Los Angeles, California 90089 (Received: March 31, 1987)
The enthalpy of hydration of a crystalline salt AHohyd,,)(MaXt,)defined by AHohyd(n)(MaXb,Cr) = AfHo(MaXb.nH2?) nAfHo(H20,1)- Afffo(MaXb,cr)(1) and the value of n can be related quantitatively by a linear two-parameter equation: AHoh,p(,)(MaXb,cr)= mn + C (2) where m and C are different constants for each salt. For each salt the value obtained for m is close to -3 kcal/mol, and the value of C depends on the nature of salt, and for most mono- and divalent metal salts it ranges from -1 to -8 kcal/mol. Enthalpies of formation of solid crystalline hydrates, ammoniates, or alcoholates are quantitatively related to AfHo of the corresponding anhydrous salt and the value of n by a two-parameter equation: AfHo(MaXb-nY)= An" + AfHo(MaXb)( 3 ) where Y can be H 2 0 , NH,, or CH,OH. A and CY are different constants for each salt. For hydrates, the values obtained for CY are close to unity and the values of A and CY are related by A = +155a - 226.0 (4). For n = 1-7, the average deviation obtained for AfHo(MaXb.nY)for any series is less than 1 kcal/mol while the maximum deviation is 3 kcal/mol. For a limited number of compounds available (total of 12), the enthalpy of dilution of a salt M a x bcan be related to the added number of moles of water by the three-parameter quadratic equation AHodii(na) = uno2 bn, c (7) where no is the number of moles of added water molecules, AHodil(no) is the integral enthalpy of dilution, and a, b, and c are different constants for each salt. In the range no = 1-6, the maximum absolute deviation obtained is less than 0.1 kcal/mol.
+
+
Introduction In the course of a recent analysis of the standard enthalpies of formation AfHo2,,of solid salts M a x b , we had occasion to examine AfHo2,,for their crystalline hydrates, ammoniates, and alcoholates. Our previous investigation had revealed a number of totally unexpected quantitative empirical relationships between AfHo,,, of salts having common metals or nonmetals.'-5 While we have found no simple theoretical models to explain these results, they do appear to suggest some sort of simple additivity rules (1) (2) (3) (4) (5)
Hisham, M. W. M.; Benson, S. W. J . Phys. Chem. 1985, 89, 1905. Hisham, M. W. M.; Benson, S. W. J . Phys. Chem. 1985, 89, 3417. Hisham, M. W. M.; Benson, S. W. J . Phys. Chem. 1986, 90, 8 8 5 . Hisham, M. W. M.; Benson, S.W. J . Chem. Eng. Data 1987.82, 243. Hisham, M. W. M.; Benson, S. W. J . Phys. Chem. 1987, 91, 3631.
0022-3654/87/2091-5998$01.50/0
dominated by near-neighbor interactions. They by no means suggested the equally surprising quantitative relationships we shall present here, which describe ArHD2,, of the hydrates, ammoniates, and alcoholates. Unless stated otherwise, thermochemical data used here are taken from NBS Tables,6 and values of AfHo2,,are all in kcal/mol and a t 298 K. Enthalpies of Formation of Hydrates We shall define the molar enthalpy of hydration of a crystalline salt AHohyd(,)(MaXb) as the heat liberated or absorbed at 298 K (6) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J . Phys. Chem. ReJ Data 1982, Suppl. 11.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987
Thermochemistry of Inorganic Solids
5999
TABLE I: Parameters Obtained for Eq 2
comDd
available n
-m/kcal mol-'
1, 2, 3 1, 2, 3 4.5, 5 , 9 2, 7, 12 1, 7, 10 4, 5, 10 0.5, 2, 3.5, 7, 8, 10, 12 2, 10, 12, 18 9, 14, 19 0.5, 2, 6 2, 4, 6 1, 1.5, 3 1, 2, 4 2, 4, 6 1, 2, 4, 6, 7 1, 4, 6 1, 2, 4, 6 0.5, 1.5, 4 2, 3, 4 1, 2, 6 1, 2, 6 1, 3, 8 1, 2, 2.5, 7 1, 2, 4 1, 4, 5, 7 1, 4, 7 1, 2, 6 2, 3, 4, 6 2, 4, 6 4, 6, 7 1, 3, 5 1, 2, 4, 6 3, 4, 6 3, 4, 6 1, 6, 7 1, 2, 3 2, 3, 4 3, 4, 6 1, 2.5, 3, 3.5 1, 2, 3, 6 2, 4, 7 8 7, 10, 12 1, 2, 4, 6 0.5, 2, 3.5 4.5, 9, 16
-C/kcal mol-'
deviation/ kcal max av
3.10 3.60 3.00 2.26 2.06 2.70 2.97
1.5 3.2 5.8 1.7 1.7 4.4 0.2
0.3 0.2 1.4 0.3 0.4 0.3 3.1
0.2 0.1 0.7 0.1 0.2 0.2 1.8
2.44 1.28 3.73 2.63 3.25 3.33 5.13 2.92 2.66 3.50 -1.13 2.25 3.50 2.74 3.14 2.58 3.10 2.5 2.25 3.42 4.60 2.23 1.27 3.00 3.10 2.50 2.83 2.33 11.25 5.5 2.93 2.60 3.50 4.95 4.10 4.9 2.10 1.37
0.4 16.1 0.4 1.1 3.8 4.6 88 4.0 7.5 2.3 -3.0 3.1 6.1 3.0 1.6 6.0 2.6 0.9 4.8 1.5 -2.1 3.9 15.0 3.9 6.3 0.7 10.5 5.8 8.9 -6.0 8.2 4.4 5.5 8.5 19.5 6.3 3.1 20.1
0.4 3.3 1.7 0.5 0.9 1.0 0.9 0.7 0.6 0.8 0.1 0.2 0.6 0.5 0.4 4.8 0.6 1.0 0.1 1.0 7.3 0.8 1.0 0.4 1.4 1.0 1.2 0.7 1.1 1.0 1.4 0.5 2.1 2.7 0.4 1.8 0.1 2.1
0.2 1.6 1.2 0.3 0.7 0.9 0.6 0.5 0.5 0.6 0 0.1 0.6 0.4 0.2 1.3 0.3 0.8 0.1 0.9 1.9 0.4 0.9 0.2 0.8 0.8 1.0 0.6 0.9 0.9 1.2 0.3 1.8 1.9 0.3 1.2 0.1 1.2
'
Zn (NO,), 0 nH,O = Be SO, nH,O
A = 0
'
0
1
2
3 r
4 l
5
6
7
d
Figure 1. Relationship between A~hyd(,,(M,xb)and n (eq 1).
-I 7 6
2.4
t
2.6 2#31 2.5 2.4 2.3 2.2
2.0 I.9
(standard state 1 atm) when 1 mol of the anhydrous crystalline salt M a x b reacts with n moles of liquid water: M,Xb(Cr)
+ nHzO(1)
MaXb.nHzO(cr)
(i)
mohyd(n)(MaXb,Cr) = A$fo(MaXb.nHzO,cr) - AfHo(M,Xb,cr) - nAfHo(H20,1) (1) In Figure 1 values of are plotted against n for five different salts. The points in each case lie close to a straight line, with slopes of about -3 kcal/mol of H20. All available salts (total of 45) including main groups and actinides where data for more than two hydrates are available were examined in this manner. The plots in each series were also very close to straight lines. The equation AfH0hy,qn) = mn
+c
(2)
gives an excellent representation of the data, and, as shown in Table I, except in a few cases both the average and maximum deviations obtained are less than 1 kcal/mol. Values of m and C, maximum deviation, and average deviation for each salt are summarized in Table I. For the bulk of the cases the values of m obtained are close to -3.0 kcal/mol of H 2 0 . However, a few exceptions such as Cr,O,.nH,O, CrCl,.nH,O, and Mg(ClO,),. nHzO give high values for m. Excluding these compounds, the
1
2.1
1.8
I
1 0.1
1
1
0.2
0.3
1
1
1
1
I 1.8
0.4 0.5 0.6 0.7 b , O n Figure 2. Relationship between log (-AfHo(M,Xb.nH20) A$fo(M,Xb)) and log n. 0
average value obtained for m is -2.9 f 0.9 kcal/mol of HzO. Because of a larger contribution to AHohyd(n) by the first water molecule, the intercept C obtained in eq 2 is not zero and is always negative. The values for most of the compounds vary from -1 to -8 kcal/mol. For trivalent compounds the values are greater than -8 kcal/mol. NazSe and K2Se show exceptionally large values for C. T o explore this further we plotted, log [-AfHo(M,Xb.nH20) 4Ho(M,Xb)] (=log - [ w h y , ( , , ) + nAfHo(H,O,l)] against log n with the results shown in Figure 2 suggesting a linear relation between these quantities. All available hydrates were examined in this manner and plots obtained were all close to straight lines. W e also examined ammoniates (total of 43) and the few available alcoholates (MnCl,.nCH,OH). As shown in Figure 3, the plots were all very close to straight lines for each compound. From these observations, we propose the following relation to relate
+
6000 The Journal of Physical Chemistry, Vol. 91, No. 23, 1987
Hisham and Benson
TABLE II: Parameters Obtained for Ep 3
dev/kcal compd for Y = H 2 0 LiCl LiI Na3V04 K2CU(S04)2
K2Mg(S04)2 RbzCO, BeSO, Mg(C104)2 MgS04 MgSeO, CaCI, Ca(Nd2 Ca(NOJ2 SrI, SrCI2 Bar, MnC12 MnS04 COCI, NiC1, Zn(N03)2
La(N03)3 NazS Na,Se Na2HP04 Na2C03 Na2B407 Na4V207
Ce(N03)3 CrCI, cr203
NiS04 Co(N03)2
ZnSO, FeS0, Nd(N03)3 K,Se U02S04 U02(N03)2
ThCI4 ThBr, BaC204 WCI2
available n
a
-A/kcal mol-'
1, 2, 3 1, 2, 3 0.5, 2, 3.5, 7 0.5, 2, 6 2, 4, 6 1, 1.5, 3 1, 2, 4 2, 4, 6 1, 2, 4, 6, 7 1, 4, 6 1, 2, 4, 6 0.5, 1.5, 4 2, 3, 4 1, 2, 6 1, 2, 6 I , 2, 2.5 1, 2, 4 1, 4, 5 1, 2, 6 2, 4, 6 1, 2, 4, 6 3, 4, 6 4.5, 5, 9 4, 5, 9, 16 2, 7, 12 I , 7, 10 4, 5, 10 2, 10, 12, 18 3, 4, 6 2, 3, 4 1, 2, 3 4, 6, 7 2, 3, 4, 6 1, 6, 7 1, 4, 7 3, 4, 6 9, 14, 19 1, 2.5, 3, 3.5 1, 2, 3, 6 2, 4, 798 7, IO, 12 0.5, 2, 3.5 1, 3, 8 1, 2, 4, 6
0.992 0.962 0.995 1.016 0.997 0.974 0.967 0.966 0.971 0.954 0.981 0.979 0.987 0.960 0.984 0.956 0.983 1.003 0.995 0.974 0.966 0.973 0.988 0.963 0.993 0.992 0.985 0.998 0.969 1.023 0.943 0.955 0.995 0.961 0.970 0.975 0.979 1.004 0.979 0.979 0.970 0.962 0.994 0.974
72.63 76.37 72.48 70.76 71.60 74.97 75.98 79.49 75.32 78.03 74.39 72.55 72.64 77.81 73.59 75.76 73.84 70.9 72.64 75.03 76.67 75.74 73.83 78.33 71.75 71.88 74.08 71.11 77.03 70.06 87.55 78.23 72.38 76.87 75.18 75.89 74.87 72.12 75.75 77.68 79.73 74.44 72.59 77.73
dev/ kcal -A/kcal
max 0.2 0.6 0.8 4.7 0.3 0.7 0.8 0.1 1.6 1.3 1.7 0.2 0.2 2.6 0.1
0.1 0.1 0.4 1.2 0.6 2.6 0.7 19.6 4.8 0.9 0.4 0.5 0.3 0.9 1.1 0.3 1.5 2.3 1.6 1.9 1.3 3.4 1.3 2.5 2.6 0.3 1.1
av 0.1
0.4 0.5 2.6 0.2 0.5 0.6 0.1 0.9 0.8 1.1 0.1
0.1 1.8 0 0 0
Pb(N03)2
0.3 0.9 0.4 1.2 0.5
1.0 3.5 0.5 0.2 0.4 0.1 0.7 0.7 0.2 1.2 1.3 1.0 1.2
0.9 2.2 0.7 1.3 1.5 0.2 0.7
0
0
0.9
0.4
AfHo(M,Xb.nY) (where Y = H z O , NH,, or CH,OH), ArHo(MaXb),and the value of n: Afw(M,Xb*nY) = An*
+ AfHo(MaXb)
(3)
where Y = H 2 0 , NH,, or CH,OH, and A and a are different constants for each salt. For hydrates, when n = 1 in eq 3 we see that
A = AfHo(MaXb*H2O) - AfHo(Ma&) = AHohyd(l)
+ AfHo(H2091)
Thus A from eq 3 and C from 2 are related. When n = 1
AHohrd(l)= m
+ c = A - AfHo(H20,1)
compd for Y = NH, SbF3 CUCI, Hid2 CuBr2 CUCl CuBr CUI CUSO, AICI, AIBr, AII, GaCI, GaBr, SnBr, SnI,
(4)
Values of A and a,maximum deviation, and average deviation for each salt are summarized in Table 11. We have also examined salts where data are limited to two values of n, and for these salts, the values for parameters A and a obtained are listed in Table 111. For hydrates, it can be seen that in the majority of the cases a is slightly less than 1. The average value of A is, as expected, about -74 kcal/mol which is not far from the ArHoof the liquid water, -68.3 kcal/mol. However, we have found that the values
PbC1, PbBr, FeS0, PbI2 GaI, InCI, ZnCI2 ZnBr2 ZnI, CdClz CdBr2 LiBH, LiI LiBr LiCl AuBr AuI FeCl, FeBr, MnBr2 BeCI, CaC1, CaBr, Car2 SrI, BaBr2 BaCI2 for Y = CH30H MnC1,
mol-'
available n
a
mol-'
max
1, 2, 3, 4, 6 2, 3.3, 5, 6 1.3, 2, 6 2, 3.3, 5, 6 1, 1.5, 3 1, 1.5, 3 0.5, 1, 2,3 1, 2, 5 1, 3, 5, 6 1, 3, 5, 6 1, 3, 5, 6 1, 3, 5, 6 1, 5, 6 1, 2, 3, 5 1, 2, 3, 5 1, 3, 6 1, 1.5, 2, 3.25 1, 2, 3, 5.5 1, 2, 3, 4, 6 0.5, 1, 2, 5
0.8970 0.8102 0.7299 0.8430 0.8173 0.8463 0.9055 0.9020 0.8314 0.8052 0.9562 0.7792 0.8293 0.8992 0.9322 0.9167 0.9155 0.8775 0.8961 0.9264 0.8673 0.9090 0.8206 0.8695 0.8684 0.8626 0.9097 1.0570 0.9165 0.9448 0.9785 0.761 5 0.8554 0.8610 0.9017 0.8850 0.7005 0.9001 0.9087 0.9238 0.9107 0.9619 0.9403
25.13 36.82 31.71 35.39 29.24 27.8 1 26.863 33.797 44.775 5 1.808 44.572 45.247 42.531 29.061 26.683 24.802 24.598 26.702 31.865 24.791 39.116 34.907 35.034 34.227 34.399 31.010 28.463 19.028 27.853 24.144 22.166 33.546 25.807 33.674 32.025 32.794 52.618 27.586 28.996 30.370 29.446 22.883 25.502
1.5 1.1 5.7 1.3 0.6 0.7 0.4 0.6 3.5 2.3 9.3 1.5 1.0 1.5 0.5 2.5 0.3 0.3 1.1 0.8 0.4 4.7 0.8 1.5
1.6 1.6 0.5 0.1 0.3
1.9 0.2 0.6 0.5 0.7 0.8 0.8 1.3 1.5 1.6 2.9 0.8 1.2 1.2 0.3 0.1 0.2
0.9662
62.44
0.8
0.6
1, 2, 3
1.5
2.0 2.4 0.4 1.0
1.1 1.0 1.6 1.5 1.7 2.0 2.1 4.2 1.1
av 0.8
0.6 4.3 0.8 0.4 0.5 0.2 0.5 1.8 1.2 4.7 0.8 0.7 0.8 0.3 1.7 0.2 0.2 0.6 0.4 0.3 2.5 0.5 0.8 1.0 1.1
of A decrease with increasing values of CY.As shown in Figure 4, A and CY are linearly related by -A = - 155a 226.0 (5)
+
The average deviation obtained for A by this equation is only 0.7 kcal/mol with a maximum deviation of 3.5 kcal/mol. Equation 5 can also be written as AHohyd(l) = 155a - 157.7 = 1 5 5 ( ( ~- 1) - 2.7 (6) For ammoniates, values of CY are also usually less than unity but show a much greater range from 0.73 to 1.06. The values obtained for A also show a much larger variation from -23 kcal/mol to as much as -52 kcal/mol. This is in contrast to hydrates for which the overall range for A is about 10 kcal/mol. We have also noticed an important feature of the enthalpy of dilution, AHodil,and the number of moles of added water molecules, 4.Generally, the overall change in enthalpies with dilution is largely achieved in the initial stages with the addition of water. Once no reaches the value of 6 further changes are small, and, in majority of the cases, from no = 6 to infinity, the net enthalpy change is less than 3 kcal/moL6 We noticed that in the very early stages 1 5 no 5 6 , Nodil can be related quantitatively with no by the three-parameter quadratic equation (7)
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987
Thermochemistry of Inorganic Solids
TABLE IV. Parameters Obtained for Eq 7
TABLE III: Parameters Obtained for Eq 3 a
-A/kcal mol-'
Na2Zn(S04)2 Na2PtC1, MgS0, ZnSe04 Cu(N03)2
0.9414 0.9565 0.9884 1.0031 0.9385 0.9894 0.9592 0.9979 0.9723 0.9930 0.9822 0.965 1 1.0105 1.ooo 0.9841 1.0074 0.9717 0.9791 0.9941 0.9697 0.9499 1.0033 0.9760 0.9950 0.9716 0.9405 0.9738 0.9863 0.9971 0.9698 0.9727 0.9809 0.9906 1.0040 0.9871 0.9927 0.9981 0.9724 0.973 1 0.9777 0.9862 0.9704 0.9648 0.9838
78.0 76.5 75.6 70.8 80.5 71.8 76.9 70.9 73.2 71.9 74.0 75.3 69.5 71.2 71.4 69.6 74.5 75.0 72.2 74.3 77.5 70.9 74.0 72.4 74.4 79.1 73.9 74.5 71.1 75.5 74.5 71.9 71.3 70.4 72.9 71.1 70.8 74.3 75.4 72.4 73.3 76.0 76.1 74.1
for Y = NH, MgBr SnCI2 PbS04 InBr, InI, CdI2 HBC12 AgCl AgBr Ad AuCl NiBr2 COC1, CoBr2 FeI, CrC12 CeCI, ThCId BeBr2 MgC12 SrBr2 Sr(C104)2 Ba(C104)z NaBr NaBHa
0.9607 0.8249 0.9434 0.8620 0.9397 0.7363 0.9249 0.9675 0.9886 0.891 1 0.7945 1.0045 0.926 0.9684 0.8531 0.9414 0.9200 0.8791 0.5719 0.9294 0.8924 1.0035 0.9809 0.8515 0.9563
33.4 31.2 22.3 37.2 32.4 33.3 29.8 22.9 21.7 21.7 35.4 31.8 33.0 32.3 36.0 25.7 31.3 36.4 65.2 32.4 27.8 21.9 21.2 25.4 20.6
comDd for Y = H 2 0 '41203
MnBr2 KMgCI, ZrF4 zr(s04)2 AgF ZnS04 CdC12 CdS04 Cd(N0h Feci2 FeS04 Ca(I0,)2 CaS04 Ca(CH20HC02)2 Sr(103)2 Sr(C104)2 SrBr2 BaCI, BaBr2 KOH K2S K2S4 K2Zn(S04)2 K2Mn(S04)2 RbOH Rb2Te03 BeS04 Zn(CH3C02)2 LiC104 LiBr LiRe04 HCOONa NaCN NaBO, NaIO, NaH2P04 Na3HP207 Na2B401
available n
6001
where no is the number of moles of added water molecules, AHodil(,,,,) is the enthalpy of dilution of salt Maxb,and a, b, and c are constants.
-AfH("o)-
(M,X,)/kJ compd and uarameters NaOH a = -1.093, b = 13.46, c = 425.4 NaC104 a = -0.024, b = 0.212, c = 379.54
mol-'
calcd 2.5 452.2 3.0 456.0 4.0 461.8 4.5 463.9 3.25 378.6 3.5 378.5 4.0 378.3 4.5 278.1 5 377.9 377.4 6 712.6 NaCHpC02 3 a = -0.5111, 3.5 714.4 b = 6.967, 4 716.0 c = 696.3 4.5 717.3 5 718.4 5.5 719.2 719.2 6 469.5 KOH 3 a = -0.533, 3.5 471.4 b = 7.333, 4 473.1 c = 452.3 4.5 474.5 475.6 5 6 477.1 KF 3.5 578.0 579.2 a = -0.40, 4 b = 5.40, 4.5 580.2 c = 564.0 5 581.0 6 582.0 KCNS 2 187.0 a = +0.05, 2 186.5 186.0 b = -1.30, 3 c = 189.4 4 185.0 4.5 183.4 6 183.4 LiBr 3.25 385.2 u = -1.152, 4 389.3 b = 13.815, 5 392.7 c = 352.46 6 393.9 Ca(N03)2 3 954.6 a = -0.383, 4 957.3 b = 5.282, 5 959.2 c = 941.9 6 960.4 Zn(N03)2 1.5 506.7 a = -1.091, 2 513.6 b = 17.561, 2.5 519.9 c = 482.8 3 525.7 3.5 530.9 4 535.6 4.5 539.7 5 543.3 6 548.9 Cd(NOd2 2.5 467.3 a = -0.657, 3 470.1 b = 9.271, 3.5 472.6 c = 448.23 4.0 474.8 4.5 476.6 5.0 478.2 6.0 480.2 Mn(N03)2 2.5 598.0 a = -0.976, 3 602.1 b = 13.612, 4 608.9 c = 570.07 5 613.7 6 616.6 Cr0, 2 594.8 a = -0.1125, 3 596.0 b = 1.725, 4 596.9 597.6 c = 591.8 5 6 598.1 nn
obsd 452.3 456.3 461.9 463.9 378.6 378.5 378.3 378.1 377.9 377.4 712.6 714.6 716.1 717.3 718.2 719.1 719.7 469.5 471.3 473.0 474.5 475.7 477.1 578.0 579.2 580.2 580.9 582.0 187.0 186.4 185.9 185.0 183.4 183.4 385.2 389.3 392.3 393.9 954.6 957.3 959.2 960.4 506.7 513.8 519.7 525.5 530.5 535.6 539.3 543.1 548.9 467.3 470.2 472.7 474.8 476.4 477.0 480.2 598.0 602.5 608.9 613.4 616.6 594.8 596.1 596.9 597.6 589.1
dev(ca1cd - A$P(M,X,) obsdl/kJ Clkcal mol-' 0.1 -0.2 0.3 0.3 0 0 -3.8 0 0 0 0 0 0
-12.5
0.2 0.1 0
-0.2 -0.1 0 0
27.5
-0.1 -0.1 0.1
0.1 0 0 0 0 -0.1 0 0 -0.1 -0.1 0 0 0 0 0 -0.4 0 0 0 0 0 0 0.2 -0.2 -0.2 -0.4 0 -0.4 -0.2 0 0 0.1 0.1 0 -0.2 -0.4 0 0 0.4 0 -0.3 0 0
-3.3
1.3
3.5
-0.9
-8.1
-6.2
2.3
0.1 0 0 0
'1 cal = 4.184 J. For a total of 12 compounds available, the results listed in Table IV show an excellent fit to eq 7. The absolute maximum deviation is less than 0.5 kJ/mol for the entire ensemble (1 kcal(therm)
6002
2"
The Journal of Physical Chemistry, Vol. 91, NO.23, 1987
p 1 ' "
2.0 -
t
-
78
-
77
-
' 2 76
-
8 75
-
74
-
73
-
72
-
71
-
70
-
r? r
1.9-
3y
-2.1
I c
79
- 2.2
T 0 2
Hisham and Benson
-
1,8-
N
:
0
LL
n
m
a-
I
a
- 2.0 a'
I+ 1.7-
a
I
r
i? -
h I
1.3
"
-
69
7
m,o Figure 3. Relationship between log [-AfHo(M,Xb.nY) - A$'(M,Xb)] and log n.
= 4.184 kJ). Because the variations in
with dilution are small and the observed values of m o d i l are more accurate, the unit used in the table is kJ/mol. It is also interesting to note that, except for KOH, for all other compounds the values obtained for c are close to those for the corresponding anhydrous salts. However, because only 12 compounds are available for the analysis, and since, except for Zn(NO&, the variation in A H o & , with dilution is small, the general validity of the relationship is difficult to confirm. Modi1
Discussion The quantitative aspects of crystalline hydrate formation do not seem to have attracted much attention despite a great deal of experimental effort in the area. Two features are very evident. The first is that the numbers are quite small. For almost all the salt types the net energy released per water molecules added is about 3 kcal/mol. If we used a hypothetical standard of solid H 2 0 extrapolated from ice to 0 to 25 OC AHm = 1.6 kcal/mol and A f P ( H 2 0 , c r ) = -70.1 kcal/mol, then the net change becomes only 1.4 kcal/mol of H20. The first water molecule always exceeds this value by from 1.5 to 4.5 kcal/mol, again not a very large change. Crystal structures of hydrates show pronounced solvation of the metal by the first water molecule with probable H bonding of the water to the nonmetal. These are extremely strong interactions. But the empirical, nearly linear relation found here suggests that the interactions are largely short-range, neighbor interaction with little modification by next neighbor and negligible next-nearest-neighbor influence. Ionic models would not readily lend themselves to such an interpretation. In the gas phase, polarization forces have been shown to be an appreciable part of
0.L
I
I 0.96
I
I
0.98
I
\
1 .oo
\ I
\
1. t2
CYFigure 4. Relationship between A and a in M,Xb-nH,O. Dashed lines are displaced from solid line by f 1 kcal in ordinate.
ion-H20 and these would not be expected to conform to linear behavior. The forms of the relations are also of interest. As n a the hydrates become dilute inclusions of salts in a hypothetical ice. In eq 2 we expect the coefficient m to approach zero so that the apparent constancy of m for the early water molecules is not general. Similarly a t large dilution the coefficient in the astonishingly more accurate eq 3 must approach unity. The relation given by eq 3 may be used to estimate the values of AfHofor anhydrous salts from the values for the corresponding compounds MaXb.nY. If values of AfH0(M,Xb.nY) are available for three or more values of n, eq 3 can be used directly to estimate AfHoof the unsolvated salt M a x b . In hydrates, if values are available for two values of n both 3 and 4 can be used to estimate the value for corresponding anhydrous salt. It is also possible to estimate AfHoof an anhydrous compound from the value of a single hydrate by taking mean values for the parameters A and a ( A = -75.0 kcal/mol, a = 0.976). However, due to uncertainties involved in the observed values of AfH0(M,Xb-nY) and the errors involved in the parameters, the estimated values may have higher uncertainties. In practical problems where such higher uncertainties are acceptable, these procedures may be used to estimate AfHO of anhydrous salts, and the values estimated may be treated as preliminary values.
-
Acknowledgment. This work has been supported by grants from the National Science Foundation (CHE-84-03761) and the U.S. Army Research Office (DAAG29-85-K-0019). (7) Gowda, B. T.; Benson, S.W. J. Phys. Chem. 1982, 86, 1544. Meot-Ner, M.; Speller, C. V. J . Phys. Chem. 1986, 90, 6616.
(8)
