J . Phys. Chem. 1987, 91, 3631-3637 irregular, real shapes, such as enzymes, is straightforward. Complex electrostatic fields can also be represented easily. Using this method, we have demonstrated for the first time that a significant enhancement of the association of superoxide to superoxide dismutase is provided by this field and that this enhancement is decreased as the ionic strength is increased from zero to physiological ionic strength. The relative decrease is very similar to the experimentally determined decrease in enzyme rate.I3 Morover,
3631
this work shows that the correct ionic strength behavior is only obtained when both the shape of the enzyme and the dielectric discontinuity at the protein surface are included in the simulations. Acknowledgment. This work was supported by grant No. GM-30518 (NIH), NOOO14-86-K-0483 (ONR), RK@l42 (NIH)v and AC02-72 (DE). Registry No. SOD,9054-89-1; Ole-,11062-77-4.
Thermochemistry of Inorganic Solids. 7. Empirical Relations among Enthalpies of Formation of Halides Mohamed W. M. Hisham and Sidney W. Benson* Donald P. and Katherine B. Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park mc-1661, Los Angeles, California 90089 (Received: October 6, 1986; I n Final Form: February 17, 1987) The general equation [ArHo(MXn)- AfHo(MY,)] = a[AfHo(MX,) - ArHo(MZ,)] + bn has been found to correlate the standard enthalpies of formation for any three halides MX,, MY,, and MZ, (all solids) of any metal M with formal valence n including cations such as NH4+. The coefficients a and 6 are the same for any particular main or subgroup of a given valence state. While values of b vary over a broad range, values of a are never far from unity. The deviations from these relations are always within the claimed accuracy of the ArHoreported. For any given group average deviations are within & O S kcal/mol with maximum deviations never exceeding f 3 kcal/mol. Estimated values are listed for 45 halides for which values of ArHo are not currently known.
with each metal, and in other cases the variation is relatively small. As shown in Figures 1 and 2, when we plotted (AfHo(MF,) ArHo(MCl,))/n against (ArH"(MF,) - ArHO(MBr,,))/n or (AfHO(MF,) - ArW(MI,))/n for group IA (including ammonium compounds) and IIA (groups 1 and 2)16 metals, respectively, the plots obtained were very close to straight lines with the slope. about 1.2 kcal/mol in all cases, suggesting a linear relation among halides. The relations between these compounds are given by eq 1-4. F/Cl/Br Series: For group IA (group 1) including ammonium halides: (AfH(MF,) - ArH(MBr,)) = 1.195(AfH(MF,) - AfH(MC1,)) 4.1 (1)
Introduction In the present paper we continue our investigation of empirical relations among the enthalpies of formation of ArHoZs8solid, inorganic salts. In earlier papers'" we have reported a number of simple relations which permit us to estimate ArHo298for large numbers of inorganic salts and their hydrates. In a recent paper,5 we have presented evidence that ArHoof any three classes of oxygen-containing compounds such as oxides, hydroxides, carbonates, sulfates, and nitrates can be related quantitatively by a two-parameter linear equation. In this paper, we show that such a relationship is also valid for the solid halides. Unless otherwise stated, thermochemical data used here are taken from NBS Tables,' and values are given for standard enthalpies of formation Arff0298 per mole of metal atom and a t 298 K in kcal/mol. The existing data on AfH02s8of all solid fluorides ( 4 P ( M F n ) ) , chlorides (A,HO(MCI,)), bromides (ArHo(MBr,,)), and iodides (A,HO(MI,)) where the data for at least three halides are available for a particular metal M are listed in Table I. The values listed for actinide compounds are taken from a recent IAEA publication.* The difference in ArHO between any two halides MX, and MY, per valence state for each metal are listed in Table 11. Although no obvious relationship is found between ArHoof individual compounds, the values obtained for differences AAfHo in Table 11 show systematic and monotonic behavior. When ArHo(MF,) is involved in the differences, the value largely varies
For group IIA (group 2) halides: (ArHWF,) - ArH(MI,)) = 1.168(AfH(MF,) - AfH(MCI,))
(1) Hisham, M. W. M.; Benson, S . W. J . Phys. Chem. 1985,89, 1905. (2) Hisham, M. W. M.; Benson, S. W. J. Phys. Chem. 1985, 89, 3417. (3) Hisham, M. W. M.; Benson, S. W. J . Phys. Chem. 1986, 90, 8 8 5 . (4) Hisham, M. W. M.; Benson, S . W. J . Phys. b e m . Ref. Dura, in press ( 5 ) Hisham, M. W. M.; Benson, S. W. J . Chem. Eng. Ref. Dura, in press. ( 6 ) Hisham, M. W. M.; Benson, S. W. J . Phys. Chem., submitted for publication. (7). 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. Ref. Data 1982, 1 1 , Suppl. No. 2. (8) Fuger, J.; Parker, V. B.; Hubbard, W. N.; Oetting, F. L. The Chemical Thermodymmics of Acrinide Elements and Compounds, Part 8; International Atomic Energy Agency, Vienna, 1983.
Unfortunately, because of the lack of data, we could not do such analyses for other main-group metal halides. However, for subgroup metal halides including transition, lanthanide, and actinide halides, when we plot (ArH(MF,) - ArH(MCl,))/n against either (ArH(MF,) - ArH(MBr,))/n or (AfH(MFn)- A,H(MI,))/n as shown in Figure 3, all the points irrespective of the nature of the compounds and the valence states were close to straight lines represented by eq 5 and 6, respectively. F/ Cl/ Br Series: (ArH(MF,) - A,H(MBr,)) = 1.203(AfH(MF,) - ArH(MCI,)) + 1.83n ( 5 )
0022-3654/87/2091-3631$01.50/0
+
For group IIA (group 2) halides: (AfH(MF,) - AfH(MBr,)) = 1.160(ArH(MF,,) - A,H(MCI,))
+ 5.4n
(2)
F/CI/Z Series: For group IA (group 1) including ammonium halides: (ArH(MF,) - AfH(MI,)) = 1.179(AfH(MF,) - AfH(MC1,)) + 7.8 (3)
'
0 1987 American Chemical Society
+ 24.ln
(4)
3632
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
Hisham and Benson
TABLE I: Standard Entkaloies of Formation (.A., H d of Solid Halidesa __I.
valence metal Li Na K Rb cs TI In Ag Au
Hg
cu
Pt NH4 Be Mg Ca Sr Ba Sn Pb Cd Hg Ti V Cr Mn Fe co Ni
state 1 1 1 1 1 1 1 1 1 1 1 1 1
-A&!298/(kcal/mol) fluoride 147.2 137.1 135.6 133.3 132.3 77.6 48.9
110.9
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
245.4 268.5 291.5 290.7 288.5
3 3 3
Sb Bi Au
cu
Zn Mo Pd Pt AI
Ga In
sc
Ti V Cr Fe La Lu Tm
Er Ho DY Gd Sm Nd Pr Ce Y Ru Re U Pt Pu NP
Am
Eu Tb Yb Ti Zr Mo
Hf Pt U
chloride 96.6 98.3 104.4 104.1 105.9 48.8 44.5 30.4 8.3 3.7 32.8 13.5 75.2
bromide 83.9 86.3 94.1 94.3 97.0 41.4 41.9 24.0 3.3 24.8 25.0 9.2 64.7
117.2 153.3 190.2 109.1 205.2 77.7 85.9 93.6 53.6 122.8 108 94.5 115.0 81.7 74.7 73.0 52.6 99.2 67.4 47.5 29.5
84.5 125.3 163.0 171.5 181.0 58.2 66.6 75.6 40.8 96.0 87.3 72.2 92.0 59.7 52.8 50.7 [52.5] 33.9 78.5 62.4 24.9 19.6
359.5 278.0
168.3 125.4 128.4
126.0 92.4 102.5
3
218.8
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
86.9 389.4
91.3 90.6 28.1 221.0 172.3 138.8 133.0 95.5 256.0 [(256.5)] 266.0 [(235.6)] 235.8 [(236.9)] 238.7 [(237.7)] 240.3 [(237.8)] 239.0 [(233.5)] 240.9 [(240.8)] 245.2 [(245.2)] 248.8 [(249.0)] 252.6 [(253.1)] 251.8 [(252.9)] 239.0 [(238.0)] 49.0 63.1 207.0 43.5 229.4 214.7 233.7 223.7 [(223.8)] 238.3 [(240.7)] 229.4 [(229.4)]
4 4 4 4 4 4
158.7 167.4
185.9 170.0 165.4 155.7 129.7 182.7
359 379.0 365.4 379.6
456.8 46 1.4 457.5
(195) 234.3 114.8 236.7 55.4 243.5
62.0 (61) (1 1) 177.6 131.1 103.6 (98.0) 64.1 (215.0) [(216.8)] (1 96.0) (1 99.0) (200.0) [(200.5)] (202.0) (200.0) [(199.3)] (199.0) [( 198.1)) (205.0) [(204.9)] (209.0) [(208.7)] (212.0) [(213.0)] (21 1) (202) 33.0 39.9 167.0 [170.3] 28.9 189.5 174.6 193.5 (188) [(186.2)] (199) (190) 147.4 181.8 76.8 (185)
37.4 191.7
iodide 64.6 68.8 78.4 79.8 82.8 29.6 27.8 14.8 0 14.5 16.2 (2.4) 48.1 46.0 87.0 127.5 [125.1] 133.4 143.9 34.3 41.9 48.6 24.7 63.1 60.1 37.5 (60.0) 27.0 21.2 18.7 (6.0) 49.7 (5.3) 15.1 (5.6) 75.0 57.1 56.9 24.0 [32.4] (19) (-1 5) ( 1 22) (14) 64.7 49.0 (14) 159.4 [( 159.4)] 131.0 [(131.0)] 143.8 [(143.9)] 146.5 [(146.5)] 149.0 [(148.9)] 145.1 [(145.1)] 142.0 [(142.0)] 148.2 152.8 [(152.7)] 156.4 [( 156.3)] 155.3 [(155.4)] 147.4 15.7 (6) 111.7 (7.11 138.6 122.6 164.3 (1381 (144) (135) 89.8 115.1
(23) (111)
17.4 124.0
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3633
Thetmochemistry of Inorganic Solids
TABLE I (continued) valence state
metal Pa Th Te NP Pu Nb Ta W U Pa
4 4 4 4 4
465 501.4
5
433.5 455.0
5
-AfH298/(kcal/mol) chloride bromide
fluoride
441.9 441.3
5
5 5
496.5
249.6 283.5 78.0 235.2 230.3
197.5 230.5 45.5 184.3 (1 81.0)
190.6 205.3 118.6 253.0 273.1
132.9 143.0 75.6 193.7 206.1
iodide 125.2 160.3 (-10) (1 15) (111) 64.2 [51.5] (61 .O) (14) (1 12.0) (114)
'Values given in ( ) are estimated values from the present work. Values given in [ ] are recommended values from the present work. Values given in [( )] are taken from ref 14.
BO
-'_
'_
L
-
g -
75
65-
0 V
c
0
cz V
m
&
z
5
:-
0-
0-
55-
=a
65
-
I
I
LL
LL
I
E
0 -
=a,
0-
=a'
K
U
U
55
45
I
I
50
60
- [AfHo(MF2T - AfHo(MCI,)]/~kcoI mol-' Figure 1. Relationship among AfHO(MX,) for group IA (group 1) metal and ammonium halides.
FICIII Series: (AfH(MFn) - AfH(MIn)) = 1.465(AfH(MF,) - AfH(MC1,))
+ 5.44n
(6)
The set of equations given above can be written in a number of equivalent forms to correlate any three different halides. For example, eq 1 can be rearranged into eq 1 F, 1Br, and l a as follows: AfH(MF,) = -6.135AfH(MC1,) + 5.135AfH(MBr,) 20.9
+
(IF)
A,H(MBr,) = -1.195AfH(MCl,)
+ 0.195AfH(MF,) + 4.1 ( 1 er)
AfH(MCl,) = -0.837AfH(MBr,) - 0.163AfH(MF,) - 3.4
(la) In practice, we can estimate AfHo for any compound of interest using these equations. However, when coefficients involved in the equations are much larger than unity, deviations are correspondingly magnified. In eq 1, an error of only 1 kcal/mol in both AfH(MCl,) and AfH(MBr,) may cause uncertainties as large
Figure 2. Relationship among AfHo(MX,) for group 11A (group 2) metal halides.
as 1 1 kcal/mol in the estimated value of AfHo(MF,). It is thus not recommended that such equations be used to try to estimate AfHo for compounds for which values are not known. When coefficients are smaller than unity, the deviations become smaller, and in such cases estimates can be made with good accuracy. We recommend the set of equations given in Table 111 to estimate AfHo for compounds where values are missing. Unfortunately, in case of AfHo(MF,), it is not possible to use any of these equations for the estimation, because, in all equations, the coefficients involved are much larger than unity. Table IV shows the deviations between the calculated value obtained by using these equations and the observed value for each compound. When a value is calculated for a compound, the values reported in the literature are taken for the other two corresponding reference compounds. For comparison we also have listed in Table IV uncertainties in the observed values. Since the uncertainties involved in the observed values are not listed in the N B S tables, the uncertainties reported in Table IV are taken from a different so~rce.~ (9) Kubaschewski,0.; Alcock, C.B. Metallurgical Thermochemistry, 5th
ed; Pergamon: Oxford, 1979.
3634 The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
Hisham and Benson
TABLE 11: Difference in A , H d M X ) for Pairs of Halides -[ AfHo(MX,) - AfHo(MY,)] /n/(kcal/mol) M Li Na K Rb NH4
1 1 1 1 1
F/CI 49.6 38.8 31.2 29.2 26.4 35.7
CI/Br 13.7 12.0 10.3 9.8 8.9 10.5
Cl/I 33.0 29.5 26.0 24.3 23.1 27.1
F/Br 63.3 50.8 41.5 39.0 35.3 46.2
Br/I 19.3 17.5 15.7 14.5 14.2 16.6
F/I 82.6 68.3 57.2 53.5 49.5 62.8
Be Mg Ca Sr Ba
2 2 2 2 2
64.1 57.6 50.7 46.3 41.7
16.4 14.0 13.6 13.3 12.1
35.6 33.2 31.4 32.4 30.7
80.5 71.6 64.3 59.6 53.8
19.2 19.2 17.8 19.1 18.6
99.7 90.8 82.0 78.7 72.3
AI
3 3 3
63.7 50.9
14.1 11.0 8.6
31.1 22.8 23.8
77.8 61.9
17.0 11.8 15.2
94.8 73.6
2.6 7.4 6.4 5.0 6.9 7.8
16.7 19.2 15.6 8.3 17.2 16.6
9.8 9.7 9.0 6.4 13.4 10.4 11.2 11.0 11.0 11.2 9.4 10.4 11.3
21.7 22.0 22.5 14.5 29.9 24.0 28.5 27.4 26.8 27.2
cs
Ga In In
TI Ag Au
Hg
cu Sn Pb Cd Hg
Ti V
Cr Fe co Ni cu
Zn Pd Bi Sb sc
Ti V
Cr Fe Lu Tm Er Ho DY Gd
Sm Nd Pr Ce Ru Re U Pt La Pu NP Y Mo Hf Pt U
Th Zr Pa Te
Nb Ta W L!
n 1
1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5
5 5 5
28.8 18.5
36.4 36.9
45.7 44.2 45.4 41.4 38.6 41.8 42.5 56.1 56.9 45.4 48.0 51.2
9.8 14.5 13.7 11.7
24.7 28.0
46.2 45.9
56.8 55.2 56.3 52.5 47.9 52.1 52.3 70.6 70.7 57.1
14.1 11.8 9.2 3.3 10.3 8.7 12.0 12.4 13.5 8.1 16.5 13.6 17.4 16.4 15.8 16.0
57.7 5.3 7.7 13.3 4.9 16.0 13.3 13.4
48.0 34.1
58.4 59.4
74.2 71.5 72.1 68.5 66.5
12.7
64.9
13.0
70.1 76.0
61.6
86.3 92.3 81.1 89.9 5.8
32.3
64.5
19.0
83.0
32.2 30.3 30.7
72.7 63.1 63.6
16.2 17.0 17.3
88.0 80.1 80.9
58.6 50.0 48.6
11.5 12.5 8.6 11.9
9.5 31.2 29.8 31.6 25.3
5.0 66.4 67.3 68.8
60.1 62.4 60.4
65 mol-'
TABLE 111: Recommended Equations for the Estimation of A,H2% of Group I A Metal Halides Including Ammonium H a AfH(MCI) = 0.837AfH(MBr) 0.163AfH(MF) - 3.4 AfH(MCI) = 0.702AfH(MI) + 0.298AfH(MF) - 8.8 AfH(MBr) = 0.839AfH(MI) + 0.161AfH(MF) - 6.5 AfH(MBr) = 0.459AfH(MI) 0.541AfH(MC1) - 1.7 AfH(M1) = 1.192AfH(MBr) - 0.192AfH(MF) + 7.7 AfH(MBr) = 1.195AfH(MCI) - 0.195AfH(MF) + 4.1 AfH(M1) = 1.425AfH(MCI) - 0.425AfH(MF) 12.5
+
Group IIA Metal Halides AfH(MCI2) = 0.856AfH(MI-J 0.144AfH(MF2) - 41.2 AfH(MC12) = 0.862AfH(MBr2) + 0.138AfH(MF2) - 9.3 AfH(MBr2)= 0.993AfH(M12) + 0.007AfH(MF2) - 37.0 AfH(MBrZ)= 0.952AfH(M12) 0.048AfH(MC12) - 35.0 AfH(M1,) = 1 .007AfH(MBr2)- 0.007AfH(MF2) 37.3 . ,--\----', - - AiHtMIij = 1.168A;HiMCl;j - 0.168AfH(MF2) 48.1 AfH(MBr,) = 1.160AfH(MCI2)- 0.160AfH(MF2) - 10.8
+
+
11.1
55 /fi/kcol
+
9.5 4.5 13.0 13.2 13.1 13.1 8.1
25 35 45 - [ A , Ho(MF,) -A,Ho(MCI,)]
+
56.2 53.9 54.1 55.6
20 (5
Figure 3. Relationship among AfHo(MX,) for subgroup metal halides.
14.4 4.9
31.7 30.7 30.7 30.4 31.3 33.0 32.3 32.0 32.1 32.2
59.9 49.1
56.7 49.9 50.2
22.4
10.5
56.7 55.9
51.2
24.8 16.2
36.2 24.9
17.9 16.7 18.5
85.2 85.4
13.7
73.9
+ +
Subgroup Metal Halides AfH(MC1,) = 0.683AfH(MIn) 0.3l7AfH(MFn) - 3.71n AfH(MCI,) = 0.831AfH(MBr,) + 0.169AfH(MF,) - 1.52n AfH(MBr,) = 0.562AfH(MC1,) + 0.438AfH(MI,) - 0.551 AfH(MBr,) = 0.822AfH(MI,) + 0.178AfH(MF,) - 2.64n AfH(M1,) = I.217AfH(MBr,) - 0.217AfH(MF,) + 3.21n AfH(M1,) = 1.464AfH(MCIn)- 0.464AfH(MFn) + 5.43n AfH(MBr,) = 1.203AfH(MCI,) - 0.203AfH(MF,) + 1.83n
+
Discussion
Considering the uncertainties involved in the reported values listed in Table IV, the maximum deviations usually obtained are less than 2 kcal/mol. The larger deviations obtained in certain cases may be attributed uncertainties in the reported values. For example, for SbC13the deviation obtained is 5.6 kcal/mol when AfH(Sb13)and AfH(SbF3) are used as reference compounds. This deviation is not unexpected, because the experimental errors reported are 1 7 and 14 kcal/mol, respectively. A similar explanation holds for other estimated values where the deviations obtained exceed 1 3 kcal/mol. The equations given in Table 111 can be used to estimate the AfHoof compounds where values are not known or to correct the values where uncertainties are very high.
The Journal ofPhysica1 Chemistry, Vol. 91, No. 13, 1987 3635
Thermochemistry of Inorganic Solids
TABLE I V Deviations Obtained (in kcsl/mol) for the Set of Equations Given in Table 111 AfHo(MCI,)
M
n
deviation (calcd)
AfHo(MBr,)
exptl accum
A d o (MI,)
exptl accum
deviation (calcd)
deviation (reported)
deviation (calcd)
Group I A Li
Na K
Rb cs
NH4
1 1 1 1 1 1
0 -0.3 -0.1 0 0.3 0.4
av:
0.2
0.4 -0.3 -0.2 0.4 0.5 0.4
2 0.1 0.2 2 0.4 0.2
0.35
0.5 0 0 0.6 0.3 0
0.3 0.2 0.1 0.3 0 -0.2
0.1 -0.3 -0.1 2.0 0.3 0.6
0.2
0.2
0.2
2 0.3 0.2 2 3 0.20
0.6 0 0 0.7 0.3 0
0.6 -0.5 -0.2 0.6 0.6 0.6
0.3
0.5
2 0.2 0.3 2.5
Group IIA Be Mg Ca Sr
Ba
2 2 2 2 2
av:
-1.2 1.1 -0.2 -0.9 -0.1
-1.3 1.o 2.1 -0.8 -.7
0.7
1.2
0.8 0.2 0.9 0.6 0.6
-0.1 0 2.6 0 0.9
-0.1 -0.1 2.5 0 0.8
-1.4 1.2 -0.2 -1 .o -0.1
0.7
0.7
0.8
1.2 3 0.6 0.6
-0.1 0 2.7 0 1.o
-0.1 -0.1 2.1 0 0.9
-1.6 1.2 2.4 -1 .o 0.8
0.8
0.8
1.4
1.2 2.5 0.5 0.8
Subgroup Ag Au
Hg
cu
In TI
1 1 1 1 1 1
-0.7
-1.1
0.2
0.2
0.3
0.4
-0.5
0.6
0.1 1.9 -0.1 1.1 -4.2 -0.5
-0.8
0.3
0.2 1.o 0.3 0.3 2.0 0.2
0.6
-1.6
0.1
-0.7
-0.4
0.2
Subgroup
Sn Pb Cd
Hg Ti V Cr
Fe co
Ni
cu Zn
Sb sc
2 2 2 2 2 2 2 2 2 2 2 2
-0.9 0.6
1.6 0.6 0.4 0.3
1.7 -0.7
-0.1 -0.4 0.2 -1.9
5.0 0.5 2.7 2.4
-3.6 -2.3 -0.7 -2.8
-0.1
0.6
0.2
1.5 4.4
3.5 1.o
5.7
-3.7
-3.0 -0.2
-0.1 1.8
-3.3 -4.0
1.o 0.5
-0.9 2.2
1.4 3.6
-4.0 -5.0
-0.7 0.6
0.4 0.1
0.2 0.3
1.4
0 -0.3 0.2 -1.5 0.5 -0.1
-2.6 -2.0 -0.4 -3.5
3 0.2 0.8 0.5 2 0.3
-3.0 -2.0 -0.7 -2.3
1.8 -3.0
5.6
4.0 1.o 1.o 1.o 0.4
4.6
0.1
0.2
1.6 1.1 -0.6 1.2 1.8
0.8 -1.6 -0.9 -0.4 -0.4 0.6 0.1
3 3 3 3 3
-2.7 -3.3
2.1 -5.3 -3.5
NP
3 3
-4.0 -2.3
-3.3 -4.2
Zr U
4 4 4 4
0.1 -0.5
3.9 1.5
0.3 0.6
4.7 2.5 1.3 1.1
2.5 1.7 -0.2 1.2
0 -0.7 -1.1 -1.4
5 5 5
0.7 -1.8 -0.6
5.0
1 1.8 3
10.5
5.1
0.8 -2.4 -0.8
1.2
2.5
Er U
Pu Am
Pa Th Nb Ta
av:
2.3
1.5
In the case of Nb, for example, if AfH(Nb15)is taken as a reference value, the estimated AfH(NbBr5) and AfH(NbC15)values have high uncertainties. We feel that the value AfH(Nb15) = -64.2 kcal/mol reported in the literature is questionable. If the value is -51.5 kcal/mol, the deviations are reduced to less than 1 kcal/mol. Such consistency considerations permit us to suggest what we believe are better values for five other compounds. The values corrected by this procedure are listed in Table I. The set of equations given in Table 111 can be used to estimate the AfHo of chlorides, bromides, or iodides of any metal provided the AfHo of the reference compounds are known. The accuracy of the estimated value mainly depends on the uncertainties in the reference values. We can estimate the uncertainties in any given prediction as
1.5
0.6 0.1
0.2 0.8
-3.7 2 -0.6 -5.0
2.5 2.0
0.1
0.2
-3.7 -0.1
3.1 -7.7 -5.1
1.o 0.6
0.8 0.3
1.o 2.8
-5.9 -3.4
0.5 1.7
1.o 0.6 3.1 0.5
5.8 3.2 -I .4 1.4
5.8 2.3 -2.7 -0.4
1 0.7 3.7 0.5
12.5
13.6
-2.9
1.4
2.0 2.7
2.9
3.4
the vector sum of the coefficient-weighted uncertainties in the equation used. When AfH(MF,) is taken as one of the reference values, it can be seen that, because of the lower values for the coefficient of AfH(MF,), the accuracy of the estimated values are largely determined by the other reference value. As example, using eq 2M,C1, an error of f5 kcal/mol in the value of AfH(MF,) can contribute only $1.5 kcal/mol in the estimated value for AfH(MCln). Using the set of equations given in Table 111, we are able to estimate values for 45 compounds for which the values are not currently known. These estimated values are also listed in parentheses in Table I. Whenever possible, the estimated values are compared with the observed values which are reported in other sources, and also compared with other independent methods which
3636 The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 TABLE V: Some Estimated ArHoValues (kcal/mol) halide (MX,)
215 212 209 205 199 200 200 211 199 202 199 190 186 188
EuI, YBr, PtI PtI, Ptl, TbI, YbI,
138 202 2.4 5.6 7.1 144 135
MnI,
60.0 58 i 3
CUI, Fell CrBr, BiBr, Bil,
6.0 14' 98 94b (61) (19)
AuBr, Ad3
11 -15
TiCI, PuBr,
19Y 195 at 0 K 181 185 53 122 (74) (6) 23d 111 -1.0 115 111 61 14 112 114
Hfk
Mol2 Scl, Til, Rel,
Mol, HfI, Te14 NPI4 Pu14 Tal,
w1s
UI, Pal,
217 213
209 205 198 199 200 213 203 198 201 191 203 191 (180* 8)* 129
142 134
TABLE VI: Deviations Obtained for the Set of Equations lL,cl, lL,*" 1L.I
-ArH(MX,)I (kcal/mol) est reported
LaBr, PrBr, NdBr, SmBr, GdBr, DyBr, ErBr, CeBr, TbBr, HoBr, TmBr, YbBr, LuBr, EuBr,
Hisham and Benson
deviation (obsd - calcd)/(kcal/mol) ref and remark 13 13 13 3 3 3 3
I , estmated value I , estimated value I , estimated value 1, estimated value 1, estimated value 18 estimated value 13 1 18 estimated value
using method using method 14, estimated 14, estimated
described in ref 2 described in ref 2 value value
6, estimated value from hydrates
taking the value for FeF3 from ref 9
method described in ref 4. CTakingthe value "From ref 12. for TiF4 from ref 9. dDetermined from MoC14 and MoBr,.
we suggested previously. The results are shown in Table V. In all cases we find good agreement. The following comments can be made concerning these estimated values. For lanthanides, we are able to estimate AfHofor all trivalent bromides from the reported values of AfH(MC1,) and AfH(MF,) of the corresponding metals. As shown in Table V, these estimated values are in good agreement with the experimental values given by Hurtgen et al.,I3 and the values (except LuBr, and EuI,) are also in good agreement with the estimated values given by Bratsch'O whose estimates are based on the ionic model equation relating values for A,Ho of aqueous ions and the values for ionic radii of cations and anions involved. Recently, Bard et al.I4 have compiled the critically evaluated
M La Lu Tm Er Ho DY Gd Sm Nd Pr Ce Eu
AAfH(MC1,)
1.5
-1.4
4.4 -4.3 -0.9 -0.8 -0.5
-4.1 4.0 0.8 0.7 0.4
2.1
-2.0
Bratsch, S. G.; Lagowski, J. J. J. Phys. Chem. 1985, 89, 3310. Smith, D. W. J . Chem. Educ. 1986, 64, 228. Rard, J. A. Chem. Rev. 1983, 85, 555. Hurtgen, C.; Brown, D.; Fuger, J. J. Chem. Soc., Dalton Tram. 1980,
70. (14) Bard, A. J.; Parsons, R.; Jordan, J. Standard Potentials in Aqueous Solution; International Union of Pure and Applied Chemistry, 1985.
AAfH(MI,) -0.7 15.7 -0.9 0.8 -1.2 -0.5 7.5 -0.3 -0.6 1.6
thermochemical data for halides of the rare earths. Most of the cases,the reported values particularly for the chlorides and iodides, are in good agreement with NBS Tables. Additional data are also available for fluorides and bromides. It is interesting to note that, as shown in Table I, the bromide values are in good agreement with the estimated values illustrated in this paper. Most of the fluoride values are available for lanthanides, and as we reported e l ~ e w h e r e ~it. 'is~ possible to treat these data separately for lanthanides. A set of equations (lL,cI,lL,Br,lL,,)obtained by treating the data is given; except for LuI, and GdI,, as shown in AfH(MBr3) = 0.9333AfH(MC1,) 0.0667AfH(MF3) 49.7 ( IL.B~)
+
+
AfH(MI3) = 0.5846AfH(MC13) + 0.0667AfH(MF,)
+ 159.9 (1 L,I)
AfH(MC13) = 1.0715AfH(MBr3)- 0.0715AfH(MF3) - 53.3 ( 1L,CJ Table VI, the absolute deviations obtained are very low. The higher deviations obtained for LuI, or GdI, are probably due to the uncertainties involved in the observed values of corresponding fluorides, iodides, or botkhalides. However, more detailed evaluation of the data available from various sources will be presented elsewhere together with other independent methods we developed for the estimation of enthalpies of formation of inorganic solids. The value estimated for CrBr, is in good agreement with the value obtained by using another independent method we reported previously! In the latter AfHO of CrIBr, was related to the AfHo of CrI, and CrBr, by simple additivity relations. We have recently found6 that AfW for solid hydrated compounds can be correlated quantitatively by the equation AfHo298(MXn-nH20) = AfH298(MX,)
+ An"
(6)
where n is the number of water molecules involved in the hydrated compounds. AfHo298(MX,.nH20)and ArHozss(MXn)are the standard enthalpies of formation of hydrated compounds MX,.nH20 and the corresponding anhydrous salt MX,, respectively. A and a are constants. Using eq 6 we obtained a value for Mn12 from the values of Mn12.2H20 and Mn12.4H20 of 58 f 3 kcal/mol, in good agreement with the value obtained in the present work. For trivalent halides of Eu, the only value available is for EuC1,. However, for EuF,, the value for the monohydrate is available. Using eq 6 the value obtained for EuF3 is -373 kcal/mol, and when M.;Benson, S. W. J. Phys. Chem., to be published. (16) In this paper the periodic group notation in parentheses is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the pblock elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., I11 3 and 13.) (15) Hisham, M. W.
(10) (1 1) (12) (13)
AAfH(MBr3) -0.1
-
J . Phys. Chem. 1987,91, 3637-3639 we use these value as a reference compound together with the value for EuCI, in eq 3 the value obtained for EuBr, is -188 kcal/mol in good agreement with -180 f 8 kcallmol recommended recently by Rard.'* In certain cases, however, values are available only for the chlorides and bromides of certain metals. In these cases, a rearrangement of eq 1 and 2 may be used to estimate the values for the iodides. Because the coefficients involved are larger than unity, the estimated values have high uncertainties. Therefore, these values may be treated only as preliminary values. In recent we have also shown that, for binary solid compounds of formula MX, with multiple valence states, the AfH of compounds can be related quantitatively with the value of z by the two-parameter equation log (-AfHo(MX,)/z) = a bz (7)
+
This equation may also be used in estimating the AfH for the halides of multivalence compounds. For example, we are able to estimate values for PtI, and PtI, by using these equations. When we used these values together with the values for the chlorides as a reference in estimating the values for the bromides, the deviations obtained for PtBr2 and PtBr, are only f0.5 and f0.3 kcal/mol, respectively. For some metals, values for only one halide are available. However, as shown in Table 11, the differences in the value between any two halides (except fluoride) are almost constant for some groups of metal. As an example, for group IIA (group 2) metals the difference in value between AfHo(MBr2)and AfHo(M12)per valence state varies only by 1 kcal from Be to Ba. Similarly for lanthanides, the difference between AfHO(MC1,) and AfHo(M13) per valence is almost constant and is equal to 31 f 1 kcal/mol.
3637
For actinides, the difference in values between AfH0(MCl4)and AfHo(MBr4)per valence state is 13 kcal/mol. Such relationships may also be used to deduce values for other halides. For example, the values for BiBr3, TbBr,, and YbBr, are estimated by this method. However, because of the absence of uncertainties in the reported values, the estimated values obtained by using this procedure are preliminary. It is also interesting to note that AfHo obtained for certain compounds such as CUI,, A d , , and FeI, are in line with the unsuccessful attempts to obtain these compounds for which the lower valence states compounds are thermodynamically more stable. Although a quantitative relationship exists among the halides, the reason for such a relationship is difficult to understand theoretically. However, the relationship illustrated in this paper is very useful in estimating AfHofor a number of halides of various metals for which AfH values are not currently known. Acknowledgment. This work has been supported by Grants from the National Science Foundation (CHE-84-0376 1) and the U. S. Army Research Office (DAAG29-85-K-0019). Registry No. PtI, 13779-77-6; MnI,, 7790-33-2;CUI,, 13767-71-0; Ho12, 14055-74-4; PtI,, 7790-39-8;BiBr,, 7787-58-8;Bil,, 7787-64-6; AuBr3, 10294-28-7; A d , , 13453-24-2; ScI,, 14474-33-0; TiI,, 1378308-9;CrBr3, 10031-25-1; FeI,, 15600-49-4; LaBr,, 13536-79-3; LuBr,, 14456-53-2; TuBr,, 14456-51-0; HoBr,, 13825-76-8; CeBr,, 14457-87-5; YBr,, 13469-98-2; Rel,, 15622-42-1; EuI,, 13759-90-5; TbBr,, 14456YbI,, 1381 3-44-0; Tic&, 47-4;Tb13, 138 13-40-6;YbBr3, 13759-89-2; 7550-45-0;HfBr,, 13777-22-5;Mo14, 14055-76-6;HfI,, 13777-23-6; TeI,, 7790-48-9; NpI,, 15513-95-8; PuBr,, 15608-34-1; h1415513-97-0; , TaI,, 14693-81-3; WI,,13782-91-7; VIS, 13775-20-7; PUIS, 17497-66-4.
Theoretical Thermochemistry. 3. A Modified Procedure for Ionization Energies of AH,, Species John A. Pople Chemistry Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania 1521 3
and Larry A. Curtiss* Chemical Technology Division/Materials Science and Technology Program, Argonne National Laboratory, Argonne, Illinois 60439-4837 (Received: January 9, 1987)
The ab initio theory of AH,' monocations (A = C to F and Si to CI), presented in part 2, is modified to give singlet-triplet separations in a manner consistent with the treatment of neutral species given earlier. New theoretical ionization energies are generally within 0.1 eV of experimental values when the latter are definitive.
In parts 1 and 2 of this series,'q2 we have presented a general theory of the energies of AH, molecules and their cations (A in the first or second row of the periodic table). A key feature of this treatment is the use of isogyric comparisons with the hydrogen molecule (an isogyric process being one leaving the number of unpaired electron spins unchanged). Thus, in part 1, the dissociation energy (0,) of an isogyric bond rupture (e.g., BH2 BH H ) was calculated directly from a set of quantum mechanical BH2 + H), on energies., For nonisogyric rupture (e.g., BH, the other hand, the total energies were used to calculate the energy
-
+
-
(1) Pople, J. A.; Luke, B. T.;Frisch, M. J.; Binkley, J. S. J . Phys. Chem. 1985, 89, 2198.
(2) Pople, J. A.; Curtiss, L. A. J . Phys. Cfiem. 1987, 91, 155.
0022-365418712091-3637$01.50/0
+
-
+
-
of the related isogyric comparison AH, H AH,-, H2 (1) This result was then combined with the exact value of D,(H2), to give D,(AH,, - H). In a manner consistent with this procedure, singlet-triplet separations can be determined by the isogyric comparison AH,(triplet) H2 AH,(singlet) + 2H (2) with some S U C C ~ S S . ~
+
(3)The total energies used are MP4SDTQ/6-311+G(2df,p)//HF/6-31G* for first row molecules and MP4SDTQ/6-31 +G(2df,p)//HF/6-31G* for second row molecules, assuming additivity for the basis set extensions for diffuse, double-d, and f-polarization functions. Full details are given in ref 1.
0 1987 American Chemical Society
