J . Phys. Chem. 1986, 90, 885-888 measurements of thermodynamic and kinetic data on metalloproteins in aqueous media may lead to erroneous conclusions as to the situation that exists in biological media. The major contribution of solvation to the thermodynamics is expected to reside in the AEs term due to changes in ligand conformations and metal-ligand bond lengths. For instance, it has been well demonstrated that hydrogen bonding to a histidine ligand in the axial position of metalloporphyrin complexes can influence the redox potential by at least 100 mVSm8 Clearly, whether or not electron transfer takes place in biological membranes and whether or not (66) Doeff, M. M.; Sweigart, D. A.; O'Brien, P. Inorg. Chem. 1983, 22, 85 1-852.
(67) OBrien, P.; Sweigart, D. A. Inorg. Chem. 1985, 24, 1405-1409. (68) Quinn, R.; Mercer-Smith, J.; Burstyn, J. N.; Valentine, J. S. J . Am. Chem. SOC.1984, 106, 4136-4144.
885
solvent molecules or ions with the ability to change ligand conformations or hydrogen bond to ligands are present will be important in tuning the thermodynamics and kinetics of electron transfer. It should also be-said that the practice of the use of cross reactions in aqueous media for determining the self-exchange rates of metalloproteins may lead to calculated self-exchange rate constants which are in error by orders of magnitude due to the noncancellation of solvation contributions. Acknowledgment. The receipt of a CSIRO Postdoctoral Fellowship is gratefully acknowledged by the author. After the initial submission of this manuscript, Professor M. J. Weaver and Professor D. A. Sweigart kindly supplied copies of various manuscripts in press. The author is grateful for the receipt of these manuscripts prior to publication and to Drs. R. J. Geue and P. Bernhard for communication of unpublished results.
Thermochemistry of Inorganic Solids. 3. Enthalpies of Formation of Solid Metal Oxyhalide Compounds 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, Los Angeles. California 90089- 1661 (Received: March 6, 1985; In Final Form: October 4, 1985)
Examination of available of standard enthalpies of formation of solid oxyhalide compounds (total of 35) of various metals from main groups to actinide series shows that the standard enthalpies of formation of these compounds can be correlat. d quantitatively with the enthalpies of formation of the corresponding oxides and halides of the same oxidation states by the equation AHf"(MO,Xy)= a [ ( 2 ~ / z ) A H f " ( M 0 ,+, ~( )y / z ) A H f " ( M X , ) ] + C, where z = 2x + y = the formal oxidation state of the metal, MO,X, is the oxychloride, and MOZl2and M X , are the corresponding oxide and halide of the same oxidation state z . Cis a correction factor in kcal/mol. For main and first transition-metal compounds, a = 1 and C = 0. For trivalent-state lanthanides, a = 2.155 f 0.12 and C = 257.8 f 1.3 or 250.4 f 1.2 kcal/mol. For tetravalent oxychlorides, a = 1 and C = 5 kcal/mol. For penta- and hexavalent compounds, a = 1 and C = 0.
Introduction
As a part of a program to understand the bonding and kinetic behavior of solid inorganic catalysts, we have been exploring the known thermochemistry of inorganic solids. In the course of this, we have discovered simple empirical relations which permit us to estimate the enthalpies of formation of inorganic salts and their compound hydrates; no comparable estimation methods now exist for these substances. In recent papers'*2we have shown that, for binary solid metal compounds of the formula M X , (where X is either metal or nonmetal) with multiple valence states, there is a quantitative relationship between the enthalpies of formation of the compounds and the value of z . The relationship can be expressed by -AHfo2,,(MX,) = a'z
- b'z2
(1)
or, with smaller average deviation, by
compounds and the corresponding oxides and halides of the same oxidation states. Unless otherwise stated, thermochemical data used here are taken from NBS table^,^ and values are given for standard enthalpy of formation AHf",,, per metal atom and at 298 K in kcal/mol. Divalent Oxyhalides
In this series, the only compound for which the necessary experimental values are available is Cu20Cl2. The standard enthalpy of formation of this compound can be related to standard enthalpies of formation of the corresponding oxide and chloride of the same oxidation states by a simple additivity relation: AHf"(Cu00,sCl) = '/zAHfo(CuO)
+
'/2AHf0(C~Cl2)= '/,(-37.6) '/2(-52.6) = -45.1 kcal/mol (obsd, -45.1 kcal/mol)
+
Trivalent Compounds
where a', b'and a", b"are, in general, different pairs of constant for each metal. The applicability of these two-parameter equations was demonstrated for 86 different compound series of various metals from main groups to actinide series. Examination of the available standard enthalpies of formation of solid oxyhalide compounds of metals reveals an interesting feature concerning the standard enthalpies of formation of these (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.
0022-3654/86/2090-0885$01.50/0
The metals forming trivalent oxyhalides for which experimental data exist are main group metals [groups I11 and V (groups 13 and 156)], first transition metals, and lanthanides; all of the compounds are oxychlorides. For main group metals, experimental data are available for only four compounds (AlOCl, SbOC1, Sb405C12,and BiOCl) and the corresponding oxides and halides of the same oxidation states. Except for BiOC1, the additivity relations illustrated below show (3) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, C.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Re$ Data 1982, 1 1 , Suppl. 2.
0 1986 American Chemical Society
886
The Journal of Physical Chemistry, Vol. 90, No. 5, 1986
Hisham and Benson
TABLE I: Calculated Values from Ea 3 (Trivalent Comwunds)
compd main group metals AlOCl SbOCl Sbol
2SC10.5
BiOCl first transition metals TiOCl VOCI FeOCl lanthanide metals LaOCl CeOCl PrOCl NdOCl SmOCl GdOCl TbOCl DyOCl HoOCl ErOCl TmOCl YbOCl LUOCl a
1 cal = 4.184J.
-AH('/ (kcal/mol)" obsd calcd
189.2 89.4 86.7 87.7
189.6 87.8 87.0 75.9
180.0 178.6 145.1 143.4 90.1 98.5 (97.3)b 241.6 239.0 242.0 239.0 237.1 234.0 233.0 235.9 239.2 237.9 236.0 229.9 227.1
228.0 227.0 228.4 227.0 227.0 225.3 228.0 228.1 229.9 230.8 229.1 221.0 225.0
dev(obsd - calcd)/ '
(kcal/mol)"
-0.4 1.6 0.3 11.8 +1.4
dev/%
0.2 1.8 0.3 13.5
+1.7 -8.4 (-1.2)b
0.8 1.2 9.3 (1.2)b
13.6 12.0 13.6 12.0 10.1 8.7 5.0 7.7 9.3 7.1 6.9 8.9 2.1
5.6 5.0 5.6 5.0 4.3 3.7 2.1 3.3 3.9 3.0 2.9 3.9 0.9
For reported value in ref 4.
good agreement between the observed and calculated values; the results are summarized in Table I. (i) AHfo(AIOCl) = 2/3AHfo(A10j.5)+ y3AHfo(AlC13) = 2/,(-200.3) + (obsd, -189.2 kcal/mol) y3(-168.3) = -189.6 kcal/mol (ii) AHfo(SbOCI) = 2/3AHfo(Sb01,5)+ f/,AHf0(SbCl3) = Y3(-86.l) y3(-91.3) = -87.8 kcal/mol (obsd, -89.4 kcal/mol)
+
(iii) AHfo(SbOl,25Clo,5) = 5/AHfo(Sb0i,5)+ y6AHfo(SbC13) = 5/6(-86.1) + v6(--91.3) = -87.0 kcal/mol (obsd, -86.7 kcal/mol) (iv) AHfo(BiOCl) = 2/3AHfo(BiOl.5)+ y3AHfo(BiCl3)= X(b68.6) )/,(-90.6) = -75.9 kcal/mol (obsd, -87.7 kcal/mol)
+
In the case of the first transition-metal series, however, the necessary experimental data are available for only three compounds (TiOCl, VOC1, and FeOCI). For these compounds, the simple additivity relation is in good agreement for TiOCl and VOCI; but, for FeOCl, the deviation is 9 kcal/mol. However, for the value reported in ref 4, the deviation for FeOCl is only 1.2 kcal/mol. (i) AHfo(TiOC1) = y3AHfo(Ti01.5)+ y3AHF(TiCl3) = y3(-l8l.8) + y3(-172.3) = -178.6 kcal/mol (obsd, -180.0 kcal/mol) (ii) AHfo(VOCl) = 2/3AHfo(VOj,5)+ 73AHfO(VCl,) = 2/,(-145.7) + (obsd, -145.0 kcal/mol) v3(-138.8) = -143.4 kcal/mol (iii) AHfO(FeOC1) = y3AHfo(FeOl,5)+ !/3AHfo(FeCl,) = 2/,(-lOO.O) + '/,(-95.5) = -98.5 kcal/mol (obsd, -90.1 kcal/m01;~-97.3 kcal/mo14) (4) Kubaschewski, 0.;Alcock, C. B. 'Metallurgical Thermochemistry", Pergamon: Oxford, 1979; 5th ed.
c
Figure 1. Plots of deviation vs. -AHro(MOCl),~d(lanthanide compounds).
The illustrations described above (including bivalent oxychlorides) suggest that the enthalpy of formation of oxychloride compounds of main and first transition-metal series may be related to the heats of formation of the corresponding oxides and chlorides by simple additivity relation of the form: AHfo(MO,X,) =
(
+ f f o ( M O z , 2 ) + Cv/Z)AHf0(MX,) (3)
+
where z = 2x y is the oxidation state of the metal. MO,X, is the oxyhalide, and MOZi2and MX, are the corresponding oxide and halide in the oxidation state, z. For lanthanide compounds, the results obtained with the additivity relation (eq 3) are shown in Table I. The maximum absolute deviation is 14 kcal/mol; however, close examination of the results indicates that the deviations vary systematically. When the deviations are plotted against observed values of oxychlorides, as shown in Figure 1, two exactly parallel lines are obtained. The slope of the lines is 0.464 (-0.5), and difference between the intercepts is 3.4 kcal/mol. The interesting feature is that, except Yb, the first half of the lanthanides are represented by the lower line and the remaining compounds are represented by the upper line. Both lines give an equation of the form AHfo(MOC1) = a[2/3AHf0(MO, 5 )
+ XAHfo(MC13)] + b
(4)
*
where a = 2.155 0.12 and b = 257.8 f 1.3 kcal/mol for the lower line and 250.4 f 1.2 kcal/mol for the upper line. Equation 4 has the same form as eq 3, but different values of the parameters, a and b. With eq 4, the estimated values for lanthanides compounds are in good agreement with the observed values. The maximum absolute deviation is only 4 kcal/mol, and the results are summarized in Table 11. Tetra-, Penta-, and Hexavalent Compounds
The lack of experimental data in this category makes detailed analysis difficult. In case of tetravalent compounds, the number of available oxyfluoro, -chloro, -bromo, and - i d 0 compounds with corresponding oxides and halides of same oxidation states are 2, 3, 2, and 1, respectively. For pentavalent compounds, only one value is available. The total number of hexavalent compounds is 5 , which includes 1, 2, and 2 oxyfluoro, -chloro, and -bromo compounds, respectively. Table I11 shows the results obtained by using the additivity relation eq 3 for these compounds. The following comments can be made concerning the table.
The Journal of Physical Chemistry, Vol. 90, No. 5, 1986 887
Thermochemistry of Inorganic Solids TABLE 11: Calculated Values from Eq 4 -AH," / (kcal/mol) obsd calcd 241.6 241.4 239.0 238.8 241.7 242.0 239.0 238.7 237.1 238.7 234.0 235.0 229.9 225.9
a, b/
compd LaOCl CeOCl PrOCl NdOCl SmOCl GdOCl YbOCl
(kcal/mol) 2.155. 250.4
TbOCl DyOCl HoOCl ErOCl TmOCl LUOCl
2.155, 257.8
233.6 233.8 237.7 239.5 235.8 227.0
dev(obsd - calcd),/ (kcal/mol) +0.2 +0.2 +0.3 -0.3 +1.6 -1 .o +4.0
233.0 235.9 239.2 237.9 236.0 227.1
301 25
-0.6 +2.1 +1.5 -1.6 +0.2 +o. 1
TABLE III: Calculated Values from Eq 3 (Tetra-, Penta-, and Hexavalene Compounds) -AH," / (kcal mol)" obsd calcd
comDd tetravalent compounds UOFZ ThOF2 NbOCl2 UOCI, ThOC12 UOBr2 ThOBr2 Tho12 pentavalent compounds NbOCI3 hexavalent compounds W02Br2 WOBr4 WO2CI2 WOCI, UO2F2
dev(obsd - calcd)/ (kcal mol)
-i5
-AH:(
dev/%
MU,-
M0,,5) /kcal
Figure 2. Plots of (MOCI-MOI,S) vs. (MC13-MOl,S). 0
358 (3 59.6) 398 185 255 294 233 284 (270)b 239
358
0
397 178 252 288 225 262
+I +7 +3 +6 +8 +22 (+8)b +13
210
205
170 130 187 162 394 (395.5)b
162 123 182 172 370
226
(0.4)b 0.3 3.8 1.2 2.0 3.4 8 (3Ib 5.4
+5
2.4
+8 +7 +5 -10 +24 (25.5)b
4.7 5.4 2.7 6.2 6.1 (6.4)b
1 cal = 4.184 J. bFor reported values in ref 5.
TABLE I V Calculated Values from Eq 5
-AH: / compd
C/kcal
NbOC12 VOCl2 ThOC12
5
(kcal/mol) calcd obsd 183 257 293
185 255 294
dev(obsd - calcd)/ (kcal/mol) +2 -2 +1
Among the tetravalent compounds, the observed and calculated values are in good agreement for oxyfluoro compounds. The calculated values from eq 3 for oxychlorides, however, are always lower than the observed values. Therefore, a correction factor C is introduced into eq 3 as in
+
1 -30 -20 - i O 0 10 20 30 40
where z = 2x y = the oxidation state of metal. MO,X, is the oxyhalide; MO, and MX, are the corresponding oxide and halide in the same oxidation state z . Cis a correction factor in kcal/mol. For C = 5 kcal/mol, the maximum absolute deviation becomes only 2 kcal/mol, as shown in Table IV. However, lack of data for other compounds precludes such analysis. Though the absolute
deviations are high for these compounds, as shown in Table 111, the maximum percentage deviation is only 6% fr the entire ensemble. The reported values available in ref 5 are also listed in Table 111, and the values were compared with the calculated values.
Discussion It is evident from the above illustrations that there is a roughly quantitative relation between the enthalpies of formation of oxyhalide compounds and the corresponding oxides and halides of the same oxidation states. The relationship between these compounds can be expressed by the following general equation:
AHr' (M 0,X y ) a( 2XAHfo(M0,/z) Z + y/zAHfo(MX,)
+
where z = 2x y = the formal oxidation state of the metal, MO,X, is the oxyhalide, MOzIzand MX, are the corresponding oxide and halide of the same oxidation state z, and Cis a constant in kcal/mol. For main and first transition metal compounds a = 1 and C = 0. For trivalent state lanthanides, a = 2.155 f 0.12 and C = 257.8 f 1.3 or 250.4 f 1.2 kcal/mol. For tetravalent oxychloride, a = 1 and C = 5 kcal/mol. For penta- and hexavalent compounds, a = 1 and C = 0. Expression 6 can be used to estimate the enthalpy of formation of any oxyhalide provided the values for the corresponding oxides and halides of the same oxidation states are known. Moreover, the relationship among the oxide, halide, and oxyhalide enables us to evaluate the enthalpy of formation of any one of these compounds provided the values for remaining two compounds are known. For example, in the first transition-metal series, values for VOClz and VOzCl are available; however, the corresponding ( 5 ) Hubbard, W. N.; Fuger, J.; Oetting, F. L.;Parker, V. B. 'The Chemical Thermodynamics of Actinide Elements and Compounds Part 8. The Actinide Halides"; International Atomic Energy Agency: Vienna, 1983. (6) 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., 111 3 and 13.)
-
888 The Journal of Physical Chemistry, Vol. 90, No. 5, 1986
TABLE VI: Calculated Values of Trivalent Oxychloride from Eq 7
TABLE V Metal Halides Parameters (Eo 2)
a", b"
compd
z
1.8234, 0.0507
VCI, VCI, VCll VC15
2 3
1.6540, 0.0525
MoCI, MoCI, MoC14 MoCl, MoCl,
4 5 2 3 4 5 6
-AHro/ (kcal/mol)" obsd calcd
Hisham and Benson
dev(obsd - calcd)/ (kcal/mol)
108 139 165' 187'
105 141 167 186
+3 -2 -2 +I av 2.0
67 93
71 94
-4
115
111
126 129b
123 131
+4 +3 -2 av 2.8
compd LaOCl CeOCl PrOCl NdOCl SmOCl GdOCl TbOCl DyOCl HoOCl ErOCl TmOCl YbOCl LuOCl AIOCl SbOCl BiOCl TiOCl VOCI FeOCl
-1
1 cal = 4.184 J. bEstimated from eq 3.
chlorides VC14 and VCl, are not known. From expression 5 the values for VC14 and VCI, can be estimated; these values are AHfO(VC14) = 2AHfo(VOC12) - AHfO(V02) = 2(-168) - (-170.6) = -165.4 E-165 kcal/mol (when a = 1, C = 0 in eq 6) AHfO(VC1,) = 5AHfo(V02C1)- 4AHfo(VOz,s) = 5(-185.6) - 4(-185.3) = -186.8 = -187 kcal/mol The values for VC12 and VC13 are known from the l i t e r a t ~ r e ; ~ from our estimate above, we obtain values for VCI, and VC15. It is interesting to note that, when these values are used in expression 2, the average deviation becomes 2 kcal/mol with the maximum deviation 3 kcal/mol between observed and calculated values; the results are shown in Table V. In case of Mo, the values for MoO2CI2and MoOC14 are known, but the value for the corresponding chloride, MoCI,, is not available. However, the two resulting estimates for MoC16, using expression 5 when a = 1 and C = 9 kcal/mol (for hexavalent compounds), differ by only 4 kcal/mol.
+
AH? (MoCl,) zs 3 [AH,' (M o O ~ C I ~-)73AHt (Moo3) c] = 3[(-171.4) - Y3(-178,1) 91 = -131 kcal/mol
+
+
AHfO(MoC16) = 3/2[AHf0(MoOC14)- '/,AHfO(Mo-O,) c] = 3/*[(-153) - y3(-178.1) 91 = -127 kcal/mol
+
The value of -129 kcal/mol estimated for M d l s (average of -131 and -127 kcal/mol) fits expression 2 very well and the data for other chlorides (where available). The results are also shown in Table V. For trivalent oxychlorides, where more data are available, the plots of -AAHfo(MOC1-M0,,5) vs. -AAHfo(MC13-M0,,5)as
(I
-AHfo/ (kcal/mol)" obsd 241.6 239.0 242.0 239.0 237.1 234.0 233.0 235.9 239.2 237.9 236.0 229.9 227.1 189.2 89.4 87.7 180.0 145.1 90.1 (97.3)'
calcd 241.4 239.2 240.4 238.2 237.1 234.5 235.5 235.9 237.5 237.5 235.5 228.0 229.5 187.0 93.1 84.9 180.8 145.3 98.3
dev(obsd - calcd)/ (kcal/mol ) 0.2 -0.2 1.6 0.6 0 -0.5 -2.5 0 1.7 0.4 0.5 1.9 -2.4 2.2 -3.7 2.8 -0.8 -0.2 -8.2 (-1.0)'
1 cal = 4.184 J. 'For reported value in ref 4.
shown in Figure 2 show another important feature. (More details of these relations will be presented elsewhere.) Except for Fe, all the compounds lie on or close to the straight line which has a slope 0.548 and intercept 4.21 kcal/mol. The line is represented by eq 7 for which the maximum absolute deviation is 3.7 kcal/mol AAHP (MOC1-MOI 3 ) = 0.548 f 0.15AAHfo(MC1~-MO~,~) - 4.21 f 0.8 (7) for all the oxychlorides, except FeOC1. Its deviation is 8.2 kcal/mol. However, the observed value for FeOCl given in ref 4 lies close to the line and has a deviation of only 1 kcal/mol. Our correlation suggests that this is a better value. The results are summarized in Table VI.
Conclusion For the 35 oxyhalides compounds of the various metals we have examined, the standard enthalpies of formation of any solid metal oxyhalide compound can be related to the standard enthalpies of formation of the corresponding halides and oxides of the same oxidation state by eq 5 . Though in certain cases the deviations are high, the relationship given by eq 5 may be useful in estimating the enthalpies of formation of the compounds, where even an error as much as 10 kcal/mol may be useful in dealing with a problem. Acknowledgment. This work was supported by the U S . Army Research Office, Grant No. DAAG29-82-K-0043, and the National Science Foundation, Grant No. CHE-79-26623.
