J . Phys. Chem. 1986, 90, 307-312
307
STATISTICAL MECHANICS AND THERMODYNAMICS Actinide Thermodynamic Predictions. 3. Thermodynamlcs of Compounds and Aquo Ions of the 2+, 3+, and 4+ Oxidation States and Standard Electrode Potentials at 298.15 K Steven G. Brats&* and J. J. Lagowski Department of Chemistry, The University of Texas, Austin, Texas 78712 (Received: June 17, 1985)
A modified ionic model is applied to selected actinide thermodynamic measurements to allow the evaluation of gas-phase ion thermodynamics across the actinide series. These are used to predict the thermodynamic properties of a number of actinide compounds and aquo ions at 298.15 K. General guidelines are offered for predicting the relative stabilities of actinide(II), -(III), and -(IV) compounds in various chemical environments.
Introduction This paper continues our investigation of the thermodynamic properties of the actinide elements and their These properties are of paramount importance to the nuclear industry, and their variations across the actinide series are of considerable theoretical interest. Therefore, simple and reliable methods of thermodynamic prediction are valuable contributions to actinide research. In previous we have developed a modified ionic model which allows the prediction of the thermodynamic properties of simple lanthanide compounds and ions. In the present work we apply our model to the actinides. Our modified ionic model allows the prediction of the standard enthalpy of formation (A&') of a solid lanthanide compound from a simple equation which is fit to the available AHf' data. The following numerical quantities must be known: the standard enthalpy of formation of the monatomic gas (AHfo(M,g)), the ionization potential sum for the oxidation state under consideration ( C f I P ( M ) ) , the crystal ionic radius of the metal for coordination number 6 (rMl+), and the correlation parameters for the compound type (halide, oxide, or ~ u l f i d e ) .We ~ have also given equations for the prediction of the thermodynamic properties of aquo ions M'+(aq) where z = 2+ 3+, and 4+.4 The direct approach cannot be used for the actinides because the ionization potentials are mostly unavailable. However, it is possible to back-calculate an internally consistent set of "thermochemical" ionization potentials from selected thermodynamic data, if two assumptions are made: 1. As with the lanthanides, ligand field effects involving f orbitals are negligible on the energy scale considered. 2. The correlation parameters derived for lanthanide compounds remain applicable to actinide compounds. We show here that the first assumption is valid within experimental error, but that the second is only approximately correct. Once the ionization potentials and gas-phase ion thermodynamics have been deduced from thermochemical cycles, they can be used to calculate thermodynamic quantities for other actinide species. Our investigation is restricted to the 2+, 3+, and 4+ oxidation states. These are generally the most important oxidation states for the actinides, and they are the only ones at present for which we have correlation parameters. Tentative thermodynamic data are also provided for compounds and aquo ions of radium and element 104. (1) Bratsch, S. G.; Lagowski, J. J. Chem. Phys. Leu. 1984, 107, 136. (2) Bratsch, S. G.; Lagowski, J. J. Polyhedron 1985, 4, 841. (3) Bratsch, S. G.; Lagowski, J. J. J . Phys. Chem. 1985, 89, 3310. (4) Bratsch, S. G.; Lagowski, J. J. J . Phys. Chem. 1985, 89, 3317.
0022-3654/86/2090-0307$01.50/0
TABLE I: Selected Key Atomic Data
M Ra
AHfo(M,g)"
IP,'
IP,g
IP+
1556 41OC 597.1 60063c 531.4 464.8 343.1 284.1 387.4 310.0 196.2 150d 125d 100d 70d 350d 540d
5.2796 5.17 6.08 5.89 6.05 6.19 6.06 5.993 6.02 6.23 6.30 6.42 6.50 6.25d 6.65 5.gd 7.0d
10.1472f 11.75h 11.9 11.20 11.53 11.39 11.44 11.64 12.09 12.02 12.20 12.38 12.56 13.06 12.90 13.0 13.0
18.9 20.6 20.0 20.0 20.7 21.8 22.4 21.2 22.3 23.6 24.1 24.4 25.4 27.0 23.0 24.0
Ac
Th Pa U Np
Pu Am Cm Bk
Cf Es Fm Md No Lr 104
IP4g 28.75h 31.0 32.6 33.6 34.6 36.2 36.8 35.6 37.3 38.7 39.3 39.8 41.0 42.6 33.0
S0(M,c)' 69 62 53.4 52 50.2 50.5 56.1 55 72 78 80 90 88d
84d 66d 5 6d 4Sd
"kJ mol-' (298.15 K): ref 10, except as noted. bReferences7 and 8. CReference9. dEstimated (this work). CeV (0 K): ref 12, except as noted. 'Reference 11. geV (0 K): estimated (this work), except as noted. *Reference 12. ' J K' mol-' (298.15 K): ref 10, except as noted.
All thermodynamic quantities tabulated in this paper refer to K except ionization potentials which refer to 0 K. We have attempted to maintain compatibility with the CODATA recommendations for chemical thermodynamic value^.^ All physical constants and energy conversion factors have been taken from Cohen and Taylor.6 298.15
Selected Key Atomic Data Table I lists "best" values of atomic data for the elements considered in this paper. Although we have accepted the literature data7-I2in well-established cases, we have found it necessary to ( 5 ) CODATA Recommended Key Values for Thermodynamics J . Chem. Thermodyn. 1978, 10, 903. (6) Cohen, E. R.; Taylor, B. N. J . Phys. Chem. Re$ Data 1973, 2, 663. (7) David, F.; Samhoun, K.; Guillaumont, R.; Nugent, L. J. In "Heavy Element Properties", Muller, W., Blank, H., Ed.; American Elsevier: New York, 1976; pp 97-104. (8) David, F.; Samhoun, K.; Guillaumont, R.; Edelstein, N. J . Inorg. Nucl. Chem. 1978, 40, 69. (9) Brewer, L. as quoted by Waber, J. T. In "Heavy Element Properties", Muller, W., Blank, H., Ed.; American Elsevier: New York., 1976; pp 29-64. (10) Ward, J. W. J . Less-Common Met. 1983, 93, 279.
0 1986 American Chemical Society
308 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 estimate many quantitites. We list here our methods of estimation, with some highly subjective uncertainties. AH,’ (Es-No,g): From thermochemical cycles involving polarographic measurements and corrections for amalgamation potential^.^,^,'^ Uncertainty = 30 kJ mol-’. Our derived Mro(No,g) is remarkably low and may indicate an error in the cycle. Mfo(Lr,104,g): By comparison with Lu and Hf, respectively. Uncertainty = 40 kJ mol-’. IPI(Md): Martin et al.I2 have given 6.58 eV on the assumption that the ground-state electron configuration of Md+ is .5fl37s1. However, Vander Sluis and Nugent14 have calculated that the 5fI4 electron configuration is 0.33 eV lower in energy than 5fI37s1; we have adjusted Martin’s IP accordingly. IPl-IP3(Lr): Extrapolated from trends in excited-state IP values for the lighter actinides for the successive ionizations M“ (5f46d17s2 or 5f47s27p1) M+(5f47s2) M2+ (5f47s’) M3+(5f4),which are ground-state processes for Lr.I4-l7 The necessary promotion energies for the lighter actinides have been taken from ref 14-17. Any deviations from a smooth trend exhibited by Lr have been assumed to parallel those exhibited by Lu in the lanthanide ser i e ~ . ~ - ’Uncertainty ~-’~ = 0.2 eV (IP,) and 0.4 eV (IP, and IP3). IPl-IP4( 104): Estimated from trends in IP values for other d2s2metals (Zr, Hf, Th). Uncertainty = 1.0 eV; uncertainty in sum = 2.0 eV. IP2(Pa-No): From the relationship between first and second ionization potentials (s electrons),18 correcting where necessary for irregular ground-state electron configurations in M+ and/or M2+.I4J7 Uncertainty = 0.20 eV. IP3(Ac,Pa): From system differences (SD) m e t h ~ d ~ - as ’~.’~ applied to other actinide IP3. Uncertainty = 0.4 eV. IP3(U-No): From thermochemical cycles involving Uncertainty = AHro(M3+,aq)and/or E0(M3+/M2+).7~8,13~20-24 0.4 eV. IP,(Pa-Bk): From thermochemical cycles involving AHf’(M02,c), MfO(M4+,aq),and/or E0(M4+/M3+).20-22 Uncertainty = 0.4 eV. IP4(Cf-Lr): From SD meth0d~3’~J~ as applied to other actinide IP,. Uncertainty = 0.6 eV. S’(Fm-104,c): Estimated by method of Ward and HilLz5 It is necessary to warn the reader at this point that significant discrepancies exist in the literature for some actinide thermodynamic data. For example, ref 10 gives a “tentative” experimental value for M?(Pa,g) of 571 kJ mol-’, which is 29 kJ mol-’ smaller than the value listed in Table I. Adoption of this value would require that our thermochemically derived IP4(Pa) be increased to 31.3 eV, which is less consistent with our selected IP4(Th,U) in Table I. As another cautionary example, ref 8 predicts a gradual decrease in AHfD(M,g)for Es to No from 142 to 130 kJ mol-’, while ref 10 lists an experimental AHfo(Es,g) = 131 kJ mol-,. However, if such values were adopted, then either IP2-
-
-+
-
( 1 1) Moore, C. E. Nail. Stand. Ref Data Ser., Natl. Bur. Stand. 1970,
No. 34.
(12) Martin, W. C.; Hagan, L.; Reader, J.; Sugar, J. J . Phps. Chem. Ref Data 1974, 3, 77 1 . (13) Hulet, E. K. In “Actinides in Perspective”, Edelstein, N. M.. Ed.; Pergamon Press: New York, 1982; pp 453-490. (14) Vander Sluis, K. L.;Nugent, L. J . J . Opt. SOC.Am. 1974, 64, 687. (15) Vander Sluis, K. L.; Nugent, L. J. Phys. Rec. A 1972, 6 , 86. (16) Brewer, L . J . Opt. SOC.Am. 1971, 61, 1101. (17) Brewer, L. J . Opt. SOC.Am. 1971, 61, 1666. (18) Ahrens, L. H. “Ionization Potentials”; Pergamon Press: New York, 1983; pp 3-6. (19) Vander Sluis, K. L.; Nugent, L. J. J . Chem. Phys. 1974, 60, 1927. (20) Nugent, L. J.; Baybarz, R. D.; Burnett, J. L.; Ryan, J. L. J . Phys. Chem. 1973, 77, 1528. (21) Fuger, J.; Oetting, F. L. “The Chemical Thermodynamics of Actinide Elements and Compounds. Part 2: The Actinide Aqueous Ions”; International Atomic Energy Agency: Vienna, 1976. (22) Fuger, J. In “Actinides in Perspective”, Edelstein, N. M., Ed.; Pergamon Press: New York, 1982; pp 409-431. (23) Fuger, J.; Haire, R. G.; Peterson, J. R. J . Less-Common Mer. 1984, 98, 315. (24) Mikheev, N. B. Inorg. Chim. Acta 1984, 94, 241. (25) Ward, J. W.; Hill, H. H. In “Heavy Element Properties”, Muller, W., Blank. H., Ed.; American Elsevier: New York. 1976; pp 65-78.
Bratsch and Lagowski
28.0 32.0 24.0
14
16.0 = 0
q
1
A c Th
2
3
4
5
Pa U Np Pu
6
7
8
910111213
-
A m C m Bk C f E s Fm Md No
Figure 1. Linearization of the ionization process M2+ (Sfq’l) M3+ (5P) + e-. Th point is spectroscopic;’’ all others are thermochemical (this work). F,(q) from ref 15.
44.0
36.0
28.0
. 6
q
O
=
1
Th P a
2
3
4
5
6
7
8
9 1 0 1 1 1 2 1 3
-
U Np Pu Am C m B k C f Es F m M d No L r
Figure 2. Linearization of the ionization process M3+ (Sf@I) M4+ (5P)+ e-. Th point is spectroscopic;12 all others are thermochemical (this work). F,(q) from ref 15.
(Es-No) in Table I would have to be modified in such a way so as to vary erratically and inexplicably, or we would have to conclude that the reported polarographic data7,8J3are in error. In summary then, future studies may well invalidate some of our selected themodynamic values, but it is believed that our general method of prediction will retain its usefulness. We have derived all thermochemical ionization potentials from experimental oxide and aquo-ion data (standard enthalpies of formation and standard electrode potentials) because these data are extensive and of relatively high reliability. As discussed below, actinide compounds appear to have covalent contributions to bonding somewhat different from that existing in the analogous lanthanide compounds. This differential bonding should be small in species where the metal atoms are associated with highly electronegative oxygen atoms. Fluorides might be a better choice, but the data are neither as extensive nor as reliable. Our thermochemical first through third ionization potential sums for U-Bk are in good agreement (*0.1 eV) with those calculated by Goldman and Morss.26 The thermochemical third and fourth ionization potentials, corrected where necessary for irregular electron config~rations,~~J’ are combined in Figures 1 and 2 with the spectroscopically derived f electron linearization parameters given by Vander Sluis and Nugent.I5 The general linearity of the points indicates that we have been justified in ignoring ligand field effects involving the 5f orbitals. If significant f orbital ligand field effects existed, the points in Figures 1 and 2 might be expected for form double(26) Goldman, s.; Morss, L. R. Can. J . Chem. 1975, 53, 2695
Actinide Thermodynamic Predictions
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 309
TABLE 11: Properties of Gas-Phase Ions at 298.15 K and Crystal Ionic Radii electron configuration" gas-phase ion ion 5f 6d 7s AHfob 'J Sof AGlOg rMi+h ion Ra2+ 1656 0.0 176.35 1612 0.1400 Ac3+ 1 2335< 2.5 191.3 2284 Ac2+ 0.1352 Th3+ 1 1
Th2+ Pa2+ U2+
Np2+ PU2+ Am2+
Cm2+ Bk2+
CP+ Es2+
Fm2+
Md2+ NoZ+
Lr2+ 1042+
2 1 3 2 1 4 3 3 2 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 14 14 14
1 2
1 2 1
1 2 1 1 1 1 1 1 1
1 1 1 1 1 2
2064' 2055 2487c 2306 2306 2316< 226 1 2377d 224V 224V 2240 2470d 2173 2222c 2044 2208' 1998 2220d 2147 2244d 2083 2286d 1994 2326< 1976 2338' 1976 2362< 1976 2455< 1969 2572< 2394< 2176 2482
1.5 0.5 4.0 (4.0) 2.0 4.5 (5.5) (4.5) 4.0 (6.0) (5.0) (6.0) 2.5 (5.5) 0.0 (4.0) 3.5 (1.5) 6.0 (5.0) 7.5 (7.5) 8.0 (9.0) 7.5 (9.5) 6.0 (9.0) 3.5 (7.5) 0.0 (5.0) 1.5 0.5 0.0
187.9 182.2 194.95 194.9 190.06 195.77 197.3 195.8 195.26 198.3 196.9 198.3 191.84 197.6 177.3 195.6 194.5 188.8 198.8 197.4 200.5 200.5 201.2 202.1 200.9 202.7 199.3 202.4 195.3 201.1 178.0 198.0 189.6 183.9 178.1
2014 2007 2432 255 1 2253 2261 2205 2322 2192 2191 2184 2413 21 18 2166 1995 2154 1944 2168 2097 2194 2034 2237 1945 2277 1930 2292 1930 2315 1930 2408 1923 2520 2342 2125 243 1
electron configuration" 5f
6d
7s
1 1
Pa'+ 0.1310 u3+
0.1273
Np3+
PU3+ Am3+ 0.1240
Cm" Bk3+
0.1211 0.1184
Cf3+ Es'+ Fm3+ Md" No3+
Lr3+ 0.1160
104)+
0.1138
Th4+
0.1118
U4f
0.1100
Pa4+ Np4+ pu4+
0.1083
Am4+ Cm4t Bk4+
0.1068
cf4+
0.1053 0.1040 0.102
Es4+ Fm4+
Md4+ Lr4+ 1044+
2 1 3 2 4 5 6 7 8 9 10 11 12 13 14 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1
1
gas-phase ion AHfob Je 3885 0.0 4242 2.5 4352< 1.5 4197 4.0 4419d (4.0) 4176 4.5 4504d (5.5) 4177 4.0 4154 2.5 4165 0.0 4199 3.5 4241 6.0 4277 7.5 4308 8.0 4337 7.5 4432 6.0 4580 3.5 4402 0.0 4804 0.5 7022 7194 7327 7425 7498 7664 7756 7682 7882 8048 8135 8279 8542 8518 7994
0.0 2.5 4.0 4.5 4.0 2.5 0.0 3.5 6.0 7.5 8.0 7.5 6.0 3.5 0.0
So/
AGfoC
176.4 191.57 188.20 194.89 194.9 196.14 197.7 195.21 192.2 177.3 194.7 198.8 200.7 201.4 201.0 199.3 195.3 178.1 183.9
3832 4182 4293 4136 4358 41 14 444 1 4115 4095 41 10 4144 4186 4222 4256 4285 4379 4523 4347 4745
0.1013 0.0994 0.0976 0.0960 0.0945 0.0932 0.0920 0.0909 0.0898 0.0889 0.0880 0.087
176.68 191.52 195.26 196.09 195.6 192.1 177.5 194.7 199.0 200.9 201.5 201.1 199.4 195.4 178.1
6960 7128 7259 7357 7432 7598 7700 7622 7822 7990 8076 8219 8477 8452 1930
0.0980 0.0959 0.0940 0.0924 0.0909 0.0896 0.0884 0.0873 0.0864 0.0855 0.0847 0.0839 0.0832 0.0826 0.0820
~
rMl+h 0.1 120
0.1088 0.1060 0.1035
0.100
"Outside radon core. bkJ mol-': Equation from ref 3. H,O(M,g) and ionization potentials from Table I. CPromotionenergy from ref 14 and 17. dPromotion energy estimated (this work). Total angular momentum quantum number (L-S coupling). Values in parentheses are less reliable because they involve ions with partially filled 5f and 6d or 5f and 7s orbitals. fJ K-' mol-': equation from ref 3. g k J mol-' from AHf" - TASfo,using So(e-) = 20.87 J K-' mol-'.3 hCrystal ionic radius (nm)(see text). humped curves similar to those formed by the d-block transition metals. 27a328a,29a
Properties of Cas-Phase Ions Thermodynamics of gas-phase ions at 298.1 5 K are presented in Table 11. The equations for deriving these quantities from key atomic data have been given previ~usly.~ Multiple sets of data have been given for several ions because, even when it is not the ground state, an electron configuration involving 6d electrons can sometimes be stabilized through ligand field effects (vide infra). A breakdown of the L-S coupling scheme for heavy elem e n t ~could ~ ~ lead ~ ,to~a ~slight ~ overestimation of the gas-phase standard entropies, So(MZ+,g). This has a small effect (2-3 kJ mol-') on the gas-phase standard Gibbs free energies of formation, AGfo(MZ+,g),which we choose to ignore. Crystal Ionic Radii Although ionic radii have been reported for many seventh period element^,^^^^^^^ a number of gaps still exist, especially for the heavy (27) (a) Huheey, J. E. "Inorganic Chemistry", 2nd 4.; Harper and Row: New York, 1978; pp 365-366. (b) Ibid., p 814. (c) Ibid., p 359. (d) Ibid., DD 681-687. rr (28) (a) Cotton, F. A.; Wilkinson, G . 'Advanced Inorganic Chemistry", 3rd ed.;Wiley-Interscience: New York, 1980; p 683. (b) Ibid., pp 1005-101 1. (29) (a) Johnson, D. A. "Some Thermodynamic Aspects of Inorganic Chemlstryn, 2nd 4,; Cambridge University Press: London, 1982; 146. (b) Ibid., pp 168-171. (30) Shannon, R. D. Acta Crystallogr., Sect. A 1976, 32, 751.
actinides. It would be convenient to obtain a simple equation which correlates the available data and makes predictions in cases where experimental measurements are difficult or impossible. We shall assume that the ionic radius ( r ) of an actinide is completely determined by the coordination number, ionic charge ( z ) and electron configuration. We shall restrict the present discussion to the standard coordination number 6. We may characterize the electron configuration by q, which represents the number of electrons outside the radon core. For an isoelectronic series (constant q), the ionic radii should decrease as z increases. Also, for consistent z, r should decrease with increasing q (the actinide contraction). Finally, actinide ionic radii should be slightly larger than the radii of their lanthanide analogues with the same z. Based on these requirements, we propose the relationship expressed by
rM1t(nm) = 1.5'(q 2*268 + 14)
+ 0.066 + Ar
(1)
where 1+ I z I 7+, 0 Iq I14, and Ar is a small correction term which is needed to produce maximum consistency with selected lanthanide ionic radii.3 F~~ = 2+, ar = +0.002 nm; for z = 3+, Ar = -0.002 nm; for all other z, Ar = 0 . Equation 1 is functionally compatible with the equations developed for lanthanide ionic radii.3 Ionic radii calculated by eq 1 are given in Table 11. As with the lanthanide ionic radii,3 the fourth decimal place in radius is significant only in a relative sense between adjacent elements. According to eq 1, no significant break in
Bratsch and Lagowski
310 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 TABLE III: Predicted Standard Enthalpies of Formation of Actinide(I1) ComDounds (kJ mol-'. 298.15 K)" MS MC12 MIz MO MF2 MBr, M -528 -428 -734 -576 -837 Ra -1183 -168 -63 -358 -201 -462 AC -817 +I57 +27 +47 -233 -128 Th -595 -30 +84 -192 -38 -297 Pa -667 -81 +37 -230 -77 -336 U -712 -174 -52 -312 -160 -419 Np -801 -304 -329 -203 -564 -456 PU -951 -398 -269 -364 -624 -515 Am -1016 -270 -138 -378 -228 -885 -487 Cm -354 -219 -304 -563 -454 Bk -965 -461 -323 -553 -404 -663 Cf -1069 -496 -356 -581 -432 -691 ES -1101 -441 -512 -369 -701 -590 Fm -1114 -451 -528 -382 -710 -599 Md -1127 -466 -548 -400 -725 -613 NO -1146 -363 -211 -418 -271 -531 Lr -956 104 -668 -238 -125 +22 -79 +76 ~
TABLE V Predicted Standard Enthalpies of Formation of ActinideUV) Compounds (kJ mol-'. 298.15 K) MBr4 MI4 M02 M MF, MCI, -672 -1225 Th -2092 -1186 -965 -579 -1136 Pa -1997 -1091 -870 -1028 -807 -519 -1079 U -1936 -990 -770 -482 -1046 Np -1899 -754 -1884 -973 -468 -1034 PU -857 -637 -353 -922 Am -1769 -811 -592 -309 -881 Cm -1724 -928 -709 -427 -1002 Bk -1842 -764 -544 -263 -840 Cf -1678 -633 -414 -134 -713 ES -1549 -79 -661 Fm -1495 -578 -359 -466 -247 +32 -552 Md -1384 -1150 -231 -12 +266 -320 NO +217 -371 Lr -1199 -279 -60 -332 -922 104 -1748 -828 -608 1300
MS2 -627 -544 -493 -465 -459 -351 -313 -437 -278 -154 -104 +3 +233 +I81 -372
-
I
I
"Ligand field stabilization energies associated with 6d' or 6d2 electron configurations have not been considered because they are usually unknown.
TABLE I V Predicted Standard Enthalpies of Formation of Actinide(II1) Compounds (kJ mol-', 298.15 K ) M MF," MCl,b MBr3' M13d Mol: MS, -805 -521 -843 -606 AC -1624 -1011 -512 -222 -534 -299 Th -1321 -701 -318 -388 -614 -621 Pa -1414 -788 -688 -386 -680 -449 -847 U -1478 -734 -427 -484 -881 -714 Np -1516 -798 -487 -538 -934 -767 PU -1574 -828 -512 -544 -951 -785 Am -1596 -830 -510 -539 -943 -777 Cm -1592 -498 -524 -822 -759 -1578 -926 Bk -815 -488 -733 -512 -1598 -911 Cf -813 -482 -725 -503 -1590 -900 ES Fm -1582 -868 -717 -494 -810 -476 -741 -403 -420 -796 -644 Md -1509 -615 -274 -289 -667 -513 NO -1378 Lr -1574 -864 -709 -484 -814 -471 104 -1192 -484 -327 -101 -437 -91
"Ac-Bk = hex; Cf-104 = rhbc. b A ~ - E= ~hex (a);Fm-104 = mncl (7).CAc-Bk = hex/rhbc; Cf-104 = rhdbr. dAc-Pu = rhbc (a); Am-IO4 = hex (6). eAc-Pu = hex (A); Am-Cf = mncl (B); Es-104 = cub (C). actinide ionic radii should occur at q = 7. This point is discussed further below. The ionic radii of Lr2+, 1042+,and 104)' in Table I1 have been extrapolated (this work) by assuming a slight break at q = 14 analogous to that exhibited by various rM* following the lanthanide series.30
Predicted Standard Enthalpies of Formation and Relative Stabilities of Actinide(II), -(III), and -(IV) Compounds Standard enthalpies of formation of various actinide(II), -(III), and -(IV) compounds may be calculated from the data in Table I1 and the equations given in ref 3; these are assembled in Tables 111-V. Agreement with experimental data22-31 is usually within 20 kJ mol-'. The AHfo values may be combined to derive the variations in the standard enthalpies of decomposition for a particular compound type across the actinide series. As with the lanthanides, there are two general decomposition reactions of interest: 1. disproportionation of an actinide(I1) compound to the metal and the corresponding actinide( 111) compound:
MI1
-
f3M
+ 2/3M111
(31) Morss, L.R.; Fuger, J.; Goffart, J.; Haire, R. G. Inorg. Chem. 1983, 22, 1993.
- z o O ~ c l ~ ~ ~ , ~ ~ , ,, lI
, ,
l
I
j
-300 0
-400 Ac
Th
Pa
U
Np P u
A m Cm
Ek C f
Es
Fm M d No
L r 104
Figure 3. Predicted standard enthalpies of disproportionation (kJ mol-') of actinide(I1) compounds to the metal and the corresponding actinide(111) compounds (reaction 2).
+600
+400
0 -200
-400 -600
Th Pa
U
Np Pu Am Cm B k C f
Es Fm Md N o
L r 104
Figure 4. Predicted standard enthalpies of decomposition (kJ mol-') of
actinide(1V)compounds to the corresponding actinide(II1)compounds with liberation of nonmetal (reaction 3). 2. decomposition of an actinide(1V) compound to the corresponding actinide(II1) compound with liberation of nonmetal: MIv -+ MI11 + X (3)
Because the reactants and products in reaction 2 are all solids, the associated entropy change should be near zero and AGO and AHo should be similar. This is also the case for reaction 3 when X = I or S. When X = F, C1, Br (to some extent), or 0, the entropy change associated with reaction 3 should be positive and AGO should be more negative than AH'. The standard enthalpy changes predicted for reactions 2 and 3 are plotted in Figures 3 and 4, respectively. On the basis of these figures, some general statements may be made concerning the relative stabilities of actinide(II), -(III), and -(IV) compounds.
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 311
Actinide Thermodynamic Predictions TABLE VI: Predicted Standard Cibbs Free Energies of Formation of Actinide 2+, 3+, and 4+ Aquo Ions (kJ mol-', 298.15 K) AGfo(M2',aq) AGfo(M3+,aq) M a b C a d AGFo(M4+,aa)a Ra -534 Ac
Th
Pa U NP
Pu Am Cm Bk
Cf Es
Fm Md No Lr 104
-167 +50 -20 -63 -149 -29 1
-300
-90
-148
-160
-103 -34
-360
-196 -24 1 -272 -276
-223
-266
-301 -405
-238 -213 -21 1
-433 -445
-458 -476 -29 1 -2
-200 -120 -19 -214
-614 -317 -41 1 -477
-416 -399
-704 -606
-360
-539
-516
-497
-571
-475
-590 -586
-356
-574
-416 -250 -1 16
-563 -554 -547 -476 -351 -546
-169
-298
-6 1 +5 1 +282 +233 -312
+8.0
-
+6.0 +4.0
-
+2 .o
-
0-
- 2.0 -
,
-4.01 Ac
Th Pa
,
,
I
I
I
Np P u
U
, , , , ,
I
,
,
I
Es F m M d No Lr 104
Am Cm B k C f
Figure 5. Predicted one-step standard electrode potentials, E0(M4+/M3') and E0(M3+/M2') (V). - 1
I
Using lowest energy (ground-state electron configuration) AGfo(M2+,g,6d')from ACro(M2+,g)from Table 11; no LFSE. Table I1 and subtracting 140 kJ mol-' for LFSE (see text). CUsing AGfo(M2+,g,6d2) from Table I1 and subtracting 200 kJ mol-' for LFSE (see text). "Using AGfo(M3+,g,6d')from Table I1 and subtracting 210 kJ mol-' for LFSE (see text).
The order of stability of the actinide(I1) compounds with respect to reaction 2 is N o > Md > Fm > Es > Cf > Am > others. In terms of an ionic model, Mz+ is stabilized by large anions with low charge (Cl-, Br-, I-) and destabilized by small anions with As with the lanthanides, even if an authentic high charge (02-). actinide(I1) compound is predicted to be unstable with respect to disproportionation, the same stoichiometry may still exist in a "metallic" m~dification.~ Therefore, the existence of compounds such as Th12 or PUS (which probably contain ThIV and PulI1, respectively) should not be surprising. Actinide(II1) compounds are usually stable with respect to neighboring oxidation states, although the 3+ state does not achieve the same level of importance as it does in the lanthanide series (where only Eu13 is unstable3). According to our calculations, all Th"', Par1', and 104"' compounds, as well as U z 0 3and Np203,should disproportionate to the metal and the corresponding actinide(1V) compounds. Also, MdI,, NoC13, NoBr,, NoI,, and No2S3 should decompose to the corresponding actinide(I1) compounds with liberation of nonmetal. The order of stability of the actinide(1V) compounds with respect to reaction 3 is Th > 104 I Pa > U > N p > Pu > Bk > Am > Cm > others. In terms of an ionic model, M4+ is stabilized most by small anions of very electronegative nonmetals (F,02-). Thus, actinide tetrafluorides and dioxides are known for at least as far into the actinide series as Cf, although other actinide tetrahalides and actinide disulfides are known only as far as U, Np, or Pu. If the AH,' values presented in Tables 111-V indicate a compound to be of borderline stability with respect to a neighboring oxidation state, it must be borne in mind that the uncertainty in the AHo of decomposition to the other state depends on the cumulative uncertaintites of the individual AHf' values. Also, entropy effects may be the determining factor in the stabilization or destabilization of a borderline case.
Predicted Standard Gibbs Free Energies of Formation of Actinide 2+, 3+, and 4+ Aquo Ions and Predicted Standard Electrode Potentials at 298.15 K Standard Gibbs free energies of formation of actinide 2+, 3+, and 4+ aquo ions may be calculated from the data in Table I1 and the equations given in ref 4; the results are assembled in Table VI. As expected, they agree well with the literature data,7*8J-23 usually within 10 kJ mol-', because the latter have been a primary basis for the evaluation of gas-phase thermodynamic properties (Table 11).
. -30
I
, ,
Ra A c
Th
,
I
Pa
V
, , Np
, ,
,
P u Am C m B k
,
,
Cf
Es
1
,
i m Md
, No
, L r '04
Figure 6. Predicted overall standard electrode potentials, Eo(Mz'/M) (VI.
An actinide 2+ ion with a 6dl electron configuration is subject to significant ligand field effects when placed in chemical environments. The standard enthalpies and Gibbs free energies of formation of chemical species containing such M2+ions are more negative than otherwise anticipated, the difference being the ligand field stabilization energy, LFSE. The spectroscopic analysis of Nugent et and the standard electrode potentials Eo(M3+/ M2+)compiled recently by M i k h e e indicate ~ ~ ~ LFSE(MZ+,aq,6d') to be somewhat greater than the lanthanide LFSE(M2+,aq,5d1). To be consistent with our previous work,4 we adopt LFSE(M2+,aq,6d') = 140 f 30 kJ mol-'. From Table VI, it may be seen that the 2+ aquo ions of Ac, Pa, U, Np, and Cm are predicted to be most stable with a 6d' electron configuration. There are two additional cases where 6d ligand field effects should be operational. The first case involves an actinide 3+ ion with a 6d' electron configuration. Simple electrostatic conside r a t i o n ~indicate ~ ~ ~ that LFSE for such an ion should be 50% greater than for an isoelectronic 2+ ion. Therefore, we adopt LFSE(M3+,aq,6d1)= 210 f 50 kJ mol-'. The second case involves an actinide 2+ ion with a 6d2 electron configuration. As a rough estimate we adopt LFSE(M2+,aq,6d2)= 200 50 kJ mol-I. From Table VI, only the aquo ions of Th are affected by these refinements, the free-ion promotion energies for other actinides being too large (Table 11). Predicted Eo values connecting various oxidation states are ~~~'~~~~~~ listed in Table VII; agreement with the l i t e r a t ~ r eis~usually within 0.1-0.2 V for the 4+/3+ and 3+/2+ potentials, and within 0.05 V for the 2+/0, 3+/0, and 4+/0 potentials. Larger discrepancies (about 0.3 V) are associated with the least reliable (most negative) 3+/2+ potentials reported by M i k h e e ~ Trends .~~ in Eo are illustrated in Figures 5 and 6.
*
Differences between Lanthanide and Actinide Chemistry: Relativistic Effects In recent years it has become evident that the properties of heavy elements are best explained by relativistic quantum me-
312 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 TABLE VII: Predicted Standard Electrode Potentials (V, M M4+/M'+ M3+/M2+ M2+/M M3*/M Ra -2.77 Ac -3.3' -1.55' -2.12 Th -3.0' -2.8',d -0.77d -1.44' Pa -2.0 -2.6' -0.83' -1.42 U -0.6 -2.9' -1.02' -1.65 Np +0.2 -2.9' -1.25' -1.78 Pu +1.0 -2.9 -1.51 -1.97 Am +2.4 -2.4 -1.87 -2.04 Cm +3.0 -3.3' -1.38' -2.02 Bk +1.6 -2.8 -1.56 -1.98 Cf +3.2 -1.6 -2.10 -1.95 Es +4.5 -1.3 -2.24 -1.91 Fm +5.0 -1.1 -2.31 -1.89 Md +5.5 -0.2 -2.37 -1.64 No +6.6 f1.3 -2.47 -1.21 Lr +8.1 -2.6 -1.51 -1.89 104 -1.5 -1.7 0.0 -0.6
298.15 K)' M4+/M
-1.82 -1.57 -1.40 -1.29 -1.23 -0.92 -0.77 -1.08 -0.65 -0.30 -0.16 +0.13 +0.73 +0.60 -0.8
"Using the most negative bCfo(Mz+,aq)from Table VI. *M3+(aq) is predicted to have a 6d' electron configuration. 'MZ+(aq) is predicted to have a 6d1 electron configuration. dMZ+(aq)is predicted to have a 6d2 electron configuration.
Bratsch and Lagowski V), because Th has been used as an auxiliary element in deriving the correlation parameters. We have not adjusted the predictions in Tables I11 and IV because we wish to maintain internal consistency with our lanthanide correlation^,^,^ and because the exact magnitude of the adjustment, or even its existence in the case of actinide( 11) compounds, it open to question.
The P ( M ) Function An important correlation technique for lanthanide and actinide thermodynamics was developed by Nugent, Burnett, and M ~ r s s . ~ ' They defined a function P(M): P(M) = AHfo(M,g)
+ AE(M) - AHf0(M3+,aq)
(4)
AE(M) is the promotion energy from the ground-state electron configuration to the fqd1s2configuration, where q varies from 0 (La, Ac) to 14 (Lu, Lr). This promotion energy is zero or near zero for the elements La, Ce, Gd, Lu, Ac, Pa, U, Np, Cm, and Lr; for other elements it is positive and usually accurately known from spectroscopic measurement^.',^^ Nugent et aL3?found that a plot of the lanthanide P(M) values vs. q is roughly V-shaped with a break at q = 7 (Gd). They attributed deviations from the plot to the tetrad e f f e ~ t . ~They ~~~* also found that the light actinides fall on a separate but parallel plot. By assuming a parallelism throughout the actinide series (including a break at q = 7 Cm)), they predicted AHf0(M3+,aq) for all actinides. Subsequent electrochemical and thermochemical measurements for certain heavy actinides prompted David and co-workers7~*to reevaluate the actinide P(M) function. They found it to remain approximately linear throughout the actinide series, with no break at q = 7. Although they derived more reliable AHfo(M3+,aq) values for the heavy actinides, they did not attempt to explain the difference in shape between the lanthanide and actinide P(M) functions. 1. According to our m0de1~9~
chanical t h e ~ r y . ~A~ primary - ~ ~ relativistic effect occurs when the strongly penetrating s and p electrons are accelerated by a heavy nucleus to velocities comparable to that of light. This results in a relativistic increase in electron mass which causes a contraction and lowering in energy of the s and p atomic orbitals. The more efficient screening of the nucleus by the s and p electrons produces a secondary relativistic effect, an expansion and raising an energy of the d and f atomic orbitals. It appears that most of the differences between lanthanide and actinide chemistry may be qualitatively explained through relativistic arguments. For example, IP, and IP2 are somewhat higher for the actinides than they are for their lanthanide analogues, IP3 are similar, and IP, (and presumably higher IP) are considerably AHfo(M3+,aq)(kJ mol-') = lower (ref 3 and Table I). This relationship is expected, because 613.4 Mf0(M3+'g) - rM3+ 0.0784 - 1293.6 = the first two ionizations usually involve s electrons, while the third, fourth, and subsequent ionizations usually involve f electrons. As a chemical consequence, some the actinides can exist in much higher oxidation states than any of the lanthanides.7~8*21*22,27d.28b The half-shell drop in IP3 and IP4 is over 4 eV in the lanCombination of eq 4 and 5 gives t h a n i d e ~but ~ only about 1.2 eV in the actinides (Table I). The P(M) (kJ mol-') = greater spatial extension of the actinide 5f orbitals compared with 613.4 the lanthanide 4f orbitals, largely a secondary relativistic effect, - 3 rM3++ 0.0784 1275.0 (6) results in a lower pairing energy. As a result, a more nearly smooth variation is observed in the relative stabilities of adjacent oxidation Based on eq 6, we offer the following analysis of the P(M) states (2+ vs. 3+, 3+ vs. 4+, etc.) across the actinide series.29b function: Spitsyn et al.36have suggested that the smaller electrostatic in1. Lanthanides and actinides fall on separate plots (although teraction of the 5f electrons may also be responsible for the absence parallel in the first halves of the series) because AE(M) of a significant break in actinide ionic radii at the half shell. C:IP(M) are not identical for a lanthanide and an actinide with The greater spatial extension of the actinide 5f orbitals increases the same value of q. their susceptibility to environmental effects, such as covalent 2. The lanthanide P(M) function is V-shaped because of the bonding.28b Thus, our assumption that the energy contributions break in ionic radius at q = 7. The actinide P(M) function is from covalent bonding depend only on ionic r a d i ~ sbegins ~ . ~ to continuous because no significant break in ionic radius occurs in lose its validity in the actinide series. This might explain why the the actinides at q = 7.36 calculated AHf' values of actinide(II1) compounds (Table IV) 3. Deviations from the P ( M ) plots could be d u e to irregularities tend to be about 20 kJ mol-' less negative than the experimental (or uncertainties) in AE(M) - C:IP(M) and do not necessarily value^.^^^^' It is suspected that a discrepancy of similar magnitude reflect the tetrad e f f e ~ t . ~ ~ , , ~ may be found for actinide(I1) compounds (Table 111) when experimental data become available. On the other hand, this type Acknowledgment. We are grateful for the generous financial of discrepancy does not exist for actinide(1V) compounds (Table support provided by the Robert A. Welch Foundation (Grant No. F081).
+
+
(32) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271. (33) Pyykko, P.; Desclaux, J. P. Acc. Chem. Res. 1979, 12, 276. (34) Ionova, G. V.; Pershina, V. G.; Spitsyn, V. I. Zh. Neorg. Khim. 1983, 28, 3107. (35) McKelvey, D. J . Chem. Educ. 1983, 60, 112. (36) Spitsyn, V. I.: Vokhmin, V. G.; Ionova, G. V. Zh. Neorg. Khim. 1983, 28, 1638.
+
(37) Nugent, L. J.; Burnett, J. L.; Morss, L. R. J . Chem. Thermodyn. 1973, 5, 665.
(38) Bratsch, S . G. Chem. Phys. L e f f .1983, 98, 113. (39) Nugent, L. J. J . Inorg. Nucl. Chem. 1970, 32, 3485. (40) Fidelis, I. K.; Mioduski, T. J. In "Structure and Bonding", Clarke, M. J., Ed., Vol. 47; Springer-Verlag: New York, 1981; pp 27-51.
