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Free energy of plutonium polymer formation
Journal
317
of the Less-Common Metals, 91(1983) 317-320
FREE ENERGY
OF PLUTONIUM
POLYMER
FORMATION
G. L. SILVER
Monsanto Research Corporation, Mound, Miamisburg, OH 45342(U.S.A.) (Received August 13,198Z; in revised form November 2,1982)
Summary The free energy of plutonium polymer is estimated as about -341.9 kcal mol- ‘. The solubility product of Pu(OH), corresponding to this number is 2.5 x lo- 56.
A form of plutonium which continues to attract attention is the “polymer”. The analysis of X-ray patterns suggested many years ago that the polymer is the hydrous dioxide dispersed as a colloid [l, 23. Research has indicated that the nature of the polymer depends upon the environment in which it forms, so that properties reported for the polymer are not always in agreement [a]. These observations have been analyzed by Davydov [3], who makes the point that no precisely fixed solubility product (or free energy of formation) is likely to be obtained for this material. The virtues of Davydov’s arguments notwithstanding, it seems desirable to obtain an estimate of the free energy of plutonium polymer so that understanding of this material might be enhanced. From time to time reports have appeared on the conditions of plutonium concentration, oxidation number and pH at the point of “incipient” polymer formation. By “incipient” it is implied that the reaction dissolved plutonium
+ polymer
(1)
is close to equilibrium. At equilibrium, AG for reaction (1) is zero. By various dilutions of a nitric acid solution of concentrated tetravalent plutonium, and by allowing the diluted solutions to equilibrate for 4 days, Brunstad [l] was able to characterize the “incipient point” of eqn. (1). Since tetravalent plutonium disproportionatea in dilute acids, eqn. (1) can be rewritten symbolically as follows: [PI?‘]
+ [PI?“] + [Pu’]
+ (4T-~[Pu”]
+ [Pu”‘] + [PuOH3 +] +
-2[Pu”‘]
- [PuOH3 +])[H,O]
= Pu(OH), + (4T-4[Pu”] 0022-5088/83/oooO-O/$03.00
-4[Pu”‘]
- [PuOH3 +])[H +] 0 Elievier Sequoia/Printed
(2) in The Netherlands
318
Equation (2) reflects the fact that, at equilibrium, a plutonium solution which is not pure plutoni~(II1) or pure plutonium~1) always consists of a mixture of four oxidation states. In the conversion of plutonium to polymer, as represented by the formula Pu(OH),, water is required as the source of the oxygen which is found in the polymer. However, 4 mol of water are not required per mole of plutonium (as might be imagined by the representation of the process as Pu4+ +4H,O + Pu(OH~~+~H’~ because the species PuOz+, PuOz2+ and PUN +, which are always present at equilibria, already contain oxygen. Similarly, less than 4 mol of acid per mole of plutonium are generated by the equilibrium process because some of the hydrogen ions generated are used in the reduction of PuO,+ and PuO,‘+ to the tetravalent state and PUN+ is already partially hydroxylated. In eqn. (2) the symbol T represents the total quantity of plutonium converted to the polymer, and a term such as [Put*‘] represents the quantity of trivalent plutonium, at its equilibrium concentration, which has been converted. Terms containing [H,O] and [H’] represent the solvent consumed and the acid generated respectively in the equilibrium process described by eqn. (2), and the term Pu(OH), represents the colloidal polymer. Since eqn. (2) represents the equilibria condition, it can be rewritten as Gpolymer = GIII+ G,, + G, + GVI+ GIVoH+ (4T- 2[Vj - 2[VI] - OV(OH)3 “1) x x (-56.69)-(4T-4[V]
-4[VI] - [IV(OH)3+])G,+
(3)
where G stands for the free energy, Roman numerals represent the corresponding plutonium oxidation states, -56.69 is the molar free energy of formation of water in kilocalories per mole, @V(OH)3’] represents PuOH3’ and H+ represents the hydrogen ion. Table 1 lists the free energy of the plutonium polymer as calculated by applying eqn. (3) to Brunstad’s data. The nitrate complexes of the various plutonium oxidation states were neglected in this calculation because the formation constants of these complexes are unreliable (ref. 2, pp. 99,110). However, the solutions studied by Brunstad were dilute in both plutonium and nitrate, and some of these complexes are only very weakly associated (ref. 2, p. 131). The equilibrium oxidation state distributions given in Table 1 (which were used in calculating the G values) were computed as described elsewhere [4-S]. The standard free energy of formation of the trivalent plutonium cation was taken as - 138.3kcal mol- ’ [7]. Other standard G” values for the plutonium ions were calculated from this value using the potential scheme given by Cleveland (ref. 2, p. 20) and Silver [S]. It can be seen in Table 1 that the G values for the polymer cluster around -341.96 kcal mol-‘. The reader may wish to make his own selection of data for these calculations but is warned that much available data purporting to represent oxidation number N = 4.66 show substantial deviations from charge conservation ([Pu”‘] = CPU’] + ~[Pu”‘]) as required by this oxidation number. Such data are not appropriate for analyses using eqn. (3). (The foregoing relation can be derived by consideration of the fate of the electrons which are exchanged among the plutonium ions during the disproportionation of pure tetravalent plutonium [4]. Alternatively, it can be obtained from the condition
319
TABLE 1 Free energy G of the plutonium polymer neglecting states (IV(OH) E PuOH’ ‘)
Solution acidity
nitrate complexes
Pu concentration W
Fractional oxidation state distribution
0.12
4.184 x 1o-3
0.16
8.368 x10-3
0.20
2.092 x 1o-2
0.26
4.184 x lo-*
0.32
6.276 x lo-’
III = 0.54317 IV = 0.11529 V = 0.08225 VI 3 0.23046 IV(OH) = 0.02882 III = 0.51823 IV = 0.16420 v = 0.05534 VI = 0.23144 IV(OH) = 0.03079 III = 0.49121 IV = 0.21159 v 3 0.03970 VI = 0.22575 IV(OH) = 0.03174 III = 0.45121 IV = 0.27803 V = 0.02613 VI = 0.21254 IV(OH) s 0.03208 III = 0.41402 IV = 0.33810 V = 0.01835 VI = 0.19783 IV(OH) s 0.03170
of the plutonium oxidation
G (kcal
mol- ‘)
(M) -341.90
-341.96
-341.80
- 341.84
-341.98
of charge conservation which always applies to isolated plutonium solutions (given as eqn. (6a) in ref. 9) by substituting for Nthe value 4.00.) The free energy of the hydrous dioxide when calculated from a widely quoted value of its solubility product (7 x 10-56) (ref. 2, p. 311) is about -341.28 kcal mol- I. Experience suggests that AG for polymer formation is more negative than AG for the precipitated hydrous dioxide (just as is reflected by this number and the G values in Table 1) because dilute plutonium solutions subjected to a slow increase in pH generally show evidence of polymer formation before precipitation of the hydrous dioxide. If the stoichiometry of the polymer is represented by the formula Pu(OH), for the purposes of calculations, the freeenergy estimate of -341.90 kcal mol-’ implies a solubility product for the polymer of about 2.5 x lo- 56. This value may be useful when studying plutonium in the environment, as environmental plutonium is sometimes thought to be in equilibrium with the polymer. The reader confronted with the problem of estimating the solubility product of the polymer or the hydrous dioxide in a plutonium solution of
arbitrary oxidation number N(3 < N < 6) can make the estimation by calculating the equilibrium concentration of Pu4+ in the solution [5, 61 and then multiplying this number by the hydroxide ion concentration raised to the fourth power. If the solution oxidation-reduction potential is known, another method [lo] can be used to calculate the concentration of the tetravalent plutonium cation.
Acknowledgment Mound is operated by the Monsanto Research Corporation Department of Energy under Contract DE-AC04-76-DPOO053.
for the U.S.
References 1 A. Brunstad, Znd. Eng. Chem., 51(1959) 38. 2 J. M. Cleveland, The Chemistry of Plutonium, Gordon and Breach, New York, 1970, Section 4.2. 3 Yu. P. Davydov, Radiokhimiya, 9 (1967) 52. 4 G. L. Silver, J. Znorg. NucZ. Chem., 33(1971) 577,400O. 5 G. L. Silver, J. Radioanal. Chem., 23(1974) 195. 6 G. L. Silver, Radiochim. Acta, 21(1974) 54. 7 J. Fuger and F. L. Oetting, The Chemical Thermodynamics of Actinide Elements and Compounds, Part 2, The Actinide Aqueous Zons, International Atomic Energy Agency, Vienna, 1976. 8 G. L. Silver, J. Znorg. Nucl. Chem., 43(1981) 2997. 9 G. L. Silver, J. Znorg. Nucl. Chem., 36(1974) 939. 10 G. L. Silver, Mar. Chem., 12(1983) 91; Plutonium Chemistry, Am. Chem. Sot. Symp. Ser., 216 (1983), round table discussion.
317
of the Less-Common Metals, 91(1983) 317-320
FREE ENERGY
OF PLUTONIUM
POLYMER
FORMATION
G. L. SILVER
Monsanto Research Corporation, Mound, Miamisburg, OH 45342(U.S.A.) (Received August 13,198Z; in revised form November 2,1982)
Summary The free energy of plutonium polymer is estimated as about -341.9 kcal mol- ‘. The solubility product of Pu(OH), corresponding to this number is 2.5 x lo- 56.
A form of plutonium which continues to attract attention is the “polymer”. The analysis of X-ray patterns suggested many years ago that the polymer is the hydrous dioxide dispersed as a colloid [l, 23. Research has indicated that the nature of the polymer depends upon the environment in which it forms, so that properties reported for the polymer are not always in agreement [a]. These observations have been analyzed by Davydov [3], who makes the point that no precisely fixed solubility product (or free energy of formation) is likely to be obtained for this material. The virtues of Davydov’s arguments notwithstanding, it seems desirable to obtain an estimate of the free energy of plutonium polymer so that understanding of this material might be enhanced. From time to time reports have appeared on the conditions of plutonium concentration, oxidation number and pH at the point of “incipient” polymer formation. By “incipient” it is implied that the reaction dissolved plutonium
+ polymer
(1)
is close to equilibrium. At equilibrium, AG for reaction (1) is zero. By various dilutions of a nitric acid solution of concentrated tetravalent plutonium, and by allowing the diluted solutions to equilibrate for 4 days, Brunstad [l] was able to characterize the “incipient point” of eqn. (1). Since tetravalent plutonium disproportionatea in dilute acids, eqn. (1) can be rewritten symbolically as follows: [PI?‘]
+ [PI?“] + [Pu’]
+ (4T-~[Pu”]
+ [Pu”‘] + [PuOH3 +] +
-2[Pu”‘]
- [PuOH3 +])[H,O]
= Pu(OH), + (4T-4[Pu”] 0022-5088/83/oooO-O/$03.00
-4[Pu”‘]
- [PuOH3 +])[H +] 0 Elievier Sequoia/Printed
(2) in The Netherlands
318
Equation (2) reflects the fact that, at equilibrium, a plutonium solution which is not pure plutoni~(II1) or pure plutonium~1) always consists of a mixture of four oxidation states. In the conversion of plutonium to polymer, as represented by the formula Pu(OH),, water is required as the source of the oxygen which is found in the polymer. However, 4 mol of water are not required per mole of plutonium (as might be imagined by the representation of the process as Pu4+ +4H,O + Pu(OH~~+~H’~ because the species PuOz+, PuOz2+ and PUN +, which are always present at equilibria, already contain oxygen. Similarly, less than 4 mol of acid per mole of plutonium are generated by the equilibrium process because some of the hydrogen ions generated are used in the reduction of PuO,+ and PuO,‘+ to the tetravalent state and PUN+ is already partially hydroxylated. In eqn. (2) the symbol T represents the total quantity of plutonium converted to the polymer, and a term such as [Put*‘] represents the quantity of trivalent plutonium, at its equilibrium concentration, which has been converted. Terms containing [H,O] and [H’] represent the solvent consumed and the acid generated respectively in the equilibrium process described by eqn. (2), and the term Pu(OH), represents the colloidal polymer. Since eqn. (2) represents the equilibria condition, it can be rewritten as Gpolymer = GIII+ G,, + G, + GVI+ GIVoH+ (4T- 2[Vj - 2[VI] - OV(OH)3 “1) x x (-56.69)-(4T-4[V]
-4[VI] - [IV(OH)3+])G,+
(3)
where G stands for the free energy, Roman numerals represent the corresponding plutonium oxidation states, -56.69 is the molar free energy of formation of water in kilocalories per mole, @V(OH)3’] represents PuOH3’ and H+ represents the hydrogen ion. Table 1 lists the free energy of the plutonium polymer as calculated by applying eqn. (3) to Brunstad’s data. The nitrate complexes of the various plutonium oxidation states were neglected in this calculation because the formation constants of these complexes are unreliable (ref. 2, pp. 99,110). However, the solutions studied by Brunstad were dilute in both plutonium and nitrate, and some of these complexes are only very weakly associated (ref. 2, p. 131). The equilibrium oxidation state distributions given in Table 1 (which were used in calculating the G values) were computed as described elsewhere [4-S]. The standard free energy of formation of the trivalent plutonium cation was taken as - 138.3kcal mol- ’ [7]. Other standard G” values for the plutonium ions were calculated from this value using the potential scheme given by Cleveland (ref. 2, p. 20) and Silver [S]. It can be seen in Table 1 that the G values for the polymer cluster around -341.96 kcal mol-‘. The reader may wish to make his own selection of data for these calculations but is warned that much available data purporting to represent oxidation number N = 4.66 show substantial deviations from charge conservation ([Pu”‘] = CPU’] + ~[Pu”‘]) as required by this oxidation number. Such data are not appropriate for analyses using eqn. (3). (The foregoing relation can be derived by consideration of the fate of the electrons which are exchanged among the plutonium ions during the disproportionation of pure tetravalent plutonium [4]. Alternatively, it can be obtained from the condition
319
TABLE 1 Free energy G of the plutonium polymer neglecting states (IV(OH) E PuOH’ ‘)
Solution acidity
nitrate complexes
Pu concentration W
Fractional oxidation state distribution
0.12
4.184 x 1o-3
0.16
8.368 x10-3
0.20
2.092 x 1o-2
0.26
4.184 x lo-*
0.32
6.276 x lo-’
III = 0.54317 IV = 0.11529 V = 0.08225 VI 3 0.23046 IV(OH) = 0.02882 III = 0.51823 IV = 0.16420 v = 0.05534 VI = 0.23144 IV(OH) = 0.03079 III = 0.49121 IV = 0.21159 v 3 0.03970 VI = 0.22575 IV(OH) = 0.03174 III = 0.45121 IV = 0.27803 V = 0.02613 VI = 0.21254 IV(OH) s 0.03208 III = 0.41402 IV = 0.33810 V = 0.01835 VI = 0.19783 IV(OH) s 0.03170
of the plutonium oxidation
G (kcal
mol- ‘)
(M) -341.90
-341.96
-341.80
- 341.84
-341.98
of charge conservation which always applies to isolated plutonium solutions (given as eqn. (6a) in ref. 9) by substituting for Nthe value 4.00.) The free energy of the hydrous dioxide when calculated from a widely quoted value of its solubility product (7 x 10-56) (ref. 2, p. 311) is about -341.28 kcal mol- I. Experience suggests that AG for polymer formation is more negative than AG for the precipitated hydrous dioxide (just as is reflected by this number and the G values in Table 1) because dilute plutonium solutions subjected to a slow increase in pH generally show evidence of polymer formation before precipitation of the hydrous dioxide. If the stoichiometry of the polymer is represented by the formula Pu(OH), for the purposes of calculations, the freeenergy estimate of -341.90 kcal mol-’ implies a solubility product for the polymer of about 2.5 x lo- 56. This value may be useful when studying plutonium in the environment, as environmental plutonium is sometimes thought to be in equilibrium with the polymer. The reader confronted with the problem of estimating the solubility product of the polymer or the hydrous dioxide in a plutonium solution of
arbitrary oxidation number N(3 < N < 6) can make the estimation by calculating the equilibrium concentration of Pu4+ in the solution [5, 61 and then multiplying this number by the hydroxide ion concentration raised to the fourth power. If the solution oxidation-reduction potential is known, another method [lo] can be used to calculate the concentration of the tetravalent plutonium cation.
Acknowledgment Mound is operated by the Monsanto Research Corporation Department of Energy under Contract DE-AC04-76-DPOO053.
for the U.S.
References 1 A. Brunstad, Znd. Eng. Chem., 51(1959) 38. 2 J. M. Cleveland, The Chemistry of Plutonium, Gordon and Breach, New York, 1970, Section 4.2. 3 Yu. P. Davydov, Radiokhimiya, 9 (1967) 52. 4 G. L. Silver, J. Znorg. NucZ. Chem., 33(1971) 577,400O. 5 G. L. Silver, J. Radioanal. Chem., 23(1974) 195. 6 G. L. Silver, Radiochim. Acta, 21(1974) 54. 7 J. Fuger and F. L. Oetting, The Chemical Thermodynamics of Actinide Elements and Compounds, Part 2, The Actinide Aqueous Zons, International Atomic Energy Agency, Vienna, 1976. 8 G. L. Silver, J. Znorg. Nucl. Chem., 43(1981) 2997. 9 G. L. Silver, J. Znorg. Nucl. Chem., 36(1974) 939. 10 G. L. Silver, Mar. Chem., 12(1983) 91; Plutonium Chemistry, Am. Chem. Sot. Symp. Ser., 216 (1983), round table discussion.