HEAT OF HYDROLYSIS OF URANIUM (IV) IN PERCHLORIC ACID SOLUTIONS1 ABSTRACT The heat of hydrolysis of uranium (IV) in perchloric acid solution has been measured by a spectrophotometric technique. A value of 10.7f 1 kcal. per mole was obtained, in good agreement with a previous value determined by a calorimetric method. The entropy of association of uranium (IV) with hydroxyl ion is $52 e.u. INTRODUCTION In a kinetic study of the oxidation of uranium (IV) by iron (111) (I), a value was required for the heat of hydrolysis of uranium (IV). This quantity, AH, is related to the temperature variation of the hydrolysis constant IC for reaction [I] according to d(ln K)/dT = AH/RT". U4++H?0 S UOH3++H+ The hydrolysis constant K is defined by: (UOH3+)(H+)/(U4+) = K, where the brackets indicate concentrations in gram-ions per liter. A value of 11 kcal./mole has been reported for AH (2). This result is based on the difference between the measured heats of solution of solid uranium tetrachloride in 0.5 M perchloric acid and in water. The accuracy of the value obtained by this method depends on the assumptions that: (i) UOH3+ is the only species of uranium (IV) in very dilute acid solutions, (ii) U4+ is the only uranium species in 0.5 Ad perchloric acid solution, and (iii) chloride ion does not form complex ions with uranium (IV). However, Kraus and Nelson (3) have shown in a careful study of equilibrium [l] at 25OC. that none of these assumptions is strictly correct. Further, the precision of the value of I1 kcal./mole depends on a single measurement of the heat evolved when uranium tetrachloride is dissolved in water (2). In the present work, the value of AH has been calculated more directly from measurement of the hydrolysis constant I< as a function of temperature. The method used depends on measurement of the changes in optical density of partially hydrolyzed uranium (IV) solutions with temperature, and is based on the technique described in Reference (3). The pri~lciple of the method may be summarized. The optical density D for a 1-cm. thickness of solution containing U4+ and UOH3+ as the only light-absorbing species is D = (Ut+)E4+ (UOH3+)E3, where E3 and E4 are the extinction coefficients of UOH3+ and U4+, respectively, [3 I 'Manuscript received Az~gust 4, 1955. Contribution front the Chemistry and imetallurgy Division, Atonzic Energy of Canada Limited, Chalk River, Ontario. Isszced as A.E.C.L. No. 235.
1776 CANADIAN JOURNAL OF CHEMISTRY. VOL. 33 for the wave length used. If the total concentratioil of uranium (IV) is a molar, then the hydrolysis constant R is given by: K = (H+)(E?-Eobs)/(Eobs-E3), [4 I where Eobs = observed extinction coefficient = D/a. It follows from equation [4] that if E 4 and E3 are kno~vn, measuremeilts of Eobs and (H+) permit the calculation of K. Icraus and Nelson (3) have shown that their data at 648 mp (the wave length at the maximum of a characteristic U4+ absorption peak) are best described by E4 = 60.0 and E3 = 6.1, independent of ionic strength. The principal assumption made in the applicatioil of this method to the present work is that the activity coefficient terms, which are implicit in the definition of the hydrolysis constailt by equation [2], are unaffected by changes in temperature between 15.2"C. and 247 C. The assumption, although not strictly correct, is frequently made in other studies of similar equilibria (see, for example, Reference (4)). A second assumption is that the extinction coefficients E3 and E4 are temperature-independent. Further discussion bearing on this latter assumption is given below. EXPERIMENTAL Solutions of UIV of the desired coilcentration and acidity were prepared by dilution of weighed portions of a stock solution 0.0787 &I in UIV, 1.010 im in perchloric acid. Other details of the preparation and analysis of the solutions are given elsewhere (1). Two series of experiments have been made. (i) The first set were carried out with 2.44 Ad perchloric acid. At this coilcentration of acid, the hydrolysis of U4+ is very largely suppressed (K 0.01 at 25 C. (3)). Such measurements served therefore to fix the value of E4, the extinction coefficient of U"+. (ii) The second set of experiments, made with 0.104 M perchloric acid, provided the values of Eob, required for the calculation of K as a function of temperature. The optical measurements were made with a Beckman DU spectrophotometer. The instrument was adapted to permit coiltrol of the temperature of solutioils in the cell compartment to &0.05"C. in the temperature range used here. The optical density at 648 mp was read vs. a blank cell coiltaining either 0.10 M or 2.44 M perchloric acid. The two 1-cm. cells used were matched to =to.lyo trailsmission at this wave length. The optical density for solutions 2.44 M in perchloric acid showed no tendency to drift with time. However a slight decrease with time was noted for the solutions 0.104 M in perchloric acid, presumably as a result of slow air oxidation of UIV which is known to occur more readily in solutions of low acidity. For these samples, the readings of optical density vs. time were extrapolated back to the time of preparation of the samples. These extrapolated values never differed by more than 0.5% from the optical density first recorded. RESULTS AND DISCUSSION Tables I and I1 give the relevant data for solutions 2.44 im and 0.104 M in
BETTS: HEAT OF HYDROLYSIS OF UR.4NIUM (IV) 1777 perchloric acid. The excellent agreement of our value of 59.9f 0.05 for E4 at 2Z C. with the value of 60.0 (3) is to be noted (Table I). However, the apparent dependence of E4 on temperature (-0.2% per degree) shown in Table I is unexpected. To account for this relatively large change in the optical density on the basis of hydrolysis alone, it would be necessary to assume that the true value of E4 is 63 or 64, and that K = 0.14 at 25OC. Such a value of K is 10 to 15 times higher than one would expect from the careful work of Icraus and Nelson. A more reasonable explanation is that I< is indeed of the order of 0.01 at 25"C., and that the extinction coefficient of U4+ is temperature dependent. This uncertainty in interpretation fortunately does not appreciably alter the value of AH calculated from the experimental results. (See below.) TABLE I EXTINCTION IN 2.44 ilf PERCHLORIC ACID COEFFICIENTS:~ OF URANIU~I (IV) Temp., OC. M UIV (X103) En En (average) 24.7 8.56 50.0 24.7 8.57 60.0 20.4 8.47 60.4 20.1 8.52 60.6 15.2 8.51 61. It 15.2 8.49 61.3 50.05 60.5 61.2 Ionic slrengtlz = 2.55. "For X = 648 7np. tthis sanzple was healed Lo 24.7OC., and gave E4 = 59.9. On cooling again lo 15.2OC., E., = 61.5, indicating a reversi6le change. TABLE I1 EST~NCTION COEFFICIENTS* OF URANIUM (IV) IN 0.10-i nf PBRCNLORlC ACID Temp., OC. ilf UIY (X lo3) E01~4 Eohs (average) Ionic strength = 0.19 (inclzbding contri6z~tion from U(C104)n). *For X = 648?np. Table I11 gives the values of the hydrolysis constants calculated from the experimental results by means of equation 141. Since Eobs >> E3, an error of ~20% in Es has only a small effect on AH, and the Kraus and Nelson value of 6.1 (3) has therefore been accepted for this constant. Because of the uncertainty regarding possible variatio~ls of E4 with temperature, K has been calculated using three sets of values for Ed. The second and third columns of Table I11 give the values of K based on E4 = 64 and 63 respectively. In the last column are shown values of K deduced on the basis that E4 is temperature-dependent. In this case, the appropriate value of E4 for each temperature is given in Table I. The values of AH listed in Table I11 were calculated from a plot of
CANADIAN JOURNAL OF CHEMISTRY. VOL. 33 TABLE 111 VALUES FOR THE EQUILIBRIUM CONSTANT AND AH FOR HYDROLYSIS OF URANIUM (IV) Temp., "C. K* Kt Kt 24.7 0.0810 0.0778 0.0680 20.4 0.0619 0.0591 0.0519 15.2 0.0450 0.0424 0.0378 AH, kcal./mo!e = 10.5 10.9 10.6 Ionic strengllz. = 0.19. *Assuming Ed = 64. tassuming E4 = 63. SAsszlming E4 is temperature-dependent. log K vs. l/t K. (Fig. 1). The values of AH obtained from these three sets of values of K are identical within experimental error, i.e., 10.7f 1.0 kcal./mole. I/TO K. IX lo5) FIG. 1. Dependence of the hydrolysis constant on temperature (Table 111). The agreement of this result with that found earlier (2) is striliing, in view of the completely different experimental methods employed; however the almost exact coincidence of the two values must be regarded as fortuitous.* Table I11 shows that K is about 0.075 at 24.7OC., the exact value depending on the value of Eq assumed. For comparison, the Kraus and Nelson result (3) is 0.05 at 25OC., for ionic strength 0.19. This agreement is as good as can be *NOTE ADDED IN PROOF: In a paper pt~blished after complelion of present nzanuscript, Kraus and lvelson (J. Am. Cl~em. SOC. 77:372?1. 1955) report AH=l1.7 kcal./n7ole for heal of I~ydrolysis of z~ranium (IV) z12 perchlorale media, in agreement wilhvalue obtained in present work.
BETTS: HEAT OF HYDROLYSIS OF URANIUM (IV) 1779 expected, since in the present study, uranium (IV) perchlorate contributes almost 50% of the total ionic strength at p = 0.19, whereas the value of 0.05 applied to solutions in which sodium perchlorate and perchloric acid were the principal electrolytic components. The entropy of association of U4+ with a hydroxyl ion can now be estimated. For this purpose the hydrolysis constailt at zero ionic strength, I<,, must be used- 0.21k0.02 at 25OC. (3). Using the relation AFO = -RT In I<,, and AFO = AH0-TASO, AS0 and AFO at 25OC. are found to be f33 e.u. and f0.92 kcal./mole, respectively. These values refer to reaction [I] above. This result may be combined with the dissociation equilibrium of water (4) to derive the thermodynamic constants for the association reaction proper: AF", AH", ASo, kcal. kcal. e.u. The large positive value of AS0 for the association reaction is in qualitative agreement with the suggestion of Rabinowitch and Stocltmayer (4), viz., the partial neutralization of charge which occurs releases water molecules from the hydration shells around the separated ions, and thereby increases the disorder (and hence the entropy) of the system as a whole. REFERENCES 1. BETTS, R. H. Can. J. Chem. 33: 1780. 1955. 2. FONTANA, B. J. Declassified Report MDDC 1452. U.S. Atomic Energy Comm., Oak Ridge, Tennessee. 3. I~RAUS, K. A. and NELSON, F. J. Am. Chem. Soc. 72: 3901. 1950. 4. RABINOWITCH, E. and STOCKMAYER, W. H. J. Am. Chem. Soc. 64: 335. 1942.