Jan., 1960
THEKINETICS OF REACTION BETWEEN URANIUM(IV) AND CERIUM(IV)
109
THE KINETICS OF THE REACTION BETWEEN URANIUM(1V) ,4SD CERIUM(1V)' BY F. B. BAKER, T. W. NEWTON AKD MILTONKAHN University of California, Los Alamos Scientijc Laboratory, Los Alamos, X e w M e x i w and the University of New Mezico, Albuquerque, New Mexico Received J u l y 80, lQ6Q
The kinetics of the reaction between uranium(1V) and cerium(1V) was studied in perchloric acid-sodium perchlorate solutions a t fi = 2, over the perchloric acid concentration range 0.80 to 2.00 M. The rate for the principal react,ion path was found to be proportional to both the CeOH+* and UC4concentrations and inversely proportional to the hydrogen ion concentration. The thermodynamic quantities of activation in 2 M perchloric acid a t 2.4" were found to be AHS = 14.0 f 0.7 kcal./mole, ASS = 6.2 f 2.5 e.u., and AFS = 12.2 f 0.2 kcal./mole. A potentiometric study of the hydrolysis of cerium( IV) in the aforementioned media indicates CeOH +a to be the predominant species in solution over the perchloric acid concentration range from 0.300 to 2.00 M.
Introduction The kinetics of the oxidation of uranium(1V) by iron(III),2 ~ x y g e n ,pl~tonium(V1)~ ~ and plut o n i ~ m ( 1 V ) have ~ already been studied. The present investigation of the oxidation of uranium(IV) by cerium(1V) was undertaken to provide further kinetic information for comparison with that already available. The rate was found t o be first order with respect to both CeOH+3 and U+4 and inversely proportional to the perchloric acid concentration. Potentiometric measurements indicate that the principal cerium(1V) species is CeOH+3 in the acid concentration ranges studied.
Experimental Reagents.-Stock solutions of cerium( IV) perchlorate were prepared by electrolytic oxidation6 of cerium( 111) perchlorate, which in turn was obtained by digestion of cerium(111) oxalate in fuming perchloric acid. Small amounts of oxalate were added cautiously to the fuming acid. In general about 90% of the cerium was present as cerium(1V). The cerium( IV) concentration was determined by titration with standardized ferrous sulfate; the total cerium concentrat,ion was determined by a standard spectrophotometric procedure .7 The acid concentration of the cerium( IV) stock solution was determined by titration with standard base after removal of the tobal cerium as cerium(II1) oxalat,e. Cerium(II1) oxalate was prepared from ceric ammonium nitrate by reduction with hydrogen peroxide and subsequent, precipitation with oxalic acid. Uranium( IV) stock solutions were prepared by electrolytic reduction of uranyl perchlorate solutions, which were prepared by dissolving pure uranium oxide ( U308)in fuming perchloric acid. Approximately 807, of the total uranium was reduced to uranium( IV). The uranium( IV) concentrat.ion was determined by titration with standard ceric sulfate. The total uranium concentration was determined by reduction with zinc amalgam, air oxidation (zinc reduction of U(V1) gives some U(II1) which is oxidized to U(1V) by O2in 1 M sulfuric acid) and titration with standard ceric sulfate. The acid concentrat.ion was determined by removing the uranium with a cation-exchange (Amberlite I R 120) column in the acid form and tit,rating with standard base. The titrations were correct,ed for the hydrogen ion equivalent of the metal ions removed. (1) This work was done under the auspices of the U. S. Atomic Energy Commission a t t h e Los Alamos Scientific Laboratory under the Advanced Study Program with the Cniversity of New Mexico a n d is based on a thesis t o he submitted by F. R. Baker i n partial fulfillment of the requirements for t h e de,zree of Doctor of Philosophy in the Graduate School of the University of New Mexico. (2) R. H. Betts, Can. J . Chen., 33, 1780 (1955). (3) J . Halpern and .J. G . Smirh, ibi4.. 3 4 , 1418 (1956). (4) T. W. Newton. THISJOURNAL. 62, 943 (1958). ( 5 ) T. W. Newton, ibid., 63, 1493 (1959). (6) G. F. Smith, G. Frank and A. E. Kott, I n d . Eng. Chem., Anal. Ea., ia, 268 (1940). (7) A. I. Medalia and B. J . Byme, A n d . Chem., 28, 453 (1951).
The perchloric acid used was prepared from concentrated acid which had been purified by boiling at atmospheric pressure and then again under reduced pressure. Sodium perchlorate was prepared by neutralizing reagent grade sodium carbonate with perchloric acid, boiling out the carbon dioxide and crystallizing from water several times. Sodium perchlorate stock solutions were analyzed gravimetrically by drying aliquots at 150" to constant weight. Distilled water was redistilled from alkaline permanganate in an all Pyrex still. Rate constants obtained from runs using sodium perchlorate which had been crystallized three times were the same within experimental error 1t8 those in which the twicecrystallized salt was used. E.M.F. Measurements.-The hydrolysis of ceriuni(1V) was studied potentiometrically by measurement of the potential of the cerium(II1)-cerium(1V) couple as a function of Derchloric acid concentration employing a procedure very similar to those reported elsewhere.8pg The total cerium concentration in all reaction mixtures was 3.51 X 10-3 M. The cerium(1V)-cerium(II1) ratios were varied by addition of hydrogen peroxide. Sodium perchlorate was used to maintain the ionic strength a t 2.0. The concentration of cerium(1V) in the reaction mixture was determined spectrophotometrically~and was found to be constant within the experimental error during the potential measurements. Measurement of Reaction Rates.-The reaction rates were determined by following the change in concentration of cerium( IV) with time spectrophotometrically. I n order to make observations on the cerium( IV) conccntration within a sufficiently short time after mixing, the following procedure was adopted. Appropriate amounts of reagents, inrluding the uranium( IV), were pipetted into a plugged, thermostated funnel which led directly into a thprmostated (zt0.1") 10-cm. absorption cell. The cerium(1V) solution was added subsequently by means of a modified hypodermic syringe with constant stirring. After about 4 seconds, when mixing was complete, the plug %-as removed to allow the mixed solution to drain into the absorption cell. It was possible to take the first reading within 10 seconds of zero time. The cerium(1V) poncentration was determined from its absorbance a t 2900 A., where the molar absorptivity is about 2000 M-1 cm.-l. The absorbance as a function of time was read from the recorder chart of a Gary Recording Spectrophotometer, Model 14, which moved at a speed of eight inches per minute. Initial cerium( IV) concentrations were determined spectrophot,ometrically as in the procedure used in the e.m.f. measurements.
Results and Discussion Hydrolysis of Cerium(1V).+herrill, King and SpoonerQfound in their potentiometric study of the cerium(II1)-cerium(1V) couple in perchloric acid (0.202 to 2.38 M ) at 25' that the hydrolysis of ceriuni(1V) could be represented by the equations (8) S. W. Rabideau, J . Am. Chem. SOC.,79, 3675 (1957). (9) M . S. Sherrill, C. B. King and R. C. Spooner, ibid.. 66, 170
(1943).
F. B. BAKER, T. W. NEWTON AND MILTONKAHN
110 and
where the brackets indicate concentrations in moles per liter. Sherrill, et al., found the hydrolysis represented by equation 1 to be essentially complete and the hydrolysis quotient for the second step to be 0.6. Because the study referred to above was carried out only a t 25" and varying ionic strength, it was necessary to extend the study of hydrolysis of cerium(1V) as a function of temperature and a t constant ionic strength in order to interpret the kinetic data. The formal potential Ef for the cerium(II1)cerium(1V) couple is related to the hydrolysis quotients K1 and Kz by the expression where the constant EO' involves the standard potentia1 and the activity coefficients. For the case where K1>> [H+],equation 3 becomes
-
In
(--) [H+] + Kz
(4)
IH'12
The formal potentials mere extrapolated to zero cerium(1Y) concentration to correct for polymerization.lO~ll At the highest cerium(1V) concentration it was estimated from the data given by King and Pandow10 that a t least 90% of the cerium(1V) was monomer. Values of the formal potentials calculated using equations 3 or 4 and limiting K1, Kz pairs are compared with the experimental formal potentials in Table I. The choice of the limits for K1, Kz pairs is based oii an experimental error of 0.4 mv. Although the values for K1 and Kz given in Table I are quite uncertain they are sufficiently precise for the analysis of the kinetic data and perchloric acid the first hydrolsuggest that in 2 ysis step is a t le,& 837, complete a t 2 5 " ; at 1.6' this hydrolysis step is at least 70% complete but not more thaii 90% complete. Considering the relatively small value of K:! a t both temperatures it is concluded that the predominant species in 2 J1 perchloric acid is CeOH+3,in agreement with Sherrill, et al. Stoichiometry.-The stoichiometry of the reaction 2Ce(IV) U(IV) = 2Ce(III) UWI) was checked by adding an excess 'of 'cerium(1V) to uranium (IV) under experimental conditions similar to those used in the rate runs. The amount of cerium(1V) reduced in excess of that equivalent to the uraniuni(I\') and \vas small (< 2%) and attributed to n trace of oxidizable impurity present in the stock solutions. Rate Law.--The rate of oxidation of uranium(1V) by cerium(1V) was investigated at 2.4" in the perchloric acid concentration range froin 0.800 to 2.00 molar and :in ionic strength of 2.00; the initial cwiuni(I\') :iud nranium(1V) concentrations ranged from 4.2 to 6.0 X IO-5 31 and 2.6 to 8.8 X J 1 , respectively. The linearity of the plots de-
+
+
(10) C. L King and AI. 1, Pandow, J Am Chem S O C ,74, l9R6 (19521, (11) L Hridt and \I Smith, z h d , 70, 2478 (19-18)
Vol. 64
TABLE I HYDROLYSIS OF CERIUM( IV) IN PERCHLORIC ACID SOLUTIONS A T P = 2.00 FORX~L POTENTIALS OBT.4INED FROM THE DATACOMPARED WITH THOSE CALCULATED, FOR VARIOUS VALUESOF KI AND K P 25 O c
Best v a h e s , Q Exp., Ef Ef
[HGl,
2.000 1.000 0.500 0.300
1.7275 1.7083 1.6876 1.6706
1.7278 1.7083 1.6874 1.6706 0.1
Zd(mv.)2
Calculated Upper limit,
Lower limit,
KIC
Kib
Ef
Er
1.7271 1.7079 1.6875 1.6713 1.0
1.7268 1.7088 1.6879 1.6704 0.9
Upper limit,
Lower limit,
1.6' [Hi],
2.000 1.000 0.500
0.300 Ed( mv. 1
Exp., Er
Best values,d Ef
Kl,e hf'
Ki,f
1.7207 1.7061 1.6899 1.6759
1.7210 1.7062 1.6895 1.6758
1.7214 1.7059 1.6892 1.6761 1.1
1.7210
0.3
Ef
1.7068 1,6897 1.6752 1.1
>> [H+],K z = 0.15 and (EO' - ( R T / F ) In KI) = 1.7119. * K I >> [H+],K2 = 0.12 and (Eo' - ( R T / F ) In a
Kl
K 1 ) = 1.7108. Kr = 10, K 2 = 0.22 and Eo' = 1.7750. Ki = 8, K , = 0.08, Eo' = 1.7598. Ki 14, Kz =
'
scribed below suggested that the rate of reaction was first order with respect to both cerium(1V) and uranium(1T'). Where the concentration of uranium(1V) in moles per liter was considerably larger than one-half of the cerium(1T') concentration, plots of log[U(IV)]/[Ce(IV)] versus time yielded straight lines up to the point where the reactions were about 80% complete. For rate runs where the concentration of uranium(1V) was close to one-half that of cerium(IV), straight lines were obtained from plots of the reciprocal of the average concentrations versus time; the average concentration is defined as (Z[U(IV)] [Ce(IV)])/2 a t time t. The second-order rate constant k' a t a particular hydrogen ion concentration is defined by the equation
+
-d[ Ce( IV) I/dt = 2b'[ U(IV)][ Ce(TV)]
The constancy of the second-order rate constant, k' a t a hydrogen ion concentration of 2.00 M is shown in Table 11. Similar experiments were done a t other hydrogen ion concentrations, and the results are summarized in Table 111. VALCESOF Run
1 2 3 4 )
6 7
THE
TABLE I1 RATECOXSTANT k' IC 2 00 M PERCHLORIC ACID AT 2.4' A N D j~ = 2.00 lU(IV)Io, [Ce(IV)11, k', ,M x 105 M x 105 J f - 1 set.-' 6 06 3 50 7 08
s 85 8 02 'J 62
2 62
5 4 4 4 6 5 5
05 25 28 27 01 OB
06
464 455 472 44i 183 462 138
Because the rate was found to be proportional to the reciprocal of the hydrogen ion concentration
THEKINETICSOF REACTION BETWEEN URANIUM(IV) AND CERIUM(IV)
Jan., 1960
111
TABLE I11 can be shown that reaction 11 cannot contribute significantly to the experimentally established rate VALUESOF THE RATECONSTANTS k' AND kl IN PERCHLORIC law. ACID SODIUMPERCHLORATE SOLUTIONS AT 2.4' AND p = 2 No.
LH+ ,I'
Av. obsd. k', M - 1 sec.-l
determ.a
kit seo. -1
Calod. k', M - l s e c . -1
2.00 7 460 1190 480 7 1.25 810 1240 820 1.00 5 1030 1240 1040 0.80 5 1380 1320 1310 a The mean deviation from the average k ' was in the range from 2 to 2.5Y0 and the maximum deviation ranged from 2 to 4.37,.
It is of interest to compare the net activation process (equation 8) with that of the analogous reaction between plutonium(1V) and uranium(IVI6
+
P u + ~ U+*
+ 2Hz0 = [activated complex]+6 + 2H+
Although cerium(1V) is principally CeOH+3 and in acid solution plutonium(1V) principally P u + ~ the activated complexes are formally the same for both reactions. the following rate law is proposed, which is written Temperature Dependence.-The rate of reaction in terms of the predominant species in solution has been studied over the temperature range from - dICe(1V)I = 2kl [U+4][CeOH+a] 2.4 to 15.6" at a perchloric acid concentration of 2.00 (5) M . The results are summarized in Table IV; dt [H +I Inasmuch that the hydrolysis of U+4is negligible12J values of kl were calculated from the experimenin the acid concentration range studied [U+4] = tally determined values of k' using equation 7 and the appropriate values of KIand K2. Because Ki [U(IV)]. From equations 1 and 2 was evaluated only a t one temperature, the [CeOH+3]= [Ce(IV)I[H+l/([H+12/K~ [H+l K d values given for K1 in the last column of Table IV (6) were estimated by assuming (from consideration The dependence of k' on the hydrogen ion con- of the relative ionic radii of P u + ~Ce+4 , and U+*) centration obtained from equations 5 and 6, is that the entropy of hydrolysis is 24 f 6 e.u., given by the expression for the reaction Ce+4 HzO = CeOH+3 H+, which is within the range of the entropies of hykl k' = (7) drolysis for the analogous hydrolytic reactions of [H+I2/Ki [H+l Kz P u +and ~ U+4.3J812The values of Kz were obtained The values of kl given in the fourth column of by interpolation on a log K, versus 1/T plot using Table I11 were calculated using equation 7. The the data given in Table I. small increase in kl with decreasing hydrogen ion concentration (see Table 111) can be explained by TABLE IV assuming a lack of constancy of the pertinent TEMPERATURE DEPENDENCE FOR THE RATE OF REACTION activity coefficients or by postulating an addiAT 2.00 M PERCHLORIC ACID CONCEWI7RATION tional path which would not contribute significantly Temp.. k', ki, OC. M-1 see.-' sec.-l K I , A4 K2, hf to the over-all reaction rate. Because the systematic variation in kl was almost within the esti2 4 460 f 9" 1190 8 0 08 mated probable error of kl it was decided to elim8.0 810 rt 20 2030 10 .10 inate this minor path from further consideration. 15.6 1670 f 40 4050 1.1 .14 The values of k' given in the last column of a These uncertainties are the average deviation from the Table I11 which were calculated using the average mean. of kl,1250 f 150 sec.-l, are in satisfactory agreeThe constants log A and E, in the Arrhenius ment with the experimental values of k' indicating that the rate law given by equation 5 is satis- equation were obtained by a method of least squares and are 14.6588 and 14.6 kcal./mole, respecfactory. Mechanism.-The rate law (equation 5 ) for the tively; values of the rate constants calculated rate-determining reaction shows that the forma- using these values of log A and E a agree with the tion of the activated complex from the principal average values tabulated in the second column of species in solution can be represented by the net Table IV within 1%. The values of the entropy, heat and free energy of activation were calculated16 process13 for the net activation process (equation 8) and are CeOH+3 + li+4 HzO = [activated complex] +e H+ ASZ = 6.2 rt 2.5 e.u., AH$ = 14.0 f 0.7 kcal./ (8) mole and AFt = 12.2 f 0.2 kcal./mole. These This rate-determining reaction is probably values pertain to the reaction in 2.00 M perchloric acid at 2.4'. The uncertainties were estimated by IT(IV) Ce(lV) +U(V) Ce(II1) (9) combining the probable error of the rate constants followed by the fast reaction and the uncertainty of the hydrolysis quotients TJ(V) + Ce(1V) --+ U(V1) Ce(II1) (10) K1and K2. Effect of Sulfate.-Several runs were made a t An alternative to reaction 9 is 2.4" and 2 M perchloric acid with added sodium U(V) + U(V) --f U(V1) U(1V) (11) sulfate. The sulfate concentration was varied On the basis of published rate c o n ~ t a n t s 'it~ ~ from ~ ~ 0.0010 to 0.10 M . The rates in this range in(12) K. A . Kraus a n d F. Nrlson, J . Am. Chem. Soc., 72, 3901 (1950)' creased with increasing sulfate concentration and (13) 1'. W. Newton and S. W. Rabideau, J . P h y a . Chem., 63, 365 were immeasurably faster than in pure 2 M per(1959).
+
+
+
+
+
+
+
+
+
+
+
+
(14) D. M. H. Kern and E. F. Orlemann, J . Am. Chem. Soc., 71,2102
(1949). (15)
H.Imai, Bull. Chem. Soc. Japan, SO, 873 (1957).
(16) S. Glasstone, K. Laidler and H. Eyring, "The Theory of Rate Processes," MoGraw-Hill Book Co., New York. N. Y., 1941,pp. 195199.
HERBERTS.HARNED
112
chloric acid. However, in 1.1 M sulfuric acid in which the sulfate concentration was estimated to be 0.45 M , the rate was measurable and only 1.3 times as fast as the rate under comparable conditions of 1.5M perchloric acid a t I.( = 2. These results suggest that the effect of sulfate is similar to that found in the neptunium(1V)neptunium(T’1) reaction which has been extensively studied. l7
Vol. 64
Acknowledgments.-The authors gratefully acknowledge many helpful discussions with Professor G. Scatchard primarily concerning the hydrolysis of cerium(1V). They also acknowledge discussions with Dr. C E. Holley, Jr., and especially with Dr. J. F. Lemons, under whose general direction this work was done. (17) J. C. Sullivan, D. Cohon and J. C . Hindman, J. Am. Chem. SOC., 79,4029 (1957).
THE THERMODYKAIIC PROPERTIES OF THE SYSTEM : HYDROCHLORIC ACID, POTASSIUM CHLORIDE AND WATER FROM 0 TO 40’ BY HERBERT S. HARXED Contribution X o . 1630from the Department of Chemistry of Yale University, New Haven, Connecticut Recezved July 87, 1959
Parameters of equations which permit the calculation of the activity coefficients of both electrolytic components and the activity of water in the system, hydrochloric acid, potassium chloride and water from 0 to 40°J have been obtained. The magnitude and sign of the excess heat of mixing as a function of temperature has been estimated.
In an earlier communication, a thorough investigation of the thermodynamic properties of the system hydrochloric acid, sodium chloride and water from 0 to 50’ has been recorded.’ The present contribution contains a similar calculation for aqueous solutions containing hydrochloric acid and potassium chloride. The calculations are based on the equations log 7 1 = log log 12 = log
- orlmm~- h2m?2 ( 0-) orzmml - SzIml1
YNO) ~ ~
(I) (2)
+
to be applied a t constant total molalities m = ml m2. In these equations yl, ml and y 2 , m2 represent the activity coefficients and molalities of the acid and the salt in their mixtures, respectively, y!(o) is the activity coefficient of the acid of molality m in mater and ~ 2 ( ~ the ) , activity coefficient of the salt in water at molality m. The quantities 0(12(c), a 2 1 ( 0 ) , p 1 2 and pzl are the empirical coefficients of the linear and quadratic terms. Calculations of the Parameters of Equations 1 and 2.-The coefficient a 1 2 ( 0 ) was obtained by reconsideration of the electromotive force data of Harned and Hamer2 and Harned and Gancy3 for the activity coefficient of the acid, q l l in the mixtures. The activity coefficients, yl(o),of the acid in water were obtained from the data of Harned and Ehlers4 as tabulated by Harned and Owen.5 The values of log ylc0)and 0(12(0)from 0 to 40’ at 5’ intervals are given in Table I for the system at total molalities 1, 2 and 3. Since all the experimental evidence indicates that log y1 varies linearly with the acid or salt concentration a t constant total molality, it is assumed that p 1 2 equal zero. The parameter azl = a21(o) &ml was computed by the method of ;IlacKay.6 Values of log YZ(C)
+
(1) H. S. Harned, J . P h y s Chem.. 63, 1?99 (1959). (2) H . S. Harned and W. J Hamer, J . Am. Chem. Soc.. 86, 2194 ( 1933). ( 3 ) II. P. Ilarned and A. €3. Gancy, t b ~ d .62, , 627 (1958). (4) H. S. Harned arid R . W.Ehlers, ibad., 56, 2179 (1933). ( 5 ) H. S. Harned and B. B. Owen, “The Physical Chemistry of
Electrolytic Solutions.” 3rd Ed., Reinhold Publ. Corp., New York, N. Y.,1958, p. 716.
TABLE I
DATAFOR COJIPUTINGTHE ACTIVITYCOEFFICIENTSOF HYDROCHLORIC ACID, yl, IS
t
A N D POTASSIUM CHLORIDE,yzJ SOLUTIONS OF 1, 2 A N D 3 m TOTAL MOLALITIES 021 = -0.006
log
Yl(0)
m
o J
10 15 20 25 30 35 40
i.9253 1.9224 1.9188 i- ‘3153 1 9118 1 9079 -1,9041 1 8999 1.8957
log YZ(0) = ml + m a
1.7694 -i.7745 1.7767 i.7188 -1.7810 1.7824 -1 ,7810 -1.7810 1.7803
m = ml
0 5 10 15 20 25 30 35 40
0.0326 .0286 ,0224 .016ti ,0103 - ,0039
-1.9967 1.9894 i.9824
5 10 15 20 25
UlItO)
0.0670 .0650 .0625 ,0605 ,0585 ,0558 ,0540 .05?0 ,0500
-0 -
-
0740 0714 ,0681 ,0655 ,0629 0602 0586 0568 0560
+ m2 = 2
1 7380 1.7435 -1.74‘37 1 7*54:3 -1.7582 1 . 7604 1 . 7619 1 7627 1.7619
+ +
0
alz(o1
+1
ml rn? 3 0.1620 1.7419 .1544 1.7396 ,1464 -1.7451 ,1377 1.7497 .1287 -1.7526 .1192 1.7566
0.0680 ,0665 ,0645 ,0625 .Of305 . 0.590 ,0570 ,0550 ,0530
-0 -
0640 0615 0585 0555 0535 0514 0485 0470 - 0435
= -0.005
0.0690 ,0680 -0660 ,0650 ,0640 ,0630
-0.0585
-
.(‘Si5
.b545 - ,0510 - ,0485 - ,0440
required for this calculation were obtained from the data of Harned and Cook’ and are recorded in the third column of Table I. (6) H. A. C. MacKay. Trans. Faraday Soc., 61. 903 (1955). See also ref. 5, p. 628, 629. (7) H. 6. Harned and AI. A. Cook, J. Am. Chem. SOC.,69, 1920 (1937). See also ref. 5 , p. 727.
