S. W. RABIDEAU, AND R. J. KLINE
1502
Vol. 63
THE KINETlCS OF THE REACTION BETWEEN PLUTONIUM(V1) AND TITANIUM(II1) IN PERCHLORATE SOLUTION1 BYS. W. RABIDEAU AND R. J . KLINE Contribution f r o m the University of California, Los Alamos Scien ti$ c Laboratory, Los Alamos, New Mexico Received March 20, 1969
The kinetics of-the reaction between Pu(V1) and Ti(II1) has been studied as functions of temperature and acidity using
spectrophotometric methods. Since the reductions of Pu(VI) and Pu(1V) by Ti(II1) are measurable, whereas the reductipn
of Pu(V) 1s very rapid, the data were treated as com etitive consecutive second-order reactions. The rate law wntten In The inverse first power terms of the rate of disappearance of Pu(V1) is -d/bu(VI)]/dt = kl[Pu(VI)][Ti(III)][H+]-l. of the hydrogen ion concentration in the rate law suggests that the slow step may consist of the reaction PuOz++ TiO H f + d hoe+ TiO++ H+. With values of the specific rate constant for the reaction between Pu(IV) and T i W I ) obtaiped from independent experiments, the spectrophotometric data were coded for the IBM-704 computer and the calculation was made usin an iterative procedure to evaluate the specific rate constant for the reaction between Pu(Y1) a$ Ti(III). At 25" in moyar perchloric acid, the rate constant for the Pu(V1)-Ti(II1) reaction was found to be 108 sec. The reduction of perchlorate ion by Ti(II1) has been considered, and it has been shown that reductions of Pu(V1) and pu(Iv) by Tl(III) are not catalyzed by chloride ion. The thermodynamic quantities for the activation process wntten in terms of the principal species are AF+ = 14.7 f 0.01 kcal./mole, AH* = 10.3 i 0.4 kcal./mole and A S * = -14.7 =I=1.3 e.u.
+
+
+
Introduction Rapid reductions of the plutonyl ion can be followed spectrophotometrically with high precision a t plutonium concentrations as low as M because of the relatively large molar absorptivityo of the plutonyl ion (ca. 550 M-I cm.-l) a t 8304 A. using the Cary Model 14 Spectrophotometer. As part of continuing research on the effect of size and charge type upon the thermodynamic quantities of activation for oxidation-reduction reactions of plutonium, the kinetics of the reaction between Pu(V1) and Ti(II1) has been studied. I n the reduction of Pu(V1) with Ti(II1) it is necessary t o consider the reactions
-
b Pu(V) + Ti(1V) + Ti(II1) -+ ICs Pu(1V) + Ti(1V) Pu(V) + Ti(II1) Pu(1V) f Ti(II1) -% Pu(II1) + Ti(1V) Pu(V1)
(1)
(2) (3)
I n exploratory experiments, it was found that the reactions of Pu(V1) and Pu(1V) with Ti(II1) OGcurred a t measurable rates; however, the reduction of Pu(V) as shown in equation 2 was too rapid to measure. Thus, considering equation 2 fast in comparison with (1) and (3), it is possible to consider this system as a competitive consecutive second-order reaction system, that is kl + 2Ti(III) + Pu(1V) + 2Ti(IV) ks Pu(1V) + Ti(II1) +Pu(II1) + Ti(1V) Pu(VI)
(4)
(5)
Frost and Schwemer2 have considered a system somewhat analogous t o the present work, and the differential rate equations were derived for the special case of stoichiometrically equiva.lentamounts of the reactants. Since Ti(II1) reacts with perchlorate ion as a side reaction, it was not practical to use predetermined concentrations of reductant in the present rate experiments. Experimental Plutonium(VI) was prepared from an especially selected lot of high purity metal by removal of the oxide film, dis(1) This work was done under the auspices of the U. 8. Atomic Energy Commission. (2) A. A. Frost and W. C. Sohwemer. J . Am. Cham. SOC..74, 1268 (1952).
solution of the metal in the appropriate weighed quantity of boiled and standardized Baker and Adamson reagent grade 71% perchloric acid, and oxidation with ozone. The titanium(II1) perchlorate stock solution was pre ared by the dissolution in hydrochIoric acid of a sample oPtitanium hydride obtained from Metal Hydrides, Inc., Beverly, Mass. The stock solution was filtered and stored ?der .an atmosphere of helium. Prior to use in the reaction wlth Pu(VI), a portion of .the stock solution was added t? a deaerated perchloric acid solution which was then laced in a thermostat. Periodically samples of the Ti(III7 were removed ?nd quenched in solutions of cerium(1V) sulfate. The cerium(1V) sulfate solutions were analyzed with the Model 14 Cary Spectrophotometer at 25' at a wave length of 4390 d. With the use of cerium(1V) sulfate solutions standardized against U. S. Bureau of Standards As& sample 83a, it was found that the molar absorptivity at this wave length is 191.1 f 0.3 M-1 om.-' Pseudo fnst-order plots. of log[Ti(III)] versus time gave straight lines which permitted the titanium( 111)perchlorate concentration used in the experiment to be determined. All solutions were prepared with distilled water which had been redistilled from alkaline permanganate in an all-Pyrex apparatus. Sodium perchlorate was obtained by the neutralization of C.P. sodium carbonate with erchloric acid and double recrystallization of the salt. %he perchloric acid was standardized by weight against Baker Analyzed Grade mercuric oxide. I n each determination of the rate constant. for the reaction between Pu(V1) and Ti(III), the moIar absorptivity of PUOZ++was determined in the solution environment and at the temperature to be used in the kinetic experiment. NO correction was required for absorption by the TI(JII) or Ti(1V) or by the plutonium species produced during the course of the reaction, since these concentrations were 1n the lo-' M range and their molar absorptivities are small. Weighed quantities of a diluted plutonium(.VI) perchlorate stock solution, together with the approprlate amounts of acid and salt, were placed in one leg of a double chambered ten cm. spectrophotometric absorption cell. After flushing the cell with nitrogen, a known volume of diluted Ti(II1) stock solution was added t o the second leg of the absorption cell. The solutions were brought to temperature in a water thermostat, mixed uickly, and laced in the cell compartment of the spectrop%otometer. k i t h circula ting water, the temperature of the bath-water in the cell compartment was maintained at f 0 . 2 " . The first readings w?re obtained within 20 to 25 seconds after the start of mixing. The experimental observations consisted of the determination of the concentration of puOz++as a function of time through use of the strong absorption peak at 8304 d. measured with the Cary Model 14: Recording Spectrophot0.meter. The initial titanium( 111) perchlorate concentration was known, and the concentration of this species as a.function of time was computed from the observed change in the concentration of PuOn++ plus a small correction for the reaction of Ti(II1) with the Pu(IV) formed. The specific
.
KINETICS OF REACTION BETWEEN PLUTONIUM(VI) AND TITANIUM(III)
Sept., 1959
rate constants for the reaction between Pu(1V) and Ti(II1) have been determined3 from independent work. Under the conditions of the present work, the reaction between Pu( 111) and Pu(V1) has been found to be negligible. Stoichiometry.-Since it was found that a solution of PuOa+, prepared by the reaction ?f Pu( 111).and PuOz.++, was reduced to Pu( IV) by Ti(II1) within the time of mixing, the initial approximation of the titanium( 111) perchlorate concentration was considered to be the original concentration less twice the change in the concentration of Pu02++. The linearity of second-order plots to 30 to 40% completion supports this stoichiometry. Further, in experiments at 10' in which approximately equal molar quantities of Ti(II1) and PuOz++ were used, the ratio of the change in the titanium to the change in the plutonium concentrations at the time of essential completion of the reaction closely approximated 2.00. This result indicates that under the conditions of the experiments, the essential reduction process was the conversion of P u 0 2 + + to Pii(IV). In experiments a t 25O, the ratio of change of Ti(II1) concentration to that of PuOz++ was somewhat greater, indicating that a significant amount of Pu( IV) had been reduced a t the time of complete reaction of the Ti(II1).
Results and Discussion Theoretical.-The difficulties inherent in the use of initial slopes in the evaluation of specific rate constants in kinetic studies have been stated by Ing01d.~ However, in the case of some fairly rapid reactions, it may be difficult to improve upon the values of the rate constants derived from initial slopes. I n the present work, the kinetic data were first analyzed with the assumption that reaction 4 alone need be considered. The values of kl were then obtained in the usual way from plots of log { [Ti(III)]/[Pu(VI)] X [Pu(VI) - xJ/[Ti(III) 2x1) versus time, where x is the change in the Pu(V1) concentratioir a t any time, t. Although in all instances initially linear plots were obtained in this way, departure from linearity occurred sooner when kl and k3 were relatively large. (See equations 6 and 7). It was interpreted that the deviation from a straight line relation arose chiefly from the fact that the reduction of Pu(1V) by Ti(II1) is not negligible. Using in part the notation of earlier work12 the following derivation develops an expression for the calculation of kl which takes into consideration the amount of Ti(II1) lost through the reaction with Pu(1V). If equations 4 and 5 are rewritten
1503
Dividing equation 10 by 21c1A& and simplifying, we obtain da/dr = [(3K/2)
- l ] a p - [(3/2)-
Ao/2Bo]Ka - ( K A O O ( ~ / ~ B(12) O)
Then, making the further substitutions a = [ ( 3 / 2 )- A o / ~ B D I
(13)
b = Ao/2Bo
equation 12 becomes da/dr = [(3K/2) - l ] a p - aKa
-
bKa2 (14)
Since the rate equation in terms of the rate of disappearance of B is -dB/dt
then it follows that
=
- dp/dr
kiAB
(15)
bap
(16)
and also
- da/dp
- 2 ) / 2 R - aK/bp - K a / p (17) Multiplying equation 17 by @-R and integratiag, we =
(3K
find that = [(3K - 2)p/2b(K - I ) ]
LY
- a/b
+ cPK (18)
where c is the constant of integrat'ioll and has the value c = 1
+ a / b - (3K - 2 ) / 2 b ( K - 1)
(19)
since a = 1 when p = 1. Substituting the value of c in equation 18, gives dp/dr = (3K
- 2)p2(pK-' - 1 ) / 2 ( K - 1 ) 3pK+1/2
+ a@
(20)
Finally, transposing and inserting the limits. of integration L d r =
Sp
- 2)pZ(pK-l-
db'
-
1) - 3pK+1/2
+ ap
p _ _ _ I I _ _ _ _ -
(3K
1)/2(K
(21)
Values of r as functions of p, and consequently as functions of time, have been graphically evaluated by plotting l/denominator of equation 21 versus 0. The preliminary values of klfor use in the computation of K were obtained from initial slopes of sccond-order rate plots assuming no loss of Ti(II1) kl through reaction 5 . The values of ks used with IC1 B 2A +C 2E (6) in the evaluation of K at various acidities and temLa peratures were obtained experimentally from iiideC+A---tD+E (7) pendent measurements. The manual graphical inthen from stoichiometry considerations tegration procedure was tedious inasmuch as iteraC = ( A - A D ) 3(Bo - B ) (8) tions were required to obtain the best value of K , where A , B, C , D and E represent the molar concen- and hence of ICl. Consequently, the integral extrations of Ti(III), Pu(VI), Pu(IV), Pu(II1) and pression in equation 21 was programmed for the Ti(IV), respectively, and the subscrilst zero corre- IBM-704 computer. A comparison was made sponds.to iiitial coGeentrations. Therate equation between the areas evaluated manually and by computer methods. The areas were found to be in in terms of the disappearance of A can be written excellent agreement. -dA/dt 2kiAB + ksAC (9) Input data for the IBM-704 consisted of initial 2kiAB k3A[(A - AD) 3(Ro - R)] (10) reactant concentrations and optical density rendiiigs A simplification in the mathematical treatment is of the plutoniym-titanium solutions a t a wave achieved through the use of the substitutions length of 8304 A. Readings were taken a t one secK = lcs/ki T = 2kiBot (11) ond intervals from the strip chart recording with the = A/Ao d r = 2lclBo dt use of a transparent plastic template which had lines 6 = B/Bo carefully ruled on it to provide divisions correspond(3) 8. W. Rabideau and R. J. Kline, THISJ O U R N A L ,t o be publislLed. ing to this time unit. The integration was per(4) C. IC. Ingold, J . Chem. Sac., 2170 (1931). formed with the computer coded to make use of the
+
+
+
+
O(
+
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S. W. RABIDEAU AND R. J. KLINE
Vol. 63
trapezoidal rule. The optical density values for the uncertainty of the mean value of the product h.1 period between the time of mixing and the first re- [H+]is given as twice the standard deviation of the corded trace on the spectrophotometer were comTABLE I puted from the value of kl derived from the initial HYDROGEN ION CONCENTRATION DEPENDENCE OF RATE slope plot and the known initial concentrations of FOR THE Pu(V1)-Ti(II1) REACTION IN PERreactants assuming second-order rate behavior. CONSTANT CHLORATE SOLUTIONS OF IONIC STRENQTH Two AT 2.5" These points were used to evaluate the integral over the limits of integration used. With the IBM-704 computer, iterations were performed until the dif2.00 12.6 25.2 0.50 56.2 28.1 ference between successive values of K were less 11.3 22.6 60.0 30.3 than 0.1%. I n most of the 7 versus time plots, the 12.6 25.2 57.4 28.7 line was constrained to go through the origin; how12.5 25.0 0.25 113 28.2 ever in those cases in which the least squares line was 1.00 22.2 22.2 113 28.2 not required to go through the origin, it was found 21.0 21.0 114 28.5 that the intercept was very small. All the values of 21.8 21.8 109 27.2 IC1 were derived from slopes of lines restricted to pass 22.3 22.3 through the origin as theoretically required. InMean 2 5 . 5 f 1 . 4 '-4.2 24.2 cluded in the computer program was the evaluation of the least squares slope of the 7 versus time plots. mern. Within the limits of uncertainty it appears I n an effort to determine the influence of the value that the rate of the reaction between Pu(VI) and of k~ upon the result obtained for kl, various k~ re- Ti(II1) is given by the rate expression -d[Pu(VI) 1sults were fed into the calculation, otherwise using /dt = Icl [Pu(VI)] [Ti(III)] [H+]-'. A possible the same experimental data. It was found that ICl mechanism suggested by this result for the ratewas not very sensitive to the value chosen for k3. determining step is The use of a ka value which differed from the experkl imentally determined value by about 10% resulted PuOz++ + TiOH++ + PuOz+ + TiO++ + H + (22) in a change of kl of only 0.1%. Temperature Dependence.-Measurements of Arbitrarily, it was decided to use data up to 40% the temperature coefficient of the specific rate concompletion of the reaction in the computation of the stant for the reaction between Pu(V1) and Ti(II1) values of kl. However, tests were made to deterbeen made in molar perchloric acid solutions. mine the influence of using data obtained a t greater have The results are given in Table 11. percentages of reaction. For the reaction a t 2.2" in 0.25 M HC1O4--1.75 dl NaC104, a difference of TABLE I1 1.8% in the values of kl was noted when experi- TEMPERATURE DEPENDENCE O F Pu(V1)-Ti(111) REACTION mentally obtained results up to 40 and 63% comple- IN MOLARPERCHLORIC i l C I D SOLUTIONS OF U N I T IONIC tion were used. It is known that a t the higher exSTREXGTH tents of reaction a greater contribution toward the ki, M-1 ki, M-1 t , "C. 1 / T X 10' sec.-1 t , "C. 1/T X l o 3 sec.-1 decrease in the concentration of PuOz++is made by 2 . 5 3.628 23.1 15.5 3.464 56.0 the Pu(II1)-Pu(V1) reaction. 23.1 56.8 As discussed in the experimental section of this 22.0 56.8 paper, it is observed that the reduction of Pu02+ 5.8 3.585 29.5 57.3 by Ti(II1) is fast in comparison with the rate of 29.6 59.1 reduction of PuOz++. This result is somewhat un31.2 20.0 3.411 81.8 expected in view of the slowness observed in the re32.5 i8.0 duction of Pu02+ by vanadium(II1) p e r ~ h l o r a t e . ~ 31.8 76.5 Further, it has become customary to consider that 1 0 . 2 3 , 5 2 9 1 2 . 7 2 5 . 0 3.364 108 reactions involving the making or breaking of 43.8 108 metal-oxygen bonds are slower than those reactions 4 2 . 4 103 involving an electron transfer, e.g., the disproporI12 tionation reactions of Pu(1V) or Pu(V) are slower than the Pu(II1)-Pu(V1) reaction. However, in the present work, the low total plutonium ion con- With the expressions of the transition state theory,6 centration precludes the disappearance of appreci- values of the free energy, heat and entropy of activaable quantities of PuOz+ by the disproportionation tion were computed using the data of Table 11. The path, and the change in the concentration of Ti(II1) values are found to AF* = 14.7 0.01 kcnl./mole, indicates that it is involved in the reduction. It is AH*, = 10.3 f 0.4 kcal./mole and AS* = -14.7 not clear why the reduction of Pu02+ by Ti(II1) f 1.3 e.u. for the reaction between Pu(V1) and should be much more rapid than the reduction of Ti(II1) in terms of the principal species, Z . C . , PuOz++ T i + + + H 2 0 -+ (I'UO~.T~.OH)+~ PUOZ ++. H+. Hydrogen Ion Dependence.--In Table I are Effect of Chloride Ion.-lnasmuch as it is imgiven the results of a study of the hydrogen ion concentration dependence of the reaction between possible to carry out an investigation of the reacPu(V1) and Ti(II1)a t 2.5". Theionic strength was tion betweeii Pu(V1) and Ti(II1) in perchlorate maintained at two by the addition of appropriate solution in the absence of CI- because of the reduc( G ) S. Glasstone, K.Laidler and H. Eyring, "The TlleorJr of Rate quantities of anhydrous sodium perchlorate. The +Z
+
+
+
Processes," McGraw-Hill Book Co., Ino., New York. N. Y., 1941, P.
(5) S. W. Rabideau, THISJOURNAL,68, 414 (1958).
417.
c
Sept., 1959
HEATCAPACITY OF SODIUM PEROXIDE AT HIGH TEMPERATURE
tion of perchlorate by Ti(", it was of interest to determine whether an increased C1- concentration altered the observed rate of reaction. A solution of 1 M HCIOl was made 0.02 M in C1-, and the specific rate constant for the Pu(V1)-Ti(II1) reaction was determined at 10.2" in this medium. A value of 45.0 M-' set.-' was obtained which is in good agreement with the value of kl determined at this temperature in 1 M HCIOl with a total C1- concentration of about 0.002 M . (See Table 11.) Ionic Strength Effect.-From measurements of the value of ICl a t 2.5" in molar perchloric acid and
1505
a t ionic strengths of 1.00 and 2.00 it was observed that I G ~was little altered by this change in ionic strength. This is in contrast to the effect of ionic strength on the reduction of Pu(1V) by Ti(III) . 3 I n this reaction the value of kl nearly doubled as the ionic strength was increased from 1 to 2. Acknowledgments.-It is a pleasure to express our appreciation to Dr. J. F. Lemons for valuable discussions and interest in this work and to Drs. D. T. Cromer and A. H. Zeltmann for their assistance in the calculations.
HEAT CAPACITY OF Naz02A T HIGH TEMPERATURES1 BY M. S. CHANDRASEKHARAIAH, R. T . GRIMLEYAND JOHN L. MARGRAVE Department of Chemislry, University of Wisconsin, Madison 6, Wisconsin Received March 28, 1969
Samples of Na20, contained in gold capsules have been studied in a drop-type calorimeter from 375 to 869°K. The heat content is given by (HT- H2g8)= 16.7T 7.8 X : O - T 2 - 5642 cal..mole-* [298" < T " K . < 869"J. A transition a t 610 i 10" has a heat of 1280 cal. mole-'. The melting point of Na202IS higher than 869°K.
+
Very little high temperature thermodynamic data for sodium peroxide have been available. Two papers,29agive the heat capacit'y and entropy of sodium peroxide up to 100'. This calorimetric measurement was undertaken in order to obtain enthalpy and heat capacity data a t higher temperatures. The apparatus is similar in design to one described by Southard4and the details of construction are given e1sewhe1-e.~A platinum-wound furnace mas used to heat the sample and was maintained at constant power by a constant voltage regulator. The constant temperature oil-bath was maintained constant to j=0.002'. The calorimeter resistance thermometer was a transposed bridge arrangement of two copper and two manganin resistances, and the change in the temperature of the calorimeter was measured in terms of the change in the resistance of this arrangement. An electrical calibration experiment yielded the factor for converting the observed change in resistance to heat content of the sample. Sodium peroxide was obtained from the Niagara Falls Laboratory of the du Pont Company and was analyzed by standard methods. The result of the analysis indicated : sodium peroxide, 98.3%; sodium carbonate, 1.5% ; sodium oxide (by difference) , 0.2%. X-Ray diffraction indicated no other phases present, and no solid.solutions were indicated in either original or quenched samples. Experimental Procedures A weighed quantity (9.6537 g.) of the sample wafi transferred into a gold capsule, which was then sealed tight and welded. Except for welding, the rest of the operation was done inside a dry box. The enthalpy of. the empty gold capsule above 298%. was determined at different tempera(1) Presented before the 134th meeting of t h e American Cheinicrtl Society, Chicago. Illinois, September 8 , 1958. (2) S. S. Todd, J . Am. Chem. Soc., 7 6 , 1229 (1953). (3) A. M.Vedeneev and 6. h i . Shuratov, Zhur. F i z . Khh.,26, 837 (1951). (4) J. C. Southard, J . Am. Chem. Soc., 63, 3142 (1941). (5) R. T. Grimley, Ph.D. Thesis, University of Wisconsin, 1958.
tures using the calorimeter assembly. This capsule plus the sample was then heated in the furnace to a measured temperature and dropped into the copper Calorimeter. The rise in temperature of this calorimeter was measured on a resistance thermometer with a White Double Potentlometer.
Results and Discussion Enthalpy differences of the empty gold capsule were measured from 100 to 800' a t 100' intervals. The results fit the analytic function (HF- H ~ o = ~ 0.4341T ) ~ ~+ 2.463 ~ ~ X ~ I ~- 131cal. where ( H T - Hs9&is the ellthalpy difference for the capsule between room temperature and the temperature T ,O K. in calories. This equation was employed for computing the heat transferred by the capsule as distinguished from the total heat trxnsferred t o the calorimeter in cooling the sample and the capsule from the furnace temperature to the final calorimeter temperature. Table I contains the experimental results, and Table I1 presents the molar heat content, entropy and free energy functions at selected temperatures as calculated from the data. In calculating the enthalpy differences for sodium peroxide, corrections for the contributions from sodium carbonate and from sodium monoxide were made. Heat capacity data for sodium oxide were taken from the thesis of Grimley5 and for sodium carbonate, data were taken from Popov and Ginzberg.6 Entropies were calculated from these enthalpy data using the method of Kelley.' Equations for the entropy and enthalpy differences for sodium peroside as a function of t#emperature have been derived by the method of 8homateu to fit the experimental data with an uncertainty of =tl%between 298.15 and 869' K., if the heat of' transition is included for temperatures above 783°K. ( 6 ) ill.ilf. Popov and D. nl. Gmzberg, J . G'cn. C/mn&.(U.S.S.H.), 26, 1103 (1956). (7) IC. IC. ICelley. Bulletin No. 476, U. S. Buieau of hlines, 1949. (8) C. H. Shomate, THIBJOURNAL, 68, 368 (1954).
