'I'lie observcd biuiolecular rate constants are greater by a factor of eight than extrapolated values for the bimolecular "Bodenstein" mechanism, for which the transition state is believed to be
crepancy is in the present work. 'I'his qucstioii requires further work, but the present in\restigagation has fairly definitely established the occurrence of both unimolecular and biniolecular s 0 0 reaction paths. ' \ / \ / Acknowledgments.----'l'hiswork has been s u p 0 (1 N . I t seeins unlikely, b u t not entirely cxluclecl, t h a t this is due to an error in extrapola- ported by the O . S . R . One of us has received tion. Possibly a simple extension of the Ashmore fellowships from the Corning Glass Works Foundaand Levitt NO3 mechanism, including reaction 21, tion and the General Education Board. An initial e m account for the additional reaction path. How- investigation of the shock pyrolysis of SO2 was ever, the data now available indicate t h a t this carried out in these Laboratories several years ago should increase the extrapolated rate only by a by Dr. W.In .__ (2) J. C. I I i n d m a n , .1. C. Sullivan a n d D. Cohen, THISJ O U R N A I . , 76, 3278 (105.0. ( 3 ) J. C. S u l l i v a n , D . Cohen and J. C. IIindrnan, rbid.. 79, 4029 i19.57 ) . ( 4 ) J. C. Sullivan, 11. Cuhen and J. C. I f i n d m a n , ibid., 79, 3072 ( 1!I 37) .
Results
I. The Np(1V) + Np(VI) + 2Np(V) Reaction..
-
The order of the reaction with respect to each of the metal ions has been determined previously.? ' The reaction is bimolecular both in perchlorate and sulfate media. The rate constant, k,,bsd, in the present work therefore was calculated by means of the integrated equation for a bimolecular reaction. The Effect of Acid Concentrations.-Table I summarizes the data on the effect of acid concentration on the rate of the reaction. Least squares analysis yields a value for n in the equation koh.d
=
k[H+]"
(1)
of -3.140 =t0.022 (99y0 confidence level) for tlic hydrogen containing solutions and of -2.134 f 0.022 (99% confidence level) for the 95% deuterium solutions. Within experimental error there is no significant effect of deuterium on the acid dependence of the reaction. The data in perchlorate solution may be analyzed in terms of more than a single reaction path. Least squares treatment of the data yields values of the rate constants for the equation kubsd
= ki[H+]-'
+ k2[13+]-3
(2)
in the hydrogen mcdiuni, k l = 4.27 X lo-? inole liter-' set.-' and k 2 = 5.04 X mole2 liter-* set.- l. I n the deuterium solutions, k l = 8.56 X l o p 3 mole liter - l set.-' and k2 = 1.02 X mole2liter-?sec.- l. The Effect of Deuterium Concentration. - E x amination of Table I shows that there is a siqnificant effect of deuterium on the reaction rate. Table I1 illustrates this in more detail. A plot of the observed rate against the percentage of deute-
KINETICS OF RE.\CTIONS INVOLVING NEPTUNIURI(IV) (T) ASD (17) Ioss
May 20, 19.59
2317
~
The Isotope Effect in Sulfate Solution.-Figure 1 is a plot of the observed rate constant kobsd for various initial concentrations of sulfuric and deuteriosulfuric acid. As shown in the figure the general TABLE I shape of the curve resembles that determined in the THEEFFECTOF HYDROGEN A N D DEUTERIUM IONCONCEN- hydrogen-containing Multiplication of T K A T I O N S O N THE RATE O F T H E Np(IV)-Np(VI) REACTIONS the rate constants for the deuteriosulfuric acid soluIU PERCHLORATE SOLUTION tions by a factor of 4.6 gives a curve that lies close CL = 2.2, t = 24.9" to that obtained in sulfuric acid. The magniObsd. r a t e [Np(VI) 1, constant, k [ ( N p ( I V )I , tude of the isotope effect supports the previous [a'I. ID'] a moles/l. moles/l. i . mole-' suggestions that the reaction mechanism is the moles/l. moles/]. x 10s x 10' min. -1 same as in perchlorate solution. The deviation of 47.2 0.271 2.61 2.77 the curves for the two media a t high sulfate con46.3 2.61 2.77 centrations may be a reflection of accumulating 2.60 4.12 47.1 effects of dissociation and hydrolysis constant dif8.07 0.634 2.60 4.12 f erences. 7.87 2.60 4.12
rium in the solution was used to obtain the rate constant for a 10070 deuterium solution. It is found that a t 2.5' the ratio k H / k D is 5.0.
1.21
2.60 2.60 1.R3 2.60 2.60 0,2i:? 2.61 2.61 2.60 0 , 500 2.60 2.60 0.996 2.60 2.60 1.97 2.60 2.60 Total deuterium content 95%.
THERATE OF
Acid
1.84 1.76 0.736 0.693 9.30 10.1 10.3 2.53 2.61 0,574 ,530 ,138 ,145
TABLE I1 Sp(1V)-Sp(\'I) REACTIOXAS A FUNCOF DEUTERIUM CONCEXTRATIOV fi = 2.2, t = 24.9'
THE
TION
D
[H +, 1) +I,
content ,
0,273 ,270 ,270 ,271
95 79.2 47.5 0
rnolesll.
4.12 4.12 4.12 4.12 2.77 2.77 4.12 4.12 4.12 4.06 4.06 4.12 4.12
. , c
Obsd. r a t e constant, k I mole -1 i n i n .
-1
9.90 12.8 23.6 4 6 . 9 (av.)
kobsd/k&I
0.211 .273 ,502 1.00
Temperature Effect in Perchlorate Solution,Table I11 gives the data on the effect of temperature on the rate. The ratio of k~ to k D increases
1 10-3
I
0
I
1
I
I
I
1.0
1.5
2.0
2.5
3.0
I
0.5
3.5
kobs TABLE I11 Fig. 1.-The effect of deuterium on the rate of the THE EFFECTOF TEMPERATURE O N THE RATE OF THE Np(1V)-Sp(V1) REACTIONI N PERCHLORATE SOLUTIONT\-p(IV)-p\:p(VI) reaction in sulfate solution; t = 25", = 2.2, [H+] = 2.2: 0 , rate observed in D2O-D?SO4 [ I f + ] = [ D + ] = 0.271 M , CL = 2.2, [Np(IV)] = 2.60 X solution (95% total D ) ; 0 , rate observed in H,O-H,SO, 11.1, [Np(VI)] = 4.06 X 10-3 M Obsd. r a t e Ohsd. rate4 solution; A, rate observed in D~O-DZSO~ solution X 4.6. Temp., O C .
a
constant, kH 1. mole-' min.-'
constant,
kD
I. mole-1 min.-I
5.0 2.08 0.370 14.9 10.1 1.92 24.9 46.9 9.90 35.1 174.9 40.4 95y0 total deuterium content.
kn/kn
5.65 5.26 4.74 4.33
with decreasing temperature. This is reflected in the slightly higher activation energy for the reaction in D20 solution. T h e least squares values of the energies of activation are 26.85 f 0.27 kcal. for D20 solutions and 25.32 f 0.28 kcal. for H20 solutions. The activation energy found in the present investigation for HzO solution is in satisfactory agreement with that previously reported, 25.2 1.6 kcaL2
*
+
11. The 2Np(V) ---f Np(1V) Np(VI) Reaction.-This reaction previously has been shown to have a second-power dependence on the concentration of N P ( V ) . ~ The observed rate constant, kobsd., was therefore calculated in the same manner as for the Np(1V)-Np(V1) reaction. Table IV summarizes the rate data. For this reaction i t is found that the rate is faster in deuterium solution. It is possible to express the results in an equation of the form previously used.3 The resulting values of k'5 and k'6 are for deuteriosulfuric acid solution, kobsd
=
k'5
[HSOa-] f k'e [HSOI-]'
(3)
k'5 = 1.17 x lo-' liter2 set.-' and k'6 = 0.58 X lo-' mole-3 liter3 set.-'. These compare with
--
--
~ 3 C 3I I 3 . . Hf , r p o # e i / l e r . .~
3:
15
2 3
where [A1Zlf]7zis the concentration of the reacting species of oxidation state +4 and [NI~T] is the total metal ion concentration o f this oxitlatioii state. The final form of the rate eciuatioii will depend 011 the number of transition states and on the M r v species assumed to be involved in the i n tial reaction. Newton took cognizance o f the two simplest possibilities, i.c., I-'$+ ant1 two reuctioii interniecliates and IJ(OH)3- with the concomitant single transition in his exai~iinationoi thca 'I---Pu system. \i7e have tested our data with similar ussumptioris. For t h e case where NpOH-:' is considered to be the initial reaction species, thr rate equation 7 is put i n the fciriii
+
Fig. 3.-- Plot of ( k u b . d . . l ( € 1 -,K r ] j for S p I I \ 7 ) - S p ( \ ' I ) :tiid I ~ ~ I \ . ] - P u ( \1 'rlc a c t i c i i ~ ~ 0 : , I'(IL-)bI'11(\'1 i rc:Ict i i i n ; 0 , S p ( l \ . )- S p ( \ ' I ' reaction.
the values of k ' b = 0.43 X lo-? liter2 sec.-* and k ' ~= 0.23 X lo-' inole-" liter3 set.-' found for sulfuric acid solution. The specific rate constants Tor the reaction are higher by :I f2ictor of 2.5 to 2.7 in tleuteriuni solutions. 11
'r.4I3LE
RATE 11.4T.4
THE DISPROPORTIOSATION
FOR
REACTION IN
TIrO SOLLTIOS I X I l ( ~ ' ~=1 ~7.50 x 10 - ? .I[, t = 250, p = 2.0, total 9;ir;, [I)-] = 2.0 .l/ 1,ntial concn
Obsd. r a t e constant, k u . I . mole-: miti.
lr)yso,!, l1il,1?51
11
I
Obsd. r a t e constant, k H , I , mole --I min. - 1
~'
(J.31
.iO(l
n=
0.15
0,:31
I
0 3x
1.21 1.14 :3 33 3.42
Oil
2 00
I00
Discussion I n a recent investigation of the kinetics of the L~(117)-P~~(VI) reaction, Xewtonj has postulated a mechanism involving a n inhibiting back reaction favored by hydrogen ion. I t was further suggested that this type of mechanisni may be general and would include the Xp(IV)-Np(VI) reaction. This suggestion is of considerable interest and we have re-examined the data on the neptunium system using the more extensive rate measurements reported in the present paper. For the M(IV)-M(VI) reactions to be considered, :i general mechanism involving consecutive steps caii lic written as ki
.lf
+J'
f
* + wT-T
ILIO.T+
k. k, iYll+
I_ k.
[U'!
--
k:,
[s,]
.-
(4)
1
+ prr '
+ products
for which the rate equation is
(5)
where h-is the hydrolysis constant of the +4 ion. li -1I-l ( x q . )
LlOH.'3 (aq.i
+ €IT
(9i
-1plot of the left side of equation S is made against hydrogen ion. The intercept will be l / k l arid the slope will depend on the number of transition states and the number of hydrogen ions evolved ( i . ~ . , the values of w,pI etc.']. For the U t 4 - P u 0 2 i 2 data. the expected straight line with a positive intercept is found, confirming t h a t the pro1)osed mechanisni is consistent with the data (see Fig. 2). Similar treatment oi the neptunium data7 also yields a reasonable straight line. However, in this case the intercept is negative, indicating t h a t the proposed mechanism does not hold for this reaction. Aisiniilar plot of our data for the case where Kp is considered as the initial reactant gives a curved line with the intercept again negative or so close to zero t h a t we cannot deduce support for the rnechanisni. I t iiiight be pointed out that if the intercept is zero or close to zero (large 1; k l ) , then the equations for the successive reactions reduce to the same form as for parallel reactions. In other words, if kl is sufficiently large it becomes difficult to distinguish between parallel and consecutive reactions. 'Turning to the deuterium isotope effect on the rates, one can make the following comments. Since the empirically observed rate laws for both the Np(1V)-Np (1'1) and the Np (1')disproportionation reaction in deuterium solution can b e espressed in the same form as in hydrogen solution. the mechanism is probably the same in both media. The problem is then to consider the probable effect of deuterium on the different stages of the reactions. The observed inverse hydrogen ion dependence of the reproportionation reaction may be formally 16) S. W. Rabideau, I,. B. Asprey, T. I;.Keenan a n d T. 1%'. Newton, paper presented before t h e 2nd International Meeting on t h e Peaceful Uses of Atomic Energy, G e n e r a , September, 1958. ( 7 ) A value of k E for S p +iof 0.039 has been estimated f r o m t h e cons t a n t s for uranium(1V) a n d plutonium(IV).s Since t h e interpreta. tion of t h e isotope effect on t h e neptunium reaction required a knowledge of K E in both HzO and Dz0, t h e constant has been determined in both media b y a combination of spectrophotometric a n d $H measurements. Surprisingly, t h e behavior of neptunium(1V) appears to be markedly different from both uranium and plutonium. In HnO. ICE is found t o be 5 & 0 3 X and in DnO t o be3.2 i 0.5 X 1 0 - p F u r t h e r reaction results in polymerization. De(, = 2 00. ClOa-). I,erimmts w i l l l) irivcn in a subsequent piihlicntion
O F DEUTERIUhZ h k y 20, 1gt39 KINETICSO F EXCIIAXGE
depicted by a number of kinetically indistinguishable postulates. The assumption previously made of a rapid and reversible hydrolytic pre-equilibrium is not overly attractive in the light of the equilibrium experiments. Although it is possible to formulate an entity such as N ~ ( 0 H ) ~ and f f attribute the observed isotope effect to the hydrolytic equilibrium, it is equally plausible to assume that if hydrogen is split off in the activated complex a deuterium effect of similar magnitude would be obtained. It is not readily apparent that the isotope effect can distinguish between these two possibilities. I n contrast to the Np(1V)-Np(V1) reaction, the rate of the Np(V) disproportionation is increased by D20. It has been suggested t h a t for the Np(V) reaction, as well as for the kinetically similar U(V) and Pu(V) disproportionation, the first step in a reasonable mechanism would be an equilibrium [CONTRIBUTION FROM
THE
BETWEEN
DIBORANE AND T E T R ~ B O R ~ N E Mot"
+ H'*
K M02Hf*
This would be followed by one or more steps MOz+
+ MOZH -+kz products
MOzH++
++
+ MOzH++
ka ---t
products
(12)
Since the species MO2H++ would be a strong acid, no isotope effect would be expected for the preequilibrium. Logically then one would interpret the observed isotope effect as arising from a tighter bonding of hydrogen in the activated complex than in reactant species such as M 0 2 H + 2or M02HS04. I t does not appear feasible to define further the condition of the hydrogen in the activated complex or draw any conclusion as to detailed mechanism of a hydrogen atom transfer from the isotope data. LEMONT,ILLINOIS
DEPARTMENT O F CHEMISTRY, THEJOHNSHOPKISSUNIVERSITY]
Kinetics of the Exchange of Deuterium between Diborane and Tetraboranel BY J. E. TODD AND IT.'.S. KOSKI RECEIVED~ - O V E M R E R 1. 19,58 The kinetics of the exchange of deuterium between diborane and tetraborane have been found to be complex. The results indicate t h a t the exchange proceeds by two different paths-one involves two hydrogen positions in tetraborane and the other involves the remaining eight or all ten hydrogen positions. The major reaction is interpreted in terms of a ratedetermining reaction of BDa from diborane with B4Hlo while the minor reaction is envisaged as a rate-determining activation of two sites in tetraborane followed by rapid deuterium exchange with Boron atoms also exchange in this system although detailed kinetics studies have not been made.
Introduction The equilibria which are the bases for understanding interconversion reactions of the boron hydrides have been investigated by two types of chemical or quasi-chemical investigations. The purely chemical method consists of studies of product formation whereas the quasi-chemical method involves kinetic studies of isotope exchange. In either case the equilibria involved are deduced by proposing mechanisms compatible with the observed change of the system. The advantage of directness inherent in the chemical method is frequently offset by complications introduced by product interference so that, in many systems, only initial-rate studies are feasiible. Frequently, isotope exchange experiments may be performed under such conditions that any chemical change is either negligible or corrigible. Moreover, the elementary steps contributing to the mechanisms of both types of reactions are often the same so that the equilibria involved may be elucidated more directly by the isotope exchange method. An example of this is the BzHe-BHs equilibrium which has been postulated in both chemical and isotope exchange reactions involving diborane.2,3 (1) This research was supported by t h e United States Air Force through t h e Air Force Officeuf Scientific Research of t h e Air Research a n d Development Command under contract No. A F 18(600)-1526. Reproduction in whole or in part is permitted for a n y purpose of t h e United States Government. (2) R . P. Clarke a n d R . N. Pense, THISJ O U R N A L , 7 8 , 2132 (19.51). (3) P. C. hlaybury a n d 'w. S. Roski, J . Chem. P h y s . , 21, 742
(1953,.
In less ideal situations the exchange results may yield information about the lability of atoms of the exchanging isotope which is chemically significant. The B2De-B4Hla exchange reaction, reported in the following paragraphs, appears to fall in this category as well as the former. In addition, i t appears to be the first gas-phase exchange reaction in which atoms of the same element in one compound exchange a t two measurably different rates.
Experimental A. Preparation of Materials.-Diborane
(BZH6, BZD6 and B1'&) was prepared by treating lithium aluminum hydride or deuteride with boron trifluoride in ether. The details of the preparation and purification have been described p r e ~ i o u s l y . ~Deuterium resulting from the thermal decomposition of the diborane ranged from 95-9870 pure, and the diluent is hydrogen. Tetraborane was prepared by the BsH~I-Hzreaction. The apparatus and procedure for this preparation are described by Burg and Stone.5 The tetraborane was purified by distillation from a trap at about -78" ( D r y Ice-acetone) to one at -119" (melting ethyl bromide) with continuous pumping to remove diborane. Tetraborane purified in this manner was free from impurities as indicated by its infrared spectrum. The purification procedures used for both and BzDe were spot-checked by vapor-phase chromatography and found to be free of detectable amounts of impurities. B. Isotopic Analysis.-Two methods were used in analyzing the boron hydrides for their specific deuterium content. (The term specific deuterium content is herein defined as the total number of deuterium atoms in a sample of compound divided by the total number of atoms of hydrogen and deuterium in the sample.) I n the more fundamental ~~
(4) W, S. Koski, P. C . hlaybury a n d J. J. Kaufman, A n d . Chem., 26, 1992 (1954). ( 5 ) A. B. Burg a n d F. G . A . Stone, THWJ O U R N A L , 7 6 , 228 (1453).
