1741
REACTION BETWEEN VANADIUM(II) AND NEPTUNIUM(IV)
The Kinetics of the Reaction between Vanadium(I1) and Neptunium(1V) in Aqueous Perchlorate Solutions1 by Mary J. Burkhart2 and T. W. Newton University of California, Los Alamos Scientific Laboratory, Los Alamos, N e w Mexico 87644 (Received November $6, 1968)
+
+
The reaction Np(1V) V(I1) = Np(II1) V(II1) was studied in acid perchlorate solutions from 0.016 to 2.0 M HC104, from 0.9 to 36.7’ at anionic strength of 2.0 M (LiC104). The rate law at 25’ is -d[Np(IV)]/dt = (2.53 (3.8 x 10-2/[H+]) (6 x 10-4/[H+]*)][Np4+][Vz+].The temperature dependence of the predominant,hydrogen ion independent term leads to AH* = 9.72 =t 0.05 kcal/mol and AS* = -24.0 i:0.2 cal/ mol deg for Np4+ V2+ = activated complex. Chloride ion causes a moderate increase in rate. For the most important chloride term the net activation process is Np4+ V2+ C1- = activated complex, for which AH* = 13.45 =k 0.15 kcal/mol and AS* = -5.5 =t 0.4 cal/mol deg. The effect of ionic strength is in accord with an extended form of the Debye-Huckel equation from 0.275 to 4.0 M . The hydrogen ion, chloride ion, and temperature-dependence data are consistent with an outer-sphere mechanism.
+
+
+
+
Introduction The kinetics of reactions in which V(I1) is oxidized to V(II1) have attracted considerable attention recently because important qualitative differences between V(I1) and the other reducing agents Cr(II), Fe(II), and Eu(I1) have been observed. Many oxidations of V(I1) are predominantly hydrogen ion independent and most of those which probably involve inner-sphere mechanisms appear to be limited by the rate of substitution on V(II).a I n the present work we have studied the reaction V(I1)
+ Np(1V) = V(II1) + Np(II1)
(1)
Np(1V) was chosen as the oxidizing agent to provide an example of a 4+ actinide ion. The oxidation potentials for neptunium4 and vanadium5 ions show that reaction 1 goes to completion; the equilibrium quotient is about 1O’O. An additional reaction must be considered (eq 2) for which the equilibVs+
+ Np4++ 2H20
V02+
+ Np3+ + 2H+
(2)
rium quotient has been determined to be (6.2 f 0.4) X M 2 a t 25’ and p = 3 M.6 We estimate that this M 2 at p = 2 M . value will rise to about 7.3 X Because of reaction 2 it is convenient to consider two regions of hydrogen ion concentration: (a) [ H + ] > 0.2 M where ( 2 ) is relatively unimportant and (b) [H+] < 0.2 M where corrections for the formation of V(1V) must be applied.’ Experimental Part Reagents. Neptunium(V1) solutions were prepared from neptunium stock solutions made up in HC104 as previously described.8 A portion of the stock solution was taken nearly to dryness and weighed to determine the 71% HC104 remaining. It was diluted with the
+
appropriate amount of standardized HClOd to give Np(V1) in the desired acid concentration. Separate experiments showed that fuming HC104 oxidizes neptunium quantitatively to the VI state. No substance capable of oxidizing Np(III), other than the Np(V1) itself, was found in these solutions. A portion of the Np(V1) solution was reduced to Np(II1) with zinc amalgam and the total neptunium content of these completely reduced solutions was determined by titrating back to Yp(V1) with standard Ce(IV).s Neptunium(1V) solutions were prepared by mixing carefully measured volumes of Np(II1) and Np(V1) in a mole ratio of 2: 1. Sufficient time was allowed for the quantitative reaction 2Np(III) Np(V1) = 3Np(IV) to go to completion.9 These Np(1V) solutions were found to be stable with respect to air oxidation for periods of at least 1 week. Vanadium(V) solutions were prepared from two sources of V206. The first was prepared by acidifying a solution of NH4V0s (Fisher Scientific Co., marked purified) and washing the precipitate thoroughly with water. The second was prepared from metal reported
+
(l! Work done under the auspices of the U. S. Atomic Energy Commission. (2) Graduate student summer employee. (3) N . Sutin, Accounts Chem. Res., 1, 225 (1968). (4) J. J. Katz and G . T . Seaborg, “The Chemistry of the Actinide Elements,” Methuen and Co., Ltd., London, 1957, p 224 (also published by John Wiley & Sons, Inc., New York, N. Y . ) . (5) W. M. Latimer, “Oxidation Potentials,” 2nd ed, Prentice-Hall, Inc., New York, N . Y., 1952. (6) E. H. Appelman and J. C. Sullivan, J. Phys. Chem., 66, 442 (1962). (7) 3. C. Sullivan, personal communication. (8) T. W. Newton and N. A. Daugherty, J . Phys. Chem., 71, 3768 (1967). (9) J. C. Hindman, J. C. Sullivan, and D. Cohen, J . Am. Chem. SOC., 80, 1812 (1958).
Volume 78,Number 6 June 1969
1742 to be 99.8% V and 0.03% Fe (Varlacoid Chemical Co.). The metal was dissolved in 5 M HNOI and taken to fumes with HC104 to precipitate V205 which was washed as before. The V20j was dissolved in 1 M HC1O4 to give stock solutions of V(V). Total perchlorate in these solutions was determined by reducing samples to V(1V) with zinc amalgam and passing aliquots through a cation-exchange resin in the acid form. Eluents were titrated with standard NaOH to the phenolphthalein end point. Vanadium(I1) solutions were prepared by reducing samples of the V(V) stock solutions on zinc amalgam. These solutions were analyzed by oxidizing aliquots with excess standard Ce(1V) and back-titrating to V(1V) with standard Fe(I1) in 6 M H2S04solutions.1° Stock solutions, about 3 'M in HClO4, were prepared by diluting commercial 71% acid which had been boiled and cooled in a stream of argon. The diluted solutions were boiled again before use; analysis was by titration with standard NaOH. Solutions of LiC104, NaC104, and La(C10& were prepared by neutralizing analytical reagent grade carbonates (or oxide for La) with perchloric acid. These were purified by two or three recrystallizations from water. The concentrations of the stock solutions were determined using Dowex 50 in the acid form. Aliquots were passed through ion-exchange columns and the eluents were titrated with standardized NaOH. Doubly distilled water was used for all solutions; the second distillation was from alkaline permanganate in an all-Pyrex still. The concentration units employed in this paper are moles per liter at 23". Procedure. Reaction rates were determined spectrophotometrically in rapidly stirred 10-cm absorption cells as previously described.* The measurements were made at 7230 where Np(1V) is the principal absorbing species. At this wavelength the extinction coefficient change for reaction 1 is close to -172 Ii!l--l cm-l for 25" and 2 M HC104. For most of the rate runs, all of the solutions except the V(I1) were placed in the cell and swept with purified argon for about 40 min while temperature equilibrium was being established in the thermostat. The reaction was started by injecting the V(I1) solution at the appropriate temperature from a calibrated hypodermic syringe with a Teflon needle. No significant effectswere observed when the order of addition of the reactant solutions was reversed. Rate Law. In the high-acid region the rate of change of absorbance with time was often relatively low at first but increased to a normal rate after 10-15 sec. This "inhibition" is very likely due to contamination of the V(I1) solutions with enough oxygen to give about 11.5% V(IV).ll The reverse of reaction 2 is much faster than the V(I1)-?Jp(IV) reaction, so a net disappearance of Np(1V) does not occur until the V(1V) is reduced to V(II1). For solutions with [H+]greater than 0.2 M the data obtained after the induction period were in accord with the second-order rate law: -d[Sp(IV)]/dt = k'[VThe Journal of Physical Chemistry
MARYJ. BURKHART AND T. W. NEWTON (II)] [Np(IV)]. Values for IC', the apparent secondorder rate constant, were calculated from the absorbance data using a nonlinear least-squares program which minimized Z ( A o b s d - Aoalod) 2.12 The uncertainty in the time at which the reaction actually started was treated as an adjustable parameter, or, alternatively, the timing was assumed to be exact and the initial absorbance was made an adjustable parameter. Differences in the rate constants calculated in these two ways were insignificant, usually less than 1%. Results of a typical run are shown in Table I where observed and calculated absorbance values are given as a function of time. ~
~~
Table I : Typical Rate Run" Time? see
Aobsd
Aaaled'
0 20 40 60 80 100 120 140 160 180 200 220 240
0,600 0.564 0.532 0.500 0,472 0,445 0.421 0,399 0,376 0,357 0,338 0.319 0.301
(0.600) 0.566 0.532 0.500 0,472 0,445 0.420 0.396 0.375 0.354 0.336 0.318 0.302
Time, sec
260 280 300 320 340 360 440 520 600 680 760 840 m
Aobsd
Acdodb
0.286 0.270 0.258 0.244 0.232 0.221 0.180 0.150 0 128 0,109 0.094 0,081
0.286 0.272 0,258 0.245 0.233 0.222 0.183 0.152 0.128 0.108 0.092 0,079 0.021
I
a Conditions: 25.2", 2.00 M HCl04, 3.58 X M Np(IV), M V(I1). This calculation gives -1.9 i and 1.30 X 0.7 sec as the effective start of the reaction. If the effective start is taken as zero, A c a l o d is 0.604 & 0.001 and k' is 2.557 M-1 sec-1. Calculated using -d[Np(IV)]/dt = 2.552, [Np(IV)][V(II)] M sec-'.
Better evidence for the correctness of the second-order rate law is provided by experiments in which the initial concentrations of the reactants were varied. The results are shown in Table 11. The effect of varying [Np(IV)]o by a factor of nearly 9 is within the experimental error of the determinations of k'. Increasing [V(II)10 by a similar factor increases lc' by an amount just beyond the experimental error. Table I1 also shows that the source of the vanadium is without significant effect. Other experiments showed that concentrations of the product ions V(II1) and Kp(111) are without effect at concentrations at least as high as M . This is about three times higher than that produced in a typical rate run. It was also found that nep(10) G. H. Walden, L. P. Hammett, and S. M. Edwards, J . Am. Chem. Soc., 5 6 , 57 (1934). (11) J. H. Swinehart, Inorg. Chem., 4 , 1069 (1965), has shown that the oxidation of V(I1) by oxygen proceeds predominantly t o V(1V). (12) T. W. Newton and F. €3. Baker, J. P h p . Chem., 67, 1425 (1963).
1743
REACTION BETWEEN VANADIUM(II) AND MEPTUNIUM(W) tunium solutions further purified by extraction into methyl isobutyl ketone gave essentially the same rates as the ordinary stock.
0
IO I
TIME
- SECONDS
20
30 I
45
I
60
90
180 3
Table 11: Effect of Initial Concentrations of Np(1V) and V(I1) on the Apparent Second-Order Rate Constant"** lO~[Np(IV)lo, M
108IV(II)lo, M
0.36 0.36 0.36 1.33 1.96 3.16
1.30 1.95 4.45 0.45 0.45 0.43
k',E
k',d
M-1 aec -1
2.60 2.58 2.67 I
8ec-l
2.56 2.60 2.72 2.63 2.56 2.54
... .
M-1
.
...
a Apparent second-order rate constant defined by: -d[Np(IV)]/dt = k'[Np(IV)] [V(II)]. Conditions: 25.2' V(I1) solution prepared from vanadium and 2.00 M HClO4. metal. V(I1) solution prepared from NH4V08.
'
Zinc(I1) was found to be without effect on the second-order rate constant. A rate run was made using V(I1) made from V(V) by reduction on zinc amalgam in the usual way. The V(I1) remaining on the amalgam was then oxidized to V(1V) with air and reduced again. This was repeated and another rate run was made. Rate constants for the two runs agreed within the experimental error, the second value being 1.2% lower than the first. This result also shows the absence of catalytic impurities from the amalgam. I n contrast to the results described above, the data from solutions with [H+]less than 0.2 M are not in good agreement with a simple second-order rate law. However when reaction 2, together with V2+
+ V 0 2 + + 2H+ = 2V3+ + HpO
dy/dt whereA
- x - y ) ( B - 2) + kay(B - X) kz(A - x - Y ) ( X - y) k--z(z + Y)Y - k3y(B - ). (4) = [n'p(IV)10,B = [V(II)10, x = B - [V(II)], =
Figure 1. Rate run at 25', p = 2.0 M , [ H f ] = 0.02 M, [V(II)IO= 1.93 X loFs M, and [Np(IV)lo = 0.359 x 10-3 M. Solid lines were calculated using kl = 5.12 M-I see-', kz = 3.64 X IOa M-l sec-l, k-z = 2.0 x 108 M-1 sec-1, and k4 = 1.6 M-' sec-l: A, absorbance X 10; B, [Np(IV)] X 104, M; c, [V(IV)I x 104, M ; D, [V(III)I x 104, M .
(3)
is considered, good agreement between observed and calculated absorbance os. time values was obtained. Equations 1-3 lead to the simultaneous differential equations dX/dt
I- INp(IU)l /[Np(IU)l,
ki(A
y = [V(IV)], and the k's are for the indicated reac-
tions. These equations were solved numerically and least-squares best values for kl were determined as previously described. l 3 These calculations required values for the rate constants kz, k-2, and k3 as well as the initial concentrations A and B. A single determination of k-, gave 400 M-' sec-' at 1' in 0.1 d4 HClOd. This rate may reasonably be expected to be proportional to [H+], to depend rather strongly on the ionic strength, and to have a small temperature coefficient. These considerations lead t o the estimate: k-2 = [H+] (1 f 0.5) X
lo5 M-' sec-'. Values for kp were taken from the expression k2 = lc-,K,, = 73/[H+]. The value k3 = 1.6 M-' sec-' was taken from previous work.14 These values were used in the calculation of kl at the various low acid concentrations. As an example, the results for a run made in 0.02 M HC104-1.98 M LiC104 are shown in Figure 1. Significant concentrations of V(1V) are seen t o persist even in the later stages of the reaction. This run was also used to determine the importance of the necessary approximations. It was found that decreasing k, and k-2 both by a factor of 2 decreased the calculated value for kl by only 2.6%. Similarly, decreasing K,, from 1.82 to 1.55 at constant k-, increased k~ by 4.5%. Reaction 3 was found to be relatively unimportant; decreasing k3 from 1.6 to 0 increased k~ by 1.2y0. The assumption that 1% of the V(I1) was oxidized to V(1V) before the start of the reac(13) T. W. Newton, G. E. McCrary, and W. G. Clark, J.Phys. Chem., 72, 4333 (1968).
(14) T. W. Newton and F. B. Baker, ibid., 68, 228 (1964).
Volume 73, Number 6 June 1969
MARYJ. BURKHART AND T. W. NEWTON
1744
tion caused the calculated value for kl to increase by 3.5%. Including both concentration ranges, the hydrogen ion dependence was studied between 0.016 and 2.00 M in solutions of constant ionic strength (LiClOJ; the results are summarized in Table 111. Between 0.1 and 0.2 M HClO4 the correction for reaction 2 was found to be negligibly small. Above 0.2 M the rate constants were essentially independent of acid concentration. For lower acids, however, the determinations became less reproducible, and the values of k l , corrected for (2) and (3), increased significantly. A rapid reversible hydrolysis of Np(1V) is known to occur, for which [NpOH3+][H+]/[Np4+]= 0.005 M115but in addition we have observed a slow hydrolytic reaction in solutions below about 0.04 M in [ H f ] . I n 0.007 M HC104
in reaction rate in 2 M acid solutions. This dependence was studied a t 13.9 and 36.7' and the results are summarized in Table IV. At both temperatures the apparent second-order rate constant increases linearly with the chloride concentration: k(obsd) = a b[Cl-].
+
Table IV : Chloride Dependence" k', M-1
k',
Mean dev
M-1
IHCll, M
No. of
0.00 0.0495 0.099 0.198 0.297 0.396 0.495
2 2 3 2 3 2 2
13.9" 1.25 2.12 3.04 4.70 6.47 8.05 9.78
0.04 0.04 0.04 0.02 0.08 0.07 0.09
1.25 2.13 3.01 4.74 6.43 8.10 9.75
0.00 0.05 0.10 0.20 0.30 0.40 0.50
2 2 4 2 3 2 4
36.7" 4.74 10.26 16.7 27.5 41.1 52.8 67.1
0.12 0.25 0.1 0.3 0.9 0.9 1.3
4.73 10.43 16.3 28.4 40.9 53.6 66.5
detns
sec-1
(av)
eeo-1
(oalodb)
Table I11 : Hydrogen Ion Dependencea k',
k',
[HC104], M
No. of
detns
(av)
2.00 1.oo 0.60 0.30 0.21 0.16 0.113 0.10 0.080 0.050 0,045 0.040 0,0355 0.030 0.025 0,020 0.016
15 5 3 2 3 2 5 2 3 2 1 1 1 3 1 1 2
2.60 2.55 2.48 2.58 2.56 2.77 2.67 2.94 2.96 3.12 3.54 3.20 3.44 4.19 4.39 5.12 5.26
M-1
sec-1
Mean dev
M - 1 880-1
0.04 0.04 0.02 0.02 0.04 0.07 0.03 0.09 0.20 0.13
2.54 2.54 2.57 2.62 2.66 2.71 2.79 2.83 2.92 3.22 3.31 3.43 3.58 3.84 4.19 4.77 5.55
...
...
...
0.14
... ,
,.
0.30
(oalodb)
Dev
$0.06 f0.01 -0.09 -0.04 -0.10 S0.06 -0.12 +O.ll +0.04 -0.10 $0.23 -0.23 -0.14 $0.35 $0.20 +0.35 -0.29
Conditions: 25.1", 2.00 M (Li,H)ClOd, 3.5 X M Np(IV), 2.0 X 10-3 M V(I1). Calculated from the expression: k' = 11 (0.005/[H+])]-'{2.53 (0.0385/[H']) (0.0006/ [H+12)]. a
+
+
+
2 M ) the first-order rate of change in absorbance at 7230 A was about 0.2 min-l at 25". These changes could be reversed by adding acid and occurred without altering the reducing titer with respect to Ce(1V). It is likely that varying amounts of the product of this slow reaction may be responsible for some of the lack of reproducibility mentioned above. The hydrogen ion dependence over the concentration range studied can be described by the equation (p =
+ +
k'(0bsd) = { 1 (0.005/ [H+])/-l X (2.53 f 0.03 ((3.8 f 0.5)10-2/[1-I+]) ((6.0 f 1.1)10-4/[H+]2)f (5)
+
Chloride ion was found to cause a moderate increase The Journal of Physical Chemistry
a Conditions: 2.00 M H(Cl,ClOd), 3.6 X M Np(IV), M V(I1) a t and 1.57 X 10-3 M V(I1) a t 13.9' and 8.2 X 36.7". Calculated from the expression k' = (1 p[Cl-])-'* (ko kcl[Cl-] kc1'[C1-]2) with the parameters calculated from the following data: AH*o = 9.74 kcal/mol, As*o = -24.10 eu (ko at 25" = 2.74 M-1 sec-1); AH*a = 13.57 kcall mol, AS*cl = -5.31 eu (kc1 at 25' = 49.2 M - 2 sec-l); AH*ci' = 20.25 kcal/mol, A.X*cl' = 17.33 eu (kci' at 25" = 56.2 M - 3 sec-I); AH@ = 3.74 kcal/mol, A& = 12.87 eu ( p at 25' = 1.19 M-1).
+
+
+
The effect of temperature was studied in 2.0 M HC104 solutions between 0.9 and 36.7"; the results are summarized in Table V. The ionic strength dependence was studied at 25.2" Table V : Temperature Dependence" Temp:
OC
0.9 13.8 25.1 36.7
No. of detns
7 6 4 6
k', M-1 sec-1
k',
(av)
Mean dev, %
M-1 sec-1
Diff,
0.570 1.31 2.60 5.06
2.3 1.8 0.4 1.o
0.566 1.32 2.62 5.01
0.7 0.8 0.8 1.0
(oalcdc)
%
M V(II), and 3.6 X a Conditions: 2.0 M HC101, 2.2 X 10-4 Np(IV). Note: these concentrations are defined at 23". Temperatures are probably accurate to &0.lo. Calculated using AH* = 9.72 kcal/mol and AS* = -24.03 cal/deg mol. (15) J. C. Sullivan and J. C . Hindman, J . Phys. Chem., 63, 1332 (1959).
REACTION BETWEEN VANADIUM(II) AND NEPTUNIUM(IV) in solutions of LiC104, NaC104, and La(C104)30.25 1%’ in HC10,; the results are summarized in Table VI. The effect was found to be rather large; in LiC104, for example, the rate increases by a factor of about 13 on going from p = 0.275 to 3.7 fM. The rates in Sac104 and La(C104)3solutions of the same ionic strength were found to agree rather closely. This is evidence that the rate is not influenced by the perchlorate ion concentration.
Table VI : Ionic Strength Dependencea
Salt
LiC104
NaCIOa
La(C10&
Ionic strength, M
k‘,
k’, M - 1
detns
M-1 sec-1 (av)
Mean dev
0.453 1.12 1.30 2.22 2.95 4.31” 4.06d 4.78 5.93
0.036 0.01 0.02 0.01 0.10 0.04 0.05
0.462 1.13 1.33 2.17 3.04 3.98
3.34 3.73
8 2 2 2 3 2 2 1 3
..,
0.18
4.99 6.00
0.275 0.741 1.394 2.14 4.00
8 2 2 2 2
0.453 0.905 1.42 2.14 4.18
0.036 0.02 0.01 0.02 0.01
0.462 0.909 1.45 2.09 4.21
0.275 0.818 1.36 2.09 3.90
8 2 2 2 2
0.453 0,897 1.36 2.07 4.00
0.036 0.007 0.02 0.03 0.03
0.460 0.937 1.36 1.96 4.07
No. of
0.275 0.849 1.024 1.71 2.31 2.85
880-1
(calcdb)
a Conditions: 25.2’, 0.25 M HC104, 3.6 X M Np(IV), Calculated using the extended Debye2.35 X 10-8 M V(I1). Huckel expression with the following parameters: for LiC104, kO = 0.01098 i 0.0010, A = 3.245 f 0.12, B = 0.1532 f 0.010; for NaC104, kO = 0.01343 f 0.0014, A = 3.508 f 0.15, B = 0.1156 f 0.011; for La(ClO& ko = 0.01537 f 0.0015, A = 3.749 i 0.20, B = 0.1302 f 0.012. “ T h e LiC104 for these runs had been crystallized four times, rather than the usual three times. The LiClOa for these runs was from the mother liquor from c .
‘
The observations were found to be in accord with the extended Debye-Huckel equation log k‘ = log kO
+ [0.509Ax2p”’/(l
+ Ap”’)] + B p
(6)
For the net activation process involved, Ax2 is 16 and the data in Table VI were used to find the least-squares best values for ko, A , and B, given in footnote b of the same table. The unreliability of the long extrapolation to zero ionic strength is indicated by the divergent ko values found for the three salt solutions. It is interesting to note, however, that the A and B values found here are approximately equal to those for the V(I1)-
1745
U(V1) reactionlGin spite of the much lower Ax2 for this reaction. Interpretation and Discussion The data show that the predominant term in the rate law is hydrogen ion independent and thus the most important net activation process is” Xp4+
+ V2+ = [Np*V‘+]*
(7)
The temperature-dependence data in Table VI are in good agreement with the Eyring equation and a leastsquares calculation leads to AH* = 9.72 f 0.05 kcal/ mol and AX* = -24.0 f 0.2 cal/deg mol. The uncertainties indicated here are the standard deviations. The experimental entropy of activation has been used to estimate the formal ionic entropy of the activated S O V ~ + complex: S*(complex) = AS* = -24 - 23 - 84 = - 131 cal/deg mol. This value is in good agreement with those for other activated complexes with a charge of 6+. Previously tabulated values range from - 116 to - 133 cal/deg molal8 The increase in rate at low acid concentrations (Table 111)indicates an additional net activation process
+
Xp4+
+
+ V2++ H20 = [Np*OH.V5+]*+ H +
(8)
This process is relatively unimportant; the rate constant ratio, ~ - H / ~ H is~ o0.015 M , where k - ~applies to (8) and kHz0 to (7). Alternatively, the inverse dependence can be described by KpOH3+
+ V2+ = [Np*OH*V5+]*
(9)
for which ~ o H / J G H ~ o = 3.0. It is of interest to compare the rates of reduction of Np(1V) by Cr(I1) and by V(I1). Although the rate of the first reaction is only twice as large as that by V(I1) in 1 M HC104, the hydrogen ion dependences differ greatly. The chromium reaction is predominantly inverse first power and a term independent of [H+]was not detected.l9 We estimate that ~ - H / ~ K ~>o 100 or k o ~ / k ~>~ 2o X lo4 for this reaction. The ratios for these chromium and vanadium reactions are to be compared with the values for the analogous ratios for known inner- and outer-sphere reactions. For example, the reduction of C O ( N H ~ ) S O N Z by~ +Ru(NH3)G2+ is ~ ~ known to be outer sphere with k o ~ / k= ~10-2.20 If Cr2+is the reducing agent, the reaction is inner sphere and the ratio is 3 X 106.21 Before concluding that the Np4+-V2+ reaction is predominantly outer sphere we must consider that the (16) T. W. Newton and F. B. Baker, J . Phys. Chem., 69, 176 (1965). (17) I n net activation processes 7-9 and 11, the compositions of the activated complexes but not their structures are indicated. (18) T. W. Newton and F. B. Baker, Advances in Chemistry Series, No. 71, American Chemical Society, Washington, D. C., 1967, p 268. (19) R. C. Thompson and J. C. Sullivan, J. Am. Chern. Soc., 89, 1096 (1967). (20) J. F. Endicott and H. Taube, ibid., 86, 1686 (1964). (21) A. Zwickel and H. Taube, ibid., 83, 793 (1961).
Volume 73, Number 6 June 1960
MARYJ. BURKHART AND T. W. NEWTON
1746
rates of a class of inner-sphere reactions of V2+ are between 13.3 and 13.6 kcal/mol. These values apply limited by the rate of substitution at the ~ a n a d i u m . ~ to the net activation process o , reaction 1 at p = 1 is quite The rate constant, ~ H ~ for Np4+ v2+ C1- = [Np*Cl*V6+]* (11) close to the values at the same ionic strength for the inner-sphere oxidation of Vz+ by CrSCN2+ (8 M-l Values for kcl' and its AH* were calculated at the same sec-1)z2 and by V 0 2 + (0.8 M-I sec-').14 However, it time; they are unreliable, however, since they depend is unlikely that reaction 1 belongs in this class since the very strongly on the estimates for p1 and pz. The resubstitution reactions of ions like Np4+are quite rapid. sults of one of these calculations are shown in Table IV. Thus an inner-sphere, water-bridged complex could be When the rates of oxidation of V2f by Fe3+ and formed without substitution on Vz+. I n addition, FeC12+ 2 9 are compared, the ratio kFeC1/kFe is found AH* for process 7 is 9.7 kcal/mol, considerably smaller to be about 25 for these outer-sphere reactions. The than the values near 13 kcal/mol for the substitutionanalogous ratio for the V2+-Np4+reaction lies between limited inner-sphere reaction^.^ The V2+-Co(NH3)s11 and 18, depending on the value chosen for 01. These OHz8+reaction, which is probably outer sphere,23 also values may be compared with the corresponding one for shows a relatively low. value for AH*, 8.2 kcal/mol. the inner-sphere reaction between Cr2+ and Fe3+;here These considerations lead us to assign reaction 1 to the the ratio is about 104.30 These comparisons show that class of outer-sphere reactions of V2+. the observed chloride dependence is consistent with the The effect of chloride on the rate may reasonably be assignment of an outer-sphere mechanism to reaction 1. explained by the rate law It should be pointed out, however, that the chloride effect alone does not rule out the possibility of a substitution-limited rate. Parker and Espenson31 have -d[Np(IV)]/dt = [Np4+][V2+]X shown that kCl/kH20 in such cases might be as large as (ko kc1[C1-1 kc1'[C1-I2 . , . > (10) 23. This upper limit is based on the assumptions that the association quotient of VC1+ is 0.2 M-' and that the I n terms of the empirical linear parameters a and b, substitution reactions of VC1+ are 100 times faster than ko = a, lccl = b (PI Pda, kcl' = b(P1 Pz) those of V2+. aP& . . . , where p1 and Pz are the association quoAcknowledgments. We wish to acknowledge helpful tients for NpC13+and VC1, respectively. Although resuggestions by Dr. J. C. Sullivan and many discussions liable values for p~ and Pz are not available, kcl can be Dr. C. E. Holley, Jr., under whose general direcwith determined fairly accurately since b is much larger than tion this work was done. a and the P values are not large. Data for NpC13+ are very fragmentary24so it is necessary to estimate from (22) M. Orhanovib, H. Po, and N. Sutin, J . Am. Chem. SOC.,90, 7224 (1968). data on UCl3fZ6and P U C ~ ~ We + . ~estimate ~ that 01 (23) P. Dodel and H. Taube, 2. Physik. Chem. (Frankfurt), 44, 92 is probably in the range from 1.2 to 1.8 M at 25" and (1965). p = 2 M. AH" is probably about 3.5 kcal/mol. The (24) R. W. Stromatt, R. M. Peekema, and F. A. Scott, Hanford Laboratories Report HW-58212, 1958. association quotient for VC1+, p2, is certainly smaller; considering published work on FeC1+ 27 and CoC1+,28 (25) R. A. Day, Jr., R. N. Wilhite, and F. D. Hamilton, J . Am. Chem. Soc., 77, 3180 (1955). we conclude that Pz is probably less than 0.5 M . Least(26) S. W. Rabideau, et al., Proc. Intern. Conf. Peaceful Uses At. squares calculations were made to determine kcl and Energy, Bnd, Geneaa, 1968, 28, 361 (1958). its AH* after assuming values of 61 p2 ranging from (27) H. Po and N. Sutin, Inorg. Chem., 7, 621 (1968). (28) M. W. Lister and P. Rosenblum, Can. J . Chem., 38, 1827 1.19 to 3.0 M. The temperature dependence of PI (1960). P 2 was assumed to be described by a composite AH" (29) B. R. Baker, M. Orhanovib, and N. Sutin, J . Am. Chem. Soc., with values chosen between 3.24 and 4.5 kcal/mol. 89, 722 (1967). These calculations gave kcl values between 49.2 and (30) G. Dulz and N. Sutin, {bid., 86, 829 (1964). 53.4 M - z sec-' for 25" and corresponding AH* values (31) J. H. Espenson, personal communication.
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