N. A. DAUGHERTY AND T. w.KEWTON
1090
on each mixture, aiid the mean value is given in the last column of Table 111. The result a t I = 1 is iii good agreement with 0.034 interpolated for X = 33.4 and t = 25’ iii the values found by dkerlof, Teare, and Turckj for a total ionic strength of unity. It has already been noted5l3 that addition of methanol to the aqueous solvent is almost without effect on the value of aI2(the value is 0.033 for aqueous mixtures of hydrochloric acid aiid sodium chloride of I
Vol. 67
= 19. The results given in Table I11 suggest that 0 1 1 ~ decreases slightly with increasing I , but the reduced accuracy with which 0112 can be determined a t ionic strengths below 1 probably makes such a conclusion unwarranted. Thus, the values of -log s y in~ the sixth column of Table 111 (calculated with a constant value of a12 = 0.035 a t each ionic strength) differ from the “observed” values on the average by hardly more than the experimental error.
THE KINETICS OF THE REACTIOS BETWEEN YAKADIUM (V) AND I R O S (11) BY X.A. DAL-GHERTY~ AND T. W. NEWTON Cnzversaty of Cal?fornia, Lo8 Alamos Scientific Laboratory, Los Alanzos, New Mexico Received iYovember 16, 196d
+
+
The kinetics of the reaction ]‘(IT)Fe(I1) = V(1V) Fe(II1) have been studied in acid perchlorate solutions from 0.047 to 1.0 M in HC104 over a temperature range from 0 to 55.6” a t fi = 1.0. The rate law found is -d[V(V)]dt = k’[V(V)I[Fe(II)I, where k‘ may be given by: k‘ = a[H+]-’ b c[H+]. The e[“] term strongly predominates the others; values of AH* and A S * for this path were found t o be 1.52 i 0.16 kcal./mole and -37.3 f 0.6 e.u.
+ +
Introduction It has been found that the rapid reaction between V(V) and Fe(I1) can be studied by an extension of ordinary spectrophotometric techniques. This reaction is of interest to us for two reasons. First, V(T’) in acid solution is probably Toe+ and is structurally similar to the +5 actinide i 0 q 3 and a comparison of the kinetics of its reduction reactions with the analogous ones of the actinide ions should help elucidate some of the factors which determine such rates. One of these factors is the formal ionic entropy of the activated complex which for reactions involving actinide ions appears to be predominantly determined by the charge on the complex.4 The second reason for interest is to see whether this correlation extends to reactions between transition metal ions. Previous kinetic work on the reduction of V(V) by inorganic ions in non-complexing solutioiis is that of Ramsey, et al., who studied the reduction by iodide iom5 Experimental Reagents.-Two stock solutions of T7(T’) perchlorate were prepared. For the first, Fisher Scientific Co. “purified” ammonium meta vanadate was recrystallized from hot water and heated to about 900” in an electric muffle to convert the ammonium salt t o the oxide. This was dissolved in 3.34 M HClO4 and treated with ozone to oxidize traces of V(1V) to V(T7). Excess ozone was removed by passing oxygen through the solution for 16 hr. The second solution was prepared by dissolving vanadium metal in 5 HNO, and fuming with HC104 to remove nitrate and to oxidize the vanadium t o V(V). The V(V) content of these solutions was determined by titration of aliquots with standard FeS04 solution, according to the method of Hammett.6 The titrations were done in 6 X HzS04 to the ferrous phenanthroline end point. The two stock solutions were found t o be 0.16 and 0.02 M in V(T7). The free acid in the first stock solution was estimated (1) Talk done under the auspices of the U. S.Atomic Energy Commission. (2) Los Alamos Scientific Laboratory, Summer Staff Member. (3) hi. J. LaSalle and J. W.Cobble, J. Phlls. Chem., 59, 519 (1955). 44) T. W.Newton and S. W. Rabideau, %bid., 68, 365 (1959). (5) J. B. Ramsey, E. L. Colichman, and L. C. Pack, J . Am. Chem. Soc., 168,1695 (1946). d6) C. H. Walden and L. P. Hammatt, ibid., 66, 57 (1934)
to be 3 . 2 .Tf based on the initial acid concentration and the final I-(V) concentration. The second stock solution contained far less vanadium and the acid wa9 found to be 4.2 J f by titration with S a O H to the brom phenol blue end point. For the kinetic runs, only a small fraction of the total acid came from that present in the vanadium stock solutions; so errors in the estimation of the acid concentration in these stock solutions were completely negligible. Most of the kinetic runs were made using the first stock solution but several were made with the second. Within the experimental error the same concentrations of the two solutions gave the same results; so it is unlikely that significant concentrations of catalytic impurities were present in either stock solution. A stock solution of Fe(I1) was prepared by dissolving a weighed amount of Mallinckrodt analytical grade iron wire in 0.5 M HClOd and then adding sufficient 3 M HC10( to give a solution 0.10 .lit in Fe and 0.50 M in HC104 upon dilution to the final volume. The solution was found to contain about M c1-. Solutions of He104 were prepared by diluting analytical reagent grade concentrated acid. The concentrations of the solutions were determined from density measurements.? The concentrated acid had been freed of reducing impurities by boiling a t atmospheric pressure and cooling in a stream of scrubbed argon. Solutions of LiClOr were prepared by neutralizing analytical reagent grade Li2C03with HClO,, boiling out the COZ,and crystallizing from water a t least three times. The salt solutions were analyzed by density determinations; the concentration vs. density functions were determined from previously analyzed solutions.8 The water used in the preparation of all solutions was doubly distilled; the second distillation was from alkaline KRIn04 in an all Pyrex still. Apparatus.-Rate runs were made in specially shaped Pyrex cells which were positioned in a small water-filled thermostat in the light beam of a Cary recording spectrophotometer, Model 14. The cells were similar to small erlenmeyer flasks to which two 25 mm 0.d. tubes were sealed coaxially to provide a light path of about 10 cm. The ends of these tubes were left rounded since the water in the small thermostat eliminated most of the focussing effect which otherwise would have been present. The contents of the cells m-ere stirred from below by means of Teflon covered magnetic stirring bars. The spectrophotometer was operated in the ultraviolet range using the hydrogen lamp. Since the cover of the sample-containing cell compartment was removed during kinetic runs, measurements were made with the room darkened. The reaction was started by injec(7) I,. H. Briokwedde, J . Res. IVaatl. Bur. Std., 42, 309 (1949). ( 8 ) T . R’. Xerrton, J . Phus. Chern., 62, 943 (1958).
May, 1963
KIXETJCS OF REACTION BETWEES VAKADICM(V) AKD IRON(II)
ing one of the reagents into a stirred solution of the other already in the cell. The injection was made by meansof a5-ml. hypodermic syringe with a large stainless steel needle. With this apparatus 5 ml. from the syringe could be mixed into 60 ml. in the cell in about 2 seconds. I n spite of the curvature of the cell windows, adherence to Beer's law was found to be satisfactory. Tests with Cos01 and Pr( C104)3 solutions showed that the total spread in apparent extinction coefficients up to an absorbaiice of 1.7 waB 0.4 and 0.9%, respectively . Procedure.-The reaction was followed spectrophotometrically by measuring the absorbance of the reaction mixture as a function of tims. The "ave lengths used were in the range of 3060 to 3500 A. The general procedure for the kinetic measurements was as follows: Dilute stock solutions of V(V) and FejII) were made from the concentrated ones previously described. The concentration of Fe(1I) was determined by pipetting aliquots into a measured excess of standard Ce(1V) and titration of the excess with standard FeSOp to tlhe ferrous phenanthroline end point. A IO-ml. aliquot of the dilute pervanadyl stock and 50 ml. of HC104-LiC10a, to adjust acidity and ionic strength to the desired level, were pipetted into the reaction cell and the cell was placed in the small thermostat in the cell compartment. The analyzed Fe(I1) stock was kept in a separate vessel a t approximately the same temperature. After temperature equilibrium had been established, 5 ml. of the FejII) solution was injected into the stirred T-(V) solution a t the same time that the spectrophotometer recorder strip chart was started. The course of the reaction u'as recorded as absorbance a t the desired wave length us. time; chart Epeeds of 8 in./min. were used. The temperature of the reaction mixture was taken with a small thermometer about one minute after injection. Calculations .-The initial reactant concentrations were calculated from those of the analyzed stock solutions. The extent of reaction was determined from the initial absorbance, the final absorbance and the absorbance us. time. At the wave lengths used, the absorbance is due primarily to the V(V) in the solution. Apparent second-order rate constants were calculated from the data of each run using a nonlinear least-squares program for the IBM 7090 computer. This program minimizes the sum of the squares of the differences between the observed and calculated absorbance values.g Stoichiometry.-The reaction
VOz+
+ Fe+2 + 2H+ =
+ Fe+3 + H 2 0
(1)
is known t o be quantitative in acid solutions. The oxidation potentialsi0 lead to an equilibrium constant of 7.9 X lo3. 24 value of 6.2 X lo4 has been reported for 25' and unit ionic strength.l' Further, the reaction is used successfully in the determination of V(V).B
Results V(V) and Fe(I1) Dependences.-All of the rate r i m were consistent with the assumption that the reaction is first order with respect to both V(V) and Fe(II), that is: -d[Y(V)]/dt = -d[Fe(II)l/dt = k'[J'(T7)1. [Fe(II)1. The least squares calculations described above give absorbance values in agreement with experimental ones aiid the deviations show no systematic trends. Additional evidence is provided by the agreement of a series of runs in which the initial concentrations of V(V) and Fe(I1) were varied over a wide concentration range. These data are shown in Table I. The fit of the data for the individual rate rum is iiidicated by the standard deviations of the IC' values and the root mean square deviations between the observed and calculated absorbance values. These quantities are listed in the forth and fifth columiis of Table I. (9) We are indebted to R. H. Moore for writing this program. I t is based on R. H. nloore and R. K. Zeigler, Los Blamos Scientific Laboratory Report LA-2367, October 15, 19.59. Available from the Office of Technical SerTioes, U. 9. Department of Commerce, Washington, D. C.; $2.26. (10) R'. M . Latimer, "Oxidation Potentials," Second Edition, PrenticeHall, Inc., Xew York, N. Y . , 1969. (11) J. Kenttamaa, Suomen Kern. B . , 31B 273 (1968), quoted by Higqinson, et al., Dzseusszons Faraday Sac., 29, 49 (1960).
1091
I
a5 [HClO,] M.
1.0
Fig. 1.-Average apparent second-order rate constant,, IC', vs. HClOd concentration a t p = 1.0. Vertical lines represent the range; the numeral ir3 the number of determinations.
TABLE I APPARESTSECOND-ORDER R ~ T ECONST-ANT,k ' , 4~ L~FFERE;XT INITIAL COXCEXTRATIONS O F r ( V ) .4ND Fe(I1) Conditions: 0.2", 0.21 M PIC104, and p = 1.0 (LiClOd) Initial V(V),
M x
106
4.97 4.97 4.97 4.97 4.97 49.6 30.8 23.8 6.2
Initial FeW,
M
x
106
41.6 20.8 10.4 2.6 41.6 6.08 6.08 6.08 6.08
k' M-1 sec.
-1
521 525 551 535 529 559 571 593 570
Standard der.
6 8
4 9 7 22 13 8 6
R.m.s. deviation (Absorbance)
0.0010 ,0012 ,0010 ,0010 ,0008 ,0010 ,0012 ,0007 ,0012
Hydrogen Ion and Temperature Dependence,Rate runs mere made at' 0.2, 25.0, 34.0, 35.0, 45.4, and 55.6" iii LiC104 solut'ions of unit' ionic strength. The HClOd coiiceiitrations ranged from 0.045 to 1.00 M . The results of t~heseruns are summarized in Fig. 1 where the average k' value is plotted against [H.+]. The range of values aiid the number of determinations are also indicated. The data taken at 34' have been omitted from t'he plot for clarity. The plots at the three lower temperat'ures are essentially linear, but a decided up-turning is noticed a t the low acid ends of the two upper lines. Ionic Strength Dependence.-The effect of ionic strength on the reaction was found to be quite large. Determinations were made in 0.067 M acid at 0.2" and in 0.07 M acid a t 25.0°. The ionic strengt'h of the solutions m7as varied up to about 2.5 M by the addition
K.A. DAUGHERTY ASD T. W. SEWTOS
1092
T'ol. 67
of LiClOd. The results of these experiment,s are given in Table 11.
although c is a good measure of the rate constant for ( 5 ) , a and b are probably poor estimates of the rate constants for (3) and (4). TABLEI1 The over-all reaction, equation 1, requires t n o hydroEFFECT OF IOSICSTRENGTH O N THE AIJPARENT SECOKD-ORDER gen ions; so it is not surprising that one hydrogen ion RATE COSSTAXT is required in the most important net activation process. Results at 0.2", 0.067 N R C I O ~ Other reductions of ions of the h102+ type which Pl M 0.067 0.229 0.516 1.04 2.46 show the same hydrogen ion dependence are the reduck', 3f-I set.-' 35,44 65 102 190 516,525 tion of Np02+ by Fe+2l 8 and by Xp+j,14and the reducResults at 25.0°, O . O i 0 AI HClOr tion of PuOz+ by PuOz+ and the reduction of COS+by El, M 0.070 0.200 0.500 1.00 2.50 UOz+.'F IC', M-lsec.-l 63,67 108,109 181,181 291,291 793,801 The Thermodynamic Quantities of Activation.The thermodynamic quantities of activation for proress Interpretation and Discussion (5) have been calculated under several assumptions The Rate Law.-The plot,s of the data (Fig. 1) with respect to the minor paths. show that' the reaction rate is predominantly first I n the first two calculations a was assumed to be power in the hydrogen ion concentrat,ion. One or zero and the data giving rise to the curvature in the more additional terms in t8he rate lam- is required, plots were omitted. It was also assumed that the however, to account for the non-zero intercept's and for temperature dependence of 0,as well as e, is given by the curvature a t the ends of the two upper plots. An the expression from absolute reaction rate theoryli empirical rate law which is ii? accord wit,h the data is h , = I;b/h exp(AS,*R) exp(-AH,*R2) (6) -d[V(V)]idt = (a[H+]-' 6 c[H+])[T'02+j[Fe~*]
+ +
I n the third and fourth calculations a was not assumed to be zero, its temperature dependence was The coiicentrations of the principal species, [VOa+] assumed to be given by (6) and no data were omitted. and [I:e+2], have been used instead of the stoichioIt should be noted that even though a and b may be metric ones, [V(V)] and [Fe(II)], since neither subpartially determined by medium effects, the assumption stance is appreciably hydrolyzed in the experimental of (6) is justified on the basis of the relative sizes of a solutions.12 Approximate values for the parameters and b with respect to c and because the exponential in ( 2 ) were estimated as follovs, c and b from the slopes function is very similar t o other tm o-parameter funcand intercepts of the linear portions of the curves and tions over short ranges in T . For the fourth calculaa by difference. These values are list8edin Table 111. tion, AHb* was arbitrarily fixed a t 5 kcal. 'mole, a value which might be expected if b is the rate constant TABLEI11 of process (4). The dashed curves in Fig. 1 are given APPARENT RATECONSTlSTS FOR THE REACT~OK BETWEEN v(v) by this calculation. ASD Fe(I1) In the fifth calculation b was assumed to be zero, (6) Temp., a, b, C, e , calcd." "C. sec. ,If-1 see. -1 M - 2 set.-' M - 2 sea. was assumed for the temperature dependences of a and c, and no data were omitted. 2450 2450 0.2 0 20 3370 0 60 3400 25.0 For all of the calculations a least-squares procedure 3780 0 90 3680 35.0 was used which minimizes the sum of the squares of 4270 4240 45.4 8 120 the per cent deviations between the observed and 4710 17 240 4610 55.6 calculated lc' v a l ~ i e s . ~The results of these calculations a Calculated using AH* = 1.52 kcal./mole and A S * = -37.3 are summarized in Table Ti; the apparent values of e.u. the activation parameters (AS* and AH*) are given together with a measure of the fit of the data to the The form of the rate law suggests three paths for assumed function. For this n e have used the root the reaction described by the following net activation mean square per cent deviation, defined by processes (2)
-1
VOz+
-1
+ Fe+2 + HzO = (T'02.Fe.0H+2)* JT02+z
VOe+
+ Fe+?
+ F e i 2 $- H +
(VOz.l?e+3)*
(3) (4)
iH.V02.Fe+4)* ( 5 ) However, Table 111 shows that a and b are far smaller than e, and therefore a decision cannot be made as to whether a and b are due to medium effects or to the operation of minor paths such as (3) and (4). Changing the hydrogen ion concentration a t constant ionic strength probably makes small changes in the rate constants for the various paths. These changes for the predominant path are absorbed in the t,erms for the minor paths in the empirical rate law. Thus, =
(12) J. Bjerrum, G. Schwaraenhach, and L. G. SillBn, "Stability Constants, P a r t 11, Inorganic Ligands," The Chemical Society, London, 1958, Special Publication No. 7, also, F. Rossotti and 13. Rossotti, Acta C h e m . Seand., 10, 957 (1956); and D. Dryssen and T. %kine, i b i d . , 15, 1399 (1962).
r.m.5. yGdev.
=
100[(l/n)
(k'obs
-
k'calc)2/(fG'obs)
]'/*
The results in Table IV show that a variety of assumptions with respect to the minor paths lead to nearly the same values for the thermodynamic quantities of activation for the predominant path. Thub, we believe that although no conclusions can be reached with respect to possible minor paths, for net activation process (5) AH* = 1.52 + 0.16 kcal./mole and AS* = -37.3 f 0.6 e.u. These values have been used to calculate the values of c or kl the rate constant for the (13) J R Huizenpa and L. B Magnusson, J A m Chem. Soc , 73, 3202 (1951) (14) 3 C Hindman, J C Sulliran, and D. Cohen, z b d , 80, 1812 (1958). ( 1 5 ) S W Rahideau, z b z d , 79, 6350 (1957). (16) H Imai, BUZZ C h e m Soc J a p a n , 30, 873 (1957) (17) S Glasstone, I< Laidler, and H. Eyring, "The Theory of Rate Processes," 32cGran-Hi11 Book Co I n c , Ne75 York S I ' 1941 p 190
KINETICS OF REACTION BETWEEN VAKADICM(T') ASD IROK(II)
May, 1963
Iv
TrlBLE APPBRENT
I
THERMODYSASIIC QUAXTITIES OF 11
D a t a at
[H+l I 0.1M omitted
AS,*, e.u.
-37.1 1.57 -35.0 4.6
I11
Data at t 2 45' omitted
-37.9 1.36 -30.6 5.8
~CTIV4TION
IV
No d a t a omitted
-36.7 i AHo*, ltcal./mole 1.68f A&*, e.u. -57.9 i A H b * , kcrtl. /nl& -1.7 i ASIL*, e.u. ... .., -3.6 =t AH,*, kcal./mole , . . ... 15.9 i r.m.s. yG deviation 4.76 5.69 5.29 No. of data points 77 78 113 a AHb* fixed a t 5.0 kcal./niole and the other quantities computed by least squares. standard deviations computed by the least-squares program. 0.4& i 0.12 4: 7 . 5 f 2.3 =k
1093
f 0.4 i 0.12 f 3.3 rt 1 . 0
4Hb* fixeda
-37.5 I .46 -34.3 5 0 (fixed) -1-2.54 18.0 5.45 113 The uncertainties listed
0.3 0.08 11.4 3.1 4.0 1.3
V b term omitted
-37.2 i 0 . 2 1 . 5 4 =t0.06
... ...
-10.7 f 1 . 9 13.6 i 0 . 6 5.94 113 in this table are the
TABLE V T H E R M O D Y N A M I C Q U A N T I T I E S OF ACTIVATION,
AH*, kcal./mole
Ket activation process
+ + + + + + + + + +
FeA'2 H' = (H.V02.Fe+4)* 1. ' 1 ' 0 2 + 2. NpOz+ FeA2 H" = iH.SpOz.Fe+4)* 3 . Fe+2 Fe+" HzO = (Fe.OH.Fef4))* H + 4. Cr+2 Cr+a €LO = (Cr.0H.Cr+4)* H + 5. FeS2 Coca H 2 0 = (Fe.OH.Coc4)* Hf H20 = (V.OH.I'O+?)*+ H + 6. V i 3 + VO+'
+ + +
1.62 8.6 19.4 22
18.8 20.1 i. v - 3 + V 0 2 + = ( J F O z . \ 7 3 4 ) * 16.G Formal ionic entropy of the activated complex, S*comglex = AS* -5.43; NpOz+, -qz5; Crf2, (-24 i 3); FeCZ,-271n; -26 ( - 72 f 3); Ii&, l6.7.I0 Estimates are given in parentheses.
-
+
+
predominant path given in the last column of Table 111. The most striking feature of the V(V)-Fe(1I) reaction appears to be its low heat of activation, lower than those for other reactions in which metal-oxygen bonds are broken such as the analogous reduction of Kp(V) by Fe(II),I3 lower than that for the Fe(CS)6-4I;e(CS)6-3 electron exchange,I8 and almost as low as for the oxidation of Fe(I1) by Ir(Cl)6-2 or by Fe(phen) +j . Is I n contrast to AH", AS" for the V(V-Fe(I1) reaction is essentially what was to be expected. This is (18) C. F. Deck, Microfilm Bissert. Ab&., 16, 1578 (1956). (19) N. Siitin and B. Gordon, J . Am. Chem. S o c . , 83, 70 (1961); B. Gordon, L. Williams, a n d h-.Sutin, ihid., 83, 2061 (1961). (20) J. Silwrman and R. W. Dodson, J . Phys. Chem., 66, 846 (1952). (21) 4 . Anderson and 5. A. Bonner, J. Am. Chem. am.,76, 3826 (1954). ( 2 2 ) L. E. Bennett a n d J. C. Sheppard, J . P h w . Chem., 66, 1275 (1962). We thank these authors for making available the d a t a plotted in their Fig. 2. (23) S. C . Furman and C. 8. Garner, J . Am. Chem. Sue., 74, 2333 (1952). (24) W. C. E. Himinson, et al., Discussions Faradag SOC.,29, 49 ( 1960). ( 2 5 ) D. Cohen and J. C. Hindman. J . Am. Chem. Sue., 74, 4682 (1932).
25"
AS*, e.u.
S* complexa
From d a t a in lei.
-70 f 1 This work -37.3 It 0 . 6 - 38 - 69 13 20 S 9 . 9 f 1.4-TO i 1 -2 i 5 21 -79 f 5 22 -66 & 4 +I6 i 4 -3 =k 5 -77 f 5 23 24 $5 i 6 -65 i 6 BSoleRDtJntS.Values used for Snrewefrnts: HC, 0.00; VO?+, i 33; VA3,(-65 rfi: 3); Cr+3, (-67 =t 3); Fe+3; -io1"; Cof3,
+
shown in Table T where the thermodynamic quantities of activation are given for a series of reactions for which the charge on the activated complex is +4. It is seen that although the AX" values range from -38 to +12 e.u., the formal ionic entropies of the activated complexes range from -65 to -79 e.u. Just as in the case of actinide ion reaction^,^ the charge on the activated complex seems to be the predominant factor in determining its entropy. Since the values are similar to those for activated complexes formed from two actinide ions, the size of the complex does not seem to be an important factor. The activated complexes in Table V are shown as if oiily a single atom or group lies between two metal ions. This mas done for convenience only; as yet there is no evidence for or against the inlier-sphere structures shown. Acknowledgement.-The authors thank Dr, €7. 13. Baker for help and advice in the experimental part of this work.
