2474
F. ACCASCINA, F. P. CAVASINO, AND S. D’ALESSANDRO
the mercury surface during the adsorption period would be expected to be small and perhaps beyond experimental detection in this system. The independence of extension with molecular weight is not necessarily in conflict with Hoeve’s findings.’e The example that he discussed corresponds to a limiting case of weak interactions and large loop sizes, whereas in the case of mercury the interaction is probably strong.
We are proceeding with further studies on “pure” homogeneous surfaces to determine whether the difference in behavior between the two studies discussed above results from differences in interaction energies between surfaces or within a surface or whether the mercury surface, perhaps because of its liquid nature, provides other factors which have not been considered here.
Mechanism of Formation of FeN,2+and of Other Monocomplexes of Iron(II1)
by F. Accascina, F. P. Cavasino, and S. D’Alessandro Inatitule of Physica2 Chemistry, Unisersily of Palernto, Palernto, Italy Accepted and Tranrnitted by The Faraday Society
(June 7, 1966)
The kinetics of the formation of the monoazide complex of iron(II1) in aqueous solution has been studied by the temperature-jump method at various temperatures and a t ionic strength 0.1 M . A general mechanism is proposed which accounts for the available kinetic data on the formation of iron(II1) monocomplexes. The proposed mechanism and the activation parameters confirm the previous suggestion that the rate-determining step of iron(II1) complex formation is the release of a water molecule from the inner coordination sphere of the metal ion.
Introduction Kinetic studies on the formation of complexes of bivalent transition and alkaline earth metals in aqueous solution have shown that the rates of complex formation “e essentially independent of t~~~entering ligand and that the rate-determining step of these reactions is the release of a water molecule from the inner coordination sphere of the metal A different behavior seems to be shown by the iron(111) ; in fact the rate constants for the reactions of Fea+ with various anions (Cl-, Br-, CNS-, S04’-, F-, Na-) appear to be dependent On the nature Of the ligand, increasing with the basicity of the anion. In order to account for this dependence, two different The Journal of Physical Chemiet.ry
interpretations have been formulated. According to the first interpretation,‘-’ the ion pair formed in the first step of the reaction is supposed to undergo an (1) M. Eigen and L. De Maeyer in “Technique of Organic Chemic try,” Vol. VIII, 2nd ed, S. L. Friess, E. S. Lewis, and A. Weissberger, Ed., Interscience Publishers, Inc., New York, N . Y . , 1963, Part 2, 895, (2) F. P. Cavasino, Rk. Sei. Rend., AB, 1120 (1966). (3) F. P. Cavasino, J . Phye. c h . ,69, 4380 (1965). For other references see this pawr. (4) M. Eigen in “Advances in the Chemistry of the Coordination Compounds,” The nlacduan co.,New York, N. y., 1961, p 371. (5) M. Eigen, Pure Appl. C h m . , 6 , 97 (1963). (6) H.Wendt and H. Strehlow, 2.Eleklrochem., 66, 228 (1962). (7) F. P.Cavasino and M. Eigen, ~ ks c.i . Rend., A4, 509 (1964).
MECHANISM OF FORMATION OF FeNs2+
"inner" hydrolysis whose degree increases with the basicity of the entering ligand. Seewald and Sutin8 offered a second explanation by suggesting that, in the acid-independent path, the actual reactants are FeOH2+ and HA("-')- and not Fe3+ and An- in the case of the anions S042-, F-, and N3-. These considerations reduce the apparent ligand dependence of the rate constants. The kinetic studies so far carried out with iron(II1) have also shown that the observed rate constant, kobs, for the formation of various complexes of Fe(II1) results in either a linear function of the hydrogen-ion concentration (ie., with fluorides and azide ions*) or a linear function of l/(H+)(i.e., with chloride,6u10 bromide," thio~yanate,~t'*'~ and sulfate ions6) or (H+) independence (z.e., with sulfate ions13). In the case of FeS04+ formation, Davis and Smith13 have not observed any dependence of kobs on the (H+), unlike the observations of Wendt and Strehlow.6 The dependence of the observed rate constant on the reciprocal of (H+) has been interpreted by assuming that, in addition to the reaction between Fe3+and the anions, also the reaction of FeOH2+ with the same anions contributes to the complex formation. The linear relationship between kobs and (H+) has been explained in the case of FeF2+by considering the reaction of Fe3+with the undissociated acid ligand, HF. In the particular case of the FeNS2+ complex, whose kinetics of formation has been studied by Seewald and Sutin8 a t 25", the experimental data have been interpreted by a mechanism which involves the reactions of Fe3+ and FeOH2+with the undissociated acid, HN3. These authors have also admitted that the reaction between FeOH2+ and N3may contribute at low acidities. In order to suggest a general valid reaction mechanism for the various complexes of iron(II1) which is able to interpret the different dependence of the observed rate constant on the concentration of the hydrogen ion, we have reexamined the kinetics of formation of FeNS2+ a t various temperatures in the (H+) range in which Seewald and Sutin had supposed the contribution of the reaction between FeOH2+ and N3-. The kinetic investigation has been carried out by the temperature-jump relaxation method.
Experimental Section'4 The temperature-jump apparatus is essentially analogous to that previously Since the brassplatinized electrodes of the T-jump cell caused some instability of the solutions under investigation, goldcovered electrodes were used. Each solution examined was prepared by mixing a M fixed amount of an acidified (with HC104) 5 X
2475
Fe(ClO& solution with the appropriate amount of 5 X M NaN3 solution and then adjusting the ionic strength to 0.1 M by the addition of NaC104 (1 M ) and the pH by addition of HClOl(1 M ) or NaOH (1 M ) . The iron of the Fe(C10& standard solution was estimated, after reduction with SnCI2, by the Zimmerman-Reinhardt method. The NaC104 and NaN3 solutions were prepared by dissolving the appropriate weight of the substances (Fluka reagent grade) in doubly distilled water. The measurements were performed at the wavelength a t which the FeNa2+ ion exhibits the maximum absorbance (A = 460 mp) a t 15, 25, 31, 32, and 38", the temperature-jump of 8" being included. All the solutions exhibited a relaxation spectrum characterized by a single relaxation time.
Results and Discussion Conductometric and spectrophotometric studiesl6 have shown that the following equilibria exist in the aqueous acid solutions containing Fe3+ ions in the presence of low azide concentrations Fe3+
+ N3-
HN3 Fe3+
+ H20
N3-
Kc
FeN32+
+ H+ FeOH2+
KH
+ H+
KOH
Under the conditions used in this investigation, the presence of the species Fe(OH)2+and Fe(OH)2Fe4+ may be neg1ected.l' Taking into account the various equilibria existing in solution with the above assumptions, the complete mechanism for the formation of the monoazide complex of iron(II1) is as follows. (8) D. Seewald and N. Sutin, Inorg. Chem., 2, 643 (1963). (9) D. Pouli and W. MacF. Smith, Can. J. Chem., 38, 567 (1960). (10) R. E. Connick and C. P. Coppel, J. Am. Chem. SOC.,81, 6389 (1959). (11) P. Matthies and H. Wendt, 2. Physik. Chem. (Frankfurt), 30, 137 (1961). (12) J. F.Below, Jr., R. E. Connick, and C. P. Coppel, J. Am. C h a . , Soc., 80,2961 (1958). (13) G. G. Davis and W. MacF. Smith, Can. J . Chem., 40, 1836 (1962). (14) The experimental part of this work was performed at the Max Planck Institut fur Physikalische Chemie, Gottingen, West Germany. (15) A. I. Vogel, "A Text-book of Quantitative Inorganic Analysis," 3rd ed, Longmans, Green and Co., London, 1961,p 287. (16) (a) B. Ricca, Gazz. Chim. I h l . , 75, 71 (1945); (b) J. BadozLambling, Bull. SOC.Chim. France, 1195 (1950); (c) H. K. ElShamy and F. G. Sherif, Egypt. J. Chem., l, 35 (1958); ibid., l, 257 (1958); (d) R.M.Wallace and E. K. Dukes, J. Phye. Chem., 65, 2094 (1961); (e) D.Bunn, F. 8. Dainton, and S.Duckworth, Trans. Faraday SOC.,57,1131 (1961). (17) R. M. Milburn and W. C. Vosburgh, J . Am. C h a . SOC.,7 7 , 1352 (1955).
Volume 71, Number 8 July 1967
F. ACCASCINA, F. P. CAVASINO, AND S. D'ALESSANDRO
2476
H+ H+
+ FeOHZ++ HNs
%&
+ FeOH2+ I t + Na- + H 2 +d
Since the protolytic reactions occur fast relative to the metal complex formation reactions, by assuming the Fe(OH)Ns+ ion to be in a steady state, the rate equation for the formation of FeNs2+is given by d(FeNs2+)/dt = kobs(Fe3+)(N3-) - k',b,,(FeNB2+)
(1)
where kobs
+ ka4KoH/(H+)
= ksz(H+)/K~
+ kdoH/KH k2a(H+) + k d j / ( H + ) + + k12
k'obs
=
(2)
k21
( K , represents the equilibrium constant for the hydrolysis of FeN32+.) After an expansion analogous to that previously described,2 eq 1 yields the following expression, valid in the neighborhood of equilibrium dA[FeN3"]/dt
= -A[FeNP]/r
where A[FeNs2+]is the deviation of the concentration of FeNa2+from its equilibrium value. The reciprocal relaxation time is found to be 1/T
(3)
= kob,B
Fe(OH)N3+
I+G H+ + H+
peratures examined and at p = 0.1 M has been made by using the equilibrium concentrations obtained from the total iron and azide concentrations (Table I) and from the corrected equilibrium constants, KH, KOH,and KC (Table 11). The equilibrium hydrogen-ion concentrations were calculated from the measured pH values, using activity coefficients evaluated by the equation of Wenger and co-workes. 18,19 The dissociation constant for hydrazoic acid, K H , a t various temperatures and p = 0.1 M has been estimated by the van% Hoff equation with AH = 3.6 kcal mole-' 16e,m and by using the value of 3.50 X M a t 20". The latter value was obtained by interpolating at p = 0.1 M the K H values measured by Quintin21ai, various ionic strengths and a t 20". As to the association constant for the complex ion, Kc, we have calculitted the value of 3.33 X lo4 M-' at 20" and p = 0.1 from the extrapolated value of K c K H ' ~ ~ M for and by using the above value of 3.50 X KH. The association constant a t the other temperatures has bem obtained by using the AH value of - 1.1 kcal mole-l.lse The equilibrium constant for the hydrolysis of ferric ion, KoH, has been evaluated by the Milburn expression and by setting AH = 10.4 kcal
where
+ Y) + [Na-l/(l + 4 + 1/Kc
The relaxation times concerning each solution examined have been evaluated as previously dewith scribed.*JJ Each r value (Table I) is the average of a t least four runs and is affected by a maximum [H+l{[H+l KOH [FeOH2+l] Ko~[Na-l error of about 8%. r = KH([H+l KOH [FeOH2+l F"] As Table I shows, the observed second-order rate constant, koba (= 1/7B),is practically independent of KOH{[H+l KH [Na-I [Fe*+lf = [H+l([H+l KH [Na-I] K H [ F ~ O H ~ + I the hydrogen-ion concentration at the various temperatures investigated. Therefore, according t o eq 4, we (The square brackets indicate equilibrium concentrahave to deduce that the two terms involving (H+) tions.) From eq 2 and 3 we obtain
B
= [Fe3++l/(l
+ + + + + + + + + + + +
1lrB
= kbs =
~ M ( H + ) / K4H k,XoH/(H+>
*
k (4)
with k =
+ kdoH/KH
(5) The evaluation of the quantity B a t the various temki2
The Journal of Phyeical Chmietry
(18) P. E. Wenger, D. Monnier, and I. Kapetanidis, Helv. Chim. Acta, 40, 1456 (1957). (19) G . Saini and G . Ostacoli, J. InoTg. Nucl. Chem., 8 , 346 (1958). (20) B. L. Evans, A. D. Yoffe, and P. Gray, Chem. Rev., 59, 515 (1959). (21) M. Quinlin, Compt. Rend., 210, 625 (1940). (22) R. M. Milburn, J . A m . Chem. SOC.,7 9 , 537 (1957).
MECHANISM OF FORMATION OF FeNa2+
2477
Table I: Kinetic Data for FeNaB+Formation
(p =
0.1 M)
Table 11: Equilibrium Constants and Formation Rate Constants for FeNa*+Complex" ( p = 0.1 M )
1/+B Z:P e l
Z:IN:]
x lo',
x
108,
IH +I
x
x lo',
M
M
M
1.00 1.00 1.00 1.00
5.00 3.40 2.20 1.20
71.6 32.7 16.4 8.8
t =
7
lo',
sec
x M
-1
10-6, 8ec -1
38' 14.8 13.8 11.6 12.4
18.2 18.6 21.4 20.0
Av 19.5 f 1.6 5.91 1.52 3.00 5.36 1.52 1.52 1.24 2.14 0.33 0.65 0.33
76.6 76.6 38.3 38.3 38.3 15.3 15.3 15.3 12.1 7.7 7.7
28.0 25.8 27.3 21.5 25.1 21.1 26.2 20.8 24.0 23.7 25.4
11.7 11.1 10.0 11.7 11.1 12.6 10.3 12.4 10.3 11.0 9.7 Av 11.1f 1.4
t = 31'
1.00 1.00 1 .00 1.00
5.00 4.00 1.40 3.00
69.8 35.0 22.6 15.6
27.9 26.0 24.0 22.8
10.0 10.2 11.6 10.8 Av 10.7 f 0.8
t = 25'
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
5.00 5.00 4.90 4.00 3.92 3.00 2.94 2.00 2.94 2.00
87.8 80.0 71.3 43.0 36.6 28.3 25.9 17.9 16.3 10.5
59.0 57.8 56.1 55.8 51.4 55.5 51.0 52.0 44.9 51.5
5.06 5.13 5.24 5.11 5.45 5.33 5.43 5.29 5.78 4.97 Av 5.28 f 0.40
1.00 1.00
5.00 3.00
t = 15' 76.1 28.2
134 131
2.37 2.31
Av 2.34 f 0.03
are negligible compared to k in the (H+) (=[H+J) range examined by us. Consequently, as kobs is equal to k = k12 ~ B Q K o H / (eq K H5 ) ) it is not possible to determine the individual rate constants klz and k64 from the experimental data. On the other hand, the evaluation of one of the two rate constants, either klz or k64,
+
x KH x lo*, los,
KOH
T.
lo-',
oc
44-1
M
M
38 32 31 25 15
2.99 3.09 3.11 3.23 3.44
5.74 4.12 3.89 2.75 1.49
5.01 4.47 4.38 3.88 3.14
koba ( - k) X lo-',
M-1
sec-1
19.5 f 1.6 11.1 f 1.4 10.710.8 5.28f0.40 2.34f0.03
ka x lo-*, M - 1 sec-1
17.0 f 1.4 12.0 f 1.6 12.0f0.9 7.45f0.56 4.93f0.06
The estimated value of kx a t 25' is in the range -3 M-1 sec-1.
X lo*
to -4 X 10'
t = 32'
0.80 3.09 0.83 1.83 1.65 0.77 0.92 0.80 2.71 1.07 1.94
KC x
= hobs
may be made from the experimental k value if it is possible to ascertain indirectly either kdOH/KH to be > k 6 4 K o ~ / K ~ , k12 = 127 sec-'; if klz
