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Kinetics of formation of Fe(III) complexes in aqueous DMSO
J iewr?,, ~I~*li Ckem \'ol. 4~. pp 1267 !2~<, 1981
0022-1902/81]1~61267~g)$02.00]0 1981 Pergamon Press Lid
Pril!i~'d ill Gre,*t I1r[latrl
KINETICS OF FORMATION OF Fe(lII) COMPLEXES IN AQUEOUS DMSO G. KRISHNAMOORTHYand B. S. PRABHANANDA* Chemica! Physics Group, Tara Institute of Fundamental Research, Bombay 40(10(15, India
(Receir.ed 2 July 1979: received [.or publication 25 August 1980) Ahstraet--Spectrophotometric observations have been used to study equilibria and temperature jump relaxation associated with the formation of Fe(lll) complexes in aqueous DMSO in the presence of SCN . The [SCN ] dependent relaxation observed at 315 nm could be assigned to the formation of Fe DMSO~, Fe DMSO OH-~, Fe DMSO SCN2+ and Fe DMSO SCN OH + from Fe~÷ and Fe OH~, The relaxation observed at 450nm could be assigned to the formation of Fe SCN~" by paths similar to that in aqueous solutions and a pH dependent path in which the rate determining step is the displacement of DMSO from Fe DMSO SCN OH' by H20. The rate constants suggest that coordination by a DMSO instead of a H20 has lhe effecl of labilising the other H.,O coordinated to Fe OH~+, The observed decrease in relaxation rates with increase in [DMSO] have been explained as dominantly due to the reduction in the acid dissociation constant KH associated with the aquocomplex of Fe{lll). INTRODUCTION In previous work on the kinetics of formation of a typical monocomplex Fe SCN 2~ in aliphatic acid-water mixture[l], the enhancement in relaxation rate (observed in T-jump experiments) was explained as dominantly due to the participation of the aliphatic acid in the reaction scheme. In contrast, experiments on the formation of monocomplexes of Fe(IlI) in aqueous DMSO at constant pH ~DMSO-dimethylsulphoxide), show a decrease in relaxation rate with increase in the DMSO component. This was found to be the case even in experiments at constant perchloric acid concentration instead of monitoring the pH. Such behaviour may be due to the alteration of equilibrium constants and rate constants with solvent composition. However, only a detailed study can tell us whether a reaction scheme similar to that observed in aliphatic acid-water mixtures is operating in the present system. For this purpose, it is relevant to investigate the dominant solvent coordinated species present in aqueous DMSO. Since DMSO has two donor sites and DMSO coordinated AI(III)[2, 3] and Cr(III)[4] have been observed in aqueous DMSO mixtures, one can also expect DMSO coordinated Fe(Ill), though the activity of DMSO is known to be reduced in ;he mixed solvents[5,6]. Ion exchange procedures which were used in the case of the Cr(Illl complex [4] cannot be adopted in the present case since the rate constants associated with the formation and dissociation of Fe DMSO 3~ are high. NMR methods[2, 3] are also not easy to use in this case since the concentration of DMSO coordinated to Fe(III) will be small compared to DMSO in the solvent mixture, and the lines are broadened due to paramagnetic Fe(IIl) which reduces the sensitivity. Use of high concentrations of metal ion complicates the situation by dimerisation reactions. Attempts to observe the formation of Fe DMSO s~ from spectral changes (Fig. la) were also not successful since the Benesi-Hildebrand plots[7] gave unreasonable values for the extinction coefficient and formation constant, the complications probably arising from the changes in the spectral features of Fe DMSO 3~ *Author to whom correspondence should be addressed. JIN( Vo~~ go ~-g
with solvent composition and the formation of "conlEact species" similar to those described by Orgel and Mulliken[8]. However, from Fig. l(a) we can expect spectral changes associated with the formation of Fe DMSO 3+ to take place in the 300-350nm region. Recently, amplitudes of relaxation behaviour of perturbed equilibria[9, I0] have been used to determine the equilibrium constants associated with simple equilibria. However, such a procedure is difficult when sew~ral coupled equilibria are present. In addition one must be able to get sufficient experimental points on either side of the equilibrium, which may not be possible when formation constants are small. In the present case we also have to contend with the change in enthalpy of the reaction with solvent composition which affects the amplitudes. However, the relaxation times "r measured for different concentrations of the ligands could also be used in the estimation of formation constants, as can be seen from eqn (8) of Ref.[ll] for the typical formation of Fe SCN 2+. A preliminary examination showed, that the exponential relaxation observed at 315 nm in the T-jump experiments on Fe(lll) solutions in aqueous DMSO, increased in amplitude with the mole fraction of DMSO in the mixed solvent. This is consistent with the formatior, of monocomplex Fe DMSO 3+. (Since only one exponential was discerned, it is reasonable to expect the concentration of other DMSO coordinated species to be small under the conditions of the experiment). However. the relaxation rate 1/rl decreased with [DMSOJ at a given pH, which appears inconsistent with the expectations of eqn (8) in[ll], unless the equilibrium constants and rate constants alter with solvent composition as mentioned above. The formation of a large number of mono-complexes of Fe(IlI) in aqueous solutions have shown (see references cited in[12]) that these could be described in terms of the Eigen-Tamm-Wilkins mechanism[13, 14], the rate determining step being the loss of water from the inner coordination sphere of Fe(H20),~' in the pH independent path and from Fe(OH)(H20)~" in the pH dependent path. Thus, one should expect similar pH dependence and solvent composition dependence for lhe relaxation time associated with the formation of a typical complex such as Fe SCN 2+ if our assignment of the relaxation at 315 nm to the formation of Fe DMSO ~' is
1267
1268
G. KRISHNAMOORTHY and B. S. P R A B H A N A N D A
I0 i 0
O9 09
08
07 o
06 (,')1---- 06 I Z b,J a 05
05
04
t.~
()4
g 03
O3
\
oI
O2
O
0
0
250
500 WAVELENGTH
350
'
0 300
400
do
350
4 5'0
WAVELENGTH
(rim)
(a)
5;o
(nm)
(b)
O7
Z
6
--105 C~
o
300
350
I
I
I
J
400
450
s00
5s 0
WAVELENGTH
(nm)
(c) Fig. 1. Spectral behaviour of Fe(III)-DMSO--SCN- system at 29°C, pH 1.25, ionic strength 1.0 M and [Fe z] = 2.5 × 10-4 M; (A) [SCN-] = 0.0 M [DMSO] = 0.6 M (a), 1.1 M (b), 1.52 M (c), 1.92 M (d), 2.49 M (e) and 3.05 M (f); (B) in aqueous solutions with [SCN-] = 1.0 x 10-3 M (a), 2.5 x 10-3 M (b), 4.0 x 10-3 M(c), 5.5 x 10-3 M(d), 7.0 x 10-3 M(e) and 10.0 x 10-3 M(f); (C) in 25% DMSO-75% water (v/v) with [SCN-] variation same as in (B).
,;
1269
Fe(lll) complexes in aqueous DMSO correct. In this paper, we describe a study of the solvent composition dependence of relaxation times in aqueous DMSO. We also give estimates for the formation constant of Fe DMSO > obtained from equilibrium studies and temperature jump relaxation studies. A reaction scheme for the formation of a typical complex Fe SCN > in aqueous DMSO is also given. In this scheme, the possibility of further coordination of other ligands such as SCN and HN3 to Fe DMSO > has also been included.
where y is the activity coefficient of DMSO in the mixture. We are neglecting species in which more than one DMSO is coordinated, since their concentration can be expected to be small under these conditions. We also have the acid dissociation constants. Ks - [Fe OHZ+][H+]* v D [ ]
[Fe DMSO OH~I[H~] * [Fe DMSO > ]
KS
EXPERIMENTAL Acetonitrile (B.D.H) and DMSO (Baker analysed) were used. Experiments were restricted to a DMSO content of less than 25% v/v (mole fraction <0.08)in aqueous DMSO. Sodium azide was obtained from B.D.H. (AnalaR).Sodiumperchlorate was used to regulatethe ionic strength to 1.0 M, The pH of the solutionswere adjusted by adding drops of 60%HCIO4 (B.D.H. AnalaR). Hydrogen ion activities [H*I* calculated from the pH of the solutions were used in the expressions for acid dissociation constants followingthe practice of many laboratories[15, 16].The preparation of stock solutionsand other experimentaldetails have been described elsewhere[l]. A Hanovia 901 B-I xenon-mercury lamp was used for the observation at 315nm, instead of the tungsten halide lamp used at 450 nm. The experimentswere carried out in the temperature range 20-40C. RESULTS Dependence of acid dissociation constant KH on solvent composition in aqueous DMSO Spectral changes due to the formation of a monocomplex such as Fe SCN 2~ in aqueous solutions and in aqueous DMSO (Figs. Ib and lc) can be explained within the limits of experimental error ( < 10%) considering the equilibria: k,7 Fe 3+ + SCN ~-~ Fe SCN > (1) k71
[Fe SCN OH+][H+] * [Fe SCN >] KDs [Fe DMSO SCN OH+][H+] * H : . [Fe DMSO SCN z+]
tl0)
The number of water molecules coordinated to the metal ion have been omitted in writing the above equations for convenience. Since our experiments have been restricted to pH ~<3, the deprotonated species of equilibria (6) and (7) are not important in the discussion of the spectral changes. (This can be seen by noting that K s < K , from the values given in[ll]. By analogy we can expect K~S,~K~.) The observed optical density using lcm path length will then be given by O.D. = ~,[Fe SCN >] + e2[Fe DMSO SCN 2. ] + E~[Fe:~'] + e4[Fe D M S O s+] + es[Fe OH > ]
+ t6[Fe DMSO OH > ] + e7[Fe (SCN)~I
lilt
where e¢(i = 1, 7) are the extinction coefficients of the species which occur in eqn (11). We also have the conservation relation [Fe v] = [Fe SCN >] + [Fe DMSO SCN>] + [Fe > ] + [Fe DMSO 3+] + [Fe OH 2+] + [Fe DMSO OH ~-~]
k12
Fe 3+ + DMSO ~ Fe DMSO 3~
(2)
k21
+ [Fe (SCN)~]
(il2)
k26
Fe DMSO > * S C N
~
Fe DMSO SCN >
(3)
k62
Fe OH 2+ ~ H" ~ FeDMSOOH 2~+H' ~
Fe 3+ FeDMSO >
Fe SCN OH + + H + ~ Fe SCN 2+ FeDMSOSCNOH'aH + ¢
At 450nm as = e4 = e5 = E6=0 from observations. Using (9)-(12) we get
(4)
Q'[FeT] Ks + Kc'Kcs[DMSO]
O.D.
Q'[FeT][SCN ] P
(5) (6)
F e D M S O S C N 2+
(8)
Under our conditions [Fe (SCN)~] is small. This can be seen from the known equilibrium constants[17]
O.D.
K'~[SCN ]
(13)
Kh O.D. {1 + K~[SCN ] + K~s[SCN 12}[H'J*
(7) Fe 3+- 2SCN ~ Fe (SCN)L
O.D. =
experimental
(14) where Q = t,Ks + a~KcKcs[DMSO] + eTKss[SCN ] (15)
[FeSCN>J . K~ Ks=~-FeS+][SCN_ J, :
[FeDMSO 3+] _ [FeS+][DMSO] yK*:
[FeDMSOSCN >] K [Fe (SCN)~] K(s = iFe DMSO 3 ][SCN ]; ss = [FeS+][SCN-]/ (9)
K~=
P = 1 + Kc[DMSO] + Ks[SCN-] + KcKcs[SCN-] [DMSO] + Kss[SCN-] 2
Ks + KcKcs[DMSO] 1 + Kc[DMSO] + Kss[SCN ]2 + (Ks + K~Kc[DMSO])/[H+] *
(16)
(17)
1270
G. KRISHNAMOORTHYand B. S. PRABHANANDA , _ Ks + KcKcs[DMSO] Ks1 + Kc[DMSO] K~s -
(18)
Kss 1 + Kc[DMSO]
07
(19)
K~ = K , + K~Kc[DMSO] i + Kc[DMSO]
(20)
K~ and K~s are determined from experiments at low pH ( - 1 . 0 ) such that KH "~ [H+] * and the term involving [H+] * in eqn (17) can be neglected. (It will be shown later that K~ ,~ [H+] * at this pH.) The departure from linearity of O.D. vs O.D./[SCN-] plots is used to estimate ~7( 9000M-~ cm -~) and K s s ( - 1 2 7 6 M -2) in aqueous solutions in addition to e~(~5100 M-~ cm -~) and Ks at I M ionic strength. The values obtained are comparable to those obtained by others[17] under slightly different experimental conditions. The values of K~ in aqueous DMSO are determined to a first approximation using Kc = 0. This is used to determine Kr~ from an analysis of the pH dependence of the optical density at constant [SCN-] according to eqn(14). These K~ are then used in the analysis of T-jump data using eqn (22) (v. inf) to obtain an estimate of K o K~ and Kr~ are finally ctbtained by iteration using such estimates of K o Figure 2 gives plots obtained from the pH dependence of the O.D. in typical mixed solvents used in the determination of K~ at 21°C. Table I gives the estimates of K~ and K~ at 25°C and their temperature dependences in mixtures of different compositions. It can be seen that although the variation of Ks' is small, K d decreases significantly when the DMSO component of the mixed solvent is increased.
Dependence o[ relaxation times on solvent composition in aqueous DMSO. Fe DMSO 3+ formation
06
o o
05 !
O3 200
10 0
t200
6OO
/
4oo / 50C
200
•
o
(21)
Q
2o
~o
6o
I/ [H+]"
k43
along with the fast protonating steps (4) and (5). An expression for the relaxation times ~'1 can be derived
800 N
Fig. 2. Plots of OD vs OD/[H+]* (eqn (14)) at 450 nm for the estimation of Kfi at 21°C. A, 0% DMSO; D, 7% DMSO; 0, 15% DMSO; O, 25% DMSO.
k34
Fe DMSO OH 2÷
600
OD/ [H']
The relaxation times zl associated with the temperature jump relaxation behaviour observed at 315 nm in typical DMSO-water mixtures with [FC] = 1.25 x 10-3 M, are plotted in Fig. 3. As mentioned earlier this can be assigned to the formation of FeDMSO 3÷ (which is further confirmed from the similar pH dependence and mixed solvent composition dependence of relaxation times in the case of formation of Fe SCN 2+ to be discussed later in this section). To account for the pH dependence of ~'~ in addition to the acid independent path (reaction(2)) we include an acid dependent path Fe OH 2+ + DMSO ~
400
8;
,go
(M-')
Fig. 3. Typical "rT ) vs I/[H+]* plots for Fe DMSO3÷ formation at 25°Cwith ILl = 0.; O, 1% DMSO; II, 3% DMSO;0, 7% DMSO; IS], 15% DMSO and A, 25% DMSO.
Table 1. Equilibrium parameters for the formation of Fe SCN2+ in various mixed solvents at 25°C and ionic strength 1.0 M. Activity coefficients y were calculated by extrapolation formula (eqn (1)) and data given in Ref.[6]. Temperature dependence given by K~ = K~ exp( - AEdRT) and Kh = K:~exp( - AE2/RT) K~ determined using K~ = 3.2 M-t and eqn (18) Solvent composition [DMSO] Mole fraction M of DMSO. 0 0.422 0.986 2.11 3.52
0 0.0079 0.0189 0.0432 0.0786
y
Ks + KcsKc[DMSO] M~
K~ M~
AEI kcal. mole-~
K~ × 103 M
0 0.060 0.063 0.070 0.082
114.5_+1.0 129.9-+0.8 141.8-+1.6 149.9+ 1.4 149.5_+1.5
114.5-+1.0 118.9-+1.8 118.5-+3.9 101.9_+6.2 76.8+-7.0
-1.2 -1.0
2.98+-0.09 2.39 +-0.22 1.39-+0.07 0.516_+0.008 0.129_+0.005
AE2 kcal. mole 8,9 7.7 6.8 6.1
1271
Fe(lll) complexes in aqueous DMSO based on the above mentioned paths for the formation of FeDMSO 3+ following the procedure given in Ref.[ll] and taking due note of the reduced activity of DMSO in aqueous-DMSO[5,6]. If 3' is the activity coefficient of DMSO in the mixed solvent, since [Fe3+]<[DMSO] under the experimental conditions we can write
400
//
300
-l- = B ~ - -kDMK~ r,
[
/
[H+] *
J with B = { y[DMSO] + ~-~ / k,2
kDM = 3,[DMSO]+
k34~
(22)
(The activity coefficients of Fe 3+ and Fe OH > in the mixed solvents have been taken to be unity to be consistent with the observations on Fe SCN 2+ formation to be discussed later.) Using K~ from Table 1 the values of kDM and their temperature dependence were obtained from plots similar to Fig. 3. These are listed in Table 2 for typical [DMSO]. Since kDM increases more or less linearly with [DMSO] we can take k34KH/K~I t o be nearly constant and get on estimate of K* (-~3.2 +0.6M ') (see "Discussion" also). It is clear that the unusual decrease of l/z, with [DMSO] was due to the decrease in K~.
Formation of monocomplexes of Fe(llI) in aqueous DMSO in the presence of SCN and H N 3 The T-jump experiments in this system showed the relaxation associated with the formation of Fe DMSO 3. in the time range 1-50 m sec. This could be conveniently observed at 315 nm and showed a reduction in amplitude as well as an increase in relaxation rate l/r, when the concentration of the SCN o r HN3 was increased. Figure 4 gives the typical dependence of r, on [L] (L = SCN , HN3) which could be expressed as
[wl* In addition to this a relaxation with time constant r: in the range 10--400m sec. could also be observed. This had a maximum amplitude around 450nm and could be associated with the formation of Fe SCN 2+ or Fe N] +. The pH and [DMSO] dependence of r, and r2 were
I/ [H~'"j (M') Fig. 4. Typical z [i vs l/[H+]* plots for Fe DMSO3' formation at 25°C and 15% DMSO with [L] = 0(@), [SCN ] = 1x 10 " M(O). [SCN ]=2× 10 2M(A) and [HN~=4x 10 " M(~71).
similar confirming that we are observing the monocomplex formations in both relaxations. Although eqn (23) suggests ligand catalysed formation of Fe DMSO > , this is unlikely since the equilibration for FeSCN 2+ and FeN3z+ formation is much slower than that for a Fe DMSO 3+ formation and the observed values of "C" cannot be accounted for by such a path. Alternatively, we could be seeing the effect of coordination of L to the DMSO coordinated metal by a path such as
k45 FeDMSOOH > + S C N
~
FeDMSOSCNOH"
k54
(241 (since we are making observations at 315 nm) in addition to the fast protonating steps (5) and (7). In order to get an expression similar to (23) we suppose the equilibration of FeDMSOSCN 2 takes place along with that of Fe DMSO J+. This is reasonable since we do not observe a separate relaxation associated with this equilibration. Also, it is not necessary to include the reactions associated with the formation of Fe SCN > (while discussing the situation when L = SCN ) since 1/r~->'> 1/r~ from
Table 2. Kinetic parameters defined by eqns (22) and (33) for the formation of Fe D M S O 3÷ and Fe SCN> in aqueous-DMSO for typical solvent compositions at 25°C and ionic strength 1.0M. Temperature dependence given by koM = k~Mexp( AE3/RT) and kc = k°sexp(-AEo/RT)+k°exp(-AE4/RT) with AEo 10.1kcal mole i Solvent c o m p o s i t i o n mole fraction of DMSO
kDM X l0 3 sec ]
0 0.0026 (!.0189 (!.0432 0.0786
2.45 -+0.08 2.90-+0.15 4.07 -+0.07 4.70_+0.69
AE3 kcal.mole z
,,12.8 14.0
kc x 10 4 M Esec I
0.86 ~+0.05 0.92 ~ 0.04 1.01 ~+0.08 2.40 ~+0.09 3.31 _+1.10
mE 4 kcal.mole
18.5 16.9 16.9
1272
G. KRISHNAMOORTHY and B. S. PRABHANANDA
experimental observation. For this case we can write d { [ F e DMSO 3+] + [Fe DMSO OH2+]}
Table 3. Typical Values of kbM=k34KH{I/K~+7[DMSO]} + k45K~lL] and k45KD/KHvalues obtained at 25°C and ionic strength 1.0 M for the ligands SCN- and HN3 Solvent composition mole fraction of DMSO
= k~2T[Fe3+][DMSO] + k347[Fe OH2+][DMSO] - k2~[Fe DMSO 3+] - k43[Fe DMSO OH 2+] + k54[Fe DMSO SCN OH +]
0.0079 L = SCN-
- k,5[Fe DMSO OH2+] [SCN -] + k62[Fe DMSO SCN 2+] - k26[Fe DMSO3+][SCN-]. (25) An expression for the relaxation time similar to the observed behaviour eqn (23) can be obtained from (25) if we use the condition 8[Fe DMSO SCN 2+] -- 8[Fe DMSO SCN OH +] = 6[SCN-] = 0
(26)
which leads to the conservation condition $[Fe 3÷] + ~[Fe OH 2÷] + 8[Fe DMSO 3+] + $[Fe DMSO OH 2+] = 0
(27)
0.0189 L = SCN0.0432 L= SCN 0.0432 L = HN3
1
--=
0 1.0 2.0 3.0 0 1.0 2.0 0 1.0 2.0 0 4.0
kbM sec ~
KH × l0 5 M-j sec l
6.42 -+0.20 10.50 +0.20 12.90 ___0.60 16.90_+0.20 3.92-+0.16 5.13 -+0.57 6.31 _+0.51 2.10--.0.10 2.64_+0.10 3.79 _+0.08 2.1 _+0.1 3.9_+0.2
1.71 1.36 1.46 0.87 0.86 1.05 1.65 -
0.87
In addition, we could have two more reaction paths k58
Fe DMSO SCN OH* ~
Fe SCN OH + + DMSO
k85
(30) k67
FeDMSOSCN 2+ ~
FeSCN2++DMSO
(31)
k76
as shown in the proposed overall reaction scheme (Fig. 5). An expression for ~'2 can be derived taking note of the above observation that the equilibration of Fe DMSO 3+, Fe DMSO SCN 2÷ and Fe 3* takes place faster than the equilibration of Fe SCN 2÷ with these species (i.e. l/z~ >> l/z2). For the pH range ( < 2.0) used in our experiments we can write --2
1
{R~[Fe3_/] + ~[SCN ] +
1
k~7 + k76KsT[DMSO]
+k~ K ~ [H+],j
(32)
R = 1 + K~3,[DMSO] + KcsK~3,[DMSOI[SCN-] R~ =- 1 + K~[DMSO] and
1
kc = { k3s+ ks,Ks-~n y[DMSO]} ~
T1
+
k45K~
*The maximum error in k45K~/K,estimated and given in last column is + 0.43 × l05.
(6X(t) = X(t) - Xo where
Xo is the equilibrium value of X consistent with the new equilibrium constant at the new temperature. X approaches Xo by relaxation). This appears to be a valid condition since we could not observe any additional relaxation which could be associated with the equilibration of Fe DMSO SCN 2÷. Equation (27) implies that when the temperature is changed the concentration changes in [FeDMSO 3+] and [FeDMSOOH 2+] at the expense of [Fe 3+] and [Fe OH 2+] is sul~cient to satisfy the new equilibrium constants of both (1) and (2). That such a situation is reasonable, can he seen as follows. From the observed direction of change in optical density associated with the relaxations at 315 and 450nm, it could be concluded that increase in temperature would cause an increase in [FeDMSO3+]/[Fe 3+] and a decrease in [Fe SCN2+]/[Fe3+]. We can expect Fe DMSO SCN 2÷ to behave similar to Fe SCN 2÷. Thus to expect a decrease in [Fe DMSO SCN2+]/[Fe DMSO 3+] to be achieved substantially, by an increase of [FeDMSO 3+] (at the expense of [Fe3+]) to satisfy the new equilibrium situation, is not unreasonable. The expression for relaxation time ~', under this condition will be
[L] × 102 M
K~
k26[SCN-] + k,, ~
[SCN ]
(28)
The negligible variations in the intercepts of Fig. 4 suggests that the term k26 [SCN-] is small. The estimated values of k45K~/Kn at 25°C in typical aqueous-DMSO mixtures are listed in Table 3 for the ligands SCN- and HN3. To account for the pH dependence of the relaxation observed at 450 nm we have to include a path expected from studies in aqueous solutions [ l l], k38
Fe OH 2+ + SCN- ~
k83
Fe SCN OH +.
(33)
(29)
similar to expression (22) in Ref. [1]. Table 4 gives typical values of 72 as a function of [SCN-] in aqueous solution and a typical DMSO-water mixture. For [DMSO] = 0, plot of 1/~'2 vs [SCN-] gave Ks = 115 M -~ which agrees with the estimate from equilibrium studies (Table 1). For the situation [DMSO] = 3.52 M this plot was linear even upto [SCN-] = 3 × 10-2 M. This implies Kcs[SCN-] (K~3,[DMSO]+ 1) which gives an upper limit Kcs'~ 70M -1. The estimated value of Ks/(1 +K~7[DMSO]) ( = 7 9 M -1) from this plot is close to the estimated K~ (Table 1) from equilibrium studies. This again would imply K~7[DMSO]Kcs~Ks from eqn (18). This is
1273
Fe(lIl) complexes in aqueous DMSO
3+ FeDMS-----~ + SCN ~ ' ~
k2s ~
- - - 2 + FeDMSO SeN
k62
KOS / / ~
- - 2 + __ k45 "-.. FeOMSOSCNOH FeDMSOOH+ SCNk5 4 kL
k85]/ [ kSs k76 k67 + DMSO[ + DMSO
k43
k
+ DMS
+ DMSO
k~,8... ge C~-.-C.-~-O-~ + k85 ~--~KSH
Fe~)H2++ SC---N-
\
/3 +~ +Y~ H +
Fe
kl 7
\ --2"t" fe SCN
+ SCN
k7~ Fig. 5. Proposed reaction scheme for the formation of various species discussed in text, in DMSO-water mixtures. consistent with the above mentioned upper limit. Table 4 also gives the calculated ~'2 using eqn (32) with Ks/R estimated from the above plot and kc estimated from the pH dependence of 1/~'2 (Table 2). Figure 6 gives the representative behaviour of l/r2 with pH at 25°C. Analysis of intercepts to get k76 is difficult, due to experimental errors in intercepts being large. The evaluated kc (Table 2) show a definite increase with [DMSO] and increase more or less linearly with Ks',/[DMSO]. This suggests that k85KS/K~i remains more or less constant with solvent composition. As will be pointed out below we can take the rate constant ks~ to vary only slightly with solvent composition. Thus K s and Kh both decrease with [DMSO}, keeping KS/Kh nearly constant.
Formation of Fe SCN 2÷ and Fe DMSO 3÷ in acetonitrilewater mixtures The values of Ks measured in 95% CH3CN - 5% H20, 85% CH3CN-15% H~O and 20% CH3CN-80% H20 were 830M -1, 380M -1 and 155 M -~ respectively. Thus Ks shows an increase with increase in the non-aqueous component. The formation of Fe DMSO 3+ could also be
studied using Benesi-Hildebrand type plots (Fig. 7) in the first two mixtures with high acetonitrile content. The values thus obtained were Kc = 9.3 M ~ and 6.3 M ' in these mixtures. DISCUSSION
Solvent composition effects Change in solvent properties such as viscosity and dielectric constant could alter the equilibrium constants and rate constants[18, 19]. Variations in the acid dissociation constants with solvent composition in the case of organic acids has been reported[20]. (This may be due to the hydrogen bonding property of DMSO). The present results show a marked decrease in K , with increase in DMSO. (It will be shown in the next subsection that K~=KH.) KS also behaves similarly. However, one does not expect large variations in 1the metal complex formation constant in the aqueous DMSO mixtures used, where the mole fraction of DMSO was restricted to < 0.1. This can be seen by examining Ks in different solvent mixtures. A comparison of Ks obtaivted from K~ (Table l) using a constant value of K* shows a
Table 4. Observed and calculated relaxation times "r2 as a function of [SCN ] at pH - 1.54, ionic strength 1.0 M and at 25°C for [DMSO] = 0. and 3.52M. ~2 calculated using (32) with Kcs-0 k~7=120M-Jsec ~, 3.52k76 Ks y= 80 M-l sec-l, KH(= Kn) and Ks from Table 1and kc fro m Table2, [FeT] = 1 × 10 -3 M
Solvent composition mole fraction of DMSO
0.0786
[SCN-] × 102 M
"r2observed m sec
r2 calculated m sec
O.I 0.3 0.5 0.8 1.1 1.4 1.7 2.0
96.6 84.4 72.5 60.2 52.9 37.9 36.9 30.8
94.3 81. l 70.8 59.1 50.6 44.1 39.1 35.1
0.1 0.3 0.5 1.1 1.4 1.7 2.5 3.0
358.4 353.4 292.4 210.1 209.2 175.7 160.8 127.6
356.6 323.8 294.8 228.7 204.8 185.2 147.0 130.1
1274
G. KRISHNAMOORTHYand B. S. PRABHANANDA
40
outer-sphere complex formation constant Kos to vary slightly with solvent composition in these mixtures. Thus, it is reasonable to treat the rate constants associated with different paths for complex formation as not significantly altered. Similar observations have been made in the case of displacement of DMSO by water from Co(NH3)sDMSO3+ in ethanol-water mixtures[21].
/
_~- 5 0 'k)
g~
°.
2c,o 0
I 20
I 40 I / [ H ÷]
I 60
I 80
I I00
Dissociation constant K D The coordination by a charged ion such as SCN changes the KH of the water coordinated to the metal by a factor of - 40. However, the coordination by a neutral ligand such as DMSO instead of H20 is not likely to affect the Kr~ to this extent. That K ~ = K , can be concluded from the analysis of results on the basis of the proposed reaction mechanism (Fig. 5). This can be seen as follows. An examination of different sets of data (typical values Table 2) at different temperatures showed that the variation of kDM with [DMSO] could be represented as kDM= a + b[DMSO]
(M)
Fig. 6. Typical r7 t vs 1/[H+]* plots for Fe SCN2÷ formation at 25°C in DMSO-watermixtures.O, 0% DMSO;@, 7% DMSO;~, 15% DMSO and A, 25% DMSO...
03
I-0.2
(34)
where a and b are constants. This suggests that Kn/KG varies insignificantly with [DMSO] since k3a can be taken to be constant for reasons given above. From equation (20) we see that this will be satisfied for either of the conditions (i)K D= KH; (ii) Kc[DMSO] and K~Kc[DMSO]/KH are negligibly small compared to I. The latter condition is not consistent with the variation of kDM when we recognise that KH/K~ was required to be constant. (This can be seen from equation (22).) It may be added that the near constancy of k45K~/KH given in Table 3 for a given ligand shows that K D varies to the same extent as KH with solvent composition, since the variation of k45 is expected to be small as explained above. Such a behaviour of K g is to be expected since Kn° = K..
tD iQ_ 0
"~ol
O
i 05
&{OPTICAL
I I0
I 15
DENSITY}/[ DMSO] o
Fig. 7. Hildebrand-Benesiplot at 330 nm for the formation of Fe DMSO3÷ in 95% acetonitrile-5%water (v/v) at 29°C,pH 1.25 and ionic strength 1.0 M, [FeT]= 1.25× 10 4M. small increase, from - lI5M ~ to - 150M-~, when [DMSO] is changed from 0.0 to 3.52 M (mole fraction = 0.079). If we provide for a small increase in K* with [DMSO], the variation of Ks is reduced. A comparison of Ks obtained in 20% CH3CN-80% H20 mixtures with that obtained in aqueous solution also shows similar behaviour. The results on aliphatic acid-water mixtures[l] are consistent with this. Such a small variation of the metal complex formation constant can be explained as due to the small variation in dielectric constant as long as we restrict the mole fraction of DMSO or CH3CN to <0.1. Thus in the expression for the formation rate constant in terms of the EigenTamm-Wilkins mechanism[13, 14] we can expect the
Estimation of K~ and rate constants The estimate of K~(--3.2-+0.6M ') made from the dependence of koM on [DMSO] is also close to the extrapolated value of Kc determined in CHaCN-H20 mixtures. Such an extrapolation assumes a similarity in the behaviour of Kc and Ks with solvent composition and the reasonable value of 3, = 1. (The reduced 3' in DMSO-H20 mixtures can be attributed to the hydrogen bonding property of DMSO.) It has not been possible to estimate Kcs in the present work. However, we can say K c s < 7 0 M -1. The rate constant k34(-8 × 103M l sec ') estimated using this value of K~ and eqn (22) is consistent with the expectations for neutral ligands on the basis of the general mechanism proposed for the formation of monocomplexes of Fe(III),[12]. Since K ~ = KH = K~, from Table 3 we get k45 ~ 10' M-~ sec-L Comparing this with k38 ( - 1 0 4 M - l s e c -', from kc corresponding to [DMSO]= 0 given in Table 2), we note an order of magnitude increase in the rate of displacement of a water molecule by a ligand such as SCN- or HN3 when a water molecule of Fe OH 2÷ is substituted by DMSO. Since the outersphere complex formations can be expected to be similar for both these reactions, we can say, on the basis of Eigen-Tamm-Wilkins mechanism that coordination by DMSO instead of H20 enhances the further water release from the inner coordination sphere of Fe OH 2+.
1275
Fe(lll) complexes in aqueous DMSO This is similar to the observations of Margerum et a/.[22,23]. It can also be noted that k45 for HN3 and SCN determined in the present work differ by a factor close to that of k38(6.8×103M ' s e c " for HN3 and 9× 103M ' s e c ' for SCN )[24]. This is also consistent with the above statements since the differences in k38 are to be associated with the differences in the outsphere complex formation constant. We can compare the rate of water loss and rate of DMSO loss from Fe DMSO OH -'+ by comparing k ( - k , , f l K o s , where Kos is the outer sphere complex formation constant ~ I M i) and k43( 2.5 × 10~ sec ', using ka3 = k~dK*). The observation k > k4~ is as expected for a stronger coordinating DMSO tcompared to HeO). Using the value of KnS=6.5× 10 ' M ~[11], and the value of K , determined in the present work in aqueous solution, we can make use of the observation that K S/KH varies insignificantly with solvent composition to estimate kss(2.8 × 104 M ' sec '! from the analysis of data according to eqn (33). This compares well with that expected for neutral ligands from the study in aliphatic acid-water mixtures (1 >: 104-6~ 104M 'sec ~)[1].
CONCI,US1ON A detailed examination of the equilibrium data and T-jump data has enabled us to come to the following conclusions. Solvent composition dependence of the relaxation rate associated with the formation of monocomplexes of Fe(lll) in aqueous-DMSO is mainly due to the dependence of K . lacid dissociation constant of water coordinated to the metal ion) on the concentration of DMSO. However, the presence of a DMSO coordinated to the metal ion, instead of in the surrounding medium does not affect KH. When these factors are taken into account the data suggest a reaction scheme for the formation of a typical complex Fe SCN 2+ in aqt,eous DMSO (Fig. 5) similar to that in aliphatic acid-water mixtures[l]. In this scheme, Fe SCN 2+ can also be formed by a path in which DMSO will be coordinated in the intermediate state. The rate determining step in the pH dependent path is the displacement of DMSO by H20 in Fe DMSO SCN OH +. The presence of a coordinated DMSO instead of water enhances further loss of water from the inner-coordination sphere of Fe OH > similar to that observed, when aliphatic acid was used instead of DMSO[1]. The estimated values of rate constants on the
basis of the proposed reaction scheme are consistent with chemical intution. REFERENCES
1. B, S. Prabhananda, J. lnorg. Nucl. Chem. 40, 525 (1978). 2. A. Fratiello, R. E, Lee, V. M Nishida and R. E. Schuster J. Chem. Phys. 47, 4951 (1967) 3. S. Thomas and W. L. Reynolds, lnorg. Chem. 9, 78 (1970). 4. L. P. Scott. T. J. Weeks, Jr., D. E. Bracken and E 1,. King J. Am. Chem. Soc. ql, 5219 11969). 5. J. Kenttiimaa and J, J, Lindberg, Soumen Kemistilehti B33, 32, 98 (I960). 6. S. Y. I,am and R L. Benoit, Can. J. Chem. 52, 718 (1974). 7. H, A. Benesi and J. H. Hildebrand, J. Am. Chem. Soc. 71, 2703 (1949). 8. L. E. Orgel and R. S. Mulliken, J. Am. Chem. So(. 79, 4839 (1957). 9. C. F. Bernasomi, Relaxation Kinetics. Academic Press, New York 11976). 10. D. Thusius, G. Foucault and F. Guillain, Dynamic Aspect,s o/ Conformational Changes in Biological Macromolecul'es (Edited by C. Sadron), p. 271. Reidel, Dordrecht (19731. I 1. D. M. Goodall, P. W. Harrison, M. J. Hardy and C. J. Kirk, J, Chem. Educ. 47, 675 11972). 12. G. Calvaruso. F. P. Cavasino, E. Di Dio and R. Triolo, lnorg. Chim. Aeta 22. 61 (1977) and refs 1-13 cited therein: F. P. Cavasino and M Eigen, Ric. Sci. A4, 509 (1964): F. Accascina, F. P. Cavasino and E. Di Dio, Trans. Faraday Soc. 65, 489 (19691: E. Mentasti, E. Pelizzetti and G, Saini, J. lnorg. Nucl. Chem. 38. 785 (1976). 13. M. Eigen and K. Tamm, Z. Electrochem, ~m. 93, 107 {t962) 14. R. G. Wilkins and M. Eigen, Adv. Chem. Ser. 49, 5~ (1965). 15. D. D. Perrin. J, Chem. Soc. 1710 11959). 16. G. M. Fleck, Equilibria in Solution, p. 44. Holt, New York (1966). 17. G. S. LaurenCe, Trans. Faraday Soc. 52, 236 (1956): I). D. Perrin, J. Ant. Chem. Soc. 80, 3852 (1958). 18. H. K. Bodenseh and J B. Ramsey, J. Phys. Chem. 67, 140 (1963). 19. J. E. Gordon, I'he Organic Chemistry of Electrolyte Solutions, p. 393. Wiley. New York 11975). 20. E. Buncel and H. Wilson, Advances in Physical Organic Chemistry (Edited by V. Gold and D. Bethell), Vol. I4. p. 133. Academic Press, New York (1977). 21. M. Glavas and W. E. Reynolds, J. Chem. So(. (Dalton) 1706 (1975). 22. ,1. P. Jones, le. J. Billo and D. W. Margerum../. Am. Chem. So('. 92. 1875 (I970), 23. J, P. Jones and D. W. Margerum, J. Am. Chem. Soc. 92, 480 {1970). 24. F. Accascina, F. P. Cavasino and S. D'Alessandro, ,/. Phys. Chem. 71, 2474 (1967).
0022-1902/81]1~61267~g)$02.00]0 1981 Pergamon Press Lid
Pril!i~'d ill Gre,*t I1r[latrl
KINETICS OF FORMATION OF Fe(lII) COMPLEXES IN AQUEOUS DMSO G. KRISHNAMOORTHYand B. S. PRABHANANDA* Chemica! Physics Group, Tara Institute of Fundamental Research, Bombay 40(10(15, India
(Receir.ed 2 July 1979: received [.or publication 25 August 1980) Ahstraet--Spectrophotometric observations have been used to study equilibria and temperature jump relaxation associated with the formation of Fe(lll) complexes in aqueous DMSO in the presence of SCN . The [SCN ] dependent relaxation observed at 315 nm could be assigned to the formation of Fe DMSO~, Fe DMSO OH-~, Fe DMSO SCN2+ and Fe DMSO SCN OH + from Fe~÷ and Fe OH~, The relaxation observed at 450nm could be assigned to the formation of Fe SCN~" by paths similar to that in aqueous solutions and a pH dependent path in which the rate determining step is the displacement of DMSO from Fe DMSO SCN OH' by H20. The rate constants suggest that coordination by a DMSO instead of a H20 has lhe effecl of labilising the other H.,O coordinated to Fe OH~+, The observed decrease in relaxation rates with increase in [DMSO] have been explained as dominantly due to the reduction in the acid dissociation constant KH associated with the aquocomplex of Fe{lll). INTRODUCTION In previous work on the kinetics of formation of a typical monocomplex Fe SCN 2~ in aliphatic acid-water mixture[l], the enhancement in relaxation rate (observed in T-jump experiments) was explained as dominantly due to the participation of the aliphatic acid in the reaction scheme. In contrast, experiments on the formation of monocomplexes of Fe(IlI) in aqueous DMSO at constant pH ~DMSO-dimethylsulphoxide), show a decrease in relaxation rate with increase in the DMSO component. This was found to be the case even in experiments at constant perchloric acid concentration instead of monitoring the pH. Such behaviour may be due to the alteration of equilibrium constants and rate constants with solvent composition. However, only a detailed study can tell us whether a reaction scheme similar to that observed in aliphatic acid-water mixtures is operating in the present system. For this purpose, it is relevant to investigate the dominant solvent coordinated species present in aqueous DMSO. Since DMSO has two donor sites and DMSO coordinated AI(III)[2, 3] and Cr(III)[4] have been observed in aqueous DMSO mixtures, one can also expect DMSO coordinated Fe(Ill), though the activity of DMSO is known to be reduced in ;he mixed solvents[5,6]. Ion exchange procedures which were used in the case of the Cr(Illl complex [4] cannot be adopted in the present case since the rate constants associated with the formation and dissociation of Fe DMSO 3~ are high. NMR methods[2, 3] are also not easy to use in this case since the concentration of DMSO coordinated to Fe(III) will be small compared to DMSO in the solvent mixture, and the lines are broadened due to paramagnetic Fe(IIl) which reduces the sensitivity. Use of high concentrations of metal ion complicates the situation by dimerisation reactions. Attempts to observe the formation of Fe DMSO s~ from spectral changes (Fig. la) were also not successful since the Benesi-Hildebrand plots[7] gave unreasonable values for the extinction coefficient and formation constant, the complications probably arising from the changes in the spectral features of Fe DMSO 3~ *Author to whom correspondence should be addressed. JIN( Vo~~ go ~-g
with solvent composition and the formation of "conlEact species" similar to those described by Orgel and Mulliken[8]. However, from Fig. l(a) we can expect spectral changes associated with the formation of Fe DMSO 3+ to take place in the 300-350nm region. Recently, amplitudes of relaxation behaviour of perturbed equilibria[9, I0] have been used to determine the equilibrium constants associated with simple equilibria. However, such a procedure is difficult when sew~ral coupled equilibria are present. In addition one must be able to get sufficient experimental points on either side of the equilibrium, which may not be possible when formation constants are small. In the present case we also have to contend with the change in enthalpy of the reaction with solvent composition which affects the amplitudes. However, the relaxation times "r measured for different concentrations of the ligands could also be used in the estimation of formation constants, as can be seen from eqn (8) of Ref.[ll] for the typical formation of Fe SCN 2+. A preliminary examination showed, that the exponential relaxation observed at 315 nm in the T-jump experiments on Fe(lll) solutions in aqueous DMSO, increased in amplitude with the mole fraction of DMSO in the mixed solvent. This is consistent with the formatior, of monocomplex Fe DMSO 3+. (Since only one exponential was discerned, it is reasonable to expect the concentration of other DMSO coordinated species to be small under the conditions of the experiment). However. the relaxation rate 1/rl decreased with [DMSOJ at a given pH, which appears inconsistent with the expectations of eqn (8) in[ll], unless the equilibrium constants and rate constants alter with solvent composition as mentioned above. The formation of a large number of mono-complexes of Fe(IlI) in aqueous solutions have shown (see references cited in[12]) that these could be described in terms of the Eigen-Tamm-Wilkins mechanism[13, 14], the rate determining step being the loss of water from the inner coordination sphere of Fe(H20),~' in the pH independent path and from Fe(OH)(H20)~" in the pH dependent path. Thus, one should expect similar pH dependence and solvent composition dependence for lhe relaxation time associated with the formation of a typical complex such as Fe SCN 2+ if our assignment of the relaxation at 315 nm to the formation of Fe DMSO ~' is
1267
1268
G. KRISHNAMOORTHY and B. S. P R A B H A N A N D A
I0 i 0
O9 09
08
07 o
06 (,')1---- 06 I Z b,J a 05
05
04
t.~
()4
g 03
O3
\
oI
O2
O
0
0
250
500 WAVELENGTH
350
'
0 300
400
do
350
4 5'0
WAVELENGTH
(rim)
(a)
5;o
(nm)
(b)
O7
Z
6
--105 C~
o
300
350
I
I
I
J
400
450
s00
5s 0
WAVELENGTH
(nm)
(c) Fig. 1. Spectral behaviour of Fe(III)-DMSO--SCN- system at 29°C, pH 1.25, ionic strength 1.0 M and [Fe z] = 2.5 × 10-4 M; (A) [SCN-] = 0.0 M [DMSO] = 0.6 M (a), 1.1 M (b), 1.52 M (c), 1.92 M (d), 2.49 M (e) and 3.05 M (f); (B) in aqueous solutions with [SCN-] = 1.0 x 10-3 M (a), 2.5 x 10-3 M (b), 4.0 x 10-3 M(c), 5.5 x 10-3 M(d), 7.0 x 10-3 M(e) and 10.0 x 10-3 M(f); (C) in 25% DMSO-75% water (v/v) with [SCN-] variation same as in (B).
,;
1269
Fe(lll) complexes in aqueous DMSO correct. In this paper, we describe a study of the solvent composition dependence of relaxation times in aqueous DMSO. We also give estimates for the formation constant of Fe DMSO > obtained from equilibrium studies and temperature jump relaxation studies. A reaction scheme for the formation of a typical complex Fe SCN > in aqueous DMSO is also given. In this scheme, the possibility of further coordination of other ligands such as SCN and HN3 to Fe DMSO > has also been included.
where y is the activity coefficient of DMSO in the mixture. We are neglecting species in which more than one DMSO is coordinated, since their concentration can be expected to be small under these conditions. We also have the acid dissociation constants. Ks - [Fe OHZ+][H+]* v D [ ]
[Fe DMSO OH~I[H~] * [Fe DMSO > ]
KS
EXPERIMENTAL Acetonitrile (B.D.H) and DMSO (Baker analysed) were used. Experiments were restricted to a DMSO content of less than 25% v/v (mole fraction <0.08)in aqueous DMSO. Sodium azide was obtained from B.D.H. (AnalaR).Sodiumperchlorate was used to regulatethe ionic strength to 1.0 M, The pH of the solutionswere adjusted by adding drops of 60%HCIO4 (B.D.H. AnalaR). Hydrogen ion activities [H*I* calculated from the pH of the solutions were used in the expressions for acid dissociation constants followingthe practice of many laboratories[15, 16].The preparation of stock solutionsand other experimentaldetails have been described elsewhere[l]. A Hanovia 901 B-I xenon-mercury lamp was used for the observation at 315nm, instead of the tungsten halide lamp used at 450 nm. The experimentswere carried out in the temperature range 20-40C. RESULTS Dependence of acid dissociation constant KH on solvent composition in aqueous DMSO Spectral changes due to the formation of a monocomplex such as Fe SCN 2~ in aqueous solutions and in aqueous DMSO (Figs. Ib and lc) can be explained within the limits of experimental error ( < 10%) considering the equilibria: k,7 Fe 3+ + SCN ~-~ Fe SCN > (1) k71
[Fe SCN OH+][H+] * [Fe SCN >] KDs [Fe DMSO SCN OH+][H+] * H : . [Fe DMSO SCN z+]
tl0)
The number of water molecules coordinated to the metal ion have been omitted in writing the above equations for convenience. Since our experiments have been restricted to pH ~<3, the deprotonated species of equilibria (6) and (7) are not important in the discussion of the spectral changes. (This can be seen by noting that K s < K , from the values given in[ll]. By analogy we can expect K~S,~K~.) The observed optical density using lcm path length will then be given by O.D. = ~,[Fe SCN >] + e2[Fe DMSO SCN 2. ] + E~[Fe:~'] + e4[Fe D M S O s+] + es[Fe OH > ]
+ t6[Fe DMSO OH > ] + e7[Fe (SCN)~I
lilt
where e¢(i = 1, 7) are the extinction coefficients of the species which occur in eqn (11). We also have the conservation relation [Fe v] = [Fe SCN >] + [Fe DMSO SCN>] + [Fe > ] + [Fe DMSO 3+] + [Fe OH 2+] + [Fe DMSO OH ~-~]
k12
Fe 3+ + DMSO ~ Fe DMSO 3~
(2)
k21
+ [Fe (SCN)~]
(il2)
k26
Fe DMSO > * S C N
~
Fe DMSO SCN >
(3)
k62
Fe OH 2+ ~ H" ~ FeDMSOOH 2~+H' ~
Fe 3+ FeDMSO >
Fe SCN OH + + H + ~ Fe SCN 2+ FeDMSOSCNOH'aH + ¢
At 450nm as = e4 = e5 = E6=0 from observations. Using (9)-(12) we get
(4)
Q'[FeT] Ks + Kc'Kcs[DMSO]
O.D.
Q'[FeT][SCN ] P
(5) (6)
F e D M S O S C N 2+
(8)
Under our conditions [Fe (SCN)~] is small. This can be seen from the known equilibrium constants[17]
O.D.
K'~[SCN ]
(13)
Kh O.D. {1 + K~[SCN ] + K~s[SCN 12}[H'J*
(7) Fe 3+- 2SCN ~ Fe (SCN)L
O.D. =
experimental
(14) where Q = t,Ks + a~KcKcs[DMSO] + eTKss[SCN ] (15)
[FeSCN>J . K~ Ks=~-FeS+][SCN_ J, :
[FeDMSO 3+] _ [FeS+][DMSO] yK*:
[FeDMSOSCN >] K [Fe (SCN)~] K(s = iFe DMSO 3 ][SCN ]; ss = [FeS+][SCN-]/ (9)
K~=
P = 1 + Kc[DMSO] + Ks[SCN-] + KcKcs[SCN-] [DMSO] + Kss[SCN-] 2
Ks + KcKcs[DMSO] 1 + Kc[DMSO] + Kss[SCN ]2 + (Ks + K~Kc[DMSO])/[H+] *
(16)
(17)
1270
G. KRISHNAMOORTHYand B. S. PRABHANANDA , _ Ks + KcKcs[DMSO] Ks1 + Kc[DMSO] K~s -
(18)
Kss 1 + Kc[DMSO]
07
(19)
K~ = K , + K~Kc[DMSO] i + Kc[DMSO]
(20)
K~ and K~s are determined from experiments at low pH ( - 1 . 0 ) such that KH "~ [H+] * and the term involving [H+] * in eqn (17) can be neglected. (It will be shown later that K~ ,~ [H+] * at this pH.) The departure from linearity of O.D. vs O.D./[SCN-] plots is used to estimate ~7( 9000M-~ cm -~) and K s s ( - 1 2 7 6 M -2) in aqueous solutions in addition to e~(~5100 M-~ cm -~) and Ks at I M ionic strength. The values obtained are comparable to those obtained by others[17] under slightly different experimental conditions. The values of K~ in aqueous DMSO are determined to a first approximation using Kc = 0. This is used to determine Kr~ from an analysis of the pH dependence of the optical density at constant [SCN-] according to eqn(14). These K~ are then used in the analysis of T-jump data using eqn (22) (v. inf) to obtain an estimate of K o K~ and Kr~ are finally ctbtained by iteration using such estimates of K o Figure 2 gives plots obtained from the pH dependence of the O.D. in typical mixed solvents used in the determination of K~ at 21°C. Table I gives the estimates of K~ and K~ at 25°C and their temperature dependences in mixtures of different compositions. It can be seen that although the variation of Ks' is small, K d decreases significantly when the DMSO component of the mixed solvent is increased.
Dependence o[ relaxation times on solvent composition in aqueous DMSO. Fe DMSO 3+ formation
06
o o
05 !
O3 200
10 0
t200
6OO
/
4oo / 50C
200
•
o
(21)
Q
2o
~o
6o
I/ [H+]"
k43
along with the fast protonating steps (4) and (5). An expression for the relaxation times ~'1 can be derived
800 N
Fig. 2. Plots of OD vs OD/[H+]* (eqn (14)) at 450 nm for the estimation of Kfi at 21°C. A, 0% DMSO; D, 7% DMSO; 0, 15% DMSO; O, 25% DMSO.
k34
Fe DMSO OH 2÷
600
OD/ [H']
The relaxation times zl associated with the temperature jump relaxation behaviour observed at 315 nm in typical DMSO-water mixtures with [FC] = 1.25 x 10-3 M, are plotted in Fig. 3. As mentioned earlier this can be assigned to the formation of FeDMSO 3÷ (which is further confirmed from the similar pH dependence and mixed solvent composition dependence of relaxation times in the case of formation of Fe SCN 2+ to be discussed later in this section). To account for the pH dependence of ~'~ in addition to the acid independent path (reaction(2)) we include an acid dependent path Fe OH 2+ + DMSO ~
400
8;
,go
(M-')
Fig. 3. Typical "rT ) vs I/[H+]* plots for Fe DMSO3÷ formation at 25°Cwith ILl = 0.; O, 1% DMSO; II, 3% DMSO;0, 7% DMSO; IS], 15% DMSO and A, 25% DMSO.
Table 1. Equilibrium parameters for the formation of Fe SCN2+ in various mixed solvents at 25°C and ionic strength 1.0 M. Activity coefficients y were calculated by extrapolation formula (eqn (1)) and data given in Ref.[6]. Temperature dependence given by K~ = K~ exp( - AEdRT) and Kh = K:~exp( - AE2/RT) K~ determined using K~ = 3.2 M-t and eqn (18) Solvent composition [DMSO] Mole fraction M of DMSO. 0 0.422 0.986 2.11 3.52
0 0.0079 0.0189 0.0432 0.0786
y
Ks + KcsKc[DMSO] M~
K~ M~
AEI kcal. mole-~
K~ × 103 M
0 0.060 0.063 0.070 0.082
114.5_+1.0 129.9-+0.8 141.8-+1.6 149.9+ 1.4 149.5_+1.5
114.5-+1.0 118.9-+1.8 118.5-+3.9 101.9_+6.2 76.8+-7.0
-1.2 -1.0
2.98+-0.09 2.39 +-0.22 1.39-+0.07 0.516_+0.008 0.129_+0.005
AE2 kcal. mole 8,9 7.7 6.8 6.1
1271
Fe(lll) complexes in aqueous DMSO based on the above mentioned paths for the formation of FeDMSO 3+ following the procedure given in Ref.[ll] and taking due note of the reduced activity of DMSO in aqueous-DMSO[5,6]. If 3' is the activity coefficient of DMSO in the mixed solvent, since [Fe3+]<[DMSO] under the experimental conditions we can write
400
//
300
-l- = B ~ - -kDMK~ r,
[
/
[H+] *
J with B = { y[DMSO] + ~-~ / k,2
kDM = 3,[DMSO]+
k34~
(22)
(The activity coefficients of Fe 3+ and Fe OH > in the mixed solvents have been taken to be unity to be consistent with the observations on Fe SCN 2+ formation to be discussed later.) Using K~ from Table 1 the values of kDM and their temperature dependence were obtained from plots similar to Fig. 3. These are listed in Table 2 for typical [DMSO]. Since kDM increases more or less linearly with [DMSO] we can take k34KH/K~I t o be nearly constant and get on estimate of K* (-~3.2 +0.6M ') (see "Discussion" also). It is clear that the unusual decrease of l/z, with [DMSO] was due to the decrease in K~.
Formation of monocomplexes of Fe(llI) in aqueous DMSO in the presence of SCN and H N 3 The T-jump experiments in this system showed the relaxation associated with the formation of Fe DMSO 3. in the time range 1-50 m sec. This could be conveniently observed at 315 nm and showed a reduction in amplitude as well as an increase in relaxation rate l/r, when the concentration of the SCN o r HN3 was increased. Figure 4 gives the typical dependence of r, on [L] (L = SCN , HN3) which could be expressed as
[wl* In addition to this a relaxation with time constant r: in the range 10--400m sec. could also be observed. This had a maximum amplitude around 450nm and could be associated with the formation of Fe SCN 2+ or Fe N] +. The pH and [DMSO] dependence of r, and r2 were
I/ [H~'"j (M') Fig. 4. Typical z [i vs l/[H+]* plots for Fe DMSO3' formation at 25°C and 15% DMSO with [L] = 0(@), [SCN ] = 1x 10 " M(O). [SCN ]=2× 10 2M(A) and [HN~=4x 10 " M(~71).
similar confirming that we are observing the monocomplex formations in both relaxations. Although eqn (23) suggests ligand catalysed formation of Fe DMSO > , this is unlikely since the equilibration for FeSCN 2+ and FeN3z+ formation is much slower than that for a Fe DMSO 3+ formation and the observed values of "C" cannot be accounted for by such a path. Alternatively, we could be seeing the effect of coordination of L to the DMSO coordinated metal by a path such as
k45 FeDMSOOH > + S C N
~
FeDMSOSCNOH"
k54
(241 (since we are making observations at 315 nm) in addition to the fast protonating steps (5) and (7). In order to get an expression similar to (23) we suppose the equilibration of FeDMSOSCN 2 takes place along with that of Fe DMSO J+. This is reasonable since we do not observe a separate relaxation associated with this equilibration. Also, it is not necessary to include the reactions associated with the formation of Fe SCN > (while discussing the situation when L = SCN ) since 1/r~->'> 1/r~ from
Table 2. Kinetic parameters defined by eqns (22) and (33) for the formation of Fe D M S O 3÷ and Fe SCN> in aqueous-DMSO for typical solvent compositions at 25°C and ionic strength 1.0M. Temperature dependence given by koM = k~Mexp( AE3/RT) and kc = k°sexp(-AEo/RT)+k°exp(-AE4/RT) with AEo 10.1kcal mole i Solvent c o m p o s i t i o n mole fraction of DMSO
kDM X l0 3 sec ]
0 0.0026 (!.0189 (!.0432 0.0786
2.45 -+0.08 2.90-+0.15 4.07 -+0.07 4.70_+0.69
AE3 kcal.mole z
,,12.8 14.0
kc x 10 4 M Esec I
0.86 ~+0.05 0.92 ~ 0.04 1.01 ~+0.08 2.40 ~+0.09 3.31 _+1.10
mE 4 kcal.mole
18.5 16.9 16.9
1272
G. KRISHNAMOORTHY and B. S. PRABHANANDA
experimental observation. For this case we can write d { [ F e DMSO 3+] + [Fe DMSO OH2+]}
Table 3. Typical Values of kbM=k34KH{I/K~+7[DMSO]} + k45K~lL] and k45KD/KHvalues obtained at 25°C and ionic strength 1.0 M for the ligands SCN- and HN3 Solvent composition mole fraction of DMSO
= k~2T[Fe3+][DMSO] + k347[Fe OH2+][DMSO] - k2~[Fe DMSO 3+] - k43[Fe DMSO OH 2+] + k54[Fe DMSO SCN OH +]
0.0079 L = SCN-
- k,5[Fe DMSO OH2+] [SCN -] + k62[Fe DMSO SCN 2+] - k26[Fe DMSO3+][SCN-]. (25) An expression for the relaxation time similar to the observed behaviour eqn (23) can be obtained from (25) if we use the condition 8[Fe DMSO SCN 2+] -- 8[Fe DMSO SCN OH +] = 6[SCN-] = 0
(26)
which leads to the conservation condition $[Fe 3÷] + ~[Fe OH 2÷] + 8[Fe DMSO 3+] + $[Fe DMSO OH 2+] = 0
(27)
0.0189 L = SCN0.0432 L= SCN 0.0432 L = HN3
1
--=
0 1.0 2.0 3.0 0 1.0 2.0 0 1.0 2.0 0 4.0
kbM sec ~
KH × l0 5 M-j sec l
6.42 -+0.20 10.50 +0.20 12.90 ___0.60 16.90_+0.20 3.92-+0.16 5.13 -+0.57 6.31 _+0.51 2.10--.0.10 2.64_+0.10 3.79 _+0.08 2.1 _+0.1 3.9_+0.2
1.71 1.36 1.46 0.87 0.86 1.05 1.65 -
0.87
In addition, we could have two more reaction paths k58
Fe DMSO SCN OH* ~
Fe SCN OH + + DMSO
k85
(30) k67
FeDMSOSCN 2+ ~
FeSCN2++DMSO
(31)
k76
as shown in the proposed overall reaction scheme (Fig. 5). An expression for ~'2 can be derived taking note of the above observation that the equilibration of Fe DMSO 3+, Fe DMSO SCN 2÷ and Fe 3* takes place faster than the equilibration of Fe SCN 2÷ with these species (i.e. l/z~ >> l/z2). For the pH range ( < 2.0) used in our experiments we can write --2
1
{R~[Fe3_/] + ~[SCN ] +
1
k~7 + k76KsT[DMSO]
+k~ K ~ [H+],j
(32)
R = 1 + K~3,[DMSO] + KcsK~3,[DMSOI[SCN-] R~ =- 1 + K~[DMSO] and
1
kc = { k3s+ ks,Ks-~n y[DMSO]} ~
T1
+
k45K~
*The maximum error in k45K~/K,estimated and given in last column is + 0.43 × l05.
(6X(t) = X(t) - Xo where
Xo is the equilibrium value of X consistent with the new equilibrium constant at the new temperature. X approaches Xo by relaxation). This appears to be a valid condition since we could not observe any additional relaxation which could be associated with the equilibration of Fe DMSO SCN 2÷. Equation (27) implies that when the temperature is changed the concentration changes in [FeDMSO 3+] and [FeDMSOOH 2+] at the expense of [Fe 3+] and [Fe OH 2+] is sul~cient to satisfy the new equilibrium constants of both (1) and (2). That such a situation is reasonable, can he seen as follows. From the observed direction of change in optical density associated with the relaxations at 315 and 450nm, it could be concluded that increase in temperature would cause an increase in [FeDMSO3+]/[Fe 3+] and a decrease in [Fe SCN2+]/[Fe3+]. We can expect Fe DMSO SCN 2÷ to behave similar to Fe SCN 2÷. Thus to expect a decrease in [Fe DMSO SCN2+]/[Fe DMSO 3+] to be achieved substantially, by an increase of [FeDMSO 3+] (at the expense of [Fe3+]) to satisfy the new equilibrium situation, is not unreasonable. The expression for relaxation time ~', under this condition will be
[L] × 102 M
K~
k26[SCN-] + k,, ~
[SCN ]
(28)
The negligible variations in the intercepts of Fig. 4 suggests that the term k26 [SCN-] is small. The estimated values of k45K~/Kn at 25°C in typical aqueous-DMSO mixtures are listed in Table 3 for the ligands SCN- and HN3. To account for the pH dependence of the relaxation observed at 450 nm we have to include a path expected from studies in aqueous solutions [ l l], k38
Fe OH 2+ + SCN- ~
k83
Fe SCN OH +.
(33)
(29)
similar to expression (22) in Ref. [1]. Table 4 gives typical values of 72 as a function of [SCN-] in aqueous solution and a typical DMSO-water mixture. For [DMSO] = 0, plot of 1/~'2 vs [SCN-] gave Ks = 115 M -~ which agrees with the estimate from equilibrium studies (Table 1). For the situation [DMSO] = 3.52 M this plot was linear even upto [SCN-] = 3 × 10-2 M. This implies Kcs[SCN-] (K~3,[DMSO]+ 1) which gives an upper limit Kcs'~ 70M -1. The estimated value of Ks/(1 +K~7[DMSO]) ( = 7 9 M -1) from this plot is close to the estimated K~ (Table 1) from equilibrium studies. This again would imply K~7[DMSO]Kcs~Ks from eqn (18). This is
1273
Fe(lIl) complexes in aqueous DMSO
3+ FeDMS-----~ + SCN ~ ' ~
k2s ~
- - - 2 + FeDMSO SeN
k62
KOS / / ~
- - 2 + __ k45 "-.. FeOMSOSCNOH FeDMSOOH+ SCNk5 4 kL
k85]/ [ kSs k76 k67 + DMSO[ + DMSO
k43
k
+ DMS
+ DMSO
k~,8... ge C~-.-C.-~-O-~ + k85 ~--~KSH
Fe~)H2++ SC---N-
\
/3 +~ +Y~ H +
Fe
kl 7
\ --2"t" fe SCN
+ SCN
k7~ Fig. 5. Proposed reaction scheme for the formation of various species discussed in text, in DMSO-water mixtures. consistent with the above mentioned upper limit. Table 4 also gives the calculated ~'2 using eqn (32) with Ks/R estimated from the above plot and kc estimated from the pH dependence of 1/~'2 (Table 2). Figure 6 gives the representative behaviour of l/r2 with pH at 25°C. Analysis of intercepts to get k76 is difficult, due to experimental errors in intercepts being large. The evaluated kc (Table 2) show a definite increase with [DMSO] and increase more or less linearly with Ks',/[DMSO]. This suggests that k85KS/K~i remains more or less constant with solvent composition. As will be pointed out below we can take the rate constant ks~ to vary only slightly with solvent composition. Thus K s and Kh both decrease with [DMSO}, keeping KS/Kh nearly constant.
Formation of Fe SCN 2÷ and Fe DMSO 3÷ in acetonitrilewater mixtures The values of Ks measured in 95% CH3CN - 5% H20, 85% CH3CN-15% H~O and 20% CH3CN-80% H20 were 830M -1, 380M -1 and 155 M -~ respectively. Thus Ks shows an increase with increase in the non-aqueous component. The formation of Fe DMSO 3+ could also be
studied using Benesi-Hildebrand type plots (Fig. 7) in the first two mixtures with high acetonitrile content. The values thus obtained were Kc = 9.3 M ~ and 6.3 M ' in these mixtures. DISCUSSION
Solvent composition effects Change in solvent properties such as viscosity and dielectric constant could alter the equilibrium constants and rate constants[18, 19]. Variations in the acid dissociation constants with solvent composition in the case of organic acids has been reported[20]. (This may be due to the hydrogen bonding property of DMSO). The present results show a marked decrease in K , with increase in DMSO. (It will be shown in the next subsection that K~=KH.) KS also behaves similarly. However, one does not expect large variations in 1the metal complex formation constant in the aqueous DMSO mixtures used, where the mole fraction of DMSO was restricted to < 0.1. This can be seen by examining Ks in different solvent mixtures. A comparison of Ks obtaivted from K~ (Table l) using a constant value of K* shows a
Table 4. Observed and calculated relaxation times "r2 as a function of [SCN ] at pH - 1.54, ionic strength 1.0 M and at 25°C for [DMSO] = 0. and 3.52M. ~2 calculated using (32) with Kcs-0 k~7=120M-Jsec ~, 3.52k76 Ks y= 80 M-l sec-l, KH(= Kn) and Ks from Table 1and kc fro m Table2, [FeT] = 1 × 10 -3 M
Solvent composition mole fraction of DMSO
0.0786
[SCN-] × 102 M
"r2observed m sec
r2 calculated m sec
O.I 0.3 0.5 0.8 1.1 1.4 1.7 2.0
96.6 84.4 72.5 60.2 52.9 37.9 36.9 30.8
94.3 81. l 70.8 59.1 50.6 44.1 39.1 35.1
0.1 0.3 0.5 1.1 1.4 1.7 2.5 3.0
358.4 353.4 292.4 210.1 209.2 175.7 160.8 127.6
356.6 323.8 294.8 228.7 204.8 185.2 147.0 130.1
1274
G. KRISHNAMOORTHYand B. S. PRABHANANDA
40
outer-sphere complex formation constant Kos to vary slightly with solvent composition in these mixtures. Thus, it is reasonable to treat the rate constants associated with different paths for complex formation as not significantly altered. Similar observations have been made in the case of displacement of DMSO by water from Co(NH3)sDMSO3+ in ethanol-water mixtures[21].
/
_~- 5 0 'k)
g~
°.
2c,o 0
I 20
I 40 I / [ H ÷]
I 60
I 80
I I00
Dissociation constant K D The coordination by a charged ion such as SCN changes the KH of the water coordinated to the metal by a factor of - 40. However, the coordination by a neutral ligand such as DMSO instead of H20 is not likely to affect the Kr~ to this extent. That K ~ = K , can be concluded from the analysis of results on the basis of the proposed reaction mechanism (Fig. 5). This can be seen as follows. An examination of different sets of data (typical values Table 2) at different temperatures showed that the variation of kDM with [DMSO] could be represented as kDM= a + b[DMSO]
(M)
Fig. 6. Typical r7 t vs 1/[H+]* plots for Fe SCN2÷ formation at 25°C in DMSO-watermixtures.O, 0% DMSO;@, 7% DMSO;~, 15% DMSO and A, 25% DMSO...
03
I-0.2
(34)
where a and b are constants. This suggests that Kn/KG varies insignificantly with [DMSO] since k3a can be taken to be constant for reasons given above. From equation (20) we see that this will be satisfied for either of the conditions (i)K D= KH; (ii) Kc[DMSO] and K~Kc[DMSO]/KH are negligibly small compared to I. The latter condition is not consistent with the variation of kDM when we recognise that KH/K~ was required to be constant. (This can be seen from equation (22).) It may be added that the near constancy of k45K~/KH given in Table 3 for a given ligand shows that K D varies to the same extent as KH with solvent composition, since the variation of k45 is expected to be small as explained above. Such a behaviour of K g is to be expected since Kn° = K..
tD iQ_ 0
"~ol
O
i 05
&{OPTICAL
I I0
I 15
DENSITY}/[ DMSO] o
Fig. 7. Hildebrand-Benesiplot at 330 nm for the formation of Fe DMSO3÷ in 95% acetonitrile-5%water (v/v) at 29°C,pH 1.25 and ionic strength 1.0 M, [FeT]= 1.25× 10 4M. small increase, from - lI5M ~ to - 150M-~, when [DMSO] is changed from 0.0 to 3.52 M (mole fraction = 0.079). If we provide for a small increase in K* with [DMSO], the variation of Ks is reduced. A comparison of Ks obtained in 20% CH3CN-80% H20 mixtures with that obtained in aqueous solution also shows similar behaviour. The results on aliphatic acid-water mixtures[l] are consistent with this. Such a small variation of the metal complex formation constant can be explained as due to the small variation in dielectric constant as long as we restrict the mole fraction of DMSO or CH3CN to <0.1. Thus in the expression for the formation rate constant in terms of the EigenTamm-Wilkins mechanism[13, 14] we can expect the
Estimation of K~ and rate constants The estimate of K~(--3.2-+0.6M ') made from the dependence of koM on [DMSO] is also close to the extrapolated value of Kc determined in CHaCN-H20 mixtures. Such an extrapolation assumes a similarity in the behaviour of Kc and Ks with solvent composition and the reasonable value of 3, = 1. (The reduced 3' in DMSO-H20 mixtures can be attributed to the hydrogen bonding property of DMSO.) It has not been possible to estimate Kcs in the present work. However, we can say K c s < 7 0 M -1. The rate constant k34(-8 × 103M l sec ') estimated using this value of K~ and eqn (22) is consistent with the expectations for neutral ligands on the basis of the general mechanism proposed for the formation of monocomplexes of Fe(III),[12]. Since K ~ = KH = K~, from Table 3 we get k45 ~ 10' M-~ sec-L Comparing this with k38 ( - 1 0 4 M - l s e c -', from kc corresponding to [DMSO]= 0 given in Table 2), we note an order of magnitude increase in the rate of displacement of a water molecule by a ligand such as SCN- or HN3 when a water molecule of Fe OH 2÷ is substituted by DMSO. Since the outersphere complex formations can be expected to be similar for both these reactions, we can say, on the basis of Eigen-Tamm-Wilkins mechanism that coordination by DMSO instead of H20 enhances the further water release from the inner coordination sphere of Fe OH 2+.
1275
Fe(lll) complexes in aqueous DMSO This is similar to the observations of Margerum et a/.[22,23]. It can also be noted that k45 for HN3 and SCN determined in the present work differ by a factor close to that of k38(6.8×103M ' s e c " for HN3 and 9× 103M ' s e c ' for SCN )[24]. This is also consistent with the above statements since the differences in k38 are to be associated with the differences in the outsphere complex formation constant. We can compare the rate of water loss and rate of DMSO loss from Fe DMSO OH -'+ by comparing k ( - k , , f l K o s , where Kos is the outer sphere complex formation constant ~ I M i) and k43( 2.5 × 10~ sec ', using ka3 = k~dK*). The observation k > k4~ is as expected for a stronger coordinating DMSO tcompared to HeO). Using the value of KnS=6.5× 10 ' M ~[11], and the value of K , determined in the present work in aqueous solution, we can make use of the observation that K S/KH varies insignificantly with solvent composition to estimate kss(2.8 × 104 M ' sec '! from the analysis of data according to eqn (33). This compares well with that expected for neutral ligands from the study in aliphatic acid-water mixtures (1 >: 104-6~ 104M 'sec ~)[1].
CONCI,US1ON A detailed examination of the equilibrium data and T-jump data has enabled us to come to the following conclusions. Solvent composition dependence of the relaxation rate associated with the formation of monocomplexes of Fe(lll) in aqueous-DMSO is mainly due to the dependence of K . lacid dissociation constant of water coordinated to the metal ion) on the concentration of DMSO. However, the presence of a DMSO coordinated to the metal ion, instead of in the surrounding medium does not affect KH. When these factors are taken into account the data suggest a reaction scheme for the formation of a typical complex Fe SCN 2+ in aqt,eous DMSO (Fig. 5) similar to that in aliphatic acid-water mixtures[l]. In this scheme, Fe SCN 2+ can also be formed by a path in which DMSO will be coordinated in the intermediate state. The rate determining step in the pH dependent path is the displacement of DMSO by H20 in Fe DMSO SCN OH +. The presence of a coordinated DMSO instead of water enhances further loss of water from the inner-coordination sphere of Fe OH > similar to that observed, when aliphatic acid was used instead of DMSO[1]. The estimated values of rate constants on the
basis of the proposed reaction scheme are consistent with chemical intution. REFERENCES
1. B, S. Prabhananda, J. lnorg. Nucl. Chem. 40, 525 (1978). 2. A. Fratiello, R. E, Lee, V. M Nishida and R. E. Schuster J. Chem. Phys. 47, 4951 (1967) 3. S. Thomas and W. L. Reynolds, lnorg. Chem. 9, 78 (1970). 4. L. P. Scott. T. J. Weeks, Jr., D. E. Bracken and E 1,. King J. Am. Chem. Soc. ql, 5219 11969). 5. J. Kenttiimaa and J, J, Lindberg, Soumen Kemistilehti B33, 32, 98 (I960). 6. S. Y. I,am and R L. Benoit, Can. J. Chem. 52, 718 (1974). 7. H, A. Benesi and J. H. Hildebrand, J. Am. Chem. Soc. 71, 2703 (1949). 8. L. E. Orgel and R. S. Mulliken, J. Am. Chem. So(. 79, 4839 (1957). 9. C. F. Bernasomi, Relaxation Kinetics. Academic Press, New York 11976). 10. D. Thusius, G. Foucault and F. Guillain, Dynamic Aspect,s o/ Conformational Changes in Biological Macromolecul'es (Edited by C. Sadron), p. 271. Reidel, Dordrecht (19731. I 1. D. M. Goodall, P. W. Harrison, M. J. Hardy and C. J. Kirk, J, Chem. Educ. 47, 675 11972). 12. G. Calvaruso. F. P. Cavasino, E. Di Dio and R. Triolo, lnorg. Chim. Aeta 22. 61 (1977) and refs 1-13 cited therein: F. P. Cavasino and M Eigen, Ric. Sci. A4, 509 (1964): F. Accascina, F. P. Cavasino and E. Di Dio, Trans. Faraday Soc. 65, 489 (19691: E. Mentasti, E. Pelizzetti and G, Saini, J. lnorg. Nucl. Chem. 38. 785 (1976). 13. M. Eigen and K. Tamm, Z. Electrochem, ~m. 93, 107 {t962) 14. R. G. Wilkins and M. Eigen, Adv. Chem. Ser. 49, 5~ (1965). 15. D. D. Perrin. J, Chem. Soc. 1710 11959). 16. G. M. Fleck, Equilibria in Solution, p. 44. Holt, New York (1966). 17. G. S. LaurenCe, Trans. Faraday Soc. 52, 236 (1956): I). D. Perrin, J. Ant. Chem. Soc. 80, 3852 (1958). 18. H. K. Bodenseh and J B. Ramsey, J. Phys. Chem. 67, 140 (1963). 19. J. E. Gordon, I'he Organic Chemistry of Electrolyte Solutions, p. 393. Wiley. New York 11975). 20. E. Buncel and H. Wilson, Advances in Physical Organic Chemistry (Edited by V. Gold and D. Bethell), Vol. I4. p. 133. Academic Press, New York (1977). 21. M. Glavas and W. E. Reynolds, J. Chem. So(. (Dalton) 1706 (1975). 22. ,1. P. Jones, le. J. Billo and D. W. Margerum../. Am. Chem. So('. 92. 1875 (I970), 23. J, P. Jones and D. W. Margerum, J. Am. Chem. Soc. 92, 480 {1970). 24. F. Accascina, F. P. Cavasino and S. D'Alessandro, ,/. Phys. Chem. 71, 2474 (1967).