Polyhedron Vol. 7, No. 4, pp. 291-295, 1988 Printed in Great Britain

0277V538?/88 $3.00+.00 0 1988 Pergamon Iournals Ltd

EVALUATION OF ABSOLUTE STABILITY CONSTANTS OF COMPLEXE~I. THEORY AND APPLICATIONS TO THE INORGANIC ONE-TO-ONE COMPLEXES OF IRON(II1) IN

PERCHLORATE MEDIA

QI FENG and HIROHIKO WAKI*

Department of Chemistry, Faculty of Science, Kyushu University, Hakozaki, Higashiku, Fukuoka, Japan

(Received 7 April 1987 ; accepted after revision 26 August 1987)

Abatraet-A method for evaluating a true stability constant termed the “absolute stability constant” is presented and the absolute stability constants for some first complexes of iron(II1) with inorganic anionic ligands, are evaluated by s~ctrophotomet~c measurement and mathematical treatment. The k; values obtained are : 2.1 for Fe(CIO,)Z*, 7.6 for FeCI’+, 3.6 for FeB?, 383 for Fe(SO,)+ and 3.2 for Fe(N03)2+ at I = 0.4 M and 20°C. These values are much larger than the apparent constants, that is, than the values which have conventionally been reported as “stability constants”.

In expe~mentaliy dete~ining stability constants of complexes, an inert medium electrolyte has been added to maintain the activity coefficients of all ions involved constant within a series of solutions to be measured. In all cases no pa~icipation of the supporting medium ions in complex formation has been assumed. Nevertheless, it seems unde- niable that poly-valent ions can form ion-pairs to some degree with medium ions of opposite charge, though these ion-pairs are in general not very stable. This side reaction should affect the complex for- mation to be investigated, giving an erroneous stability constant. The conventional treatment has only been that perchlorate anion or tetramethyl- ammonium cation is employed as an “inert medium ion” and the stability constants with these medium ions are assumed to be zero.i-4 However, the relative error produced by ignoring complex formation with the medium ion may be very pro- nounced in investigating an especially weak com- plex whose stability is of comparative magnitude to that of the medium ion complex. This erroneous stability constant should not only lead to a false recognition of the species distribution in a practical solution but also to an incorrect evaluation for physical quantities such as molar absorptivity.

*Author to whom wrrespondence should he addressed.

Johanson’ discussed these problems with per- chlorate as a typical medium electrolyte in his review and concluded that the estimation of such a medium ion contribution may be impossible by means of an equilib~um calculation only, unless more than one method directly distinguishing the species involved can be applied simultaneously. However, it may not be easy to find out such an effective direct method. The authors thought that the medium ion effect could be estimated by suitable mathematical treatment of the experimental equi- librium data. We use the term “absolute stability constant” for the pure stability constant obtained by estimating the ion-pair formation with the weak- est medium ion, which has been thought so far to be undete~inable. In this paper a theoretical background to obtain such an absolute stability constant and the application to practical simple complex systems are presented.

THEORY

We restrict the determination of absolute stability constants by absorption spectrophotometry, to the simplest case of a Mm+ -L-- complex system con- taining a monovalent medium anion B- where only one-to-one complexes ML’“-“- and MB@+‘)- are formed, as is often observed in weak inorganic ligand complexes. Assuming that the MB complex

291

292 Q. FENG and H. WAKI

has no absorptivity at a wavelength of the measure- ment for ML, the apparent molar absorptivity E is expressed by

A EIWLI

s = c,l = [M] + [ML] + [MB] (1)

where A is the absorbance, CM the total con- centration of the sample metal, I the light path and E, is the molar absorptivity of the ML complex. If the medium anion is added to the system in such a way that the ionic strength of a series of solutions is kept constant, i.e. Z = [L-l + [B-l = const., eq. (1) can be transformed to

& &,K, K,-KB -=---.E

[L-l l+K,Z l+K,Z (2)

where K, and KB are the absolute stability constants of ML and MB at ionic strength Z, respectively.

In a conventional treatment, KB for the weakest medium anion such as the perchlorate ion is assumed to be zero and a simpler equation has been adopted,

approximate absolute stability constant derived from simultaneous equations at two selected ionic strengths, to the midpoint of these two ionic strengths.

Let these ionic strengths be Z-AZ and Z+ AZ for simplification, Z being the ionic strength where the stability constants are to be investigated, then eq. (5) is written as

KaP _ = KI(I-AI, - KB(I- AI)

I(1 AI) I+ KB(I- A#- A0 (6)

or

G~I+AI) = K l(I+A.I) - KB(I+ A,)

1+ KB(,+ A,@+ AZ) ’ (7)

If a relationship

K,par, KW -= -= Kw, K f (8)

l(l+AI)

is assumed and the ratiofis assumed to be the same for a ligand ion and medium ion of similar types when AZ is not very large, then

obtaining K, from the slope of E/[L-] vs E plot. However, the assumption of KB = 0 cannot be con- sidered as a generally acceptable one. Thus

& = const. - Kypc (4)

K=” _ = fK,(o --~KB(I)

I(/ AI) 1 +fK~d- AI)

(9)

G~I+AI) = KI(,, - KB(I)

f+ KB&+ AZ) ’ (10)

Using eqs (9) and (lo), the absolute stability con- stants K,(,, and KBc,) can be written as

'K;PI-A~-~K~~,+A,~+K~~,-A,~K~~~+A~~

f

+(I+ AZ) -f(Z- AZ) 1 K,(I) = K"~~*+A,,(Z+AI)-K~~~-A,)(Z-AZ)

(11)

'K~$-AI,-~G&+AI~

'KB(I) =

f

K",~~+A,,(Z+AZ)-K",~~-A,,(Z-AZ)'

(12)

K;P = K,-KB

1 +&I (5)

and the slope of the s/[L-] vs E plot gives only an apparent constant K”ip which is smaller than the absolute stability constant. Since KB for the weakest medium ion cannot be determined experimentally, K, is also undeterminable. An extrapolation of K”ip to zero ionic strength only gives a stability constant difference of K, - KB, not K,. Neither could simultaneous standing of eq. (5) at arbitrarily different ionic strengths produce the absolute con- stants through the alteration of K, and/or KB values due to the activity coefficient change.

The best and only possible treatment in such a case may be by a reasonable extrapolation of the

Although KlcIj and KB(,) cannot be solved from these equations, these absolute stability constants may be determined by an extrapolating treatment described below.

If f is set to be unity, approximate absolute stab- ility constants KY and Kg at ionic strengths Z+ AZ and I- AZ can be calculated by

KaP _ -KaP

K&I*AIJ = KaP

I(1 AI) l(I+AI)

I(I+A,)(Z+AZ) - K”,~,-A&--~) .

(14)

Evaluation of absolute stability constants of complexes-I

The differences between KY and K, and between g and KB

M ferric perchlorate, and sulphuric acid and per- chloric acid of different concentrations at ionic strength of 0.4 M was measured at 330 nm. In an iron(IIIknitrate complex system, the absorbance of solutions containing 8.0 x 10d4 M ferric per- chlorate, and hydrochloric acid and nitric acid of

~G~I-AI~G~I+A~ 2AZ- f (Z+ AZ) +j-(Z- AZ) 1

293

K&~AI,-KI(I, = &, J '

d

,(,+A,,(I+A~)--~~,-A,~(~-A~+ K";~+A,,(Z+AI)-K~~~~A~(Z-AZ) - (16)

approach zero with decreasing AZ

lim (K&*AI) - &(I)) = AI+0

=o (17)

(18) RESULTS AND DISCUSSION

Therefore, the absolute stability constants K, and KB at ionic strength Z can be determined by extra- polating Kj’clkAr, and K&,kAr) from ionic strength Z+ AZ to I. Once the absolute stability constant KB of the medium anion becomes clear, the absolute stability constant of any other ligand anion at the same ionic strength can easily be obtained using eq. (5) through the experimental measurement of Kyp in the binary system with B-.

Evaluation of absolute stability constants for FeCl*+ and Fe(C104)2+ complexes

The first step for evaluating absolute stability constants is to determine the conventional stability constants according to an ordinary method. The iron(III)-chloride-perchlorate system seemed to be convenient for our purpose, since aquated ferric iron and the perchlorate complex are non-absorptive at the wavelength of 336 nm, with the maximal absorption by the chloro complexes. The ~;,3~/[Cl-] vs s&? plot based on eq. (4) gave a straight line in all ionic strengths studied, indicating that the chlor- ide or perchlorate complexes higher than one to one are negligible. The presence of hydroxo complexes of iron can also be neglected under this condition (pH < l), as log /I, for FeOH2+ is less than 3.0.’ The plot with an ionic strength of 0.4 M is shown in Fig. 1 as an example. The apparent stability constants obtained in this way at different ionic strengths are given in Fig. 2. The constant first decreased, then seemed to pass through a minimum with increasing ionic strength. This change is caused by an increased formation of the iron-perchlorate complex and the variation in ionic activity coefficients.

EXPERIMENTAL

Apparatus and chemicals

A Hitachi Recording Spectrophotometer EPS- 3T was employed with a 1 cm quartz cell for absorb- ance measurements. All chemicals used were of commercially available reagent grade.

Spectrophotometric measurement for determination of apparent stability constants

In an iron(III)-chloride complex system, the absorbance for a series of solutions containing 8.0 x lop4 M iron(II1) perchlorate, and hydro- chloric acid and perchloric acid of different con- centrations at different ionic strengths was mea- sured at 336 run. In an iron(IIIFbromide complex system, the absorbance of solutions containing 7.7 x 10m3 M iron(II1) perchlorate, and hydro- bromic acid and perchloric acid of different con- centrations at ionic strength of 0.4 M was measured at 403 nm. In an iron(III)-sulphate complex system, the absorbance of solutions containing 4.0 x 10s4

different concentrations at ionic strength of 0.4 M was measured at 355 nm.

All measurements were carried out at room tem- perature 20 + 1 “C, with a reference cell containing water.

The second step for evaluating the absolute stab- ility constants is to remove the effect of the activity coefficient change from these apparent constants by an appropriate extrapolation treatment. The ionic strength region around Z = 0.4 M seems to be con- venient for analysis, since the activity coefficients of at least the chloride ion and perchlorate ion may be sufficiently constant.6 Also, the ratios yFe3+/~reC12+

294 Q. FENG and H. WAKI

3 I I I I

200 4.00 600 800 1000

ET ( M-’ cm-‘)

a4 0.45 a5 0.35 a3 :.z EY :,E

Ionic strength

Fig. 1. Determination of the apparent stability constant for the FeCl’+ complex by spectrophotometry at Z = 0.4

(HCl+ HClO,).

and ~~~~~~~~~~~~~~~ z + may be similar to each other and both change only gradually with ionic strength. For extrapolation, pairs of ionic strengths of equal difference from the central ionic strength Z = 0.4 M, i.e. Z= 0.35 and 0.45, Z= 0.30 and 0.50, Z= 0.25 and 0.55 M and so on, were taken and the corrected apparent stability constants of FeCl*+ with these pairs of ionic strengths were taken from the smooth curve which best fits experimental points, as shown in Fig. 2. By inserting these values into eqs (13) and (14), the approximate absolute stability con- stants of the FeCl*+ complex and also of the Fe(ClO,)‘+ complex were calculated, respectively. These values were extrapolated to Z = 0.4 M as indicated in Fig. 3. A good linearity from the extrapolation was obtained, from which the true absolute stability constants were evaluated to be K, = 7.6 for FeC12+ and KB = 2.1 for Fe(C10J2+. Almost the same value, i.e. 2.0 for Fe(C10,)2f can be obtained by substituting K, = 7.6 and the experimental value Kyp = 3.05 into eq. (5).

Fig. 3. Determination of the absolute stability constants for FeCl*+ and FeClOj+ complexes at Z = 0.4 by extra- polation of log K: and log Kg. l : log K:; A : log Kg.

Evaluation of absolute stability constants for other complex systems from the stability constant with medium anion determined

Since the stability constant of the iron(II1) com- plex with perchlorate ion in a medium electrolyte, together with that of the FeC12+ complex, is known, other iron(II1) complex systems could easily be ana- lysed using the same perchlorate medium.

The iron(IIIkbromide-perchlorate system was analysed in order to evaluate the absolute stability constant of FeBr*+ at Z = 0.4 M. The &3/[Br-] was plotted against &,03 to determine the apparent stab- ility constant (Fig. 4a). A straight line was drawn by an error-weighted least square technique, from whose slope KyP was obtained. The absolute stab- ility constant of FeBr2+ was calculated from the equation

K FeBr*+ - K K”iP =

Fe(C10J2+

1 +KwcIo,)~+ x 1 (19)

using the KFe(~I~,) Z+ value determined in the fore- going section.

In a similar way, the iron(III)-sulphate-per- chlorate system was analysed to evaluate the absol- ute stability constant of Fe(S04)+ at Z = 0.4 M. In this case the free sulphate concentration as the ordinate of Fig. 4b was calculated from the first protonation constant [HSO;]/[SOi-][H+] = 18.8 at Z = 0.4 M*. With the apparent stability constant obtained from the E~,~~/[SO:-] vs E$!,~O plot (Fig. 4b), the absolute stability constant was calculated using

0.2 a3 0.4 Cl5 06 0.7 a8 0.9

Ionic strength

Fig. 2. Ionic strength dependence of the apparent stability constant for the FeCl*+ complex.

*This value was determined by the present authors using a separate experiment whose details are omitted in this paper.

Evaluation of absolute stability constants of complexes-I 295

I(b)

E330(~ld M-' cm-’ I Fe

$3 ’ _I--- •---*--.w*~ .-•-_

0 2 3 4

Ezz5 (x IO’ WI-’ cm+ 1

Fig. 4. ~ete~nation of the apparent stability constants of some other iron(II1) complexes. (a) FeCl’+(HBr- HC103; (b) FeSO$(H,SO,+-HCIO,,); (c) FeNO$+(HCI-

1,

HNO,). 2.

the equation

Generally speaking, if the absolute stability con- stant with one ligand in a binary ligand system is known, the constant with another iigand can be determined. The absolute stability constant of the Fe(NO# complex cannot be dete~ined spec- trophotometrically in a perchlorate medium, because of non-absorptivity of the complex. Instead the iron(III)-chloride--nitrate system could be util- ized for the analysis. First the apparent stability constant of FeCl’+ in a nitric acid media was deter-

mined (Fig. 4c), then the absolute stability constant of Fe(NO$‘” at I = 0.4 M was calculated from the

equation K

K”1P = FeC12+-1YfjefNo~~2+

1 +KF~(No,)~+ X 1 (211

by inserting the known absolute stability constant K F&l*+*

The absolute stability constants evaluated are tabulated in Table 1, as well as the apparent con- stants. Some of these apparent constants were in good agreement with “stability constants” reported by other investigators,‘-’ considering the difference

in ionic strength. It can be seen from the table that the error produced by taking the apparent stability constant as the true constant may become signifi- cant when the value of the stability constant is small.

The extension of the present method for eval- uating the absolute stability constant using ionic strengths other than I= 0.4 M in HCI-HClO,, media, for other metal complex systems, and for the evaluation of other constants such as Kz or &, will be tried and reported elsewhere.

3.

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5. 6.

7.

8.

9.

REFERENTS

R. M. Smith and A. E. Martell (Eds), ~r~tica~~tability Constants, Inorganic Complexes, Vol. 4. Plenum Press, New York (1976). E. Hogfeldt (Ed.), Stability Constants of Metal-Ion Complexes, Part A: Inorganic Ligands. Pergamon Press, Oxford (1982). L. G. Sillen and A. E. Martell (Eds), ~tff~i~~ty Con- stants of MetakIop2 Complexes, Special Publication No. 17, London (1964). L. G. Sillen and A. E. Martell (Eds.), Stubifity Con- stants of Metal-km Complexes, Special Publication No. 25, London (1971). L. Johansson, Coord. Chem. Rev. 1974,12,241. W. J. Hamer and Yung-Chi Wu, J. Phys. Chem (Ref. Data), 1972,1, 1047. E. Rabino~tch and W. H. Stockmayer, J. Am. C/tern. sot. 1942,64,335. D. F. C. Morris and A. R. Wilson, .Z. Znorg. Nucl. Chem. 1969,31,1532. D. F. C. Morris and P. J. Sturgess, Electrochim. Actu. 1969,14,629.

Table 1. Absolute and apparent stability constants for some iron(II1) complexes at Z = 0.4 M, 20°C

Complex Absolute (Z = 0.4 M) Apparent (Z = 0.4 M) Relative error of

= conventional conventional constant (%)

Fe(ClO,)* + 2.1 0 - 100 FeC12 + 7.6 3.1 -59 FeBr* + 3.6 0.81 -78 Fe(S03 + 383 196 -49 Fe(NO,)*+ 3.2 (0.60) -81