ROBERTN. HEISTANDAND ABRAHAM CLEARFIELD
2566 3 c
POTENTIAL,
-
volts YO
SCE,
Fig. 1.-Polarograms of titanium in 0 1 M HCI: curve I, residual current polarogram for 0.1 M HC1; curve 11, polarogram of solution of titanium halides prepared after Forbes and approximately two millimolar in titanium in 0.1 M " 2 1 ; curve 111, polarogram of the same solution with Ti(II1) partially oxidized.
tial and approximately twice the size of the first, indicating a one-electron reduction t o Ti(I1) followed by a two-electron reduction t o Ti(()). Considering the dif-
[COHTRIBUTION FROM SIAGARA UNIVERSITY AND
THE
Vol. 85
ference in solvation energies of Ti(II1) between water and acetonitrile t o be expected by analogy with other triposit ive transit ion metals, the aqueous pot en t ial corresponding to - 1.3 v. vs. s.c.e. in acetonitrile would be a t least - 2 v. vs. n.h.e. This estimate more nearly coincides with the theoretical work of George and McClure,* who applied ligand field correction t o the hydration energies of diand tripositive ions of the first transition series in relating standard potentials of the metal ion couples t o the third ionization potential of the free metals. Their calculations agreed with known standard potentials for the first transition series except in the case of the Ti(II1)-Ti(I1) couple. They estimated that the true Eo of the Ti(II1)-Ti(I1) couple should be approximately - 2 . 3 v. in aqueous solution. Such a potential would well explain the absence of Ti(I1) in aqueous media. Acknowledgment.-Taken in part from a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy a t the Massachusetts Institute of Technology, June, 1961. This work was supported in part by the U. S. Atomic Energy Commission under Contract AT (30-1)-905. (7) I . M . Kolthoff and J . F. Coetzee, J . A m . Chem. Soc., 7 9 , 1652 (1957) (8) P . George and D . S . McClure in "Progress in Inorganic Chemistry,' F. A. Cotton, E d . , Interscience Publishers, Inc., New York, K Y . , 1959.
SATIONAL LEADCO., TITANIUM ALLOYMANUFACTURING D I ,~NIAGARA FALLS
N.Y . ]
The Effect of Specific Swamping Electrolytes upon the Formation Constant of the Monochloroiron(II1) Complex1 BY
ROBERTN. HEIST AND^
AND
ABRAHAM CLEARFIELD3
RECEIVED JASUARY24, 1963 The ultraviolet absorption spectrum of the monochloroiron(II1) complex in perchloric acid and sodium perchlorate-perchloric acid mixtures was examined. The formation constant increased with increasing swamping electrolyte Concentration but decreased when the ratio of sodium perchlorat2 to perchloric acid increased a t constant total molarity. These results were correlated with the effect of the swamping electrolyte upon the activities of the species involved in the equilibria.
The chloro complexes formed by the hydrated iron(111) cation have been the subject of numerous spectrophotometric studies. 4-g Gamlen and Jordang reviewed this work in detail and concluded that 4 species, FeCl", FeC12+,FeC13, and FeC14-, were formed in the system. Desesa and RogerslO observed that the absorption spectra of iron(II1) solutions containing chloride ion were greatly influenced by changes in hydrogen ion concentration. However, these investigators were interested in developing an analytical method for the drterrnination of iron and did not examine the nature of the acid effect further. Subsequently, Coll, Nauman, and West" determined the (1) Presented before the 140th National hleeting of the American Chemical Society, Chicago, Ill , Sept. 3 . 1901. ( 2 ) This paper is based u p o n the thesis submitted by Robert N . Heistand in partial fulfillment of the requirements for the degree of Master of Science, Niagara University. ( 3 ) Address. Sational Lead Co., Titanium Alloy Mfg. Div., Box C , Bridge Station, Siagara Falls, S.Y . , for all inquiries. ( 4 ) A . VunKiss, J. Abraham, and I . Hegedus, Z.anorg. oiigcm. Chem., 144, 98 ( l Y 4 0 ) . , 508 (1941). ( 5 ) H . E. Rent and C . I,. French, J . A m Chem. S O L .63, (0) E. Kilbinowitch and W. H . Stuckmayer, i b i d . , 64, 336 (1942). (7) H Olcrup, Si'eiislr. Kern. T i d s k r . , 66, 324 (1943). (81 1) &. lfetzler and R . J. hleyers, . I . A m . Chem. Soc., 74, 3772, 3776 (19.50). (9) G. A. Gamlen and D. 0. Jordan, J . Chein. Soc., 1-135 (1953). ( I O ) M . A . Desesa and L. B. Rogers, A n d . Chim. Acto, 6, 634 (1952).
effect of perchloric acid concentration and mixtures of perchloric acid and perchlorates upon the absorption spectrum of the monochloroiron(II1) complex. They found an enormous increase in the value of the formation constant with increasing perchlorate concentration and attributed this to the dehydration of the hydrated iron(II1) cation by perchlorates. However, these authors felt that this was not the only factor responsible for the observed changes in the formation constant. The present study was undertaken to elucidate further the nature of the perchlorate ion effect upon the chloroiron (I11)complexes. Experimental Reagents and Solutions.-Reagent grade iron( 111) chloride was recrystallized from aqueous solution untii free of metallic impurities. Iron (111) perchlorate was prepared from the chloride by the method of Mulay and Selwood.L2 The resulting violet crystals were dissolved in 0.1 'If HClOd and diluted with the acid to a concentration 0.05 M total iron. The solution was analyzed for iron( 111) and iron( 11) by the Zimmerman-Iieinhart method and for chloride ion by the Yolhard method.13 There (11) H. Coll, R. V. Nauman, and P. W. West, J . A m . Chem. SOL.,81, 1284 (1959). (12) I,. N. Mulay and P . W. Selwood, i b i d . , 77, 2095 (1955). (13) I . M. Kolthoff and E. B. Sandell, "Textbook of Quantitative Inorganic Chemistry," 3rd Ed., The Macmillan Co., New York, K. Y . , 1952, pp. 545, 572-573.
FORMATION CONSTANT OF MONOCHLOROIRON (II I ) COMPLEX
Sept. 5 , 1963
was less than 0.001% chloride and iron(I1) present. Hydrochloric acid and perchloric acid solutions were standardized by titration against standard sodium hydroxide solution. Sodium perchlorate and lithium perchlorate solutions were prepared by carefully weighing out the required amount of recrystallized C.P. crystals (G. F . Smith Chem. Co.) and diluting to a specific volume. Double distilled water, free of carbon dioxide and chloride ion, was used in all the preparations. Instrumentation.-All of the absorption spectra were recorded with the use of a Beckman DK-2 spectrophotometer. The reference spectrum was recorded with purified water in both cells. Samples were run at ambient temperatures which averaged 23 f 4". Except for the initial experiments, the concentration of all solutions was such as to give absorbances in the range of 0.2-0.8. Several solutions were examined twice within a 24-hour period after preparation to determine their stability. The spectra of the pairs were identical within the experimental error of the instrument.
2567
mp was taken as evidence t h a t only two absorbing
species, Fe3+ and FeC12+, were present. An isosbestic point was expected at X 282 mp from a consideration of the molar absorptivity coefficient curves of the species Fe3+ and FeC12+ as given by Gamlen and J ~ r d a n . ~ A t high chloride ion concentrations the curves did not pass through the isosbestic points. When this occurred, it was assumed that higher chloro coniplexes were present. Thus, i t was possible t o define those conditions for which only the species Fe3+ and FeC12+ were present in the solutions. 5000
,
I
4000
Results I n the first set of solutions t h e iron(II1) chloride concentration was maintained constant a t 5 X lop3 M while the hydrogen ion concentration was varied from 1 to 5 M with perchloric acid. The total electrolyte concentration was kept constant a t 5 M with NaC104. Thus, in all of these solutions the perchlorate ion concentration was also constant a t 5 M. The spectra for a portion of the ultraviolet region in which the chloro complexes absorb strongly are shown in Fig. 1.
3000
rrj
2000
lOOU
240
260
280
300
320
340
360
380
400
Wave length, mp
Fig 2 -The effect of chloride ion concentration upon the ultraviolet absorption spectra of iron(II1) perchlorate, 1 0-cm cell [ F e ( I I I ) ] = 1 X 10-3 M, [ H + ] = 3 31, [C104-] = 5 Jf; [Cl-] = a, 0 00, b, 1 X lo-* X ; c, 4 X Alf
e
0.5
Similar sets of absorption curves were now obtained at three different iron(I1I) concentrations (2.5, 5 , and 10 X lOP4M ) and a t acidities of 1, 2 , 3 , 4, 5 .Id, all a t 5 M total electrolyte concentration. The formation constants for the monochloro complex were then calculated from the relationships
0.4
< 0.3
+ [FeCI2+])= eo[Fe3+]+ el[FeCI2+]
(1)
K 1 = [FeCl2+1/[Fe3+1 [CI-]
(2)
A = E([Fe3+] 0.2
where A = absorbance, E is the total absorptivity of the solutions and eo, e t , e,, are molar absorptivity coefficients of individual species. Applying the technique of Olsen and Simonsenl4 to eq. 1 and 2 and assuming that the total chloride ion concentration. [Cl-I,, equals the free chloride ion concentration, [Cl-1, gives
0.1
0 300
320
340
360
350
400
Wave length, mp
Fig 1 --Ultraviolet absorption spectra of ferric chloride in '11; SaC104-HC10a solutions, 0 1-cm cell: [FeCh] = 5 X [C104-] = 5 M ; [ H + ] = a, 1 M; b, 2 M ; c, 3 X ; d, 4 X ; e, 5 h1
I t is seen that the absorbance increased markedly with increasing hydrogen ion concentration. The increased absorbance could not be due to the dehydrating effect of perchlorate ion since the concentration of this ion was constant throughout. I n the next set of experiments, the chloride ion concentration was varied while the hydrogen ion and iron(I1I) concentrations were kept constant a t 3 *If and 1 X lop3 M , respectively. The total electrolyte concentration was again maintained constant a t 5 M. The absorbances of these solutions in the ultraviolet region of the spectrum are shown in Fig. 2. The appearance of the isosbestic points a t 282 mp and 235
ElC1-10
+ E/Ki
=
eo/Ki f ~ [ C l - l o
(3)
Equation 3 was solved for K1, €1, and eo from sets of simultaneous equations derived from the spectral data a t about 23 different wave lengths. Only those curves which passed through the isosbestic points were used. The validity of the assumption that [C1-]0 = [Cl-] was checked by calculation using the initially derived values of ICl. The error was only appreciable when the chloride ion concentration approached the total iron(111) concentrfition and such values were not used for the final calculation of K 1 . The values of eo and el are plotted in Fig. 3 and compared with the results of earlier studies."lj The agreement between our values of eo and those obtained by Turner and Miles from hydrclysis studies of iron(II1) perchlorate solutions is quite good. However, our el values are higher than those given by Gamlen and Jordan. Absorption spectra were now obtained for solutions in which the total electrolyte concentration was 1, 2 , 3, (14) A . R. Olsen a n d T. R Simonsen, J . Chem. P h y s . , 17, 1322 (1919) (15) R. C. Turner a n d K. E. Miles. Can. J C h e m . 36 1002 (1957).
ROBERTN. HEISTAND AND ABRAHAM CLEARFIELD
2568
Vol. 85
TABLE I OUSERVED A N D CALCULATED VALUESOF K I FOR PERCHLORIC ACIDAND PERCHLORIC ACID-SODIUM PERCHLORATE SOLUTIONS Molarity
_-__
_--__
of HCIO,
Obsd.
Calcd.
5 4 3
48f7 42 i 6 35 f 5 28 f 5 20 f 4
42 37 32 27
7
2 1
5---
1
---
Obsd.
Calcd.
Obsd.
Calcd.
Obsd.
Calcd.
Obsd.
20 i 4 18 f 3 15 f 2 10 i 2
22 17.7 15.5 13.5
7.8 f2 6.8 f 1.6 5.2 f0.8
11 6.9 6.2
5 i 1 4.1 f 1
6.4 4.5
3.9 f 0.7
Calcd.
, .
and 4 ,I8 and the acidity varied from 1 t o x M , where x is the total electrolyte concentration for t h a t particular set of solutions. Values of K , were calculated from these data using the values of €0 and E ] determined from the data a t 5 ‘$1. The results are given in Table I in the columns marked obsd.
6000
___--
Total electrolyte molarity _--- _-__3-_--_-___ 2------.
4
I I ’
4.3
07
1
06
5000
0.5 4000
q 0.4 3000
2000
0.3
1000
0.2 240
260
280
300
320
340
360
380
400
Wave length, m p
Fig 3 -The ultraviolet absorption spectra of the iron(II1) ion, €0, and E , the monochloroiron(II1) complex. Solid line represents data of this study, dashed line is d a t a of Gamlen and Jordan, dotdashed line is data of Turner and Miles
The question now arises as t o whether the observed changes in absorbance are due to some special hydrogen ion effect. If this were so, then similar results should be obtained with lithium perchlorate-perchloric acid mixtures. That this is not the case is shown in Fig. 4. The decrease in absorbance on substituting lithium perchlorate for perchloric acid is much smaller than was obtained with sodium perchlorate. This difference cannot be attributed to concentration differences of the swamping electrolyte since in all of these solutions the total electrolyte concentration was 6.48 formal t o within 0.5qlo. Thus, the absorbance depends not only upon the total “inert” electrolyte concentration but also upon its composition.
The possibility that the variations in K 1 result from changes in the activities of the species involved in the equilibrium with changing swamping electrolyte composition will now be explored, For the reaction we have
+ C1-
Fe(HzO),-lCIZ+
0 320
360
340
Wave length,
380
400
rnp
Fig 4 -Comparison of ultraviolet absorption spectra of ferric chloride in several electrolyte mixtures, [Feci31 = 1 8 X M, [C104-] = 5 M: a, 5 M HCIO,, b, 4 HCIOa-l M LiCIO4, c, 3 J!f HCIO4-2 ,M LiCIOa, d , 4 A!f HCI04-1 .M iYaC104, e, 3 A4 HC104-2 A!f Sac104
where parentheses represent activities, I’i is the molar activity coefficient of species i. The waters of hydration have been omitted from eq. 5 and subsequently for simplicity. Following the treatment given by Gamlen and Jordang for solutions a t high ionic strength, viz. P F ~ C I ~ + / Y= F ~C,Yci~+ E Y*HCI
Discussion
Fe(H20),3’
0.1
+ HzO
eq. 5 becomes
for any two such solutions
(4)
Equation 7 can be used t o determine approximately how K l will vary with changes in the swamping electrolyte concentration or composition.
Sept. 5 , 1963
FORMATION CONSTANT OF MONOCHLOROIRON(III) COMPLEX
The first case t o be considered is that in which the swamping electrolyte is perchloric acid only. The mean molal activity coefficients of HC1 in perchloric acid have been determined16 u p t o I = 1. Although plots of log Y + H C I 'us. molality of HC1 were only approximately linear, i t was feltI6 that the HCl-HC104 system obeyed Harned's rule.'' Therefore, we drew the best straight line through the data a t I = 1 and its slope (-0.0147) was used to calculate values of ~ + H C I at higher ionic strengths from the equation log
YkHCl
= log Y&HCI(O)
+ 0.147(m)
(8)
where m = total electrolyte molality and Y & H C I ( O ) is the mean molal activity coefficient of m molal hydrochloric acid. As a check on the above procedure the experimentally determinedI6 activity coefficients were fitted t o the equation
The constants obtained from this fit were a = 0.460 =k 0.011 and b = 0.156 f 0.007. Equation 9 was then used to calculate activity coefficients at ionic strengths greater than 1. The two sets of activity coefficients differed by only 2-3y0. Water activities for aqueous perchloric acidla were used in place of the water activities of the actual solutions. This procedure is justified since the perchloric acid concentrations were very nearly equal to the total electrolyte concentrations. The mean molal activity coefficients were converted to mean molar activity coefficient^'^ from the known densities of perchloric acid solutions.20 Values of KIS* were now calculated for solutions 4 , 3 , 2 ,and 1M i n HCIOh using KISl = 48 at 5 M perchloric acid. The results, shown in Table I, are in quite good agreement with the observed data considering the nature of the assumptions made in the calculations. The second case t o consider is that in which sodium perchlorate is partially substituted for perchloric acid a t a constant total electrolyte concentration. The required water activities and activity coefficients have not been measured. Therefore, the following treatment was adopted. Harned's rule has been shown to apply precisely to the HC1-NaC104 systemz1 up t o I = 1. We again assumed that the rule would apply a t higher electrolyte concentrations since this is true for other similar systems.22 Thus, values of Y*HCI were calculated for concentrations greater than 1 molal by means of eq. 8 using the slope (0.0244) determined experimentally a t I = 0.1-1.0. These values were converted to mean molar activity coefficients.2Y It was then assumed that, a t constant total electrolyte concentration, the molar activity coefficient of HC1 in HC1O4NaC104 mixtures ( Y + H c I ( ~ ~was ) ) , given by the relationship Y3zHCllns)
where
=
Yd=HCl(n)
-
X(Y3zHCl(n)
-
Y&HCI(s))
x is the mole fraction of NaC104 and
(16) P. G. Murdock a n d R . C . Barton,
2569
Y*HcI(~)are the mean molar activity coefficients of HC1 in perchloric acid and sodium perchlorate, respectively, An analogous procedure was used to obtain approximate water activities of HClO4 -"aC104 mixtures using water activities of sodium chloride solutions in place of those for sodium perchlorate solutions. Values of K 1 were now calculated for each set of solutions a t constant total electrolyte concentrations using as KIS1the experimentally determined formation constants for those solutions in which only perchloric acid was the swamping electrolyte. The results are shown in Table I . The agreement with the observed data is poorer than it was in the previous case but is still good in view of the very approximate nature of the calculations. The activity coefficients required for eq. 5 are those based on standard states in which Y j = 1 a t infinite dilution of species j in each of the particular electrolyte solutions u s e d , t o obtain the K1 values. However, the activity coefficients actually used in the above calculations were based on a standard state in which Y + H c ~ = 1 a t infinite dilution in water. This was done because data based on the correct standard states were not available. Some idea of the magnitude of the error incurred by the incorrect choice of standard states may be obtained from the following treatment. The activity coefficients of HC1 in perchloric acid solutions and in sodium perchlorate solutions were determined from measurements16,21of the e.ni.f. of cells of the type Hz/HC1(MI) salt (Jln)/AgC1 Ag. For such cells
+
+
E,
=
E,' - 2 k log Mi Y , y s
(11)
where E," is the standard electrode potential, YWs is the mean molar activity coefficient of HC1 in a particular electrolyte solution, S , referred to a standard state in which a = m in dilute solutions of HC1 in water and k = 2.303 R T l F . The activity coefficients actually required are given by the equation E,
=
E,'
- 2k
log ilf, Y,S
(12)
where E," and Uss are the standard electrGde potential and activity coefficient, respectively, referred to a standard state in which a = m in dilute solutions of the particular electrolyte medium S. Combining 11 and 12 we obtain E,,.n = E
- 2k log ( YS*/Y,,')
(13)
For any two electrolyte solutions SIand SZ
Rewriting eq. 7 in the same notation as above gives
(10)
Y&HCl(a),
In calculating KIS2we used the activity coefficients in the form YWsso t h a t
J. A m . Chem. S o c , 66, 4074
(1933). (17) R . A. Robinson a n d R . H. Stokes, "Electrolyte Solutions," Academic Press, I n c , New York, N . Y., 1959, p. 483. (18) R . A. Robinson a n d 0. J . Baker, Trans. Proc. Roy. SOL.A'ew Z e d a n d , 76, 2JO (1046). (19) Reference 17, p p , 30-33. (20) "International Critical Tables," Vol. 111, McGraw-Hill Book Co., Inc., New York, N . Y., 1926, p. .54, (21) S. J. Bates and J. W. Urston, J . A m . Chem. Soc., 66, 4068 (1933). (22) J E. Hawkins, ibid., 64, 4480 (1032). (23) Densities of sodium perchloratc solutions determined a t 1 8 O (ref. 20, p . 84) were used for t h i s calculation.
where KIS?'is the calculated formation constant and KIs1 the formation constant obtained from extinction data in the electrolyte solution sl. Dividing eq. 1.5 by 16 and substituting back into eq. 14 gives E.,'
K 62 - E s I o= 2k log --!K,W
(17)
2570
ROBERTN. HEISTAND AND ABRAHAM CLEARFIELD
Thus, the error incurred by using activity coefficients of the type Y,' in place of YSsis a function of the difference in the standard potentials of the two electrolyte solutions. The difference will be small for solutions which do not differ greatly in electrolyte concentration and composition. This trend is generally observed by the data in Table I. The agreement between calculated and observed K ' s becomes poorer as one proceeds down the columns of the table, i.e., as the difference in composition of the two solutions S1 and Sz increases. J0 40
30
20
10
'
G
8 6
4
2
0
1
4
2
5
6
Molarity
Fig 5 -Plot of log K I Z'S molarity of perchloric acid Dashed lines represent extrapolated values Extrapolation of Rabinowitch and Stockmayer's data based on their eq 136: 0, Clearfield and Heistand; A, Rabinowitch and Stockmayer; 0 , Olerup, C , Coll, Xauman, and West
Data for the activity coefficients of HCI in the presence of lithium perchlorate are not available. However, since the activity coefficients of lithium perchlorate and perchloric acid do not differ greatly, lithium perchlorate would be expected to have much the same
VOl. 85
effect on Y+HCI as does perchloric acid. The much smaller changes in absorbance which result when LiC104 rather than NaC1O4 is used to replace part of the HClOl as swamping electrolyte can be rationalized on this basis. The formation constants determined in this work for solutions in which only perchloric acid was the swamping electrolyte are compared to those of other workers in Fig. 5 . Our values are in good agreement with those of Rabinowitch and Stockmayer6 and Olerup,' but are somewhat higher than those of Coll, Nauman, and U'est. l 1 These latter workers measured the absorbance a t A,,, for solutions in which [Fe (111) ] / [Cl-] E 100. They assumed t h a t FeC12+ would be the only chloro complex present under these conditions and that the limiting absorbance would be obtained a t high (9 M ) perchloric acid concentrations. These assumptions permitted them to calculate the concentration of FeC12+ in solutions of lower acid concentrations from the measured absorbances. However, the value of E,,, which they obtained in 9 34 HC1O4, 2010, is much higher than our value of El, 1980, determined in 5 214 HC104. Furthermore, they observed a shift in Amax from 336 t o 352 mp with increase in the acidity of the solutions from 2.5 to 9 M. We observed a similar shift in A,,,, but this was brought about by increasing the amounts of higher chloro complexes in solution, i . e . , by conditions which produced increased divergence of the absorption curves from the isosbestic point at X = 282 mp. Thus, either higher chloro complexes are present in the solutions 9 in perchloric acid or the absorption curves are altered by medium effects. Either reason could account for the differences in K 1 as determined in this work and by Coll, Nauman, and West. In conclusion, our results show that the ionic strength principle is not valid for dilute solutions of F e e l 2 + in the presence of large concentrations of noncomplexing electrolytes. Instead the effect of the specific electrolyte medium upon the activity coefficients of the species involved in the equilibrium must be considered. Similar conclusions were reached by Zielen and Sullivan** from their study of the electrochemical potentials of several oxidation-reduction systems. Acknowledgment.-R. N. H . wishes to express his thanks to the Union Carbide Metals Co. and the Xational Lead Co., T A M Division, for the use of their laboratories and equipment. (24) A . J. Zielen and J. C . Sullivan, J . P h y s . C h e m . , 66, 1065 (1962):
