COMPLEXINC OF IRON(III)BY FLUORIDE IONS
May 5, 1956 [CONTRIBUTION FROM
THE
1827
UNIVERSITY OF CALIFORNIA RADIATION LABORATORY AND THE DEPARTMENT OF CHEMISTRYAND CHEMICAL ENGINEERING,UNIVERSITY OF CALIFORNIA. B E ~ L E Y ]
The Complexing of Iron(1II) by Fluoride Ions in Aqueous Solution: Free Energies, Heats and Entropies BY R. E. CONNICK, L. G. HEPLER,2 2. HUGUS,JR., J. W. KURY,W. M. LATIMER AND MAAK-SANG TSAO RECEIVED OCTOBER 20, 1955 The potential of the ferrous-ferric half-cell has been studied as a function of hydrofluoric acid concentration a t 15. 25 and 35”. Equilibrium quotients and free energy, heat and entropy changes a t an ionic strength of 0.50 are calculated for H F = FeF+’ H+, FeF+P H F = FeF2+ H + a n d FeFz+ H F = FeF3 H+. the reactions: F e f 3
+
+
+
I n order to investigate the fluoride complexing of sundry cations1-3 as a function of temperature using the “ferri’’4Jmethod, i t was necessary to extend the work of Dodgen and Rollefson6 with iron to 15 and 35’. The experimental technique used in the present investigation of the fluoride complex ions of iron(111) is essentially the same as theirs.s Several experiments were also carried out a t 25’, the results of which deviated slightly from those of the above investigators. Experimental The cell, solutions and potentiometer circuit used in these experiments have been described previous1y.ls6 Experiments were carried out a t 15,25 and 35”. Before each run the assembled cell and the stock solutions were brought to the temperature of the experiment. Onehundred-milliliter aliquots of stock solution containing the desired concentrations of Fe( ClOa)z, Fe( C104)3,HCIOl and Naclo4 were pipetted into each half-cell. The stirrers were activated and after observing the small initial potential (usually less than 0.2 mv.) standard sodium fluoride solution was added to one half-cell. The potential of the cell was read after each addition. The stirrers were left on both while adding sodium fluoride and reading the potential. The potential became constant to within 0.02 tnv. approximately one minute after each addition. The variation of potential with total fluoride concentration a t 15, 25 and 35“ as well as the initial concentrations of HC1O4, Fe( C10& and Fe( C1O4), are given in Table I for a typical run a t each temperature. In all runs the initial compositions of the two half-cells were the same. Sodium perchlorate was used to bring the initial ionic strength to 0.50. The half-cell to which fluorid:, was added is desigThe measured ponated as “B” and the other as “C. tential after each addition of sodi:m fluoride minus the initial potential is designated as “E. The total fluoride concentration in half-cell B is (ZF-). The equal initial volumes in the half-cells is Vi; V is the volume in half-cell B after adding sodium fluoride. The total initial concentrations are designated with the symbol “2” and the subscript “i.” Several experiments were run a t each temperature with varying hydrogen ion concentrations and with smaller ferrous and ferric concentration changes. The initial conditions and the range of fluoride concentration are given in Table 11. In each experiment anywhere from seven to eighteen e.m.f. determinations were made a t different fluoride concentrations. The complete data may be found in references 6 and 12.
Analvsis of Results The experimental results may be interpreted by considering the following equilibria (1) L. G.Hepler. J. W. Kurp and Z. 2. Hugus, Jr., J . P h y s . Chcm.. 68, 26 (1954). (2) R . E. Connick and M. Tsao, TEISJOURNAL,7 6 , 5311 (1954). (3) Complexing of Sc+* by fluoride ion, to be published. (4) C. Brosset and G. Orring, Sncnsk. Kcm. T i d . , 66, 101 (1943). (5) H . W. Dodgen and G. K. Rollefson, Tars JOURNAL, 71, 2600 (1949). ( 6 ) J. W. Kury, University of California Radiation Laboratory Repdrt, UCRL-2271, July,
1953.
+
+
+
+ + + + + + H F = H + + FFe+3 + HzO = FeOH+P + H + Fe+3 H F = FeF+2 H + FeF+2 H F = FeF2+ H+ FeF2+ H F = FeFa H+
Qi
Qz Q3
QHF
QH
(1) (2) (3) (4) (5)
The Q’s are equilibrium quotients, for example Q1
(FeF+z)(H+) ______ (Fe +3)(HF)
where ( ) signifies concentration in moles/l. TABLE I DATAFOR TYPICAL RUNSAT DIFFERENTTEMPERATURES (G = 0.50) (zF-)x 104. E, V, moles/l.
14.97 f 0.03’ (ZHi+) = 0.01838 M (ZFei+’) = 2.315 X IO-‘ M (ZFei+9 = 5.866 X lO-‘M Vi = 110.0 ml.
25.00 f 0.01” (ZHi+) = 0.04946 M (ZFeif2) = 6.338 X lO-‘M (2Fei+9 = 4.277 X lO-‘M Vi = 104.9 ml.
35.00 f 0.02’ (ZHi+) = 0.05645 M (ZFei+*) = 6.338 X IO-‘M (ZFei+*) = 4.277 X lO-‘M vi = 104.9
9.08 18.10 27.13 36.12 45.08 54.00 62.86 71.73 80.52 89.38 98.09 106.79
mv.
39.88 71.56 92.82 109.75 124.30 136.99 148.78 159.50 169.60 179.40
ml
.
197.90
110.2 110.4 110.6 110.8 111.0 111.2 111.4 111.6 111.8 112.0 112.2 112.4
3.78 7.55 11.31 15.07 18.83 28.77 38.68 48.55 68.18 87.66 107.0 126.2
13.83 26.32 36.65 45.17 52.57 68.22 80.24 90.28 107.32 121.46 133.84 144.98
105.0 105.1 105.1 105.2 105.3 105.5 105.7 105.9 106.3 106.7 107.1 107.5
4.57 13.21 20.06 27.03 34.18 43.16 56.93 79.95 104.3 119.8 133.4
14.69 38.76 51.91 62.54 71.30 81.12 93.39 110.34 125.56 134.17 141.51
105.0 105.1 105.2 105.3 105.5 105.6 105.8 106.2 106.6 106.9 107.1
188.88
CONNTCK, HRPLER, HUGUS,KURY,LATIMER AND TSAO
1828
TABLE I1 CONDITIONS FOR INDIVIDUAL EXPERIMENTS ( p = 0.50) 14.97' M , ( Z F e , + + ) = 2.315 X 10-4iM (ZFei+3) = 5.866 X Run
(ZHi'), M
Highest (ZF-). M
1
0.0944 ,0437 ,01838 ,00994
0.028 ,022 ,011 ,009
2 n
6
4
Highest
(ZFei ++)
x io+',
(ZFei+a) 10+4, M
x
Run
(ZHi'), M
(ZF-),M
1 2 3 4
0.04946 .09443 ,09246 ,09490
25.00' 0.0126 .0075 .0072 .0073
6,338 6.338 6.050 9.09
4.277 4.277 4.083 6.133
1 2 3 4 5 6
0.0975 .0957 ,0975 ,05975 ,1060 ,05645
35.00' 0.0090 .0082 ,0045 ,0062 .0077 .0133
6.717 2.635 6.717 6.717 6.050 6.338
4.367 1.748 4.367 4.367 4.083 4.277
M
Both Brosset and Gustaver' and Babko and JXleine? were able to interpret their experimental data on the complexing of iron(II1) with fluoride by assuming the presence of such species as FeF+2, FeFzf, FeF3, FeF4- and FeFG-. Dodgen and Rollefson6 discuss the nature of the complex fluoride ions present in solutions similar to ours. Based upon their conclusions we have assumed the presence of FeF+2, FeF2+ and FeF3 and are able to account for our experimental results. The equations necessary for the numerical evaluation of Ql, Qz and Qa will now be developed. From stoichiometric considerations we obtain
Vol. 78
I
Combining (lo), (11) and (12), we obtain ( Z F e +9 ~
( F e +3)
1'
eSE/RT
+ (H+)c[
(13)
Combining equilibrium expressions (1)-(4) with equation 7 one obtains
With the justifiable approximation that
Also, by using equilibrium expressions (1)-(5) and equations 6 and 7 we obtain
Neglecting H + from ferric hydrolysis
From equations 13 and 15
We are able to solve equations 16 and 17 for Ql, Q2 and Q3 by successive approximations. Neglecting terms containing Q1, Q 2 and Q3, we obtain a first approximation for the ratio (HF)/ (ZF-) = ( H F ) (F-) (FeF+z) 2 ( F e F z t ) f 3(FeF3) (H+) from equation 17. These values are then (6) used with estimated Q's to obtain a better set of (ZFef3) = ( F e + 9 (FeOH+z) (FeF+2) (HF)/(H+) values from equation 17. (FeFs+) (FeF3) (7) As seen from equation 16, we are able to obtain ( Z F e + 9 , = ( F e + 3 ) -I~ (FeOH+l)c (8) values for Q1, Q2 and Q 3 by plottingg the quantity The reference half-cell C has been designated by the subscript "C," while for simplicity B has been left undesignated. The potential of the concentration us. (HF)/(H+) a t low (HF)/ (ii-*)diid the quantity cell B-C is given by
+
+
+
+
+
RT E=--1n 5
+ +
( F e 9 F e c2)c (Fet2)(Fet3)c
(9)
us. (HF)/(H+) a t high (HF)/(H+). This procedure was repeated until consistent values for Q1, Qz
One obtains from equation 9
Combining equilibrium expression ( 5 ) and equation 8, one obtains (Fe+3)c =
( ZFeC3)c
1
+ QH/(H+)c
also (ZFef3)
=
Vi (ZFet3)c V
(12)
(7) C. Brosset and B. Gustaver, Svensk. K e m . T i d s k r . , 64, 185 (1942). (8) A. Bahko and K. Kleiner, J . Gcn. Chem. (U.S.S.S.R.), 17, 1259
(1947).
and Q3 were obtained. In the above treatment i t has been assumed that the pertinent activity coefficient ratios remained constant a t the nearly constant ionic strength of the experiments. Following Dodgen and Rollefson's5 reasoning, complexing of ferrous ion was taken to be negligible. The hydrolysis of ferrous ionlo and the formation of HFz-" are too small to be detected. Any complexing by perchlorate ion would be absorbed in the equilibrium quotients. The values of QHF and QH used in the calculations (9) I. Leden, 2. p h y s i k . Chcm., 188, 160 (1941). (10) D. L. Leussing and I. M. Kolthoff, THISJ O U R N A L , 7 6 , 2470
(1952).
COMPLEXING OF IRON(III)BY FLUORIDE IONS
May 5 , 1956
1829
TABLE IV are given in Table 111. The values for QHF at 15 and 35' were calculated from the 25' value using EQUILIBRIUM QUOTIENTS FOR FLUORIDE COMPLEXINC ou the temperature dependence for this equilibrium a t FERRICION( p = 0.50) zero ionic strength measured by Broene and DeRun QI Qz Vries." The value a t 25' was determined experi15" mentally12 for an ionic strength of 0.50 (NaC104, 0.84 10.7 1 191.5 HC104) by measuring the hydrogen ion concentra0.95 12.0 2 194 tion spectrophotometrically, using the indicator 1.09 11.8 3 192 Tropeolin 00, in solutions containing sodium fluo0.95 4 192 11.5 ride and hydrofluoric acid. The value is estimated Mean value 192 -f 1 11.5 =t 0.4 1 . 0 z!= 0.1 to be accurate to a t least 6%. QJ
TABLE I11 FOR FERRICIONAND IONIZATION HYDROLYSIS QUOTIENTS FOR H F ( H = 0.50) QUOTIENTS 15'
QE QEF
1.18 x 10-3 1.42 x 10-3
25'
1 . 9 x 10-3 1 . 2 3 x IO-'
350
3 . 2 x 10-3 1.01 x 10-3
The value of QH a t 25' and an ionic strength of 0.5 is that used in references 1, 2 and 5 ; i t is in excellent agreement with the recent results of Milburn and V 0 ~ b u r g h . l ~The value at 15' was obtained12 spectrophotometrically using molar extinction coefficients for Fe+3and FeOH++ taken from the work of Olson and Simonson.I4 It could be in error by 15%. The 35' value was extrapolated from the 15 and 25' values. The final values of QI, Q2 and Q3 are presented in Table IV and in Table V are given A F l AH and A S for reactions (1) and ( 2 ) and AF for reaction ( 3 ) a t 25' and an ionic strength of 0.50. Because of the relatively large uncertainty in Q3, values of AH and A S for reaction (3) have not been tabulated. It is to be noted that the value of Q3 a t 15' is more reliable than the others because the fraction of iron converted to the third complex was greatest in these experiments. The values for QI, QZ and Qa a t 25' of 184, 10.3 and 1.0, respectively, compare well with those reported by Dodgen and Rollefson,b ;.e., 189, 10.4 and 0.58, except for Q3, which is highly uncertain in both cases. Using the entropy of ionization of H F at 25015 and estimating the value at a n ionic strength of (11) H.Broene and T. DeVries, THISJOURNAL, 69, 1644 (1947). (12) M S. Tsao, Thesis, University of California, 1952. (13) R. M.Milburn and W. C. Vosburgh, THIS JOURNAL, 77, 1352 (1955). (14) A. R. Olson and T. R. Simonson, J. Chcm. Phyr., 17, 1322 (1949). (15) L. G.Hepler, University of California Radiation Laboratory Report, UCRL-2202 May, 1953.
1 2 3
25 O 11.1 10.1 183 10.2 184 10.0 184 f 1 10.3 =t 0 . 4 184 185
4 Mean value
1.0
1.0
350 1
178
2 3
175 179
4
179
5 6 Mean value
178 178 178 f 1
9.7 9.7 10.6 10.3 9.5 10.2 10.0 f 0 . 4
1.0 1.0
TABLE V THERMODYNAMIC QUANTITIES FOR FLUORIDE COMPLEXINC OF FERRICIONAT ~.r= 0.50
+ + +
+ + +
AFwa kcal./mble
Fe+8 H F = FeF+2 H + -3.09 FeF+2 H F = FeF2+ H + -1.38 FeF*+ H F = FeFs H+ -0.0
AHasa, kcal./mole
ASas, e.u.
-0.65 -1.2
8.2 0.6
0.50 to be -22.0 e.u., the values for the entropy of complexing of ferric ion by fluoride ions (at p = 0.50) are obtained FF-
+ Fe+3 = FeFfZ + FeF+Z= FeFz+
A S = 30 e.u. A S = 23 e.u.
These entropies compare closely with those for the corresponding reactions of aluminum ionlB which are 32 and 26 e.u., respectively. The corresponding value for the third complex of ferric ion was not fixed accurately by these experiments, but the data are not inconsistent with a value of 18 e.u. found for the aluminum ion.'G BERKELEY, CAL. (16) W. M. Latimer and W. L. Jolly, THISJ O U R N A L , 76, 1548 (1953).
