Feb. 5, 1957
537
HYDROLYSIS OF IRON(III)ION [CONTRIBUTION FROM
THE
DEPARTMENT O F CHEMISTRY, DUKEUNIVERSITY]
A Spectrophotometric Study of the Hydrolysis of Iron(II1) Ion. 111. Heats and Entropies of Hydrolysis BY RONALD M. MILBURN RECEIVED AUGUST27, 1956 The hydrolysis of iron(II1) ion has been studied over a range of ionic strengths up to 1.00 a t the temperatures 18, 25 and 32'. Free energy, heat and entropy changes are calculated for the reactions Fe3+ HzO FeOH2+ H + and 2FeOH2+ Fe(OH)2Fe4+. Over the range investigated, increases in temperature or decreases in ionic strength shift the first hydrolysis equilibrium to the right, and the dimerization equilibrium to the left. A negative value of AS" found for the dimerizatiou reaction is discussed in qualitative terms. For comparative purposes thermodynamic quantities are calculated for the derived reactions 2Fe8+ 2H20 Ft Fe(OH)2Fe4+ 2 H + and Fe8+ OH- Ft FeOH2'.
+
+
+
+
+
I n part 111 the hydrolysis of iron(II1) ion was studied a t 25' and the experimental results were interpreted in terms of the reactions Fe3+ H20 I_ FeOH2+ H + (1)
+
+
and 2FeOH2+
Fe(OH)2Fe4+
(2)
Equilibrium quotients for these reactions were reported as a function of ionic strength. An extension of this work to cover a temperature range has now made possible the calculation of heat and entropy changes for reactions 1 and 2, and for derived reactions 3 and 4. 2Fe3+
+ 2H20 Fe(OH)2Fe4+ + 2 H + Fe3+ + OHFeOH*+
(3) (4)
Experimental Procedure.-The preparation of materials and standard solutions, and the spectrophotometric technique have been previously described.' The thermostat on the spectrophotometer was adjusted to allow soloutions to be held a t either Astock0.0997Miron18 I 0.1, 25 f 0.1,or32 f 0.1 (111) perchlorate solution, 0.1263 M in perchloric acid, was used for the preparation of all other iron(II1) solutions. Ionic strengths were adjusted by the addition of the required amount of sodium perchlorate. Temperature Dependence of the First Hydrolysis.-Four M iron(II1) perchlorate solutions were pre9.97 x M in perchloric acid, and one a t pared, each 1.113 X each of theionic strengths 1.17 X lo-*, 2.17 X 10-2,3.17 X 10-2 and 1.00. The absorbance of each solution a t 340 m p was measured at 18, 25 and 32'. Values for k l , the equilibrium quotient for reaction 1, were calculated from equation 2 of part 11,' with el = 925. As before, preliminary values for k l were first estimated making the approximations [H+] = ho and dh = d . This procedure permitted calculation of the fractions of iron( 111) hydrolyzed, a, and hence the corrected acidities, [ H + ] , and the corrected absorbances, &. Final values for k l a t the various temperatures and ionic strengths are presented in Table I.
.
EQUILIBRIUM QUOTIENTS FOR REACTION 1 AT 18,25 AND 32"
x
102
k , X 103, 18" kl X 103,250 kl X 10',32'
1.17 2.83 4.25 6.43
2.17 2.51 3.80 5.65
-
TABLE I1 EQUILIBRIUM QUOTIENTS FOR REACTION 2 AT 18,25 A N D 32" X 10 18" k d , 25" kd,32' M
kd,
1.03 270 220 170
2.03 420 320 240
3.17 2.35 3.53 5.25
100 1.10 1.64 2.47
At each temperature the results for the three lowest ionic strengths were used to extrapolate k1 to zero ionic strength, using the equation log ki log k10 - 4Ap1/z/(1 2.4p1/2) (5)
+
with A eaual to 0.503, 0.509 and 0.516 for the respective (1) R. M. Milburn and W. C. Vosburgh, THISJ O U R N A L , 77, 1352 (1955).
3.03 500 390 300
10.0 980 730 510
Following the procedure of part 11,'log k d o values for each temperature were obtained by plotting log k d - ( 8 A p ' / z ) / (1 2.1y1h) against p, and extrapolating to p = 0.2 The dimerization quotients obtained, with estimated uncertainties, were T = 18", kdO = 47 16; T = 25', kdo = 36 12; T = 32', k d o = 26 Z!C 9. The value for 25" agrees satiifactorily with our previous result.' Most of the estimated
+
TABLE I fl
temperatures 18, 25 and 32°.293 The results of the extrapolation were: T = IS0, klo = 4.2 X T = 25', k10 = 6.4 X 10-3; T = 32', klo = 9.5 X Thevaluefor25' is in satisfactory agreement with our previous w 0 r k . l ~ ~I n a plot of log k10 against 1/ToA the points fall on a straight line within the experimental limits of error, showing that AH' is sensibly constant over the temperature range investigated. The least squares slope gives AH' = 10.4 kcal. An uncertainty of f 0 . 2 kcal. is estimated. Equation 6 AS = ( A H AF)/T'A (6) with AHo = 10.4 f 0.2 kcal. and AF' = 2.96 f.0.04 kcal.,6 gives AS" = 25.0 I 0.7 e a . When the log kl values corresponding to unit ionic strength are plotted against l/T'A, a straight line is again obtained within the limits of experimental error, and the least squares slope gives AH = 10.2 kcal.6 The estimated uncertainty is I 0.3 kcal. From equation 6, with AH = 10.2 f 0.3 kcal. and A F = 3.80 3t 0.04 kcal., AS = 21.6 f 1.0 e.u. Temperature Dependence of the Dimerization.-Four 9.97 X 10-3 Miron(II1) perchlorate solutions were prepared, M i n perchloric acid, and one a t each of the each 4.12 X ionic strengths 0.103, 0.203, 0.303 and 1.00. The absorbance of each solution a t 340 mp was measured a t IS,25 and 32'. Before calculating values for k d , the equilibrium quotient for reaction 2, i t was necessary to have knowledge of kl a t each temperature and ionic strength. For p = 1.00, the kl values quoted above were used. For each of the three other ionic strengths, k1 was calculated from equation 5, with the appropriate values for k? and A , also given above. For each solution, the corrected acidity, [ H + ] , and the corrected absorbance, d h , were estimated by taking the first hydrolysis into account in accordance with the method of part 11.' Values of k d were then calculated from equation 10 of part 11, with el = 925 and ed = 3.0 X lo3. The results are shown in Table 11.
*
+
(2) The values of A were interpolated from the values of G. G. Manov. R. G. Bates, W. J. Hamer and S. F. Acree, i b i d . , 65, 176:
(1943). (3) The empirical constant 2.4 previously has been used for the representation of kl values a t 25O.l
(4) T. H. Siddall and W. C. Vosburgh, THISJ O U R N A L , 73, 4270 (1951). ( 5 ) All free energy values used in this paper for calculation of e n tropy changes have been taken from equilibrium quotients reported in part 11.1 (6) Throughout this paper, t h e superscript zeros are limited to symbols for true thermodynamic properties a t y = 0.
RONALD M. MILBURN
538
Vol. 79
TABLE I11 EQUILIBRIUM QUOTIENTSAND FREEENERGY,HEATAND ENTROPY CHANGES FOR HYDROLYSIS REACTIONS OF IROX(III) ION AT 2Soa Reaction
P
+ HzO F? FeOH*+ + H +
fi
AF
AH
AS
0 6.7(f0.4) X l O F 2.96f0.04 10.4f0.2 25.0f0.7 1 1.65(&0.10) X lo-$ 3 . 8 0 5 0.04 1 0 . 2 f 0 . 3 21 i 1 2FeOH2+ e Fe(OH)*Fe4+ (2) 0 30(i10) -2.0 f 0.2 -7.3 f 1.0 - 1 8 i 4 1 700(f200) - 3 . 9 i.0 . 2 - 8 . 2 f 1.0 -14 i 4 2E'e3+ 2H20 Fe(OH)*Fe'+ 2H + (3) 0 1.4(=t0.4) X lo-' 3.9 i0.2 13.5 f 1 . 0 32 f 4 1 1.9(&0.6) X 3.7 i0.2 12.2 1.2 28 i 5 a Equilibrium quotients and thermodynamic quantities for reaction 3 were calculated from the corresponding values for reactions 1 and 2. The equilibrium quotients for reactions 1 and 2 are those given in part 11.' A F values, in kcal. mole-', were calculated from the corresponding equilibrium quotients; AH values, also in kcal. mole-', were calculated from the temperature dependent measurements of the present study; and AS values, in entropy units, were obtained from the corresponding values of A F and AH, using equation 6 . Fe3'
+
(1)
+
*
uncertainty in the absolute magnitude of each kdo value arises from a corresponding uncertainty in ed a t 340 mp. The assumption of various values of ed within the limits of error given in part 11' has little effect on the trend of k d o with temperature. This fact lends confidence to a calculation of A H o . A plot of log k d @ against l / P A gives a straight line within the experimental limits of error. From the least squares slope, A H o = -7.3 kcal. An uncertainty of 1 1 . 0 kcal. is estimated. From equation 6, with AH0 = -7.3 i 1.0 kcnl. and A F o = - 1.99 5 0.20 kcal., ASo = - 18 f 4 c.u. .At p = 1.00, log k d against 1 / P A gives a straight line within experimental limits of error, and the least-squares slope gives AH = -8.2 kcal. An uncertainty of f 1 . 0 kcal. is estimated. From A F = -3.89 i0.20 kcal., A S = -14 =t 4 c.u. In Table I11 is given a summary of the thermodynamic data obtained. Figure 1 illustrates the plots of log k against 1j T n A used for the determination of the heats of reaction.
Discussion The first stage in the hydrolysis of iron(II1) ion iiiay be represented by either equation 1 or 4. I n part 11' a comparison was given of our equilibrium quotients for reaction 1 a t 23' with other values reported for this t e m p e r a t ~ r e . ~ Heat and entropy changes for reaction 1, reported by Rabinowitch and StockmayerIswere calculated both from their temperature dependent measurements and from the k l 0 values of Bray and H e r ~ h e y . ~Rabinomitch and Stockmayer utilized 0.1 :If iron(II1) perchlorate solutions, 0.50 144 in perchloric acid and with an ionic strength of 1.10. Their determination was based on the assumption that reaction 1 alone would be important. Neglect of dimerization may explain the discrepancy between their AHvalue (12.3 i 1.0 kcal., p = 1.10) and ours (10.2 i: 0.3 kcal., p = l.OO).'O Bray and Hershey deduced k10 a t 25' from the experimental work of Popoff, Fleharty and Hanson,"" and k1° a t (7) The value kl = 1 .O X 10-3 a t 2.5' a n d p = 0.5 reported by A . 8' Wilson and H. Taube, THISJ o U R N . ~ L , 7 4 , 3909 (1992), was omitted frvm part 11.1 ( 8 ) E. Rabinowitch and W. H. Stockmayer, i b i d . , 64,335 (1042). ( 9 ) W, C . Bray a n d A. V. Hershey, ibid., 56, 1889 (1934). ( I O ) A calculation shows the importance of dimerization in the solutions of Rabinowitch and Stockmayer. Using our values of ki and />
33" from the work of Fleharty.12 At each temperature sufficiently dilute iron(II1) solutions were used to avoid serious error from polynuclear species. .I recalculation of AHo, using the kI0 values and limits of error reported by Bray and Hershey, gives 12.6 f 3.0 kcal. The possible margin of error pIaces this value in satisfactory agreement with our work ( A H " = 10.4 i: 0.2 kcal.). Rabinowitch and Stockmayer,8 using their own A H value, calculated ASo for reaction 1 both from the k1° value a t 25' reported by Bray and H e r ~ h e y , ~ and from the kIn value a t 25" given by Lamb and Jacques.12 The first calculation gave ASo = 31 e.u.; the second gave A S o = 30 e.u. For reaction 1 we obtain ASn = 25 (i 0.7) e.u.; the differences between this result and those reported by Rabinowitch and Stockmayer can be largely attributed to the different values of AH used. Several papersi3 have made use of the kl values 1.18 X a t 13" and p = 0.5 obtained by Connick, et 1.9 X l o p 3 a t 25' and p = 0.5 obtained by Bray and H e r ~ h e y and , ~ 3.2 X loF3 a t 35" and p = 0.5 calculated by e ~ t r a p o l a t i o nof~ ~ ~ ~ ~ the 15 and 25" values. Postmus and King13dhave observed that the A H and A S values for 23' calculable from the above values of kl are 8.8 kcal. and 17 e.u., respectively. Published details concerning the measurements of Connick, et al., a t 13' do not permit an estimate of the uncertainties in the above values of A H and AS. From our thermodynamic data for reaction I , together with that accepted for the reaction H + f OH- $ H20 l 4 a recalculation for reaction 4 gave A F o = -16.i kcal., ANo = -3.0 kcal., and ASo = 44 e.u.15 The heat changes for reactions 2 and 4 have the same sign and favor the forward reactions. But the entropy changes have opposite signs; for reaction 2, AS0 = -18 (*4) e.u., while for reaction 4, ASo = 4-44 (f1) e.u. Entropy changes for reactions such as 4, involving the combination of oppositely charged ions in aqueous solution, are generally positive. The (12) A. B. L a m b a n d A. G. Jacques, i b i d . , 60, 1215 (1938). (13) (a) L . G. Hepler, J . W. K u r y a n d Z. Z. Hugus, Jr., J . Phrs. Chem., 58, 26 (1954); (b) R . E. Connick a n d M. Tsao, THISJOURNAL, 76, 5311 (1954); (c) R . E. Connick, L. G. Hepler, 2. 2. Hugus, Jr., J. W. Kury, W. M. Latimer a n d M.Tsao, ibid.,78,1827 (1956); (d) C. Postmus and E. L . King, J . Phys. Chem., 59, 1208 (1955). (14) Values of A F " , A H ' and AS' for this reaction were calculated from the d a t a of Table 11, p. 39, W. M. Latimer, "Oxidation Potentials,'' Prentice-Hall, Inc., New York, N. Y.,second edition, 1952. (15) These values for reaction 4 may be compared with those given b y Rabinowitch a n d Stockmayera: AF' = -1fi.O kcal., A f f o 1.2 kcal., and AS" 50 e.u.
-
-
Feb. 5, 1957
539
HYDROLYSIS O F IRON(II1) I O N
positive values are usually attributed t o the 1.4 water molecules having greater freedom in the -3.2 field of the complex ion or molecule than in the fields of the separate ions.16-19 The magnitudes of the entropy changes have been found t o de1.6 -3.0 pend both on the charges and sizes of the reactant ions and of the complexes, and on the number of water molecules replaced upon complex formation from the first coordinated spheres 1.8 -2.8 of the reactant ions.16-18 Calculated values of A S for complex formation, using the empirical relation proposed by Cobble," are in reasonable 2.0 -2.6 agreement with experiment for reactions of the type Fe3+ X- $ FeX2+. Application of this relation t o reaction 4 gives A S = +34 e.u.,20 2.2 compared with the experimental values of +44 4 M -2.4 0 e.u. obtained in the present paper, and +50 e.u. found by Rabinowitch and Stockmayer.8 The dimerization of iron(II1) may be repre2.4 -2.2 sented by either equations 2 or 3 . For 25' and an ionic strength of 3, HedstromZ1reports an equilibrium quotient for reaction 3 of 1.22 2.6 -2.0 (*0.10) X l o v 3 ; our work' corresponds to 2.6 ( A 0.9) X while Mulay and Selwood22report a value of 7.3 X 10-3.23 Because of approximations made, Mulay and Selwood consider 2.8 -1.8 their value t o be in satisfactory agreement with Hedstrom. Mulay and Selwood have made an approximate determination of the temperature 3.0 -1.6 dependence of the quotient, from which they 8 commte AH for reaction 3 to be ~ 9 . kcal.. witg p = 3. A t p = 1 we find A H = 12.2 3.25 3.30 3.35 3.40 3.45 ( h 1 . 2 ) ; a t p = 0 we find A H o = 13.5 (=kl.O). 1 0 3 / ~ 0A . The agreement between the three values is not unreasonable. Fig. 1.-Determination of AH for the first hydrolysis and dimDimerization reactions have been reportedz4 erization reactions from plots of log k against l / T " A : curve for a number of other ions of the type MOH+". Ia, log kI0; curve Ib, log kl for /J = 1.00; curve IIa, log kd'; Heats and entropies have been measured for the curve I I ~log , kd for = 1.00. dimerization of CeOH3+ ion bv Hardwick and Robert~on,~h and for the dirnerizition of the ScOH2+ their values may be a consequence of neglect of ion by Kilpatrick and Pokras.26 The latter work- equilibria involving higher polymers. Hardwick ers found that A H and A S varied greatly over the and Robertson2j explained their experimental work temperature range 10 to 40" ; this lack of constancy on the basis that the CeOH3+ ion dimerizes, and does not permit a comparison of their results for have assumed the reaction t o be scandium with ours for iron(II1). Kilpatrick and 2CeOHaf I- CeOCea+ H20 (7) Pokras have suggested that the trends found in ( 1 6 ) W. M. Latimer and W. L. Jolly, THISJOURNAL,76, 1548, The possibility that dimerization proceeds accord4147 (1953). ing to reaction 8 was not considered.
+
5-
_I_ +
( 1 7 ) J. W. Cobble, J . Chem. Phys., $1, 1446 (1953). (18) R. J. P. Williams, J. Phys. Chem., 68, 121 (1954). (19) E. L. King, J . Chem. Educ., SO, 71 11953). ( 2 0 ) I t mas assumed t h a t the O H - ion takes t h e place of one water molecule in the first hydration sphere of t h e Feat ion; see Cobble.l7 T h e ionic radius of t h e O H - ion was taken as 1.53 8.(see A. F. Wells, "Structural Inorganic Chemistry," Clarendon Press, second edition, 19.50. p. 7 0 ) , and the ionic radius of t h e F e 3 + ion as 0.67 A. (see R. W. G. Wyckoff, "Crystal Structures," Vol. 1, Interscience Publishers, Inc., S e w York, N. Y . , 1951, Chap. 3, table p. 15). ( 2 1 ) B. 0. A . Hedstrom, Avkiv Kemi, 6, 1 (1953). (22) L. N. Mulay and P . W. Selwood, THISJouRNaL, 77, 2693 (1955). (23) I n table 9 of a stimulating review by L. Pokras, J . Chem. Educ., 33, 223 (1950), Hedstrom's value for this quotient should read 1.22 X 10-2 instead of 12.2 X 10-3, and Milburn a n d Vosburgh's value a t w = 3.00 should read 2.6 X 10-3 instead of 26 X 10-8. (24) Refer t o table 11, L. Pokms, J . Chem. Educ., 93, 223 (1956); see also reference 25 below. (25) T. J . Hardwick and E. Robertson, Ca%. J . Chem., SS, 818 (1951). ( 2 6 ) M. Kilpatrick and L. Pokras, J . Electrochem. SOL.,101. 39 (1954).
2CeOHaf
Ce(OH)&eaf
(8)
Whichever formulation describes the actual reaction, Hardwick and Robertson's measured values of A H and A S would be equally valid. For an ionic strength of 2 , they reported AH = -16 I 1 kcal., and A S = -45.3 e.u: Both the heat and entropy changes are negative, as they are for reaction 2 in the present work. It is generally assumed that a rapid and reversible dimerization of MOHf" ions will result in the formation of M(OH)2Mf2"ions. The general reaction may be represented by 2[M(OH)(HzO)vI.',"
)J [M(OH)zM(HzO)(z,-.,I:~
+ zH~O
where y and y - 2/2 indicate the number of water molecules in the first hydration sphere of a single
540
BERNARDD. BLAUSTEIN AND JOHN W. GRYDER
two monomeric ions of charge +n. As yet no satisfactory approach has been made toward the quantitative estimation of entropies for these dimerization reactions. Before this problem can be attacked profitably, entropies for other dimerization reactions should be obtained. Acknowledgment.-The author wishes to express appreciation to Professor W. C. Vosburgh for his valuable advice concerning the present work.
metal atom in the monomer and dimer, respectively. Although z will be positive, and may generally equal +2, the measured entropy changes for dimerization of both the FeOH2+and CeOH3f ions are negative. The loss in independent motion that the monomeric ions experience upon combination would contribute toward negative entropy changes. I t is also likely that a dinieric ion of charge +2n would exert a greater restrictive influence over surrounding water molecules than would
[CONTRIBUTION FRO%
THE
DEPARTMENT
OF
VOl. 79
DURHAM, NORTHCAROLINA
CHEMISTRY, THE
JOHNS I I O P K I N S
USIVERSITY]
An Investigation of the Species Existing in Nitric Acid Solutions Containing Cerium(II1) and Cerium(1V)' BY BERNARD D. BLAUSTEIN AND JOHK W. GRYDER RECEIVEDAUGUST 29, 1956 Extraction data and electromotive force measurements are interpreted as indicating the existence of ccrium(1V)-ceriuni(IV) and cerium(1Y)-cerium(II1) polymers in 5.5f nitric acid solutions. If the polymers are assumed to be dimers, the Ce3 = Ce4Ce3in this medium are 17 =I= 2 and 2.0 i 0.7 a t association constants for the reactions 2Ce4 = (Ce4)2,Ce4 30.0 =t0.03' where total concentration of monomer and of dimer are used in the equilibrium expressions. Contradictory reDorts in the literature are reconciled bv the existence of these dimeric species. The cerium(1V) species extracted by ether is'shown to contain no ionizable hydrogen.
+.
Introduction The fact that ceric cerium forms complex ions with various anions has been known for some time.2 The formal electrode potentials vary from - 1.2 to - 1.7 depending upon whether the solution contains hydrochloric, sulfuric, nitric or perchloric acids. Cerium(1V) migrates to the anode in 1 f 3 b sulfuric acid and in 6 f nitric acid; but it travels to the cathode in 1.Sf sulfuric acid and does not migrate in 2 f nitric acid. The formation constants for the various sulfate complexes of cerium(IV) have been measured.4 More recently the ability of cerium(II1) to form complex ions has been ver5ed.j Several independent methods have been employed6 to show the existence of cerium(1V) polymers in perchloric acid solutions even a t high acidities. In spite of the existence of cerium(1V) complexes with nitrate, Noyes and Garner7 present evidence that the cerium(1V)-cerium(II1) electrode potential in nitric acid is essentially independent of nitric acid concentration. Yost, et U L . , ~ postulate mixed hydroxide-nitrate complexes 3al
(1) This work was presented a t t h e 130th meeting of the American Chemical Society a t Atlantic City and is abstracted from a thesis suhmitted by B . D. Blaustein t o t h e Faculty of Philosophy of T h e Johns Hopkins Cniversitp in conformity with t h e requirements for the degree of Doctor of Philosophy (2) See, for example D. BI. Yost, €1. Russell and C. S . Garner, "The Rare Earth Elements and 'Their Compounds." John Wdeg and Sons, Inc., New York, N. Y . , 1947, p . 61. (3) (a) Concentration will be expressed in formality, f, formula rreights per liter of solution. (b) V. J. Linnenbom and A. C. Wahl, THISJOURNAL, 71, 2589 (1949). (4) T. J. Hardwick and E. Robertson, C a n . J . Chem.. 29, 828 (1951). ( 5 ) (a) R E. Coniiicli and S \$'. hIayer, Tius J O G R N A L , 73, 1170 (1951); (b) 1'.1%'. N e w t u n and G. R I . Arcand, ibid., 7 5 , 2449 (1953). (6) ( a ) L. J . Heidt and b1. E. Smith, ibid., 70, 2470: (1948); (b) E. I,. King and RI L . Pandow, i b i d . , 74, 19BG (1952); (c) T. J. Hardwick a n d E. Koliertson, C a n . J . C h e m . , 29, 818 (1951); (d) K. A. Kraus. I
