DISSOCIATION OF LANTHANIJM FERRICYANIDE I O N PAIRS
IN
WATER
375
The Effect of Pressure on the Dissociation of Lanthanum Ferricyanide Ion Pairs in Water
by S. D. Hamann, P. J. Pearce, and W. Strauss C.S.I.R.O. Chemical Research Laboratories, Division of Physical Chemistry, Fishermen’s Bend, MelbourTie, Austyalia, and Department of Chemical Enginwring, University of Melbourne, Melbourne, Australia (Receiued September 25, 1903)
This paper describes conductometric measurements of the influence of pressure on the molal dissociation constant K,, of lanthanum ferricyanide ion pairs in water a t 25’. The value of K , increases by a factor of 1.7 between 1 and 2000 atm., arid the initial trend e dissociation a t corresponds to a change in partial molar volume of -8.0 ~ m . ~ / i n o lfor 1 atm. The results agree quite well with the predictions of the ion-association theories of Bjerrum and of FUOSS, if it is assumed that the “contact distance,” a, is independent of pressure and that the change of K , arises only from the increases in dielectric constant and density which occur when water is compressed.
When two oppositely charged ions in solution separate from an associated state into a free ionic state, there is inevitably an increase in the total electrostatic interaction between the ions and their surrounding solvent molecules. It is this factor which is responsible for the large decrease of entropy which usually occurs when ion pairs dissociate.‘ It might be expected also that the increase in electrostriction would reduce the volume of the solution as a whole and, as a corollary, that an increase in hydrostatic pressure would shift the dissociation equilibrium toward the free-ion state. Fisher,2 working in these laboratories, has observed such a displacement in aqueous solutions of the 2 : 2 electrolyte RIgSO,, for which the dissociation constant is almost doubled by raising the pressure from 1 to 2000 atm. a t 25’. In the present paper we report some similar measurements on solutions of the 3 : 3 electrolyte LaFe(CN)e, which we expected to show rather larger prcssure effects than YIgSOc because of its higher valence.
Experimental Method. The measurements were made by a conductivity method similar t o that used by Fisher.2 To obtain the data needed to estimate the degree of dissociation of LaFe(CN)Bunder pressure it was necessary (i) to establish the way in which pressure alters the equivalent conductance Ao of LaFe(C3)s a t infinite
dilution, and (ii) t o measure the equivalent conductance of LaFe(CI\;)e a t particula: pressures and a t different finite concentrations of the salt. The first end was achieved indirectly by measuring the conductances of aqueous solutions of KC1,2 KBFe(Cs)6 and Lac&. For each salt the ratio Ap/Al of the equivalent conductance a t the pressure P atm. to that a t 1 atm. was determined a t several concentrations. The results were then extrapolated to zero concentration and the ratios Apo/Al0 thus obtained were multiplied by the known values of illo for these salts (149.85,3 172.6,4 and 146.0,j respectively) to obtain Ap0. Then, by Kohlrausch’s law
+
Apo[1/3LaFe(CN)6]= i l ~ ~ [ l / ~ L a C : l ~ ] APO [‘/&Fe(Cr\;)6]
- APO [KCl]
The values of [‘/3Lal’e(CX)~]a t finite concentrations were measured directly. The details of the experimental arrangement and procedure have already been described by Fisher. Materials. Water. Conductivity water was obG. H. Nancollas, Discicssions Faradnu Soc., 24, 108 (1957). F. H. Fisher, J . Phys. Chem.. 6 6 , 1607 (1962). R . A. Robinson and R. H . Stokes. “Electrolyte Solutions,” Butterworths, London, 1959, p . 466. J. C. James and C. B. Monk, Trans. Faraday Soc., 46, 1041 (1950).
Volume 68, Number 2
February, 1964
8. D. HAMANN, P.-J. PEARCE, AND
376
tained from a mixed-bed deionizing column and had a conductivity of less than 5 X lo-' mho. Potassium Ferricyanide. Analytical grade salt was recrystallized from water and dried under reduced pressure over phosphorus pentoxide. L a n t h a n u m Ferricyanide. Following the method of Rlarsh,j lanthanum oxide was dissolved in an equivalent amount of HC1 and the solution diluted to give an oxide concentration of 100 g./l. To this solution, a t 4 5 O , the stoichiometric qu,antity of cold saturated K3Fe(CK)6was added drop by drop, with vigorous stirring. The temperature was held between 40 and 50" and the stirring continued until sufficient redbrown precipitate had formed. The product was washed with water and dried between filter papers for several weeks. The lanthanum content vias determined by titration with EDTA using xylenol orange as an indicator, and the ferricyanide content was determined by reaction with potassium iodide and back-titration with standard potassium thiosulfate. The analyses showed that the salt had the composition LaFe(C?J)a. 5Hz0, in agreement with the conclusion of Davies and Jarnesl6and not LaFe(CK)6.4.5H20,as suggested by Prandtl and R l ~ h r . ~ L a n t h a n u m Chloride. A solution was prepared by treating an excess of lanthanum oxide with HCI. The solution was filtered, diluted to about 0.1 N , and standardized by titration with silver nitrate using fluorescein as an adsorption indicator.
1
I
I
io00
f.5110
w.STRAUSS
""i 096
.o
500
2000
Pre.swm (otm)
Figure 1. Limiting equivalent conductance ratios of several salts.
Results The results are listed in Tables 1-111 and shown, in part, in Fig. 1 and 2 . The values of AP have been corrected for the change of conductance of the solvent and for the change of cell constant with changing
Table I1 : Relative Equivalent Conductance Ap/Al of Lanthanum Chloride in Water a t 25" P! atm.
1 480 985 1495
~ Table I : Relative Equivalent Conductance A P / of Potassium Ferricyanide in Water at 25" P, atm.
1
480 985 1495 2000
0,0441
1.0000 1.0126 1,0139 1.0054 0.9903
Concentration at 1 abm., equiv./l.-0.0220 0.00.500 0.00100 0.00050
1.0000 1,0106 1.0108 1.0013 0.9845
1.0000 1,0121 1.0112 0.9966 0.9782
1.0000 1.0103 1.0072 0.9942 0.9748
2000
1.0000 1.0196 1.0241 1.0200 1,0071
1.0000 1.0202 1.0239 1.0185 1.0063
a t 1 a t m . , equiv./l.----0.00100 0.000602
1.0000 1.0167 1,0189 1.0120 0,9975
1.0000 10164 1.0187
1.0123 0.9989
0
1,000 1.015 1,016 1,007 0.994
0
1.0000 1.000 1,0115 1.0075 0.9952 0.9758
1.011 1.007 0.993 0.973
It should be noted that these corrections introduce some uncertainty into the results and thaL the absolute errors in the final data may be as great as &0.5%, although the reproducibility was better than that. The Journal of Physical Chemistry
,----------Concentration 0.0100 0.00602
Treatment of Results There are several ways of treating the experimental data to derive values of the molal ion-pair dissociation constant K,. Some of these procedures are based on (5) (6)
J. K. Marsh, J . Chem. Soc., 1084 (1947). C . W. Davies and J. C. James, Proc. R o y . S O C .(London), A195, 116 (1949).
(7) (8)
W. Prandtl and S. Mohr, 2. anorg. allgem. Chem., 236,247 (1938). S . D. Hamann and W. Strauss, Trans. Faraday Soc., 51, 1684 (1955).
DISSOCIATION OF LANTHANUM FERRICYAKIDE 10s PAIRS IN WATER
1.20,
molal activity coefficient of the free ions. This definition assumes that the activity coefficient of ion pairs is unity. (ii) We further assume that yk may be replaced by f*, the mean rational activity coefficient. The error introduced by this assumption is no greater than 0.03%. (iii) We assume that f+ is given by the DebyeHuckel formula
I
I
377
in which B = 5.029 X 109/(~T)'/' cm.-' mole-'/' 1.'Ia (deg.)'/'; z is ionic valence; is the dielectric constant; T Is the temperature in OK.; I = ionic strength ( = 3 a c ) ; c is concentration in equiv./l.; and q is the distance of closest approach of the free hydrated ions, in cm. (iv) Following Robinson and Stokes,In we have put q equal t o the Bjerrum critical separation
I IO00
I
500
0
I
I
IS00
2wO
where k is Boltzmann's constant and e is the electronic charge. For a 3:3 electrolyte q = 32.18 A. a t 25' and 1 atm. (v) We assume that
Pressure [utm]
Figure 2. Equivalent conductance ratios of several salts a t the concentration c = 0.01 N .
=
Table I11 : Equivalent Conductance AP of Lanthanum Ferricyanide in Water a t 25" P, atm.
1 480 985 1495 2000
---0.0102 58.3 62.8 66.0 68.1 69.1
where Atheor can be calculated from the relation
Concentration at 1 atm., equiv./!.--0.00510 0.00204 0.00102 0.000.510
67.2 71.9 75.2 77.3
78.3
&xpti/AthPor
83.2 88.2 91.6 93.5 94.3
97.5 102.7 105.9 107.3 107.6
112.1 117.1 119.8 120.7 120.3
0
168.7 170.5 169.7 167.1 163 7
used by Davies, Otter, and Prue."
R =
8.204 X lo-' 1z1z2/ ____
F - 41.25 - ~ ('zll - . eqnation for activity empirical relations (e.g., coefficients) which involve parameters that may vary in an unknown way with a change of pressure: clearly they are unsuitable for the present purpose. Other, more rigorous, methods involve rather long computations which are hardly justified by the limited accuracy of our measurements. Here we have compromised by adopting the following method. (i) For a pure aqueous solution of LaFe(CN)fi we define K mby
Km
--
l - a
where m denotes the molality of LaFe(CN)fi,a denotes the degree of dissociation, and y* denotes the mean
1 -
Here
+ 1z21)
_ _ _
V(€T)"2
and v = viscosity of the solution. In applying these formulas we have, in every lnstance, allowed for the influence of pressure on the values of E ~ and ~ t -I 6 and ~ its ~ effect on .io(Table 111) (9) C. W. Davies, J . Chem. Soc., 2093 (1038). (10) See ref. 3, p. 407. (11) W. G . Davies, R. J. Otter, and J. E. Prue. Discussions Faraday Soc., 24, 103 (1957). (12) We have assumed that, at 25', e is given by the formula ep = e 1 / [ 1 - 0.4080 log (1 P / 2 8 8 5 atm.)]. whirh is based 011 Owen and Brinkley'sIa analysis of the high pressure measurements of Kyropoulos.14 The rerent data of Owen, AMiller.Milner, and Cogan'Kare undoubtedly more a r c u a t e than those of Kyropoulos, but unfortunately i t is impossihle t o extrapolate them safely beyond the experimental pressure limit of 1000 atrn.
+
Volume 68, .I'umber 2
February, 1964
S.D. HAMANN, P. J. PEARCE, AND W. STRAUSS
378
and 1 2 . ~ ~ 3 The ~ ~ values of K , so obtained are listed in Table IV and plotted on a logarithmic scale against c1'2 and P in Fig. 3 and 4. It will be seen from Fig. 3 that K , is by no means independent of c, which suggests that one or more of the assumptions used in deriving K , is wrong. Severtheless, it is probably justifiable to suppose that the intercepts in Fig. 3 are close to the true values of K,. It is, in any case, clear from Fig. 4 that the pressure dependence of K , (in which we are primarily interested) is independent of the concentration. Table IV includes values of the change of standard partial molar volume A v o for the dissociation of ion pairs, derived from the relation AVO= -
dRT In K , bP
Discussion Figure 1 shows that, at infinite dilution, the conductivity ratios Ap0/Al0 of the four salts all lie within
I
I
0
/om
500
I
1
1500
2000
PWWM (oirn)
Figure 4. The molal dissociation constant of LaFe(CN)s as a function of pressure at various molalities, m.
Table IV : Values of Km and A Pofor the Dissociation of Lanthanum Ferricyanide in Water a t 25" p, atm.
Concentration a t 1 a t m . , equiv./l.------0.00510 0.00204 0.00102 0.000510
7 -
0,0102
1 480 985 1495 2000
2.889 3.432 3.989 4.570 5.088
2.382 2.804 3.258 3.725 4,155
2.048 2.398 2.784 3.177 3.549
1.909
2.239 2.591 2.936 3.270
1.788 2.086 2 402 2.721 3.007
0
1.574 1.824 2.109
2.377 2.630
AVO, cm.s/mofe 1 2000
-9.2 -4.8
-8.4 -Ft.O
-8.2 -5 1
-8.3 -4.8
-8.1 -4.5
-8.0 -4.6
B. B. Owen and S. R. Brinkley, Phys. Reo.. 64, 32 (1943). S. Kyropoulos, 2. Physik, 40, 507 (1926). B. B. Owen, It. C. Miller, C. E. Milner, and H. L. Cogan, J . Phys. Chem., 6 5 , 2065 (1961). (16) P. 1%'.Bridgman, Proc. Am. Acad. Arts Sei., 61, 57 (1926). (17) The ch%ngeof c is very nearly proportional to the change in density of water, which we have taken from the tables of Dor-
(13) (14) (16) I
I 0
005
PI0 &E Ceguw/L)
I
ovs
Figure 3. The molal dissociation constant of LaFe(CN)e as a function of concentration at various pressures
The Jozrrnal of Physical Chemistry
(18)
sey. E. N. Dorsey, "Properties of Ordinary Urater-Sub8tance," Reinhold Publ. Co., New York, N . Y., 1940, p. 207.
DISSOCIATION OF LAXTHANUM FERRKCYANIDE IONPAIRS IN WATER
379
-
1 or 2y0 of each otheF. The maxima in the curves are quite usual for salts in water and are probably associated with the minimum in the viscosity of water which BridgmanI6 observed a t about 1000 atm. There appears to be a small but real difference between the behavior of the chlorides and the ferricyanides, possibly caused by the bulkiness of the ferricyanide ions. In contrast to the curves in Fig. 1, those in Fig. 2 show that at a finite concentration LaFe(CN)s behaves quite differently from the other salts. Its conductivity rises much more steeply with increasing pressure; in fact, the salt behaves more like a weak acid or a weak base than a strong ele~trolyte.’~Irrespective of any detailed theory we can confidently ascribe the effect to an increase in the concentration of free ions with increasing pressure. From the quantitative treatment presented in the last section, it appears that the abnormal increase in conductivity of LaFe(CN)6 arises from a 1.7-fold increase in K , between 1 and 2000 atm., corresponding to a volume change A v o , for dissociation, of --8.0 ~ m . ~ / m o laet 1 atm. Surprisingly, this value is remarkably close to the value -7.3 cm.B/ mole for the dissociation of RilgS04.2 Originally, we had expected the’ dissociation of a 3 : 3 electrolyte to cause a much greater increase of electrostriction than that of a 2:2 electrolyte; the fact that it does not indicates that factors other than the purely electrostatic one operate. In this connection it is informative to consider the results in terms of the theories of ion association ad~~ model vanced by Bjcwum2@and F U O S S .Bjerrum’s supposes that oppositely charged ions can be considered to be associated when their centers come within a critical distance q of each other, q being defined by eq. 3. The dissociation constant on the volume concentration scale is then given by
-
to a good approximation by dividing K , by the density p of water a t the temperature and pressure of the system. For a given electrolyte in water a t a fixed pressure and temperature, the theoretical value of K , depends only on the distance of closest approach a, which is usually regarded as a parameter adjustable to fit the experimental value of K,. Applying eq. 5 and 6 t o our data and to those of Fisher12we find the following values of a in water a t 25’ and 1 atm. h’fgSO4
LaFe(CN )e
Bierrum
Fuoss
4 19 A. 7 04 A.
3 87 A. 7 36 h;.
If, now, we assume that a is independent of pressure, we can calculate the way in which K , should vary with pressure, simply by allowing for the corresponding changes in eZ2 and p.’8 In particular we can estimate theoretical values of A Bofrom the derivatives
_ _b _In_K-, _-_AVO bP
RT
b In -~ -
p
bP
+
b In Q(b) be b In E -3dc bP bP
(Bjerrum) bln p - __-
bP
db be +--bebP
(Fuosa)
The first term in these formulas is simply the compressibility of the solution and the remaining terms depend only upon E and bt/bP. Table V lists the calculated and experimental values of A B o a t 1 atm. and Fig. 5 compares the calculated and experimental values of K , over a range of pressures. Table V: Values of AVO for the Dissociation of Ion Pairs in Water a t 25” and 1 .Atm.
where N denotes Avogadro’s number and &(b) is 8 tabulated function of b = 2q/a, a being the distance between the ceinters of the ions when they are actually in contact. The remaining symbols have the same meanings as in eq. 2 and 3. F U O S Son , ~the ~ other hand, suggested that the ions should only be considered to form pairs when their centers are within the “contact distance” a of each other. From this criterion he arrived a t the formula
K, =
3000 4=Na3eb _____
The values of K,.corresponding to ( 5 ) and (6) are given
_____ MgSO4
LaFe( CN)6
-
AVO, c rn.3/m01e------
Bierrum
Fuoss
-4.86 -6.89
-7.42
-7.3
-8.98
-8.0
Exptl.
S. D. Hamann, “Physico-Chemical Effects of Pressure,” Butterworths, London, 1957, p. 129. (20) See ref. 3, p. 393. (21) See ref. 3, p. 551. (22) Because the calculations are particularly sensitive to the way in which e varies with P , we have based them on t,he accurate dielectric constant data of Owen. et aL’5 As we mentioned in footnote 12, Owen’s measurements were made to only 1000 atm. and to obtain the curves in Fig. 5 it was necessary t o extrapola1.e the data to 2000 atm. The right-hand parts of the curves must therefore be considered t o be only tentative. (19)
Volume 68, Number 2
February, 1964
S.D. HAMANN, P. J. PEARCE, AND W. STRAUSS
380
61
proportional to \ z l x z ~ / ais) only slightly larger despite the higher valence of LaFe(CN)e. This compensation of effects explains the similarity in behavior of the two salts under pressure. The reason for the larger value of a may lie either in the bulkiness of the Fe(C?i)63- ion or in the existence of a permanent hydration shell around La3+. It has been suggested previously' that the observed entropy of dissociation of LaFe(CN)6 is consistent with the idea that its ion pairs contain hydrated lanthanum ions and it is certainly significant that the solid salt contains water of crystallization (see the Experimental part of this paper). In this connection, also, the small value of - A v o (about half the volume of a water molecule) suggests that the ions are almost fully hydrated in the ion-pair state. From all this evidence, it is reasonable t o suppose that an ion pair contains a t least one water molecule sandwiched between the two ions. Second, Table V and Fig. 5 show that both the theories of Bjerrum and of Fuoss agree sufficiently well with experiment to be useful in predicting ion-association equilibria a t high pressures. It would, of course, be possible to obtain an exact fit of the present experimental data by allowing a to vary with pressure, but this would necessarily be an arbitrary procedure since there is no known theoretical relationship between a and the pressure.
-
0
1iWO
500
f500
zoo0
Prassum (of/??>
Figure 5 . A comparison of the experimental results (shown as crosses) with the predictions of the theories of Bjerrum and of Fuoss.
The following points emerge from this analysis. First, the value of a is considerably greater for LaFe(cN)6 than for ;\IgS04 and in consequence b (which is
The Journal of Physical Chemistry
