Activity coefficients of hexamincobalt (III) oxalate in aqueous solutions of different electrolytes

M-1256 J.

Chem. Thermodynamics1981,

13, 161-766

Activity coefficients of hexamincobalt (I I I) oxalate in aqueous solutions of different electrolytes M. A. CASTELLANOS

and J. NUREZ

DELGADO

Departamento de Quimica Fisica. Facuftad de Ciencias Quimicas, Universidad Complutense, Madrid 3, Spain (Received 20 October 1980; in revised form 27 January 1981) Relative activity coefficients of hexamincobalt (III) oxalate, :CO(NH,),},(C,OJ~, in aqueous solutions of Lick, NaCI, KCl, NH,Br, NaBr, KBr, NH,NO,, KI, KSCN, (CHs),NBr, (C,H,),NCIOI, and (C,H,),NI have been evaluated from solubility determinations over an ionic-strength range of 6x 10e3 to 0.19 mol kg-’ at 298.15 K. The analysis of the hexamincobalt (III) oxalate solutions were performed by measuring the optical density at 476 nm. Our results are compared with the predictions of the Debye-Hiickel (DH) theory, the numerical integration of the Poisson-Boltzmann equation (IPBE), and the Mayer theory.

1. Introduction The results of this paper are part of a series of investigations on aqueous solutions of mixed electrolytes. Previous studies (I) showed that the increase in solubility of P,O,CO(NH~)~ in the presence of different electrolytes was that predicted by the Debye-Htickel (DH) equation. However, the behaviour of organic salts could not be interpreted in terms of the larger size of the cations. The purpose of this work was to study the effect of different electrolytes on the solubility of an asymmetric electrolyte. Hexamincobalt (III) oxalate has been chosen to extend our investigations because the solutions of this salt obey the Lambert-Beer law at all wavelengths and have a high ionic stability.

2. Experimental MATERIALS

Hexamincobalt (III) oxalate has been prepared by metathesis’2) in aqueous solution from Co(NH,),Cl, and Na,C,O,. Analysis gave the following mass percentages: Co, 18.1; and &Of-, 39.8. The calculated values for (C204)3(C~(NH3)6}2*4Hz0 are: Co, 17.92; and C,O:-, 40.10. Hexamincobalt (III) chloride was prepared by literature methods”) and was analysed with the following mass percentages: Co, 22.4; Cl, 39.79; and NH3, 38.15. The X-ray difFraction spectrum of a powdered sample indicated only a set of peaks that was identified as belonging to Co(NH3)&l,. 0021-9614/81/080761+06

SOl.OO/O

0 1981 Academic Press Inc. (London) Ltd.

762

M. A. CASTELLANOS

AND J. NUfiEZ

DELGADO

All other salts were Merck, Riedel, or Carlo-Erba products of analytical purity and were recrystallized from conductivity water. The salts were vacuum dried to constant mass. Conductivity water (triply distilled) was used throughout. PROCEDURE

The apparatus used in this study was similar to that described previously.“’ An excess of solid hexamincobalt (III) oxalate was stirred with a solution of the desired electrolyte for at least 3 h in a vessel thermostatted at (298.15kO.05) K. The solutions of the different electrolytes were prepared by mass from the salts in all cases. A first sample of the solution was rapidly filtered and the solubility of hexamincobalt (III) oxalate was determined. A second sample of the solution was taken from the vessel 1 h after the first and was also analysed; the solubilities of both samples were compared. The procedure was repeated with further samples until a constant value for the solubility of hexamincobalt (III) oxalate was obtained. The same results were obtained by stirring solid hexamincobalt (III) oxalate for longer periods of time (48 h). The solubility of hexamincobalt (III) oxalate was determined by measuring the optical density at 476 nm, where Co(NH,)i+ has a rather broad maximum. Occasional determinations of C,O,Z- by the potassium-permanganate method gave identical results. Owing to the low solubility of this salt, 4 cm optical-path cells were used. The relative activity coefficient y/y0 of the solute was calculated using

SOP = Yl’iO~ where So is the solubility of the saturating salt, hexamincobalt (III) oxalate, in pure water, S is the solubility of the saturating salt in the electrolyte solution under TABLE 1. Coefficients Ai and standard deviation o(S) corresponding to equation (2), relating solubility of hexamincobalt (III) oxalate with the molality m of the added electrolyte Added electrolyte

LiCl NaCl KC1 NH4NOX NaNO, KNO, NH,Br NaBr KBr KSCN

0.00039 0.00039 0.00039 0.00039 0.00039 0.00039 0.00039 0.00039 0.00039 o.ooo39

0 < m/mol 0.01242 0.01335 0.01324 0.01361 0.01185 0.01355 0.01248 0.01130 0.01258 0.01076

kg-’ < 0.15 -0.06142 -0.10755 -0.09823 - 0.08046 - 0.04959 -0.10871 -0.05572 - 0.04034 - 0.08072 -0.05333

0.21915 0.82318 0.67308 0.33638 0.15853 0.72554 0.18165 0.10513 0.4597 1 0.18568

t(dH,),NBr GWJ’JClO,

0.00039 0.00039

0.01247 0.01256 0.01036

-0.12339 -0.11065 -0.10215

0.89781 0.89223 0.72260

GH,),NI

0.00039

0 < m/mol kg-’ i 0.10 0.00641 - 0.07434

0.39288

-. - 2.34574 - 1.75075 - 1.78074 - 0.96504 - 2.64862 2.37733 - 2.07828

1.1 3.2 3.3 1.4 2.1 3.3 2.7 2.4 3.0 2.2 3.1 2.1 2.8 2.5

ACTIVITY

COEFFICIENTS

OF HEXAMINCOBALT

(III) OXALATE

763

I.0l-

? C z ';

(I,/mol

kg-‘)1’2

FIGURE 1. Relative activity coefficient (y/y,,) of {Co(NH,),},(C,O,), in the presence of different 1-t electrolytes as a function of the square root of the total ionic strength I,: l , LiCl ; V, NaCl ; 0, KC1 ; O,NaBr; n , KBr; 0, KI; Q, KSCN: A >NH,NO, ; V, NaNO,; A, KNO, ; q ,NH,Br; 4, (CH,),NBr; 0, (C,H5)4NC104; and 0, (C4H9).,NI. The dashed line corresponds to the Debye-Htickel limiting law (DHLL).

consideration, y is the (molality-based) activity coefficient of the saturating salt in the electrolyte solution under consideration, and yO is the activity coefficient of the saturating salt in water.

3. Results Experimental

results were fitted to polynomials

of the form:

S = xi A,(m/mol kg-‘)‘,

(2)

where S is the solubility of hexamincobalt (III) oxalate and m the molality of the added electrolyte solutions. The coefficients of equation (2) and the standard deviations are given in table 1.

764

M. A. CASTELLANOS

AND J. NUREZ

DELGADO

O-

5-

-J

0.2 (Z,/mol

0.3

0.4

0.5

kg-‘)1’2

FIGURE 2. Comparison between the experimental results for l-l electrolytes (solid lines) and the results obtained by numerical integration of the Poisson-Boltzmann equation (IPBE) and equation (3). IPBE : O,a=0.42nm; q ,a=0.44nm; l ,a=O.S7nm; n ,a=0.75nm. Equation (3): 0, (I = 0.418 nm; A, a = 0.438 nm; V, a = 0.57 nm; A, a = 0.76 nm; and V, a = 1.52 nm.

Values of In(r,/y) derived from experimental solubility measurements are plotted against the square root of the ionic strength in figure 1. It can be seen that the increase in solubility is smaller for potassium salts than for sodium or ammonium salts. This behaviour was also observed in previous work,“) but due to the low solubility of hexamincobalt (III) oxalate (even at high ionic strength) the specific effects of the different electrolytes are larger. Tetraalkylammonium salts give a much smaller increase in solubility as is shown in figure 1. The larger the ionic size of the organic cation the smaller is the increase in solubility. The Debye-Htickel theory in its form: In y = -A~z+z-~Z~‘~/(~ +aBZ~“),

(3) is adequate to interpret the results of l-l electrolytes up to I, = 0.12 mol kg-’ as is shown in figure 2. However, for tetraalkylammonium salts, rather large interaction

ACTIVITY

COEFFICIENTS I

OF HEXAMINCOBALT I

I

I

(III) OXALATE

765

I

I DHLL

I I / I’

/

(I,/mol

kg-l?”

FIGURE 3. Comparison between theory and experiment for {Co(NH,),J2(C,G,), in KCJl solutions. , experiment; 0. equation (3) with n = 0.429 nm; 0, IPBE with a = 0.43 nm; A, Mayer theory with n = 0.50 nm.

parameters a are required and equation (3) is adequate only for I, < 0.06 mol kg- ‘. The interaction parameters a (distance of closest approach) of equation (3) for different electrolytes are given in table 2. The different behaviour of the large tetraalkylammonium salts is not due only to the larger size of the cations. It seems that the smaller increase in solubility can be related to the increasing hydrophobic character of the cations.‘3-5’ This behaviour is again in agreement with previous works.“*6*7) TABLE

2. Interaction parameters a corresponding to equation (3) for hexamincobalt (III) oxalate in solutions of different electrolytes. 0 -z IJmol kg-’ < 0.12, unless indicated otherwise

Added etectrolyte

a/rim

Added electrolyte

n/rim

Added electrolyte

a/rim

LiCl NaCl KC1 NH,Br NaBr

0.425 0.425 0.425 0.418 0.448

KBr NH,NO, NaNO, KNO, KI

0.448 0.391 0.424 0.438 0.493

KSCN (CW4NBr GH,WCQ GWN

0.53 0.57 0.76’ 1.52”

a 0 < I,,,/mol kg-’ < 0.06.

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M. A. CASTELLANOS

AND J. NUREZ

DELGADO

We have also used the numerical integration of the Poisson-Boltzmann equation (IPBE)@) to calculate the ratio of the activity coefficients. The results are shown in figure 2 where the solid lines represent the experimental behaviour and the points are calculated, for some ionic strengths and different values of a, by IPBE. The agreement is very satisfactory for inorganic l-l electrolytes and (CH,),NBr. However, the IPBE method also fails to interpret the experimental behaviour of (C2H,)bNC10, and (C,H9),NI. The Mayer theory (9) in the form” ‘* 11)of the Debye-Htickel limiting law combined with a virial expansion (DHLL + B,) has been used to calculate ln(y,/y). The results are compared with those obtained by the DH equation (a = 0.429 nm) and IPBE method (a = 0.420 nm) in figure 3, where the solid line is the experimental behaviour in KC1 solution. The (DHLL+B,) treatment is adequate of GOdJWNW,L only for (1,jmol kg- ‘)l” < 0.25. We conclude that the effect of inorganic l-l electrolytes on the solubility of hexamincobalt (III) oxalate is that predicted by the DH equation. However, tetraalkylammonium salts differ greatly from the predicted behaviour. These results demonstrate that a more detailed model is required to describe this kind of aqueous solution. This model must take into account the structural aspects of water and ionsolvent interactions. REFERENCES I. Ferranti, F.; NCfiez, J.; Indelli, A. Electrochim. Acra 1978, 24, 115. 2. Bjerrum, J.; McReynolds, J. P. Inorg. Synrh. 1946, 2, 217. 3. Narten, A. H. J. Phys. Chem. 1970, 74, 765. 4. Eley, D. D. Trans. Faraday Sot. 1939, 35. 1281. 5. Frank, H. S.; Evans, M. W. J. Chem. Phvs. 1945, 13, 507. 6. Castellanos, M. A.; Ntitiez, J. 75 Aniversario de la R.S.E.F.Q., Symposium nr. 14 Madrid. 7. Ntiiiez, J.; Castellanos, M. A. to be published. 8. Zamboni, R.; Giacomelli, A.; Malatesta, F. ; Indelli, A. J. PhyJ. Chem. 1976, 80, 1418. 9. Mayer, J. E. J. Chem. Phys. 1950, 18, 1426. 10. Kirkwood, J. G.; Poirier, J. C. J. Phys. Chem. 1954, 58, 591. 11. Rasaiah, J. C.: Friedman; H. L. J. Chem. Phys. 1968, 48, 2742.

1978.