XVIZZ: The Solubility Product Constants of the Metallic Suljides WILLIAM H. WAGGONER University of Georgia, Athens, Georgia
T H E solubility product principle is commonly presented in elementary analytical chemistry courses in connection with the precipitation processes which form the basis of the systematic division of the ions into groups. Unfortunately, a comparison of textbooks2 reveals the great diversity and frequent inconsistency of the numerical K,, values reported for many compounds, particularly the metallic sulfides. The "textbooks" data given in Table 1 demonstrate the discrepancies existing among some of the values which are reported in the literature and quoted in the textbooks and also afford a comparison with the recommended "thermodynamic" values. Much of the textbook data on the solubilities and K,, values of the metallic sulfides can be traced to investigations made fifty years ago. The results of Weigel (3!2), and of Bruner and Zawadski (4,5) are most frequently quoted, either directly or through the recalculation of these data made by Kolthoff (17). A comprehensive discussion of the solubility problem is beyond the scope of this paper.3 We will consider here only those investigations which deal directly with sulfides and their solubility - moduct . constants. As originally given by Nernst (?24), the solubility product principle states that for a saturated solution of a difficultly soluble salt, B,A,, which ionizes com-
Application of the law of mass action yields the expression (Bt")"(A-")n
=
constant (K),,
(2)
Using this relation, the solubility product constant,
K,,, is calculated by using the ionic concentrations 'Suggestions of material suitable for this column and guest columns suitable for publication directly are eagerly solicited. They should be sent with as many details a8 possible, and particularly with references to modern textbooks, to Karol J. Mysels, Department of Chemistry, University of Southern California, Los Angeles 7, California. Since the purpose of this column is to prevent the spread and continuation of errors and not the evaluation of individual texts, the source of errors discussed will not be cited. The error must occur in at least two independent standard books to be presented. =See, for example, HARNED, H. S., AND B. B. OWEN,"The Physical Chemistry of Electrolytic Solutions,'' 2nd ed., Reinhold R. W., "Ionic Publishing Corp., New York, 1950, or GURNEY, Processes in Solution," McGraw-Hill Book Co., Inc., New York, 1953.
VOLUME 35, NO. 7, JULY, 1958
in moles per liter as derived from the molar solubility of the salt. Subsequently work on solutions of electrolytes has shown that a more accurate expression results from using the ionic activities. In spite of this limitation, the simple solubility product concept, with ionic concentrations, has proved of great value in analytical chemistry. The solubility of substances can be investigated by either direct or indirect experimental methods. For substances of moderate solubility the direct method is generally applicable. For difficultly soluble substances, however, indirect methods based on the measurement of some property of the saturated solution, followed by calculation according t o some empirical or theoretical formula, are employed. Arbitrarily, these indirect methods will be treated here under five headings: ( a ) conductance, (b) potentiometric, (e) optical, (d) equilibrium, and (e) thermodynamic. CONDUCTANCE METHOD
This involves the measurement of the electrical conductivity of the solution obtained by keeping the salt in contact with water at constant temperature until equilibrium is reached. The salt concentration corresponding to the measured conductance is calculated from the relation
where c is the salt concentration in gram equivalents per liter, k is the specific conductance of the saturated solution, and A is the equivalent conductance a t the given concentration. Provided the solution is very dilute, A may be assumed to equal Ao, the equivalent conductance at infinite dilution, which is obtained as the sum of the ionic conductances. Alternately, an expression of the general form A, = A
+ M&
(4)
may he used to relate the conductance and the concentration. In this equation, M is an empirical constant characteristic of the system, and the other symbols have the same significance as before. Among the possible sources of error peculiar to this method are: the conductance of the water itself, the uncertainty as to the nature of the ions involved, the extent of hydrolysis of the salts in such dilute 339
TABLE 1 The Solubility Product Constants and Free Energies of Formation for Metallic Sulfides at 25% &, calculated fwm Sub"Textbook" AF"' fhemodynamie stance date (kcal./mole) cuts 1.6 X lo-" - 20.6
solutions, the presence of slightly more soluble or strongly adsorbed impurities which contribute also to the conductivity of the equilibrium liquid, and the values employed for AO and/or M in calculating the equilibrium salt concentrations. The conductance method was employed by Bottger (S), Jellinek and Czerwinski (If), and Weigel (52), in their investigations.
cus
POTENTIOMETRIC METHODS
AUZS ZnS 1
Included under this heading are all of the methods involving e.m.f. measurements. Usually this involves measuring the effective concentration (the activity) of one of the ions by means of a reversible electrode. The electrode M/MA(solid), NaA (solution), is set up and its potential measured by combining it with a reference electrode. For an electrode we can write (in terms of oxidation potentials)
1.1X10-4*, O
(4)
'(Sf)
3.28 x 1 0 d a ( 2 6 ) 4.8 X (4)
< l o - l a (27)" . X l o 3( 0
beta
6.8X10-Io,
X
beta 8.0 X
- 9.62
- 43.2 ( 6 0 )
1.1 X
lo-==,
Wwtzite
- -44.2 ( 2 0 ) - 47.4
1X
.,
9.36
alpha
3ptd.
.
-
i'mhalerile
(17),c
CdS
7.8 X
Hg2S
5.8 X
HgS
3.5 X 8.6 X
lo-='
lo*'
black
TI8
7.5 X
La& Ce& Nd& SnS
2.5 7.7 8.9 1.2
PbS
8.4 X 10-28
Sb& Bi&
6.8 X
MnS
FeS
X 10-Ia
X lo-'' X lo-" X
lo-"
1.4 X IO-1L 5 . 4 X lo-", green 5 . 1 X 10-~6,
5. 4.
pptd.
green X 10-18 ( 9 )
X
nlnlrn
lo-'*
(ZO),
Fe& CoS
4.9 X 10-18,
- 23.32
alpha
OPTICAL METHOD 1.4 X 10-65 5 . 9 X lo-=',
alpha
8.7 X
beta CoA lo-'" ( 9 ) NiS 2.68 X (33) 1 . 4 X lo-¶' (5) 1.1 x (17)" 3. X (68): alpha 1. x (ZR),s beta 2. X lo-*' (28),L gamma 8. x l 0 - ' ( 2 0 ) PtS
where E and E0 are the electrode and standard electrode potentials respectively, R is the gas contant, T is the absolute temperature, n is the number of electrons involved, 5 is the faraday equivalent, and a is the activity. If the standard potential of the metal is known, the activity of the M+ ions in the solution saturated with MA can be calculated. From the known concentration of the NaA solution the approximate activity of the A- ions can be obtained by assuming it to be equal to the mean activity of the electrolyte. The. product of the activities of the ions M+ and A- then gives the solubility product of MA. Where the potential measurements are carried out in dilute solutions, the activity is assumed to equal the concentration. The most obvious sources of errors in this type of measurement are the assumptions made regarding the relation between the ionic concentrations and the activities, the magnitude of the junction potential in the cell, and the actual degree of reversibility of the electrodes employed. Potentiometric data were employed by Bernfeld (I), Bruner and Zawadski (4, 5), Immerwahr (IO), Jellinek and Czerwinski (II), Jellinek and Gordon (IZ), Knox (15, 16), Lucas (Zf), and Trumpler (SO), in their investigations.
2.6 X 10-1'' 1.8 X 10-Pl
8.0
x
1O7Z
From ref. (28)unless otherwise noted. specified. " At lS°C.
Temperature not
Biltz (t) utilized this method to determine the solubility of several metallic sulfides. The determination involves mixing dilute metal salt solutions with equimolar sodium or potassium sulfide solutions and observing by means of an ultramicroscope the metal ion concentrations at which the particles of the sulfides can no longer he detected. Supersaturation of the solutions would delay the appearance of precipitated particles and thus introduce an appreciable error. A more serious error would result from the visual limit of the microscope itself; i.e., the size and number of particles which must be present to be seen. EQUILIBRIUM METHODS
These involve the determination of the solubility JOURNAL OF CHEMICAL EDUCATION
of the sulfide under conditions of known acidity and known HzS concentration. The concentration of dissolved cation can be determined by any convenient method, including direct chemical analysis and electrodeposition, as well as those methods previously mentioned. The sulfide ion concentration is then evaluated from the ionization of hydrosulfuric acid by means of the relations Hi3
= H + + HS-
(6)
If the ionization (dissociation) constants, K 1 and Kz, are known, combination of expressions (7) and (9) permits the calculation of (S--) for solutions of known hydrogen ion concentration. Experimentally, the ionization constants are evaluated from conductance data or from thermodynamic data obtained from neutralization reaction measurements. I n solution HzS is fairly easily oxidized. As an acid in aqueous solution, H2S is weak and its salts hydrolyze extensively. These factors, in addition t o those previously cited, can cause appreciable errors in dissociation data. Among the investigators who utilized the equilibrium method in determining the solubility product constants of sulfides are Bruner and Zawadski (4, 5), Knox (16, 16), Lucas ($I), Moser and Behr (23), Thiel and Gessner (28), and Wilkinson (33).
able thermodynamic data for inorganic compounds and recommended certain self-consistent values. Kury, Zielen, and Latimer (19) have measured the heat of neutralization of H2S calorimetrically. Utilizing the value for the second dissociation constant of H B obtained by Konopik and Leberl (IS), they have calculated the standard free energy of formation of the sulfide ion to be 20.6 + 0.2 kcal. a t 25°C. This value agrees well with the figure 20.64 kcal. obtained by Goates, Gordon, and Faux (9). The "thermodynamic" solubility product constants given in Table 1 were calculated by means of equation (11) in an attempt to obtain more reliable values than have been available previously. The free energy of formation data used in these calculations are presented in Tables 1 and 2 and their sources cited. A value of 20.6 kcal. for the AFo of the sulfide ion was used in all cases. I t is important to note that the values given in Table 1 are theoretically applicable only to solutions of the individual sulfides. I n dealing with solutions containing mixtures of electrolytes, the total ionic strength of the solution and the activities of all the ions present, including those not common to the sulfides involved, must be considered. I n several instances, K,, values are reported for several forms of the same compound. This was done, vhere the data were available, in recognition of the fact that where a compound does exist in several modifications only one of these is commonly precipitated from aqueous solution. Such precipitated modifications are not necessarily the most stable, and aging generally decreases their solubilities.
THERMODYNAMIC METHOD
The evaluation of solubility product constants by means of thermodynamic data has been neglected by most authors of qualitative analysis textbooks although much recent data are readily available. Considering that such data are generally more reliable than those obtained by methods which involve the direct examination of extremely dilute solutions, this neglect is unfortunate. The calculation depends upon the equation AF' = -RT in K,, (10) where AFo is standard free energy for the reaction as given in equation (1) above and the other symbols have the same significance as before. Substitution into equation (10) of the appropriate numerical values for R and T and conversion to common logarithms leads to the equation AF0(kcal.) = -1.3643 log K., (11) for reactions at 2 5 T . The numerical value of AFo is equal to the sum of the free energies of formation of the reaction products, less the sum of the free energies of formation of the reactants, all substances being taken at unit activity. Free energy of formation data are readily available in the literature. Goates, et al. (7, 8, 9), Kapustinsky (IS), Latimer (to), and Ravitz (25), have employed the thermodynamic approach in calculations involving sulfides. PROPOSED VALUES
Rossini, et al. (261, have summarized the availVOLUME 35, NO. 7, IUL.Y, 1958
TABLE 2 F e e Energies of Formation of Aquated Ions* (kcal./mole a t 25'C.) Substance
S-Cult+ Cut+ Ag Zn++ Cd+'++
AF"
Subslanee
20.6(19) NdiS 12.0 Sn'+ 15.53 Pb++ Bi+s 18.43 - 35.184 , Mnt+ - 18.58 Fe++ 36.79 Fe Cot+ 39.38 - 7.755 Ca +a Lat8 -172.9 h,i++ Ce -170.5 Ptt+ From ref. (St)unless otherwise noted. +
+: ; !
AF" -167.6 - 6.275 (60) - 5.81 15. - 53.4 - 20.30 - 2.52 - 12.3 29.6 - 11.1 54.8(60)
Considerable confusion on the part of the students has often resulted when their calculations did not agree with their observations of solubilities in the laboratory. This may stem from using solubility figures of questionable accuracy as was discussed by Treadwell and Hall (29) in connection with ZnS. It can also come from the formation of complex ions such as those resulting from hydrolytic reactions as discussed by Van Rysselberghe and Gropp (31). Or it may come from a variation in the nature of the solution so that the classical K,, concept has to be modified as proposed, for example, by Denbigh (6). Frequently, however, the simple use of consistent and more accurate values such as those given above should help t o alleviate such difficulties.
ACKNOWLEDGMENT
The helpful suggestions of Dr. Karol J. Mysels of the University of Southern California and of Dr. Eugene L. Heric of the University of Georgia are gratefully acknowledged. LITERATURE CITED BERNFELD, I., Z. physik. Chem., 25,46 (1898). BILTZ,W., Z. physik. Chem., 58, 288 (1907). BOTTGER, W., Z. physik. Chem., 46,520 (1903). BRUNER,L.. AND J. ZAWADSKI,Z. anorg. Chem., 65, 136 (1909). L., AND J . ZAWADSKI, Z. anorg. Chem., 67, 455 (5) BRUNER, (1910)~ \----,. (6) DENBIGH, K. G., J. CHEM.EDUC.,18, 126 (1941). J. R., A. G. COLE,AND E. L. GRAY,J . Am. Chem. (7) GOATES, Soe., 73, 3596 (1951). J. R., A. G. COLE,E. L. GRAY,A N D N. D. FAUX, (8) GOATES, J. Am. Chem. Soe., 73, 707 (1951). AND N. D. FAUX,J. Am. (9) GOATES,J. R., M. B. GORDON, Chem. Soe.. 74. 835 (19521. ~iektrochem.,7, 477 (1901). (10) I~ERWAHR,'C.,'Z. Z. physik. Chem., 102, (11) JELLINEK,K., AND J. CZERWINSKI, 476 - . (19221 ,- -- ,. (12) JELLINEK, K., AND H. GORDON, Z. physik. Chem., 112, 239 (1924). A. F., Compt. rend. mad. sci. U.R.S.S., 28, (13) KAPUSTINSKY, 144 (1940). A. F.,AND I. A. MAKOLKIN, Acla Physico(14) KAPUSTINSKY, ehim., U.R.S.S., 10, 259 (1939). (1) (2) (3) (4)
*
(15) KNOX,J., Z. Elektrochem., 12, 477 (1906). (16) KNOX,J., Trans. Faraday Soe., 4, 43 (1908). I. M., J. Phys. C h . , 35, 2711 (1931) (17) KOLTHOFF, N., AND 0. LEBERL,Monatsh., 80, 781 (1949). (18) KONOPIK, (19) KURY,J. W., A. J. ZIELEN,AND W. M. LATIYER.J . Eledwchem. Soe.; 100, 468 (1953). W. M., "The Oxidation States of the Elements (20) LATIMER, and Their Potentidls in .4queous Solutions," 2nd ed., Prentiee-Hall Inc.., -New Ynrk. - - - ~, -1953. (21) LUCAS,R, Z. anorg. Chem., 41, 193 (1904). (22) MCALPINE,R. K., AND B. A. SOULE,"Qualitative Chemical AnaIy8i8," D. Van Nostrand Company, New York, 1933. (23) MOSER,L., AND M. BEHR,Z. anorg. Ch&., 134,49 (1924). (24) NERNBT, W., Z. physik. Chem., 4, 372 (1889). (25) RAVITZ,6. F., J. Phw. Chem., 40, 61 (1936). W. H. EVANS.S. LEVIRE. (26) Ross1~1.F. D.. D. D. WAGMAN. AND I. JAF& Natl. BUT. ~iandards( u . s . ~ , Cire. 500 (1950). , (27) SIDGWICK,N. V., "The Chemical Elements and Their Compounds," 2 vols., Oxford University Press, London, 1950. (28) THIEL, A., AND H. GEBSNER, Z.anorg. Chem., 86, l(1914). (29) TREADWELL, F. P., AND W. T. HALL,"Andytical Chemistry, Vol. I, Qualitative Analysis," 9th English ed., John Wiley &Sons, Inc., New York, 1948. (30) TRUMPLER, G., Z. physik. Chem., 99, 9 (1921). (31) VANRYSSELBERGHE, P., AND A. H. GROPP,J . CHEM.EDUC., 21, 96 (1944). (32) WEIQEI.,O., Z. phy8S. C h a . , 58, 293 (1907). (33) WILKINSON, J. R., M.S. Thesis, Department of Chemistry, University of Georgia, 1949. ~
~~~~
~
.
JOURNAL OF CHEMICAL EDUCATION
