9 46
JULIUS STIEGLITZ.
thc industrial chemist ancl the metallurgist, since arsenic in a great number of cases is a constituent of the metallic sulphides, especially those of copper. Large amounts of arsenic are given off by the sineltcrs of Salt Lake, Utah ; Everett, Washington; Great Palls, and Butte, Montana; and from many of the smelters of Germany, Englantl, and other countries. In 1854and 187j , Haubner investigated the smelter smoke disease in the Preiburg district, and various other cases have bcen studied to a slight extent. In the decision of Judge Narsliall of the Circuit Court ol the United States a s made November ,j, 1906, the conditions existing in the S:~ltLake smelter district arc described in such :I way as t o make an interestiiig comparison with the results of this series of papers. In sp(,akingof the sulphur dioxide he says: "This gas is heavier than air, and when cooled, falls to the ground a t a distance from thcs smelters dependent upon the air currents. When it is brought in contact with moisture, either in the form of raiii, lrcshly irrigated ground, or the moisture present in growiiig plarits aiid the foliage of trees, sulphurous or sulphuric acid is lormed, which is destructive to yegetation. Besides the cArriission of gas, soiiic' flue dust is einittetl froin the smclters which contains pc~rcr~pti1)le yu:mtitir~sof arsenic resulting in the d w t h of horses and co\vs." In conclusion, the writers wish to thank Ilr. Johii Maxson Stillman lor thtx many suggestions which ha1.e bren Iiclpful iii this work. THE U N I V E R S I T Y01'
MONTANA A N D STANFORD C X I V E R S l T Y .
March
14,
1908.
NOTE ON THE SOLUBILITY PRODUCT. BY JCLIVS S T I E G L I T X .
Received A p r i l
2,
1908.
Nernst2 was the first to advance t h e tlieory that at a given temperature the solubility of a difficultly solublc electrolyte in water or in aqueous solutions of other electrolytes is dcpendcnt on a constant called thc solubility product, which is proportional to the concentrations of the ions of the salt, each raised t o t h e power corresponding to the number resulting from one molecule. 'l'he constant is an important one in t h r theory of precipitation and solution and particularly useful in calculatioils of the solubility of L: precipitate in mistures that are not too concentrated. In Nernst's test -book 011 physical chemistry, the relation for a difficultly soluble binary salt-such as silver acetate-in water and in solutions containing a salt with it common ion, is developed 3 s follows: calling the total concentratioiis of the dil'ficultly soluble salt wz, ant1 in the saturated watcr soltition atid iii thc salt solution respectively, Reported at the Chicago meeting of the iZlllerican Chemical Society Z. p h y s i k . Chent., 4, 372 (1889). "'l'ranslation of the 4th Gerrrinn Edition (rgoq), 11. 527.
NOTE ON THE SOLUBILITY PRODUCT.
9 47
and the corresponding degrees of ionization CY, and CY we have first by the application of the isotherm of dissociation, i. e., on the basis of the law of mass action for the two cases:
(moa,)' and
=
Km,(Z-~n,)
(1)
+
(ma x ) m a = Km ( I -a), (2) in which (ma+ x ) represents the total concentration of the common ion. Then, on the basis of the theorem that the undissociated substance has a constant solubility-derived from the law of heterogeneous or physical e quilibrium, na, ( I - a, ) = m ( I - a ) . (3) Combining the three equations we have ( ~ , c Y , ) ~ = (~mcaY fx), and as (m, a,)', the product of the concentrations of the ions in a saturated, pure aqueous solution a t a given temperature, has a definite value, we have in general, 'ma: f E KSolubility product' (4) Substituting the variable symbols CAg, CCHsCOOand CCH3COOAg, we can express the first principle for silver acetate by CAg -.
x CCHsCOO -
- KIonization (5) CCHaCOOAg and the principle of the constant solubility of the undissociated silver acetate by CCH$200Ag =k' (6) Then for the constant solubility product we have simply cAg XCCH3CO0 = KSolubility product' (7) in which CAP and CCHBCOO represent the concentrations of the silver and acetate ions in any saturated solution of silver acetate, whether in aqueous solution where CAP= CCHsCOO or in the presence of other salts, where they will usually have different values. It has long been known, however,' that the ionization of strong electrolytes does not conform to the law of mass action-in other words that equations ( I ) and ( 2 ) a s used above to develop the theory of the solubility prod uct do not agree with the facts in the cases of such electrolytes, e. g., salts, for which the theory of the solubility product is especially important. The real relation for a salt like silver acetate is t h a t the proportion on the left side of equation ( 5 ) grows larger with increasing concentration.' This difficulty was recognized by A. A. N o y e ~to , ~ whom we owe a large part of the 1
Translation of the 4th German Edition (1904),p 498.
* Rudolphi, 2. p h y s 3 . Chem., 17,38.5 (1895). Ibid., 6, 241 (1890); 9, 613 (1892); 16, 125 (1895); 26, 152 (1898); 42, 336 (1903)
948
JULIUS STIEGLITZ.
most exact experimental work on the solubility product, and Xoyes attempted to meet the dificulty by assuming that for all solutions in which the concentration of the undissociated substance was kept constant, the product of the ion concentrations is also a constant. Noyes calculated his results on the basis of this :muniption and used it even as a method of determining the degrees of ionization of salts in the mixture. Arrhenius' showed the error of such :in assumption, which cannot be reconciled with his principles of isoliyclric solution. The latter priiiciple has been established on a safv basis by the work of Xrrhenius, Manson, Barinwater, A$rchibald,McEay, Barncs a n d others, and has been found t o hold, up to a conc:.ntratioii of a t least half-iiormd, for mixtures of salts of the same type as well as for those of different typ-s.' We find thus that the application of the law of itiass action iii equations ( I ) and ( 2 ) to the question of solubility is not justified by exp:.riciicc*. 111[in important paper published iii 1899, Arrhenius3 took up the investigatioti of the second fiii:datni.iital principle involved in thc solubility of electrolytes, tlii. \vitlely aiid generally accepted theory of the constant solubility of thc undissociatcd tnokculcs, as expressed in equations (3) arid ( 6 ) . Origiri;qlly himself :ipparentl!* ilicliricd it1 conirnon with practically all chemists to accept4 i t a s a nxittcr of course, as a consequeiice of tlie law of heterogeneous or physicil equilibriiim, but later led to questioii its corrcct11css, he testcyl its valitlity b y detcrinining tlis solubility of silver salts of a llunibrr of organic acids in water : t i i d in soh.Itions containi~igan hcreasiiig excess of the correspoa(1iiig sodium salts. Calculating the proportioii of i0iiizc.d arid iion-ionizrd silver salt with tlie aid of the principle of isohydric solL1tioils, hc found tliat as :I matter of fact the iiiolecular solubility is not constant but dcerea decidedly with the increasing coiiceiitratioii of the total c.Iectrolyte.' .Z similar fact has long bceii known for the relativr solubility of gases likt. carboil dioxide, osygcii, etc., iii water and i i i salt soliltions and Xrrlii.niiis's result should iiot l i x w hem unexpccted.8 VI'(. thus find that the two f1indmieiital equations on wliicli tlic theory of the col~staritsolubility product origitially ws bascd, arc both invalid arid may well ask if this result does not thoroughly discredit a n d dispose of the tlleory. Perhaps soinc such feeling led .$rrhenius himself to refrain froin calculating tlie values for the solubility products for the silver salts in his own expcrimelits. r, if w c consider the true relations as now established for the tbV-0 cascs of cliemical and physical equilibrium, we have for the physzk. C h e w . , 11, 391 (1893)and 31, 197 (1899). of the Congress of Arts and Science, St. Louis. %. physik. Clietn., 31, 197 (1899). I b i d . , 11, 396 (1Sm). I'iife also A. A. Soyes, Reports, etc., Vol. 1x7, p. 3 2 2 (1904). l'ide also Nernst, loc. d., p. 476.
12.
* 1. X. Noyes, Xrol. I V , 1). 31 I, Reports 3
6
6
NOTE ON THE SOLUBILITY PRODUCT.
949
equilibrium between the ions and the undissociated substance of a binary electrolyte a proportion, Cpos. ion X C ~ e gion . , CMol which grows larger with increase of concentration,' and for CMol the molecular solubility resulting from the equilibrium between the solid phase and the solution, a value growing smaller with increasing concentrations of the total electrolyte present.2 Now it is obvious t h a t with a decreasing value for ChIo, and an increasing value for the whole proportion, the ion product, Cpos,ion x CXeg.ion possibly might remain constant or approximately constant after all : it is clearly a question for rigorous experiment and calculation to determine whether the ion product does or does not remain constant, that is, whether the values for the proportion and the molecular solubility are inversely porportionate, the proportion growing larger to the same extent as CMol grows smaller with increased concentrations. Even if it should not prove to be a real, mtural constant, it might still be found to be sufficiently constant to be of practical value and assistance in the study of the reactions of precipitation and solution. I have not found in the literature any discussion or investigation of the subject from this point of view; although Arrhenius's paper was published in 1899, even the new edition3 of Nernst's text-book,' as well as other recent editions of books on physical chemistry, such as Jones's "Elements of Physical Chemistry," Me1lor's"ChemicalStatics and Dynamics, "6 as well as textbooks on the application of physical chemistry to analytical chemistry, do not even refer to it or its extremely important conclusions, but develop the solubility product as given above. I should except a statement made by A. A. Noyes in his address before the Congress of Arts and Science a t St. Louis, in which the discrepancy shown to exist by Arrhenius between the principle of isohydric solutions and the old hypotheses concerning solubility is clearly pointed out and the need for further investigation on these lines emphasized.e Considerations' of the above nature led me then to complete the calculations of Arrhenius's experimental data on the solubilities of organic silver Rudolphi, LOC.ctt. Arrhenius, LOC.a t . Translation of the 4th German Edition (1904). ' p. 595. 1904, P. 2 3 1 . LOC.cit., page 321. Since the presentation of this paper, Professor Noyes has informed me that work along these lines has been continued in his laboratory since 1904. The theory of the constant solubility product formed an essential element in a chemic0 -geological investigation carried out by me for Professor Chamberlin (vide a forthcoming report, Carnegie Institution), and this study has resulted from that investig ation.
'
'
950
JULIUS STIEGLITZ.
salts in the presence of an excess of the corresponding sodium salt, by mlculating the value of the ion product in each experiment. To this end, the degrees of ionization of the sodium salts of the fatty acids in the mixtures used had to becalculated first, and this was done with the aid of the principle of isohydric solutions. On account of the form in which Arrhenius's data are presented, the following method was pursued: Arrhenius gives first a table showing the ion concentrations and degrees of ionization of isohydric solutions of silver and sodium acetate. From these data the corresponding total concentrations for the isohydric solutions of the two salts were first calculated and the results expressed in two curves in which the cube roots of the molar concentrations and the degrees of ionization were used as coordinates. The curve obtained for sodium acetate is rectilinear and that for silver nitrate only slightly curved, so the necessary interpolations for the further calculations were easily made. In his other tables, Arrhenius gives the solubility of the silver salts and their degrees of ionization, and the total concentration of the sodium salts, but not the corresponding degrees of ionization. For instance, in the presence of 0.2667 mol. sodium acetate, the solubility of silver acetate is o , 0 2 0 3 mol., of which 50.4 per cent. is ionized. To find the degree of ionization of the sodium acetate in such a mixture, I found from the curve for the silver salt that an ionization of 50.4 per cent. corresponds to a value of 0 . 7 3 for y& and consequently the molar concentration of the silver salt is (0. 73)3or 0.389 when it is considered t o be in its share of the wiiter according to the isohydric principle. Then its share of the liter of water must be o .0203/0.389 or 5 2 . 2 cc. This leaves 94s cc. for the sodium acetate atid its concentration in 948 cc. is 0,2667/0.948 or 0 . 2 8 1 3 molar. Then its degree of ionization is 69.6 per cent., according to the curve. The concentration of the acetate ions in each of the isohydric solutions, considered separately, is 0.1961 and 0.1960 for the silver and the sodium acetate, respectively-showing that they were really isohydric. 'rhe agreement was not in all cases as close as this, but with one or two exceptions mentioned below, it was satisfactory, the concentrations of the common ion being usually within one per cent. of each other. In the given case, the total concentration of the acetate ion in the mixture is therefore 0.196, that of the silver ion, as given by Arrhenius is o , 0 1 0 2 and the value of the ion product in this experiment therefore : CAPX C C H a C O O = o . ~X0.196 ~ o z or 0.00200. All the calculations were made in this way and the following tables give all the results obtained for the acetate, propionate, butyrate, valerate and chloracetate of silver. In the calculations the curves for the acetates were always used to find the degree of ionization for all these salts, following Arrhenius's method.
NOTE ON THE SOLUBILITY PRODUCT.
95 I
In the tables the first column gives the molar concentration of the sodium salt used, column 2 its degree of ionization, calculated in the way just described, column 3 the concentration of the ionized part of the sodium salt. Column 4 gives the total solubility of the silver salt, column 5 its degree of ionization, column 6 the concentration of the ionized part of the silver salt and column 7 the concentration of the undissociated part, which represents therefore the molecular solubility of the silver salt. The last column gives the value for the solubility product, CAPX CcH8coo. The value for C is 49 found in column 6, and CCHsCOO is the sum of the acetate concentrations given in columns 3 and 6. TABLEI.-SILVER ACETATEAT 1 8 . 6 ~ . Na-Acet.
dAcet.
AgAcet.
Iooa’.
IGAcet.
loaMol.
IdK.
..
...
72.0
80.0 78.0 75,O 69.6 63.0
26.6
42.7 32.3 24.7 16.4
16.6 15.1 13.7 11.8
190 190 191
10.2
10.1
200
6.3
8.4
202
Ima.
0
0.0333 0.0667 0 . I333 0.2667 0.5OOo
52.0
0.0593 0.0474 0.0384
100.0
0.0282
186.7 315.0
0.0203 0.0147
68.1 64.4 58.4 50.4 42.8
182
TABLESILVER PROPIONATE AT 18.2~. Na-Prop. 0
0.0167 0.0333 0.0667 0.I333 0.2667 O . ~ W o
Na.Butyr.
..
..
82.0
13.69
81 .o 78.9 75.3 69.8 63.2
27.00
100s.
..
0
0.0066 0.0164 0.0329 0.0658 0.1315 0.2630 0.4930
Ag-Val. 0
0.0175 0’0349 0.0689 0.I395
rolProp.
IMQ.
52.63 100.37 186.2 316.0
0,0258
0.0191 0.0131 0.0101
moa.
dProp.
108Mol.
IdK.
74.5 72.1 69.6 65.5 58.8 50.6 42.9
34.4 28.3 24.0 16.9
11.8
11.2
8.9 7.9
118.4 119.4 122.4 118.0 124.7
6.6 4.3
6.5 5.8
(137.7)
11.0
10.5
TABLESILVER BUTYRATEAT 18.2~. IdButyr.‘ Ag-Butyr.’ Iooa. 10aButyr.’ 10aMol.
...
86.0 84.9 83.0 80.0 75.9 70. I 63.3
moa.
Ag-Prop.
0.0462 0.0393 0.0345
13.9 27.3 52.6
0.0224 0.0199 0.0169 0.0131 0.0091
100.0
0.O06O
79.6 77.3 73.5 67.7 59.9
184.4 312.1
0.0040 0.0027
51.1
2.0
2.0
43.2
1.2
1.5
56.8
81.1
18.2
15.8 13.1 9.6 6.2 3.6
4.2 4.1 3.8 3.5 2.9 2.4
TABLE4 . 4 I L V E R VALERATE IdVal.’ Ag-Val. xma.
..
...
86.5 84.0 80.1 75.8
15.1 29.3 55.9 105.7
0.0095 0.0047 0.0030 0.0018 0.001.5
AT
87.3 81.1 75.5 68.1 59.7
127.1
106k.
33.0 (49.8) 35.4 35.4 36.4 37.3 36.8 37.6
18.6~.
ro*Val.’
10SMol.
8.3 3.8
1.2
2.2
1.2
0.9
0.9
0.8 0.6 0.6
r$K.
6.9 7.2 6.9 6.9 (9.6)
952
J U L I U S STIEG1,ITZ.
TABLE SILVER CHLORO-ACETAIE AT 1 6 . 9 ~ . Na-ClAcet.
Iooa.
.. 79.8 78.1 74.8 69.4
0
0.0333 0.0667 0.1333 0.2667 0.5000
63.2
103ClAcet.~ Ag-ClAcet.
IOO~.
, .
0.0614
71.1
103ClAcet.'
1oVv1ol.
IOSK.
18.6 16.2 14.6
209.8
26.6
0.0499
j2.1
0.040j
67.(> 63.9
45.8 33.7 cj.9
99.71 18j.1 316.0
0.029!,
53.1
17.4
12.5
202.3
0.0~08
50.4 42.8
10.5 6.9
10.3
20j.S
9.3
222.0
0.0162
202.2
203.3
The experimental results of Nernst's determinations of the solubility of silver acetate in the presence of sodiuni acetate and silver nitrate, respectively, were also recalculated. Neriist used the isohydric principle in determining the degrees of ionization of the salts in the mixtures, but considered the salts to ionize with about equal readiness. Such is not the case, if we accept Arrhenius's determinations of the ionization of silver acetate, the values for which, it is true, w r e very largely obtained by extrapolation. But these sanic values having bem used in bringing the proof that the inolecular solubility decreases witli the increasing concentrations of tlic total electrolyte, it seems most reasonable to use the values also for the determinations of the solubility product of the same salt. In Tables 6 and 7 thcl results of thc recalculation of Neriist's data are tabulatcd, the degrees of ionization being determined by thc application of the isohydric principle in the usual way--the two salts present being supposed to divide the water in such a way as to give solutions containing the sanie concentration of the common ion. The division of t h c water was rapidly ascertained by trial calculations with tlic help of the ciirvcs of dissociation for the third root o f the concentrations. The colunins in tlicsc. tables have in part a different significance from tlie colunms of the previous tables : coluiiin I gives the molar concentration of tlic sodiuiii acctate (silver nitrate in Table 7 ) used in excess, column 2 gives the portio11 of the water, in cubic centimeters, in which all the sodium acetate (silver nitrate) is supposed to be dissolved to form a solution isohydric with tlie solutioii of silver acetate in the rest of the water. Coluniri 3 givcs tlic degree. of ionization of the sodiuiii acetatc (silver nitrate), column 4 the concentration of the common ion in this solution, 5 the total concentration of silver acetate, 6 its degree of ionization, and coluiiiii j tlie concentration of the coinnion ion in the isoliydric silvcr acetate solution. 'flie last column gi~7esthc values for the solubility product. TABLE0; Na-Acet.
cc,
~ 2 0 .
-SILVER
ACCTATI: AT 16'
Icoa.
!oJAcet.'
Ag-Acet.
, . . .
.,.,..
o.nGoj
0
...
0061 o . I 19 o 2-39
hg0
7X.h
0.0;31
S4,3
;,j,8
n
IO.;
