EXCHANGE 'dufx>ersit of Cbicaao Intermediate and Complex Ions* V* The Solubility Product and Activity of The Ions in Bi-Bivalent Salt A DISSERTATION SUBMITTED TO THE FACULTY OF THE OGDEN GRADUATE SCHOOL OF SCIENCE IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMISTY BY H. M. PAINE Private Edition Distributed by THE UNIVERSITY OF CHICAGO LIBRARIES CHICAGO, ILLINOIS Reprinted from the Journal of the American Chemical Society Vol. XLI. No. 8, August, 1919. ZTbe '(University ot Gbicaao Intermediate and Complex Ions* V* The Solubility Product and Activity of The Ions in Bi-Bivalent Salt A DISSERTATION SUBMITTED TO THE FACULTY OF THE OGDEN GRADUATE SCHOOL OF SCIENCE IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMISTY BY H. M. PAINE Private Edition Distributed by . THE UNIVERSITY OF CHICAGO LIBRARIES CHICAGO, ILLINOIS Reprinted from the Journal of the American Chemical Society Vol. XLI. No. 8, August, 1919. EXCHANGE [Reprinted from a paper by William D. Harkius and H. M. Paine.] INTERMEDIATE AND COMPLEX IONS. V. THE SOLUBILITY PRODUCT AND ACTIVITY OF THE IONS IN BI-BIVALENT SALTS. 1 The first evidence which indicates that all salts which give, on complete ionization, 3 or more ions, ionize in steps in such a way as to give inter- mediate ions, was presented by Harkins 2 in 1911. The earlier idea was that intermediate ions are present in aqueous solution of some of the salts of higher types, but not in all cases. Thus Abegg and Spencer, 3 in 1905, considered that thallous oxalate gives rise to an intermediate ion, but potassium oxalate does not, while in 1911 Jellinek 4 concluded that inter- mediate ions are present in solutions of sodium sulfate, but not when potassium sulfate is the solute. Such salts are mercuric chloride, cad- mium chloride, and lead chloride were commonly believed to give inter- mediate ions, but the more ordinary salts were in general supposed to ionize in one step or else to give only a negligible fraction of intermediate ions. Perhaps the strongest evidence in favor of ionization in one step 1 This series of papers was begun by W. D. Harkins in the Research Laboratory of Physical Chemistry of the Massachusetts Institute of Technology and has been continued in the laboratory of the University of Chicago with the consent of Professor A. A. Noyes. 2 J. Am. Chem. Soc., 33, 1836-72(1911); Harkins andPearce, Ibid., 37, 2679(1916). 3 Z. anorg. Chem., 46 406 (1905). 4 Ibid., 76, 309 (1911)- was found in the fact that in solutions of uni-bivalent salts the transference number is independent of the concentration. The work of Harkins in- dicates, however, that the percentage of intermediate ion is not negligible, but for salts of the type of potassium sulfate is 18% for o.oi N solutions, 35% at o. i N, and rises to 46% in a normal solution, these being the per- centages for the KSC>4~ ion. In a study of the solubility of uni-bivalent salts it was found that whereas the addition of a salt with a common univalent ion decreases the solu- bility of the uni-bivalent salt very greatly, just as would be expected, the addition of a salt with a common bivalent ion has an entirely different effect from what had previously been supposed. In other words, the solubility curve in the latter case, at least where the saturating salt has a solubility of o . 05 N or more, has another form than that which would be predicted from the solubility product principle upon the basis of the usual assumptions. Instead of falling rapidly as the concentration of the added salt increases, the solubility of the saturating salt decreases 1 at first slightly but then increases. When salts of the bi-bivalent type are used as saturating salts it is im- possible to add a salt with a common univalent ion; but when salts with bivalent common ions are added to solutions of calcium sulfate (see Fig. i), the solubility curves have somewhat the same form as when the saturating salt is of the uni-bivalent type. The explanation given by Harkins for the peculiar solubility curve of the uni-bivalent salts, was that it is due to the presence in such solutions of a considerable percentage of inter- mediate ions such as KSO4~, BaCl + , etc. It was found that the presence of intermediate ions in solution could also be easily recognized from the slope of the curve representing the solubility of the un-ionized part of the saturating salt when the con- centration of the un-ionized part is calculated on the basis of the usual assumptions, which are as follows: (i) That the isohydric principle is valid, (2) that the usual method of calculating percentages ionization is correct, and (3) that no intermediate ions are present in the solution. Now, it happens that the deductions obtained by this method of detecting intermediate ions hold in all probability even if (i), the isohydric principle is not valid, and (2) if the usual method of calculating the percentage ionization is incorrect. This is true because no use is made of the abso- lute values of the solubility of the un-ionized part of the salt as calculated, and the only essential feature of the method is a proper comparison of the slopes of the calculated solubility curves for the non-ionized parts of uni-univalent and uni-bivalent salts. Thus, when calculated in the usual 1 In the case of highly soluble salts of this type this initial decrease is absent, and the curves have the form which would be expected if the added salt had no ion in common with the saturating salt. way, such curves for the uni-univalent salts slope rapidly downward as the total ion concentration (or the concentration of the added salt) in- creases. Now, if similar curves are constructed for uni-bivalent salts, it might be expected that they would have a somewhat similar form, and this is exactly what is found when the added salts used are such as would have little effect upon the calculated solubility of the un-ionized part when intermediate ions are present. The only salts of this kind are those with no -common ion. In this case the curves for uni-univalent and uni-bivalent salts lie almost exactly parallel (compare with Fig. 3). However, when the added salt contains a common bivalent ion, the curves, when calculated on the basis of the third assumption, i. e., that no intermediate ions are present, should not show the same slope if intermediate ions are present in considerable quantity. From the change in the slope of the curve it would be possible to form some idea of the amount of the intermediate ion present, although a quantitative estimate can be made much more accurately by the use of other methods. Now, if intermediate ions are present in the saturating salt, the calculated solubility of the un-ionized part should decrease much more rapidly when the added salt contains a common univalent ion, and, on the other hand, when a salt containing a common bivalent ion is added, this solubility should either decrease less rapidly or if the relative number of intermediate ions is large, the calcu- lated solubility curve should rise instead of falling, and this latter has been found to be the case for uni-bivalent salts. It will be seen that this method of showing the presence of intermediate ions, and also something of their relative amount, depends upon the deviation of the calculated solubility curves from the normal slope, since at least the greater part of the deviation is caused by the false assumption that intermediate ions are absent. When it is realized that more than half of the salts commonly used are higher type salts, it will be seen that it is important to extend this in- vestigation to a study of types still higher than the uni-bivalent type al- ready studied. l The next most important type of salts is the bi-bivalent ; and in this type of salts there is a reversion from the tri-ionic salts previously investigated to di-ionic salts, which, with respect to the number of ions formed by a simple ionization, would seem to belong to the same type as the di-ionic uni-univalent salts. Since, by their simple ionization the bi-bivalent salts would give the same number of ions per molecule it might be expected that the curve for the solubility of the un- ionized part should be of the same general form as for the uni-univalent salts, provided that the ionization of the bi-bivalent salts is entirely a simple one. 1 Harkins and Pearce, J. Am. Chem. Soc., 37, 2679 (1916) have shown that uni-triv- alent salts give a large number of intermediate ions in solution. 6 In view of these interesting ionization relations of trionic and still higher type salts, a study of sparingly soluble bivalent salts was undertaken with calcium sulfate as a type salt of this group. Its solubility and con- ductance were determined in pure water and also in solutions of various concentrations of copper sulfate, magnesium sulfate, and potassium ni- trate. Density determinations were made on all mixtures and all weigh- ings were corrected to vacuum. In the calculations the atomic weights for 1910 were used. Preparation of Salts and Solutions. The water used for this investigation had in no case a greater specific conductance than 0.7 X io~ 6 and the average value in the bottles in which it was stored was 0.6 X io~ 6 . Calcium Sulfate. This salt was made by the addition of a very dilute potassium sulfate solution to to very dilute calcium chloride solution. Kahlbaum's "Zur Analyse" salts were used and the work carried out in special vessels of resistance glass. The calcium sulfate was washed thoroughly and rotated with several successive portions until the conductivity became constant. This salt was preserved in glass-stoppered resistance glass bottles. Gypsum. For comparison some very clear plates of gypsum were obtained from Dr. A. D. Brokaw of the Geology Department. Magnesium Sulfate Kahlbaum's "Zur Analyse" salt was twice recrystallized from conductivity water and a stock solution made up and analyzed by evaporation in platinum and weighing as magnesium sulfate. Copper Sulfate. Kahlbaum's "Zur Analyse" salt was twice recrystallized from conductivity water. Potassium Nitrate. Baker's potassium nitrate was recrystallized twice from conductivity water. Methods of Analysis. Calcium. Calcium was determined by careful precipitation with ammonium oxalate from ho: solution; after standing 4-6 hours, the calcium oxalate was filtered, washed with water containing a little ammonium oxalate, ignited in tared platinum crucibles and weighed as calcium oxide. Where copper was present it was removed from a very dilute solution by precipitation with hydrogen sulfide. The separation of magnesium from calcium presented difficulties because of the well-known fact that the quantitative separation of small amounts of calcium from much larger amounts of magnesium is unsatisfactory. The method proposed by Cameron and Bell 1 leaves much to be desired from th standpoint of accuracy. A plate of pure gypsum rotated in 25 cc. of conductivity water showed a loss equivalent to solubility of 2.067 S- per 1000 g. solution. The solution from this gave 2.083 g. CaSO* per 1000 g. of solu- tion by the oxalate method, while the specific conductance was 0.0022115 ohms, almost the same as tha for the prepared salt (0.0022148). This method was used therefore only in solutions of comparatively high con entration of magnesium sulfate. For the more dilute solutions the method proposed by Richards, McCafTery and Bisbee 2 was used. Experimental Methods. An excess of the calcium sulfate was rotated with water or solution of a salt in a 500 cc. glass stoppered resistance glass bottle which had been "steamed out" and 1 J. Phys. Chem., 10, 212 (1906). 2 Proc. Am. Acad , 36, 375 (1901). thoroughly seasoned. The temperature was measured by a thermometer which had been compared with a certified Baudin thermometer. For each determination satura- tion was approached both from under-saturation and supersaturation. The solutions were filtered in the thermostat and the first 50 cc. rejected, in order to prevent errors due to adsorption. In the experiments with copper sulfate the concentration of copper was determined for each bottle separately. In the other series solutions were care- fully made up in calibrated flasks from a weighed amount of standard solution. The calcium sulfate was finally carefully washed on a platinum cone with a large amount of the solution, and quickly transferred to the bottle, which was then filled up with solu- tion and rotated as usual. The conductivity measurements were made in the usual way with a roller bridge carefully standardized. The apparatus was similar to that used by Washburn. 1 Great care was taken throughout the work to exclude carbon dioxide from the solutions. The bottles were all filled with carbon dioxide-free air and all solutions and water carefully protected from contact with the air by soda lime trains. Experimental Data. The results of the solubility determinations of calcium sulfate in solu- tions of copper sulfate are given below in Table I, in Potassium nitrate in Table Ha, in magnesium sulfate in Table 116, and those for gypsum in magnesium sulfate in Table lie. The solubility of calcium sulfate in solutions of copper sulfate, magne- sium sulfate, and potassium nitrate, together with the conductances of all of the solutions of the pure salts and of the mixtures, were determined by us, because none of the previous work on calcium sulfate gave exten- sive enough conductivity data for our purpose. The solubility data are plotted as undotted lines in Fig. i, while the dotted lines represent the work of Cameron with potassium and sodium sulfates as the added salts. Other data of a similar nature may be found in papers by Sullivan 2 and by Cameron 3 and his associates. The curves in this figure, which represent the addition of the common bivalent ions, do not have the form to be expected when a common ion is added, in fact, as is shown most clearly in Fig. i, at a very low concen- tration (0.15 AT) the copper sulfate curve changes to the form to be ex- pected when a salt with no common ion is added, while that for magnesium sulfate changes at about 0.35 N. The form of these curves is somewhat the same as that previously found when a salt with a common bivalent ion is added to a solution in which the saturating salt is unibivalent and has a solubility of 0.07 N or more. The principal difference is that the initial solubility drop is greater in the case of the bi-bivalent salts. This change in the form of the curves representing the common ion effect has 1 J. Am. Chem. Soc., 35, 177 (1913). 2 Ibid., 27, 532 (1905). 8 Cameron and Seidell, J. Phys. Chem., 5, 643-55 (1901); Cameron, Ibid., 5, 56 (i 01); Seidell and Smith, Ibid., 8, 493 (1904); Cameron and Bell, J. Am. Chem. Soc., 28, 1220 (1906); Cameron and Bell, J. Phys. Chem., 10, 212 (1906); Cameron and Brezeale, Ibid., 8, 337-40 '1904). 3*0000000 a to N cj PJ cj t w u o o o tO 00 CO O C- CO >O P< VO co a.y^oo rhoooo O * "^O O 00 vo vo oo d 9 TABLE III. EQUIVALENT CONDUCTANCE OF MAGNESIUM SULFATE AT 18 AND AT 25. (CONCENTRATIONS IN EQUIVALENTS PER LITER, CONDUCTANCE IN RECIPROCAL OHMS.) Concentration. Al8. A/A . A25. A/A O . O.OO 135.0 loo.oo 114.4 100.00 0.00050635 i 3-3 91-33 104.7 91-52 o.ooiO"47 117.4 86.96 XOO.I 87.50 0.0020094 i 10. 8 82.08 91-67 82.75 0.005023 99-o 73.33 84-35 73-73 0.010047 88.85 65.82 76.15 66.56 0.020094 78.98 58.50 67.23 58.77 0.050235 66 .05 48 . 93 56.54 49 37 0.10047 57-79 42.81 49.58 43-34 o . 20094 49.82 36.90 43-12 37.69 0.50235 40.72 30.16 35.25 30.81 1.0067 33-37 24.72 28.81 25.18 TABLE IV. CONDUCTANCE OF CALCIUM SULPATE SOLUTIONS. (a) AT 25. Equivalents Specific conduc- A. H 25 per liter X 10. tance X 10*. I/ohm. I/ohm. A/A*. U4 O.O I4O.O 100.00 0.099955 1.3657 136.63 97-59 0.19955 2.650 132.88 94.91 0-49795 6-343 127.38 90.98 0-9959 12.104 121.57 86.84 1-9975 22.612 I3.2O 80.86 0.99720 5.011 50.195 loo 15 71-53 0.99748 10.081 90.17 89.45 63.89 0.99782 30.610 221.48 72.35 51-68 0.99911 36 . 408 252.0 69.21 49-44 (Hulett) (6) AT 18. d} 8 . 0.0 119.00 100.00 0.10013 1.1644 116.28 97-80 0.19986 2.2670 113.43 95.32 0.49871 5.436 109.0 91.60 0-99755 10.407 103.82 87.24 2.007 19.446 97.19 81.67 5-023 43.270 86.20 72-44 0.99895 10.096 77.96 77.21 64.88 0.99897 TABLE V. CONDUCTANCE OF COPPER SULFATB SOLUTIONS AT 25. Equivalent concentration Specific conduc- tance X 10 I/ohm. A. I/ohm ,25 04 ' 0.025156 1.7286 86.50 o. 99950 o . 050202 2.9688 59 13 I- 0013 o. 100081 5-0609 50.56 i. 0053 0.201085 8.7545 43-53 I- 0136 0.41993 15-535 36.99 I- 0307 1-9335 46 . 082 23-83 I. 14645 10 fc o 8 &' .- CSO 71 w*^aj J 1 1* -M '3 oo cs w Ql "" "J ^J *"* WV V.^1 Q CS -< M VO CO VO -! CS to VO ON vO vO cs y Tj- T2 3 to cs cs ''t ON to M 00 co to O\ cs - . CS CO VO 3 W) OJ 00 n ~ s/ yX y a U5 y ^ CO O O O ^- to i-> M o 8 8 8 6 6 6 6 02 9 31 :8 O CO g a s I s *x S* tl It 1 <8-S> "3 g O oo O cs oo oo M VO CS rj- * * s : t s 3999' ^ ~ o o o o o = 1; VO CO ? M OOOOO t x ff a * 3 -a ~* "> *> N g n O ^,00 g _o oo r^ oo oo oo S W O O O O O wi vo O . g M VO 1+ % 2 o+ o o o 00 + M o ^o r** o to O ^ Tf co q 8 q q q q 666666 M 10 ON ou T O vO ** t*** "** rj- to r^ oo O . M vo co Q 3 S to cs to 00 Q to to M w to vo 999 666 cs cs cs to to * M Th ^ 10 Q O OO to ON to O O\ to ON CS vO to ^ M M cs cs to to q q q q q q 666666 vO O to M vo rh IH to O oo M 00 O> O ON q q q q q q 666666 oo vo co O oo (^ O -" - VO Tj- CM M 9 S 8 8 8 8 8 6666666 to vO OO M 11 i- 00 CS tO O O CS rh ON iO ON J O O ^ ^- rf O O O O O. *"* cs 6666666 3 rt O ^-^ fa .a & t J ^ .-S J ^ I 3 a ^ i H -I w ^ CS CO TJ- M?! OT 6 6 6 6 r TJ- o" o 5CS CS IO cs rt- ON ^ O O O O ^6666 <* o o _1_ CS CS tO ^999 6 6 6 6 .S q 8 8 666 cs O oo oo cs to O 5 j. ' oo ON O *~ gl - 5-^ 5g? *-P 5 04J o o o cs to cs g n, ri ^ S 2 1 r S -~ 9 9 666 cs to 00 IO to ON C + t| 5 5 8 o o o ~ O co u ON to cs : o N t>- to cs im'o + ^ *> " q q q 666 C ' 3i ^S o ^|a 9 9 g-g- 6666 Tt- to to t^ to vo vo cs to to cs 3 Sg o a Z 999- 6666 11 been shown, in previous papers of this series, to be connected with the formation of complex ions, double salts, or intermediate ions. Another indication of the presence of intermediate or complex ions is that the solubility product as calculated from the solubility measurements increases more rapidly than when such ions are absent. This is because the calculations of the ionization count a part of the material present as intermediate, as being in the form of simple ions, and since the concen- tration of the intermediate ion increases rapidly with the concentration, 0.04 o.o 0.0 0.2 1.6 2.0 0.4 0.6 o.8 i .o 1.2 1.4 Equivalents per liter of added salt. Fig. i. Solubility of calcium sulfate in solutions of other salts. Note that the solu- bility decrease when the concentration of the added salt is only o. i equiva- lents is very much less than corresponds to the solubility-product principle. At higher concentrations the curves take on the form of non-common ion curves. this leads to an apparent rapid increase of the solubility product. It has been shown in a former paper that when account is taken of the in- termediate ions in solutions of uni-bivalent salts, the solubility product as calculated becomes much more constant. Fig. 2 indicates that the solu- bility product of a bi-bivalent salt, calculated on the usual assumption that intermediate and complex ions are absent, increases with extreme rapidity as the concentration of the solution (the total ion concentra- tion) increases. Thus, when copper sulfate is the added salt, the solu- 12 bility product is increased to more than 3 times its smallest value before the total ion concentration has reached o . i N, so the apparent activity of the bivalent ions decreases very rapidly with increasing ion concentra- tion. It is, of course, possible that the whole of such a very rapid increase o.o 20 40 60 80 ioo 120 Total ion concentration (S*) in milli-equivalents. Fig. 2. The solubility product for uni-univalent, uni-bivalent, and bi-bivalent salts, calculated on the assumption that intermediate ions are absent. in the solubility product of salts of this class, cannot be explained by the assumption of the existence of complex ions. The solubility of the un-ionized part of the salt as calculated on the as- sumption that intermediate ions and other complexes are absent (Fig. 3) is much more constant than it was found to be for uni-uni- and uni-bi- 13 valent salts, except in the more concentrated solutions in which copper sulfate is the added salt. The change in the slope of these curves as com- pared with those for the uni-univalent salts, is in the same direction as that for uni-bivalent salts when the common bivalent ion is added, that is the change in slope is in the direction to be expected if intermediate ions are present. 0.4 i.o 1.2 2.0 1.4 1.6 Log. 1 total ion concentration Z*. Concentrations in milli-equivalents. Fig- 3- The concentration of the un-ionized part of uni-univalent (T1C1), uni-bivalent (Ba(IO,) 2 , Ba(BrO 3 ) 2 , Ag 2 SO 4f PbCl 2 ) and bi-bivalent (CaSO<) salts in their saturated solutions in the presence of other salts, calculated on the in- correct consumption that intermediate ions are absent. 1 The curves for barium iodate should be ten squares lower down and five squares further to the left. Note how closely these curves parallel those for barium bromate in spite of their large displacement. 14 It is to be specially noted that most of the results described above were ob- tained in dilute solutions, that is below o.i N total ion concentration, and that therefore they are not to be considered from the standpoint of much of the work in the literature in regard to the formation of double or complex salts in concentrated solutions. The formation of these latter double and complex salts is highly specific, while that for which evidence is obtained in this paper will undoubtedly be found to be gen- eral, just as the similar behavior of uni-bivalent salts described in the first paper of this series, was later proved to be perfectly general. As has been suggested in the first part of this paper, a large part of this abnormal behavior of bi-bivalent salts would be only apparent if complex bivalent ions are formed. These would have the form /SO 4 ~ /Ca+ /Ca+ /Ca + Ca< SO/ SO/ SO/ VN/Trr + /Mg + /Cu + /SO 4 ~ /SO 4 ~ /SO 4 K so/ so/ Mg<( a/ cu<( X Mg + \Zu + X SO 4 - X SO 4 - X S0 4 ~ and would form salts of a ring structure: /SO 4 \ /SO 4 \ /SO 4 v /SO 4 K Ca<^ yCa Cu<^ yCa Q/ yCu Cu<^ etc. \crj / \ ' NQfl r \Qr v o