WALKER SOLUBILITY OF BI-BIVALENT SALTS ETC. 61 IX.-Solubility of Bi-bivalent Salts in Solutions Con-taining CI. Common I o n . By OSWALD J_I>IES JVSLKER. THE investigation of thi solubility of s d t s in dilute solutions of salts with common ions has been confined mainly to the following cases 1. Uni-univalent salt + univalent common ion. 2. Uiii-bivalent salt + univalent coininon ion. 3. Uni-bivalent salt + bivalent common ion. It was shown by Noyes and his co-workers ( J . ,.lmer. C'hem. Xoc., 1911 33 1643 1807) that in cases (1) and (2) the solubility decreases rapidly and the curve obtained by plotting solubility against con-centration of added salt is roughly of the form to be expected from the solubility product principle. I n case (3)) where a salt with a common bivalent ion is added the decrease in solubility is much less than what would be expected from that principle and if the saturating salt is sufficiently soluble the common ion may actually bring about an increase in the solubility.Fewer cases have been studied in which the saturating salt is bi-bivalent and such cases as have been examined ( e . g . Harkins and Paine J.Bmer. C'hem. SOC., 1919 41 1162) havc shown that here also the solubility decrease brought about by the common ion is less than what would be expected. More recently there has been a tendency to rejec 62 WALKER SOLUBILITY OF BI-BIVALENT SALTS the conductivity method of calculating ionic concentrations which was the method used in applying the solubility product principle, and the question of solubility effects has been approached from a different point of view based on thermodynamic considerations which involve the principles of the inter-ionic attraction theory.With a view to get further evidence concerning the solubility effects in the system bi-bivalent salt + bivalent common ion, the solubilities of several salts have been investigated. For this purpose the succinates and malonates of the alkaline-earth metals afford a suitable range of concentrations. The solubilities of the various salts considered expressed in gram-molecules per 1000 grams of water varied between 0.016 and 0.082 weight molar, whilst the total salt concentration did not exceed 0-1 weight molar, except in the case of calcium succinate as saturating salt with which a maximum of about 0.3 weight molar was reached.E x P E R I M E N T A L . The saturating salts were prepared from pure reagents by pre-cipitation thorough washing and drying a t the temperature requisite to give the anhydrous salt. Sodium and magnesium succinates were obtained by crystallisation from neutralised succinic acid solutions and were recrystallised several times. Analysis confirmed the purity of the salts thus obtained. The solubility determinations were carried out in 100 C.C. Jena conical flasks closed with rubber stoppers and provided with rubber caps. Excess of the saturating salt and a weighed quantity of the other salt were added to a known weight of water in the flask, and the mixture was rotated in a thermostat kept a t 25" 5 0.1" until equilibrium had been reached (about 30 hours).The solution, after standing in the thermostat for an hour was filtered upward by suction through a small filter paper into a weighed flask which was also in the thermostat. After weighing the solution was carefully washed out into a beaker and the solubility was obtained by determining gravimetrically the amount of the metallic radical of the saturating salt. Barium was estimated in most cases as sulphate but in presence of calcium Browning's method (Amer. J . Sci. 1892 [iii] 43 314) depending on the difference in solubility of the nitrates in amyl alcohol was employed. Calcium was pre-cipitated as oxalate and weighed as sulphate the precipitation in presence of magnesium being carried out twice. Strontium was precipitated as carbonate and weighed as sulphate.In the case of strontium malonate + strontium chloride the chloride in the solution was determined gravimetrically as silver chloride and the amount of strontium as malonate was determined by subtraction o I N SOLUTIONS CONTAINING A COMMON ION. 63 the strontium present as chloride from the total stront'ium. Inde-pendent solubility determinations gave results agreeing within 0.5% -The results are shown in Table I s being the solubility expressed in gram-molecules per 1000 grams of water corresponding to the weight-molar concentration c of added salt; so is the solubility 'rABLE I. S. C. S. c . Ba succ. + Na succ. 0.01307 0.00795 0.02523 0.01828 0.01154 0.01575 0.02349 0.03103 0.00987 0.03149 0*0301'3 0.06149 0.00913 0.04726 Sr mal.+ SrC1,. so -= 0.01570. so = c).03050. S . C. Ba succ. + Mg succ. so = 0.01570. 0.01307 0.00770 0.01294 0-01538 0.01 155 0.03074 0.01063 0*04620, 0.01024 0.06149 Sr succ. + Na succ. Ca succ. +- Na succ. Ea succ. f Ca SIICC. s, = 0.02013. so = 0.05252. so = 0.01570. 0.01740 0.00938 0.08013 0.00826 0.01383 0.00798 0.01535 0.01875 0.07103 0.05OG 0.01273 0.01597 0.01322 0.03751 0-0G-l-95 0.1014 0.01153 0.03193 0.01231 0.05382 0-061:38 0.1526 0.01143 0.07457 0.05759 0.2560 Calcium succinete + Magnesium succinate. so = 0.08252. s ............... 0.07769 0.07474 0.07340 0.07173 0.07087 c ............... 0.04121 0.06179 0.08230 0-1231 0-1631 of the saturating salt in pure water. The Solubility effects however, can be more easily compared by means of the ratios s/so and c/s0, which express respectively the concentrations of the saturating salt and of the added salt in terms of the solubility of the former in pure water.These ratios correspond to the terms " fractional solubility " and " fractional ooncentraticn " employed by Harkins ( J . Arner. Chem. SOC. 1911 33 1851). I n Figs. 1 and 2 the values of s/s are plotted against the values cf c/s0 for the additicn respec-tively of uni- bivalent and hi-bivalent salt. For comparison a typical curve for the system uni-univalent salt + univalent common ion (silver propionate 4- sodium propionate Arrhenius 2. phylsikal. Ghem. 1899 31 225) is also shown (dotted curve). The curves all lie considerably above the curve for the uni-univalent salt and for any one saturating salt the curve of Fig.2 lies above that of Fig. 1 . Moreover for one type of added salt, the curves all lie in the order of the solubility of the saturating salt in pure water the curve taking a higher position the greater the solubility; this order was found to hold by Harkins (loc. cit.) for. the salts investigated by him. The lowering effects of calcium and magnesium succinstes on thc solubility of barium succinate are almost equal the cremes on cur\-e 2 (Fig. 2 ) denoting additicii of calcium succinate 64 WALKER SOLUBILITY OF BI-BIVALENT SALTS Noyes ( J . Amer. Chem. Xoc. 1924 46 1080 1098) in his critical presentation of the interionic attraction theory of ionised solutes as put forward by Milner (Phil. Mag.1912 [vi] 23 551 ; 1913 25, 742) and by Debye and Hiickel (PhysikaE. Z. 1923 24 185) uses some of the existing data on the solubility of salts in salt solutions in order to test the validity of the theory. He finds that the solu-bility effects should be given by an equation which takes the follow-1.0 0.8 -5 0.6 04 0.2 FIG. 1. --_ -_ I CaSucc + N~,,SUCC 2 SrMd+SrCI, 3 Sr S~cc+N~~,Succ. 4 BaSucc+Na,Succ. I 1.0 2.0 3.0 6 4%. FIG. 2. I 1 i - '''\.\\\-)I +CaSutc.+ I Ci6ucc+Mgbcr. 2 BaSucc+MgSucc. Q 1 1.0 2.0 3.9 4.0 C/So. ing form for bi-bivalent saturating salts so s and c being the con-centration terms hitherto employed in this paper, where cc has the theoretical value of 0.357 for dilute solutions a t 25". CC'V~ denotes the summation of ion concentration (c') x square of valence of ion ( ~ 2 ) for all the ions present half this quantity representing the " ionic strength " as defined by Lewis and Randall ( J .Arner. Chem. Soc. 1921 43 1140). In Table I1 are shown the values of the coefficient for the two least soluble salts barium succinate and strontium succinate calculated from the solubility data in Table I. The values for the system calcium sulphate + magnesium sulphate calculated from the data quoted in Noyes's paper are also shown. The values in each column are arranged in order of increasing total salt concentration and it will be seen that in this order cc in most cases decreases reaching a value of about 0.15 at ionic strengths between 0.2 and 0.45 molar. The data for the case of calcium succinate as saturating salt a salt about four times as soluble as any of the saturating salts in Table 11 give even smaller values of a about 0.09 in the most concentrated solutions.Whils I N SOLUTIONS CONTAINING A COMMON ION. tj 5 “ Ionic strength. 0.08 to 0.20 0.20 to 0.45 3 2 C ’ Y Z . Ba succ. + ” Mg succ. s,=O.O1570. ( 0.181 0.177 0-153 0.147 TABLE I1 Values of a . Ba succ. + Brz suec. -1- Sr succ. + Ca succ. Na succ. Na succ. ~,=0*01570. so=0.c)lS7@. ~ ~ - 0 * 0 2 0 1 3 . 0.173 0.105 0.1% 0.172 0.171 0.166 0.164 0.16s 0-158 0.1G5 0-152 0.145 CnS04 + 31gso4. S = 0.015 17. 0.201 0.19G 0.181 0.169 0.150 the values of cc in the first three rows of the table are constant to within about loyo they are still somewhat smaller thzn the value 0.238 which Noyes finds to satisfy the experimental facts up to ionic strengths of 0.1,12’ in the case of the three salts of higher valence type quoted by him.The differences in the values of u from one another are greater than those which could be due to experimental error in the value of the solubility. An error in the latter as great as I:( (the actual maximum error was about 0.5:;) makes a differ-ence of about 596 in the values of a. Although u increases with decreasing salt concentration extra-polation from the graph obtained by plotting conceiiiration against the corresponding values of ct does not show any tendency for 2 to reach a value as high as 0.357 even a t very small concentrations. In order therefore to obtain data a t much smaller eoncentrations than those employed so far in this paper some experiments were carried out on the solubility of barium and magnesium osalates in presence of barium chloride and magnesium sulphate respectively.It was hoped that the results of these experiments would give an indication of the value of the “ constnnt ” O( in Noyes’s equation a t these much smaller concentrations (about 0.003 to 0.0006 weight-molar) for which the equation ought to hold more closely than in the cases dready dealt with. The solubiiity was determined in each case by titration of the aniount of oxalate present in about 200 g. of solution with carefully standardised permanganate solution of such a strength that from 30-60 C.C. were used up in t he titration.From these results no ccnsistent \-clue for u was obtained in thc case of barium oxalate. At small concentrations corresponding to the solubility of barium oxalate a small error in the experiment-ally obtained value of the solubility becomes highly magnified in t lie cnlculat8ion of a which may consequently vary enormously. With the more soluble magnesium salt the influence of an experi-mental error is not so marked an error of 1-07; in the solubility causing an error of about 57; in the value of U. The results obtained with rnagr,esium oxalate (.co = 0.00307) in presence of magnesium VOL. (‘XXVII. 66 AESOHLIMANN LEES MCCLELAND AND N I C m : sulphate are as follow the values of oc being calculated from Noyes's equation : 8. C. a. 0,00235 0.00272 0.285 0*00215 0.00491 0.320 These values of u are much nearer the theoretical value of 0.357, and the agreement between the two values is fairly good as the experimental error here corresponded with an error of about 5% in the value of u.Xummary . (1) The solubility has been determined at 25" of some bi-bivalent salts vix. succinates and malonates of calcium strontium and barium in pure water and in solutions containing varying concen-trations of a common ion. Curves are given which show that the solubility is in every case greater than would be predicted by the solubility product rule and that the divergence is more marked the greater the solubility of the salt considered and greater for an added bi-bivalent salt than for an added uni-bivalent salt.(2) The solubility data have been examined from the point of view of the interionic attraction theory of ionised solutes as developed by Debye and Hiickel and especially from the solubility point of view by Noyes. The results obtained in this paper are in good qualitative agreement with this theory and in the case of the very sparingly soluble magnesium oxalate a fair quantitative agreement is obtained. In conclusion I wish to thank Professor Sir James Walker CHEMISTRY DEPARTMENT, for the interest taken in the progress of this work. EDINBURGH UNIVERSITY. [Received September 26th 1924. WALKER SOLUBILITY OF BI-BIVALENT SALTS ETC. 61 IX.-Solubility of Bi-bivalent Salts in Solutions Con-taining CI. Common I o n . By OSWALD J_I>IES JVSLKER. THE investigation of thi solubility of s d t s in dilute solutions of salts with common ions has been confined mainly to the following cases 1.Uni-univalent salt + univalent common ion. 2. Uiii-bivalent salt + univalent coininon ion. 3. Uni-bivalent salt + bivalent common ion. It was shown by Noyes and his co-workers ( J . ,.lmer. C'hem. Xoc., 1911 33 1643 1807) that in cases (1) and (2) the solubility decreases rapidly and the curve obtained by plotting solubility against con-centration of added salt is roughly of the form to be expected from the solubility product principle. I n case (3)) where a salt with a common bivalent ion is added the decrease in solubility is much less than what would be expected from that principle and if the saturating salt is sufficiently soluble the common ion may actually bring about an increase in the solubility.Fewer cases have been studied in which the saturating salt is bi-bivalent and such cases as have been examined ( e . g . Harkins and Paine J.Bmer. C'hem. SOC., 1919 41 1162) havc shown that here also the solubility decrease brought about by the common ion is less than what would be expected. More recently there has been a tendency to rejec 62 WALKER SOLUBILITY OF BI-BIVALENT SALTS the conductivity method of calculating ionic concentrations which was the method used in applying the solubility product principle, and the question of solubility effects has been approached from a different point of view based on thermodynamic considerations which involve the principles of the inter-ionic attraction theory.With a view to get further evidence concerning the solubility effects in the system bi-bivalent salt + bivalent common ion, the solubilities of several salts have been investigated. For this purpose the succinates and malonates of the alkaline-earth metals afford a suitable range of concentrations. The solubilities of the various salts considered expressed in gram-molecules per 1000 grams of water varied between 0.016 and 0.082 weight molar, whilst the total salt concentration did not exceed 0-1 weight molar, except in the case of calcium succinate as saturating salt with which a maximum of about 0.3 weight molar was reached. E x P E R I M E N T A L . The saturating salts were prepared from pure reagents by pre-cipitation thorough washing and drying a t the temperature requisite to give the anhydrous salt.Sodium and magnesium succinates were obtained by crystallisation from neutralised succinic acid solutions and were recrystallised several times. Analysis confirmed the purity of the salts thus obtained. The solubility determinations were carried out in 100 C.C. Jena conical flasks closed with rubber stoppers and provided with rubber caps. Excess of the saturating salt and a weighed quantity of the other salt were added to a known weight of water in the flask, and the mixture was rotated in a thermostat kept a t 25" 5 0.1" until equilibrium had been reached (about 30 hours). The solution, after standing in the thermostat for an hour was filtered upward by suction through a small filter paper into a weighed flask which was also in the thermostat.After weighing the solution was carefully washed out into a beaker and the solubility was obtained by determining gravimetrically the amount of the metallic radical of the saturating salt. Barium was estimated in most cases as sulphate but in presence of calcium Browning's method (Amer. J . Sci. 1892 [iii] 43 314) depending on the difference in solubility of the nitrates in amyl alcohol was employed. Calcium was pre-cipitated as oxalate and weighed as sulphate the precipitation in presence of magnesium being carried out twice. Strontium was precipitated as carbonate and weighed as sulphate. In the case of strontium malonate + strontium chloride the chloride in the solution was determined gravimetrically as silver chloride and the amount of strontium as malonate was determined by subtraction o I N SOLUTIONS CONTAINING A COMMON ION.63 the strontium present as chloride from the total stront'ium. Inde-pendent solubility determinations gave results agreeing within 0.5% -The results are shown in Table I s being the solubility expressed in gram-molecules per 1000 grams of water corresponding to the weight-molar concentration c of added salt; so is the solubility 'rABLE I. S. C. S. c . Ba succ. + Na succ. 0.01307 0.00795 0.02523 0.01828 0.01154 0.01575 0.02349 0.03103 0.00987 0.03149 0*0301'3 0.06149 0.00913 0.04726 Sr mal. + SrC1,. so -= 0.01570. so = c).03050. S . C. Ba succ. + Mg succ. so = 0.01570. 0.01307 0.00770 0.01294 0-01538 0.01 155 0.03074 0.01063 0*04620, 0.01024 0.06149 Sr succ.+ Na succ. Ca succ. +- Na succ. Ea succ. f Ca SIICC. s, = 0.02013. so = 0.05252. so = 0.01570. 0.01740 0.00938 0.08013 0.00826 0.01383 0.00798 0.01535 0.01875 0.07103 0.05OG 0.01273 0.01597 0.01322 0.03751 0-0G-l-95 0.1014 0.01153 0.03193 0.01231 0.05382 0-061:38 0.1526 0.01143 0.07457 0.05759 0.2560 Calcium succinete + Magnesium succinate. so = 0.08252. s ............... 0.07769 0.07474 0.07340 0.07173 0.07087 c ............... 0.04121 0.06179 0.08230 0-1231 0-1631 of the saturating salt in pure water. The Solubility effects however, can be more easily compared by means of the ratios s/so and c/s0, which express respectively the concentrations of the saturating salt and of the added salt in terms of the solubility of the former in pure water.These ratios correspond to the terms " fractional solubility " and " fractional ooncentraticn " employed by Harkins ( J . Arner. Chem. SOC. 1911 33 1851). I n Figs. 1 and 2 the values of s/s are plotted against the values cf c/s0 for the additicn respec-tively of uni- bivalent and hi-bivalent salt. For comparison a typical curve for the system uni-univalent salt + univalent common ion (silver propionate 4- sodium propionate Arrhenius 2. phylsikal. Ghem. 1899 31 225) is also shown (dotted curve). The curves all lie considerably above the curve for the uni-univalent salt and for any one saturating salt the curve of Fig. 2 lies above that of Fig. 1 . Moreover for one type of added salt, the curves all lie in the order of the solubility of the saturating salt in pure water the curve taking a higher position the greater the solubility; this order was found to hold by Harkins (loc.cit.) for. the salts investigated by him. The lowering effects of calcium and magnesium succinstes on thc solubility of barium succinate are almost equal the cremes on cur\-e 2 (Fig. 2 ) denoting additicii of calcium succinate 64 WALKER SOLUBILITY OF BI-BIVALENT SALTS Noyes ( J . Amer. Chem. Xoc. 1924 46 1080 1098) in his critical presentation of the interionic attraction theory of ionised solutes as put forward by Milner (Phil. Mag. 1912 [vi] 23 551 ; 1913 25, 742) and by Debye and Hiickel (PhysikaE. Z. 1923 24 185) uses some of the existing data on the solubility of salts in salt solutions in order to test the validity of the theory.He finds that the solu-bility effects should be given by an equation which takes the follow-1.0 0.8 -5 0.6 04 0.2 FIG. 1. --_ -_ I CaSucc + N~,,SUCC 2 SrMd+SrCI, 3 Sr S~cc+N~~,Succ. 4 BaSucc+Na,Succ. I 1.0 2.0 3.0 6 4%. FIG. 2. I 1 i - '''\.\\\-)I +CaSutc.+ I Ci6ucc+Mgbcr. 2 BaSucc+MgSucc. Q 1 1.0 2.0 3.9 4.0 C/So. ing form for bi-bivalent saturating salts so s and c being the con-centration terms hitherto employed in this paper, where cc has the theoretical value of 0.357 for dilute solutions a t 25". CC'V~ denotes the summation of ion concentration (c') x square of valence of ion ( ~ 2 ) for all the ions present half this quantity representing the " ionic strength " as defined by Lewis and Randall ( J .Arner. Chem. Soc. 1921 43 1140). In Table I1 are shown the values of the coefficient for the two least soluble salts barium succinate and strontium succinate calculated from the solubility data in Table I. The values for the system calcium sulphate + magnesium sulphate calculated from the data quoted in Noyes's paper are also shown. The values in each column are arranged in order of increasing total salt concentration and it will be seen that in this order cc in most cases decreases reaching a value of about 0.15 at ionic strengths between 0.2 and 0.45 molar. The data for the case of calcium succinate as saturating salt a salt about four times as soluble as any of the saturating salts in Table 11 give even smaller values of a about 0.09 in the most concentrated solutions.Whils I N SOLUTIONS CONTAINING A COMMON ION. tj 5 “ Ionic strength. 0.08 to 0.20 0.20 to 0.45 3 2 C ’ Y Z . Ba succ. + ” Mg succ. s,=O.O1570. ( 0.181 0.177 0-153 0.147 TABLE I1 Values of a . Ba succ. + Brz suec. -1- Sr succ. + Ca succ. Na succ. Na succ. ~,=0*01570. so=0.c)lS7@. ~ ~ - 0 * 0 2 0 1 3 . 0.173 0.105 0.1% 0.172 0.171 0.166 0.164 0.16s 0-158 0.1G5 0-152 0.145 CnS04 + 31gso4. S = 0.015 17. 0.201 0.19G 0.181 0.169 0.150 the values of cc in the first three rows of the table are constant to within about loyo they are still somewhat smaller thzn the value 0.238 which Noyes finds to satisfy the experimental facts up to ionic strengths of 0.1,12’ in the case of the three salts of higher valence type quoted by him.The differences in the values of u from one another are greater than those which could be due to experimental error in the value of the solubility. An error in the latter as great as I:( (the actual maximum error was about 0.5:;) makes a differ-ence of about 596 in the values of a. Although u increases with decreasing salt concentration extra-polation from the graph obtained by plotting conceiiiration against the corresponding values of ct does not show any tendency for 2 to reach a value as high as 0.357 even a t very small concentrations. In order therefore to obtain data a t much smaller eoncentrations than those employed so far in this paper some experiments were carried out on the solubility of barium and magnesium osalates in presence of barium chloride and magnesium sulphate respectively.It was hoped that the results of these experiments would give an indication of the value of the “ constnnt ” O( in Noyes’s equation a t these much smaller concentrations (about 0.003 to 0.0006 weight-molar) for which the equation ought to hold more closely than in the cases dready dealt with. The solubiiity was determined in each case by titration of the aniount of oxalate present in about 200 g. of solution with carefully standardised permanganate solution of such a strength that from 30-60 C.C. were used up in t he titration. From these results no ccnsistent \-clue for u was obtained in thc case of barium oxalate. At small concentrations corresponding to the solubility of barium oxalate a small error in the experiment-ally obtained value of the solubility becomes highly magnified in t lie cnlculat8ion of a which may consequently vary enormously.With the more soluble magnesium salt the influence of an experi-mental error is not so marked an error of 1-07; in the solubility causing an error of about 57; in the value of U. The results obtained with rnagr,esium oxalate (.co = 0.00307) in presence of magnesium VOL. (‘XXVII. 66 AESOHLIMANN LEES MCCLELAND AND N I C m : sulphate are as follow the values of oc being calculated from Noyes's equation : 8. C. a. 0,00235 0.00272 0.285 0*00215 0.00491 0.320 These values of u are much nearer the theoretical value of 0.357, and the agreement between the two values is fairly good as the experimental error here corresponded with an error of about 5% in the value of u. Xummary . (1) The solubility has been determined at 25" of some bi-bivalent salts vix. succinates and malonates of calcium strontium and barium in pure water and in solutions containing varying concen-trations of a common ion. Curves are given which show that the solubility is in every case greater than would be predicted by the solubility product rule and that the divergence is more marked the greater the solubility of the salt considered and greater for an added bi-bivalent salt than for an added uni-bivalent salt. (2) The solubility data have been examined from the point of view of the interionic attraction theory of ionised solutes as developed by Debye and Hiickel and especially from the solubility point of view by Noyes. The results obtained in this paper are in good qualitative agreement with this theory and in the case of the very sparingly soluble magnesium oxalate a fair quantitative agreement is obtained. In conclusion I wish to thank Professor Sir James Walker CHEMISTRY DEPARTMENT, for the interest taken in the progress of this work. EDINBURGH UNIVERSITY. [Received September 26th 1924.