T H E SOLUBILITIES AND ACTIVITY COEFFICIENTS O F LANTHANUM IODATE I N CONCENTRATED SALT SOLUTIONS AT 25°C. J. N. PEARCE
AND
W. C. OELKE
Division of Physical Chemistry, The State University of Iowa, Iowa City, Iowa Received June 6 , 1937
The effect of one salt, in solution, upon the solubility of another salt has long been an accepted method for the study of the properties of solutions, and for the determination of activity coefficients. This field has been well covered in the case of uni-univalent salts a t low concentrations, but little work has been done with saturating salts having high valence ions. Almost no work has been done in concentrated solutions. W. D. Harkins and W. T. Pearce (6) have determined the solubility of lanthanum iodate in water and in dilute solutions of several salts. They have interpreted their data on the basis of the stepwise partial dissociation of lanthanum iodate. La Mer and Goldman ( 7 ) have studied the solubility of lanthanum iodate in various aqueous salt solutions by the leaching method. They give two values for the solubility of the iodate in water, neither of which agrees with that of Harkins and Pearce. Their work was done in dilute salt solution, except in the case of potassium chloride where a 2.0 molar concentration was reached. Interpreting their results with reference to the Debye-Huckel limiting law, they find increasing negative deviations with increasing concentration of lanthanum nitrate and potassium chloride. At low concentrations the curves for these salts fuse into that of the limiting law, while with potassium sulfate solutions as solvent, the curves show radical positive deviations with no sign of fusion. This phenomenon was previously observed by Bronsted and Peterson (2), and has since been called the “unsymmetrical valence type effect.” La Mer and Mason (10) find similar positive deviations using cobaltammines as saturating salts, while Peterson and Meyers (12), with copper iodate, find positive deviations with potassium sulfate solvent solutions but not with magnesium sulfate. The aim of the present work has been t o redetermine the solubility of lanthanum iodate in pure water, and to extend the study of the solubility of lanthanum iodate in solutions of typical salts up to concentrations approaching saturation. 95
96
J . K. P E A R C E AND W. C. OELKE MATERIALS
The lanthanum iodate 'i\ as prepared by precipitation, following the method of La hler and Goldinan ( 7 ) . The prepared salt uas not allowed to dry, but was kept under water until used. Some of the lanthanum iodate used with potassium chloride solutions was subsequently examined under a micrometer microscope. The particles were irregular in shape and microscopically they showed no definite crystalline form. The x-ray pattern, however, showed crystalline structure The mean dimensions of the smallest particles were 0.0098 mm. x 0.0073 mm., the largest particles being five to eight times this large. The salts used in preparing the solvent solutions mere recrystallized at least twice, the last time from conductivity water. Sodium oxalate from the Bureau of Standards was used as the primary standard to which all analytical data were referred. METHOD
The work of La -Mer and Goldman in dilute solutions was done by the leaching method originated by Bronsted and La Mer (1). An attempt was made to use this method for the determination of solubilities in concentrated solutions, but it seemed impossible to obtain consistent results in this case. Accordingly, this method was abandoned and a rotating shaker was used. In determining solubilities with this apparatus, a generous portion of the lanthanum iodate paste was washed several times with portions of the solvent solution and finally transferred to duplicate oil-sample bottles Tyith the bulk of the solution. The bottles were then clamped to the shaker and rotation started. After a minimum of two weeks' rotation at 25°C. the bottles were removed from the shaker and suspended near the surface of the water in the constant-temperature bath. The suspension waq :Jlowed to settle overnight and the clear solution siphoned into simila. '-rrttles also held in the bath. After a t least three hours more of settling, the supernatant liquid was again transferred, this time to two dry 2SO-nil. flasks. Completeness of settling was checked on each solution by means of the Tyndall effect from the beam of a small arc lamp If more than a very slight cone was visible, the solutions were allowed to settle until they were optically clear. The analyses of the saturated solutions for iodate ion were made in triplicate, by titration with standard sodium thiosulfate solution of the iodine liberated according to the reaction : 103.-
-+ 51- + 6H30+ S 312 -+ 9Hz0
In the analysis, the method of La Mer and Goldman ( 7 ) was substantially followed. The best of modern analytical technique was observed
GOLUBILITT O F LANTHAKUM IODATE
97
at every step. Carefully calibrated pipets and Normax volume burets nere used. Since in the late afternoon the blue color of the sky interfered with correct determination of the starch-iodine end point, all titrations were carried out under artificial light. The light, which struck the solutions from the top and side, was furnished by a 40-watt. frosted bulb, backed by a reflector and covered by a ground glass. By this means it was possible to maintain a precision of two parts per thousand or better in all titrations. APPARATUS
The rotating shaker, mentioned above, consisted of a 12-inch brass disc fixed to a brass shaft which ran in brass bearings suspended from an angle iron frame. On each side of the disc were eight hinged bands by which sixteen 200-ml. oil-sample bottles could be clamped to the disc. The bottles were arranged with their necks toward the common center. Owing to the slight taper of the bottles, the squeezing effect of the bands tended to force the stoppers against a concentric brass ring which prevented their leaking. The u hole assembly was submerged in a specially constructed water bath. This bath was thermostated to 25°C. & 0.01" by means of a large mercury regulator, supersensitive thermionic relay, and electric heater. The shaker was rotated a t 35 R.P.M. by means of a rubber and fabric vee belt running from a countershaft above the water to a large pulley on the shaker shaft. The entire shaker mechanism was hinged so that it could be swiing out of the bath for inspection and changing bottles. THEORY
The phenomenon of solubility may be approached from either of two standpoints. The first is the kinetic viewpoint, from which one strives to explain the observed effects from the individual behavior of the ions and molecules. The second is the tlxrniodynarnic approach which systematizes the field. The discovery by means of x-rays of the ionic structure of crystals has necessitated a rearrangement of the kinetic picture of solubility. A crystal of a salt, such as lanthanum iodate, must be thought of as a space lattice of lanthanum and iodate ions. The pattern of ions in this space lattice has not been worked out to date', yet it must be such that the electrical attractions between the oppositely charged ions are satisfied. When such a crystal is placed in a polar solvent, as water, water dipoles are attracted 1 Dr. E. S. Gantz of this laboratory has kindly made for the author a n x-ray powder diffraction picture of the lanthanum iodate used. This analysis indicates that lanthanum iodate crystals have the ionic type of lattice.
98
J. 3 . PEBRCE AND W. C. OELKE
by the unbalanced electrical fields at the crystal boundaries. This orientation of water dipoles around the crystal has a tendency to weaken the attractive forces holding the ions of the crystal together. The result is that the kinetic motion of some of the surface ions is sufficieiit to free them from the attraction of their neighbors and they escape into the body of the liquid. Once the ions have escaped from the crystal, water dipoles will orient themselves completely around the ions. The external fields of these ions are thus largely satisfied by this water sheath. G. IT, Stewart (14) contends that sufficient attractive forces still exist between dissolved ions to give a “structure” to the solution. This “structure” may be considered as a mobile, videly spaced, ion lattice similar perhaps to that in the crystal itself. The process of solution will continue, following the above mechanism, until the condition which we know as saturation has been reached. In this state a condition of equilibrium exists between the solid and the dissolved solute. Evidently the forces causing the escape of ions from the crystal have been balanced by attractive forces between the ions working in the other direction. EFFECT OF SALTS
The macroscopic &pet of salts upon the solubility of a substance, as experimentally observed, is well known. The presence of salts with a common ion tends to decrease the solubility of a salt in water solution. When no common ion is present, an increase in solubility of the saturating salt is observed. The actual mechanism behind the phenomenon, however, can only be postulated. ilccording t o Butler (3), the ions of salts mutually affect each other in t v o ways: (1) directly, owing to the forces between their electrical charges, whereby they attract ions of opposite charge and repel ions of like charge; (2) indirectly, through thc effect of their electrical fields upon the molecules of the solvent. A suitable theory of solubility must take both of these effects into consideration. The latter effect, Le., the orientation of uater about the salt ions in solution, has already been discussed. I t would lower the mole fraction of free solvent water in the sdution, and hence have a depressing effect upon the solubility. The increase in solubility, observed in the present case, must obviously be due to the first of these forces mentioned. I n order t o account for this “salting-in” effect, let us visualize conditions in a potassium chloride solution saturated with the salt, lanthanum iodate. If a e consider both salts to be completely ionized, the following species will be present: LaL++,K+, H 3 0 ~IO3-, , C1-, OH-, HzO. According to Debye and Huckel (4), a given ion will, a t any time, be surrounded by a n ionic atmosphere in IT hich ions of opposite charge predominate. Thus, a
99
SOLCBILITT OF LANTHAKUM IODATE
lanthanum ion will be surrounded by an atmosphere in which iodate, hydroxide, and chloride ions predominate, while an iodate ion will be largely surrounded by potassium, oxonium, and lanthanum ions. I n order for a lanthanum iodate crystal to grow, lanthanum and iodate ions must be able to settle out on the crystal lattice. If the ionic atmosphere around the lanthanum ions is composed largely of iodate ions, the chance of lanthanum and iodate ions settling out upon the crystal lattice of some adjacent lanthanum iodate solid will be comparatively great. Equilibrium with the solution tendency of the crystal will obtain a t a low concentration, and we say that the salt has a low solubility. On the other hand, if the residual force fields about the chloride ions are greater than those around the iodate ions, the chloride ions will predominate in the ionic atmosphere of the lanthanum ions. The result of this nil1 be that lanthanum and iodate ions will have less opportunity to settle together upon the solid lattice. Thc equilibrium will thus be displaced, by the presence of chloride ions, in the direction of increased solubility. If some other negative ions with greater residual force fields than those of the chloride ions are placed in the solution, they will usurp the place of the iodate ions to a still greater extent. Thus, with sulfate ions present, a still greater increase in the solubility of the lanthanum iodate should be observed. There is, of course, the possibility of lanthanum and chloride ions or lanthanum and sulfate ions forming lattices of their own under these conditions. This does not take place, however, because the tendency toward solubility is too great, owing in part to the fact that these same chloride and sulfate ions, with their large residual force fields, are too highly hydrated. Glasstone, Dimond, and Jones (5) give the following relative hydration numbers for negative ions on the basis of the iodide ion as zero: ION
YDBATIOB
NUMBER
ION
--
Fe (CN ) 6- - - , . . . . . . . . . . . . . . . . . C l O I -. . . . . . . . . . . . . . . . . . . . . . . . . SOa- - . . . . . . . . . . . . . . . . . . . . . . . . . . Fe (CN),- - - . . . . . . . . . . . . . . . . . . . F- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CrOd--. ........................
75 31 26 23
17 14
1 HYDRATION
, NUMBER
i
CnHaOz-. . . . . . . . . . . . . . . . . . . .
c1-. . . . . . . . . . . . . . . . . . . . . . . . . .
CIOa-. . . . . . . . . . . . . . . . . . . . . . . . Br-. . . . . . . . . . . . . . . . . . . . . . . . . . Nos-. . . . . . . . . . . . . . . . . . . . . . . . / I-. . . . . . . . . . . . . . . . . . . . . . . . . . . I
13 10 9 5
2 0
The values were obtained from a study of the salting-out effect. They consider these values a measure of the strength of the electrostatic fields surrounding the ions. Randall and Faily (13) arrange the negative ions in order of decreasing salting-out effect thus: OH-> SO,--> COS--> C103-> BrOS-> C1-> Ac-> IOa-> Br-> I-. Although the iodate ion
100
J. N. PEARCE AND W. C. O E L K E
is not mentioned in Glasstone's table, it will probably have no greater value than that of the chlorate ion. I t is to be observed in both of these series that the order is SO*--> C1-> IOa-. It will be shown later that this fact, together with the theory proposed above, easily explains the solubility behavior of these solutions. There is no doubt a similar effect, with reference t o the anion of the saturating salt. Experimental evidence, however, points to the fact that in the case of lanthanum iodate, with a high valence cation, the solubility behavior is principally dependent upon the high valence ion. Thus, with a uni-trivalent saturating salt, sulfate solvent salts have a normal eflect (10). TABLE 1 The solubilities and activity coeficients of lanthanum iodate in aqueous potassium chloride solutions
-
log S Sa
I
10 0953
0.0010~0.000684 0.005 0.000737 0,010 0. ti00786 0.050 0.001014 0.100 10.001195 0.500 '0.001919 1.000 0 . 002452 2.000 I 0.003167 3.500 , 0,003898
'
1
0 8030 0.09555' 0.8025
0.0000( 0.000663-
1 000001 0 001019 1 00243 0.001202 1 020901 0 001952 1 042771 0 002531
1
0 056114 0.107212 0 511712l 1 015186
0 23688 0 32743 0 71533 1 00757
3,01347 1.04555 1.07402 I . 18508 I . 25675 1.46744 I . 58021 1.70437 3.81336
0.109021 0.7780 0.14110 0.7226 0.16957' 0 6767 0 280631 0.5216 0 35230 0.4443 0.562991 0 2735 0 675761 0.2110 0 79992 0 1585 0 908911 0.1233 ~
Note: Each of the values given above is the mean of the results from a t least two experiments. DISCCSSION OF DATA
In the present research, the work of La Mer and Goldman (7) on the solubility of lanthanum iodate in potassium chloride and potassium sulfate solutions has been repeated on a molal basis, and carried into a region of higher eonccntrations In addition, solubility data have been obtained in the presence of the bi-univalent and bi-bivalent salt types. The solvent salt solutions were made upon a molal basis. The solubilities were first determined on a molar basis, the densities were determined, and the molal solubilities then calculated from these data. Tables 1, 2, 3, and 4 give the solubilities and activity coefficients of lanthanum iodate in potassium chloride, potassium sulfate, magnesium
101
SOLUBILITP O F LAIJTHAKUM IODATE
chloride, and magnesium sulfate salt solutions, respectively. The solubility of the salt in conductivity water is also given. It is believed that the column headings are self-explanatory. TABLE 2 The solubilities and activitu coeficients of lanthanum iodate in aqueous potassium sulfate solutions
- /___I- -
ANALYSIS)
SALT
'*Ar'L'j
moles per liter
O.OOOO( 0.0006634 0.99749 0.0010;0.000824 0.09790 0.005 0.001215 0.99847 0.010 0.001488 0.99952 0.050 0.002568 1,00554
0.09421 0.26300 0.35096 0.58873
0.0955510.8025 0.18976;0.6460 0.3585510 4380 0.44651,0 3577 0.6842810.2069
Piote: Each of the values given above is the mean of the results from at least two experiments.
TABLE 3 The solubilities and activity coegicients o,f lanthanum iodate i n aqueous inagnesium chloride solutions
-________ moles per ~
liter
1 i
mole3 per 1 i I
0 0953 1 0 8030 0 095551 0 8025
0 007226 0 08503 0 02478 0 019919 0 14113 0 09072 0 0354661 0 188331 0 13634 0 157866 0 39732 0 29466 0 309648 0 55645 0 38338 1 516902 1 2316 0 62669 3 021540 1 7382 0 73200 6 026478 2.4549 0 82171 9.0299701 3.0050 0.87550
0 1203310 7580 0 18627)0 6512 0 2318g10 5863 0 39021~0 4072 0 47893 0 3319 0 72224 0 1896 0 82755'0 1487 0 91726l 0 1210 0.97105 0.1069
0.0000~0.00066341 0.99749 !
i
0 0010 0 005 0 010 0 050 0 100 0 500 1 000 2 000 3 000
1
0 000702 0 000817 0 000908 0 001306 0 001601 0 002782 0 003508 0 004209 0 004639
I
0.99757 0.99798 0.99841 1.00180 1,00589 1.03666 1 ,07255 1.13805 1.19716
0.000704 0.000820 0.000911 0.001311 0.001608 0.002ai7 0.003590 0.004413 0.0049951
!
'I
~
S o t e : Each of the values given above is the mean of the results from a t least two experiments
In figure 1 the molal solubilities of lanthanum iodate in each of the four solvents are plotted against the cube root of the molality of solvent salt. The cube root plot was resorted to in order that the points representing low concentrations would be spread more evenly upon the curve. It is THE JOURNAL OF PHYSICAL CAEMISTRY, VOL. 42, NO. 1
102
J. N. PEARCE AND W. C. OELKE
believed that the inflection points observed at high concentrations in the sulfate curves have no especial significance and are occasioned only by the TABLE 4 The solubilities and activity coeyicients of lanthanum iodate i n aqueous magnesium
0.001213 0.001452 0,002390 0,003028 0.005879 0.008227
,
1 '
0.0272781 0.048712' 0.214310 0.418168 2 035274 4:049362
0.16497 0.22071 0,46293 0.64665 1.4266 2.0123
0.33899 0.55540 0.68813 0.94627 1.09222 1.16635
0.43454 0.3677 0.650951 0.2234 0 76368 0.1763 1.04182/ 0.0908 1.18777' 0.0649 1.26190 0 0547
given above is the mean of the results from a t least
FIG. 1. Plot of molal solubilities of lanthanum iodate in salt solutions against the cube root of the molality of the solvent salt.
method of plotting. Simple solubility versus molality curves do not exhibit these inflection points.
SOLUBILITY OF LANTHANUM IODATE
103
The relative positions of the curves are important. It will be noticed that lanthanum iodate is least soluble in potassium chloride, slightly more soluble in magnesium chloride, much more soluble in magnesium sulfate, and most soluble in potassium sulfate solutions. The high solubility observed in the sulfate solutions is accounted for in the section on theory. The relative positions of the magnesium and potassium salt curves are more difficult to explain. In the section on theory it was postulated that the solubility behavior of salts depends upon the antagonistic action of two forces. One of these is the salting-out effect due to hydration. The other is the salting-in effect due to a shift in the composition of the ion atmosphere. Two chloride ions, as in magnesium chloride, should have a greater effect in increasing the solubility than the single chloride ion of potassium chloride. This is true in spite of evidence that the magnesium ion has a greater salting-out effect than the potassium ion2. The solubility should therefore be greater in magnesium chloride than in potassium chloride solutions, which agrees with experiment. If the salting-out tendency of one magnesium and two potassium ions were the same, we should expect lanthanum iodate to have the same solubility in the two chloride salts of these elements at the same chlorideion activity. It is actually found that the solubility in 1 M magnesium chloride is only 4 per cent less than that in 2 M potassium chloride, so that this expectation is almost realized. Conversely, where we have two salts which have the same anion, the salting-in effect upon a saturating salt with a high valence cation will be practically the same. The greater hydrating power and salting-out tendency of the magnesium ion over that of even two potassium ions reduces the solubility of the saturating salt in magnesium sulfate to below that in potassium sulfate solution. ACTIVITY COEFFICIENTS
Referring again to the tables, in the seventh columns are found the common logarithms of the solubility ratios. The solubility ratio is the molal solubility of the lanthanum iodate in the salt solutions divided by the molal solubility in pure water. It gives the relative increase in solubility produced by the addition of the solvent salt. I n the final two While authorities differ on the exact values of the effective radii of ions, all agree that the magnesium ion is much smaller than the potassium ion. Eldridge (The Physical Basis of Things, p. 247. AMcGraw-Hill Book Co., New York (1934)), states that if the ion is considered as a charged sphere, its potential is proportional to the charge, and inversely proportional to the radius. A small ion will therefore have a greater charge density than a large ion of the same valence. The charge density of an ion will determine its extent of hydration, and hence its salting-out effect. See also Clark: The Electronic Structure and Properties of Matter, John Wiley and Sons, New York (1934).
104
d. h-. PEARCE AND W. C. OELKE
columns are found the negati7 e logarithms of the mean molal activity coefficients, and the mean molal activity coefficients of the lanthanum and iodate ions as defined by Lewis and Randall (11). Experimental!y, the mean molal activity coefficient, y*, is obtained from thr relation.
s o _- -Y* S
7-n
from which, by taking the common logarithm of both sides, we obtain the exprrssion : -log,,
75 =
S
log,, - - log,, SO
The tonstarit value, -log y r n , is the logarithm of the mean activity coefficimt of the saturating salt ions in the pure solvent and can be obtained in several ways Two independent methods were used in the present tigation. The first method involved the plotting of the values of
As ‘“T low concentrations against 6on a large scale and extrapolating
log so
tho G U ~ T Sto Aero ionic strength. A series of extrapolations was carried out iviependently by six different persons on the potassium chloride and magnesium chloride curves. A mean of all readings on the two curves gave a ialue of -loglo yo = 0.0953. The second method involved the from the Debye-Huckel limiting law (4): calrulation of -loglo -log10 y*o =
1.814 X lo6
(DoT )3’2
ZlZZ
G
Here 2, and 22 are the valences (3, -1) of the ions of the saturating salt; Do = 78.77, Drude’s value of the dielectric constant of water a t T = 298.1”A. Calculated from this expression -log,, y i n = 0.0955, which is in excellent agreement with the experimerital value.
s
Figure 2 shows the values of log - plotted against the values of the SO
square root of the total ionic strength of the solution. If the linear relation above holds, this plot should give a straight line. The line corresponding to the limiting law given above is also shown. The curves for lanthanum iodate in potassium chloride and magnesium chloride solutions fusc into that of the limiting law a t low concentrations. Those for the salt in potassium sulfate and magnesium sulfate solutions show the characteristic “hump”, or positive deviation from the limiting law observed by other investigators (2, 7, 9, 10, 12). Instead of fusing into the limiting law line at low conrentrations, these c u r i e cross the line a t an ionic strength of about 0.0056 and finally join each othrr if continued a short distance heloir- the axis.
SOLTJBILITY O F LANTHANUM IODATE
105
The relative positions and shapes of the curves resulting from the present investigation are in agreement with the work of Bronsted and La Mer (I), La Mer, King, and Mason (9), and La Mer and Mason (lo), using cobaltammines as saturating salts, and with that of La Mer and Goldman ( 7 ) using lanthanum iodate. The results of Peterson and Meyers (12) are not entirely confirmed in that, while they find similar curves for copper iodate in potassium sulfate and potassium chloride solvents, their curves for this salt in both magnesium sulfate and magnesium chloride solutions fall below that for the salt in potassium chloride. This behavior of their magnesium sulfate curve cannot be explained on the
FIG.2. Values of log
S plotted against the values of the square root of the total
so
ionic strength of the solution.
basis of the theory postulated (see page 97), even though copper iodate has a lower valence cation and would hence be less affected by shifts in the ion atmosphere. Numerous attempts have been made to develop mathematical relations in harmony with the experimental behavior of saturating salts of unsymmetrical valence type in ion solvents. Up to the present time most of these have been only partially successful. It is probable that the Debye-Huckel extension of La Mer, Gronv-all, and Greiff (8) comes as near as any to a satisfactory solution. SUMMARY
The solubility behavior of lanthanum iodate a t 25°C. has been investigated in solutions of potassium chloride, potassium sulfate, magnesium
106:
J. N . PEARCE AND W. C. OELKE
chloride, and magnesium sulfate from 0.001 molal up to concentrations approaching saturation. The solubility of lanthanum iodate is increased by the presence of added salts. The effect of the different salt types is in the order KC1
