THE APPARENT VOLUMES OF SALTS I N SOLUTION 111. Saturated Solutions of Mixed Electrolytes BY ARTHUR F. SCOTT
Although there is a very extensive literature dealing with the effect of an added electrolyte on the properties of a saturated solution of a second electrolyte, very little attention has been paid to the apparent molal volumes of the salts in such solutions. Nicol,’ in one of his pioneer studies of solubility relationships examined this property of the solutes for a few salt pairs. His conclusions, expressed in our present terminology, were that in a majority of cases the apparent volumes of salts in a solution saturated with both of them, are the same as in saturated solutions of the individual salts. Very similar conclusions were reached by Masson2 from an investigation of the volume changes which occur on the addition of acid to saturated salt solutions. From his expression for the variation of the density of these solutions as functions of both acid and salt concentrations Masson found, assuming the density of water in solution to be that of the pure solvent, that over a wide range of concentration “the molecular volumes of the solutes are independyt of their concentration” and “that in this respect mixed electrolytes differ from single electrolytes, the molecular volumes of which vary considerably with concentration.” To extend the applicability of his density formula to high concentrations Masson was forced to assume that the molecular volume of water in solution was different from that of the pure liquid and, by taking a special value of the density of water for each solution, he was able to show that the calculated densities of the acid-salt solutions were in good agreement with the experimental data. Recently, in a series of papers Ingham3 has employed this expression of Masson to study the apparent hydration of ions. That the apparent molal volumes of solutes in saturated solutions of mixed electrolytes are in some instances independent of each other and of concentration was also pointed out in a previous article4and was offered as evidence in support of a tentative hypothesis of the significance of the apparent molal volumes of salts in solution. The object of the present study is to investigate this question of the apparent volumes of salts in solutions saturated with respect to one of them. While the scope of the study is somewhat restricted by the lack of sufficiently precise measurements, adequate data are available for a number of mixtures l Nicol: Phil. hlag. 17, 547 (1884). .4 more complete paper on the subject, which Nicol refers to later IPhil. Mag, 31, 369 ( 1 8 g 1 ) ]as forthcoming, cannot be found by the writer. J. I. 0. Masson: ,J. Chem. Soc., 99. 1 1 3 2 ( r a r ~ j . Ingham: J. Chem. Soc., 131, I ~ I ; , 2381 (1928); 132,2059 (1929); 133,542 (1930). Scott: J. Plivs. Chem., 35, 3379 (1931), At that time the writer did not know of the paper by Nicol a i d was not acquainted with the general conclusions of Wasson. In fact the validity of the rule for two cases to he discussed suhsequently was noted about two years ago in connection with R study of the apparent molal volume3 of salts in saturated solutions. \Scott and Durham: J. Phys. Chem., 34, 2035 (1930).]
APPARENT VOLCMES OF SALTS I N SOLCTIOS
1023
of uni-univalent salts, which are pretty much varied with regard to the type of ion involved. From the examination of these data it appears that the following conclusions are permissible: First, the apparent molal volumes of the electrolytes are not dependent’ directly on the amount of water present in the solution. And second, the results can be interpreted to mean that in every case the apparent molal volume of the saturating salt has the value which is characteristic of the saturated solution of the single salt; and that the apparent volume of +e added electrolyte either ( I ) is the same as when it is the saturating salt (rule of Nicol) or ( 2 ) has some different but definite value. Before undertaking to discuss the data from which the above conclusions are drawn it is desirable to review briefly the salient features of the aforementioned hypothesis because, in spite of its provisional nature, it not only affords a plausible basis for the understanding of the conclusions in question but also suggests other incidental lines of analysis for consideration. This hypothesis, it may be recalled, follows the customary procedure of other discussions of this subject in assuming that the apparent molal volume 4 of a solute in very dilute solutions is equal to the domains of the solute ions less the contraction in volume suffered by the solvent water molecules. I t differs, however, from other hypotheses in the fundamental assumption that only the solvent molecules directly adjacent to the ions undergo contraction. According to this viewpoint the increase in 4 with increasing concentration is to be attributed to the disturbance of the water molecules in contact with the ions. A possible cause’ of this disturbance may be realized in the association of the solute ions to form pairs or clusters with the consequent displacement of the solvent molecules. The importance of our basic assumption lies in the fact that the amount of contraction of the solvent (and thus the magnitude of 4) is made dependent not on the total quantity of solvent present’ in the solution but onrthe state or what, in accord with the mechanism suggested above, may be termed the “degree of association” of the solute ions. R e may now consider the bearing of this hypothesis on those properties of the 6 values in saturated solutions which we have already summarized. I n the first place we may note that the absence of a direct relationship between the $ values and the amount of solvent present is in harmony with our fundamental postulate. In the second place the fact that the 6 value of the saturating salt is constant may be taken to mean that when, at a given temperature, a solid salt is in equilibrium with a solution, its state or degree of association in the solution is definitely fixed and is not affected by the addition of a second electrolyte. Finally, since the 4 value of the added electrolyte in a given solution is constant, we must suppose that its state is the same, regardless of concentration. However, since the @ value of the added electroh similar suggestion has been put forward rerently by Butler and Lees. [Proc. Roy-. SOC.,131 A, 389 (1931):l Commenting on the fact that the molecular refractivity of lithium chloride is constant whereas its apparent volume increases with concentration, they write: “It may be suggested that a possible cause of the effect might be found in collisions between two ions, which become more frequent as the concentration is increased, and cause a certain amount of disorientation of the sheaths of solvent molecules carried hy them, and thus give rise to a n increase of volume.”
ARTHUR F. SCOTT
1024
lyte is found to be different in different solutions, we must conclude that its state is determined to some extent by the nature of the saturating salt. Having outlined briefly the viewpoint which we shall adopt we may now take up the detailed examination of the experimental data upon which our conclusions are based. The apparent molal volume .$ of a salt is defined by the expression : .$ = V-nvl
-23 -38 -37
-
X. 01 02 03 04 05 O b 01 08 0 9 I
I
I
I
I
I
I
01
02
03
X O + 0 5 O b 01 a8 09
FIG.I Plot showing the Variation with molecular composition of the solute in a saturated solution of (a) the Apparent Molal Volume and (b) the number of mols of solvent per mol of total solute.
where V is the volume of a solution containing one gram-mol of the salt; n is the number of mols of water present in the solution; and v1 is the volume of one mol of the pure solvent at the temperature of the solution. I n dealing with saturated solutions containing two electrolytes we shall find it convenient to employ the apparent molal volume of the mixed salts, which we shall designate as This quantity is calculated on the condition that the total number of mols of the two solutes in the saturated solution equals unity. The fraction of a mol of one solute in such a solution will be indicated by x. Thus, if there are x1 mols of the X1 solute and XZ mols of the Xz solute in the given solution, +s corresponds to a solution in which x1 xz = I . The quantities V, and n, will refer, of course, to saturated solutions which satisfy the same condition.
+
APPARENT VOLUMES O F SALTS I N SOLUTIOS
1025
The first type of mixtures which we shall consider will be that which a p pears to be the simplest. The necessary data for the two available examples are given in Table I. I n Fig. I b the n, values of the two salt pairs are plotted against the corresponding x values. This convenient method of portraying the isothermal relationships in a ternary system is essentially that proposed by Janecke.’ The minima of the drawn curves represent, of course, the eutectic points of the saturated solutions where both salts as solids are in equilibrium with the solution phase. Analogous to the above graph is Fig. Ia in which the values of the salt mixtures are plotted against the corresponding x quantities. I n this case the plotted points appear to fall on a straight
TABLE I Values of x, Q~ and n, for two Salt Mixtures KCl-KBr a t X
~
~
0.000
0.093 0.260 0,390 0.549 0.635 0.775
0.871 0.934 1.000
r
$8
36.6 32.1 31.6 34.2 35.5 35.7 36.6 37.6 37.8 38.4
NaCI-NaI a t 35”*
25”’
n8 11.23 11.05
10.43 9.89 9.17 9.02 9.21 9.31 9.49 9.68
XNd
$8
“s
0.000
21.7
0.187 0.216
24.5
8.97 8.74 9.04 8.54 8.02 6.84 6.56
0,303 0.535 0,797 0.840 0.950 0.956 0.981 1.000
27.1
21.0
35‘6 36.4 37.4 38.6 39.3 39.3
5.11
4.99 4.14 4.22
Fock: Taken from Comey’s “Dictionary of Chemical Solubilities,” page 7 5 The calculated value of +s for the saturated solution of KC1 is ohviously in error See $able 11. 2 From unpublished measurements made in this laboratory with Dr. E. 3. Durham.
line passing between the values of saturated solutions containing only a single salt. Since the deviations which do occur are in most instances toward the extremes where the amount of one component solute relative to the other is small, they are most likely the consequence of errors in the basic solubility measurements. For such errors would be greatly magnified in calculating the plotted quantities. From the linear relationships depicted in Fig. Ib it follows that for the two cases under consideration the apparent molal volume of each salt is independent of the other salt present regardless of which one is the saturating salt. Furthermore, a comparison of the two plots (Figs. Ia and Ib) shows quite clearly that there is no close connection between the apparent molal volumes of the salts and the number of mols of water present in the solution. In short, these two examples conform to the rule which was derived from the conclusions of Nicol. We have already interpreted the above results to mean ( I ) that the state or degree of association of the saturating solute is unaffected Janecke: Z. physik. Chem.. 51,
1 3 2 (1906).
1026
ARTHUR F. SCOTT
by the presence of the added electrolyte and ( 2 ) that the added electrolyte is in the same state as when it is the saturating salt. Regarding the condition of the electrolyte in the assumed state we cannot, however, draw any definite conclusions. Only the above two examples will be presented to show that the apparent molal volumes of solutes in saturated solutions are independent of each other and also of the number of mols of water in the solution. While the data of other salt pairs, which might be expected to belong to the same type of those
Values of x, 'HCl
&, n,
HC1-IICI 4s
TABLE I1 for Three Chloride-Hydrochloric Acid Mixtures at
- HC1-NaC1 "8
11.13 11.47 28.7 11.35 27.6 11.12 26.2 11.02 24.7 10.42 23.2 9.74 22.5 9.32 22.0 8.65 7.65 21.1 22.0 6.21
0.000 31.7 0.110 30.1
0,231
0.341 0.413 0.584 0.j11
0.766 0.832 0.903 0.959 0.969 0.981 0.983
21.0
5.20
21.2
3.90 3.45 3.33 2.99
21.4
0.982
21.5
0.983
21.7
'HCI 0.000
@s
"8
21.6 8.99 21.2 9.11 21.2 9.14 20.8 9.07 20.6 8.93 21.1 8.80 2 0 . 2 8.72 20.5 8.35 7.86 20.5
0.093 0.165 0.418 0.580 0.627 0.681 0.771 0,853 0.918 20.4 0.960 20.6 0.98'1 2 0 . 7 0.990 2 0 . 8 0.999 21.7
2;'
HC1-"IC1
7.20
6.38 5.67 4.78 2.92
'HCl 0.000
0.076 0.179 0.293 0,317 0.352 0.j0j
0.568 0.608 0.686
4s
39.6 38.0 36.0 33.7 33.1 32.6 29.6 28.6 27.8 26.3 24.4
ns
7.50 7.51 7.61 7.60 j.61 7.60 7.40 7.25 7.14
6.85 0.784 6.28 0.826 23.7 5.91 0.874 22.9 5.38 0.918 22.4 4.34 0.936 22.4 3.46 0.937 2 2 . 7 2 . 7 5
we have just considered, are to be found in solubility tables, they are for the most part so obviously irregular as to be worthless for our present purpose. We shall now turn to a different class of salt mixtures which are characterized by the fact that the linear relationship analogous to that of Fig. Ia shows one or more definite discontinuities. To introduce this type of mixtures we may consider first the changes which take place on adding an acid to a saturated salt solution, a phenomenon which has received a great deal of attention. I n Table I1 are given the values of x, &J,and , n, for three different chloridehydrochloric acid mixtures calculated from the measurements of Ingham. A plot of these quantities is shown in Figs. 2a and ab. These graphs reveal that in these cases also the value of is not related in any obvious way to n,, the amount of water present in the saturated solution. Furthermore, within the limits of experimental error' the plotted points fall on a straight 1 Although the magnitude of the experimental error ia not known exactly, its effect on the derived de uantity must amount to approximately 0.2 cc. Values of qh for saturated solutions of and NaCl a t 25' have been found from careful measurements in this laboratory to be 31.3 cc. and 21.4cc., respectively. The lines as drawn in Fig. z b pass through these values.
Kd
APPARENT VOLUMES O F S.4LTS IN SOLUTIOX
1027
line up to an acid concentration which is rather high relative to the salt concentration and also in terms of molarity. In the case of HCl-KCl solution the x = 0.903point, which falls on the line, corresponds to an acid concentration of 5.67 mols per liter. With the HCl-NH&l solutions the x = 0.874 point represents a solution in which there are 7.3 j mols HC1 per liter. The data for the HCl-KaCl solutions appear to be most irregular but the x = 0.j 7 I point is for a solution which is 4.50 molar with respect to the acid. Unfortunately the data are not sufficiently precise to permit the determination of the exact point at which the values deviate from the linear relationship. To interpret this linear relationship we can assume what was concluded from the previous examples, that the apparent molal volume of the saturating salt, is unaffected by the presence of the acid and that the acid in the salt solution has a constant value of 9. To determine the + value of the added acid we can extrapolate the drawn lines to the limiting x = 1.00 value. The fact that the three drawn lines have a common intercept (+ = 2 0 . 0 ) can be taken to indicate that the added acid is in the same state or degree of association in the three saturated salt solutions. A step toward the determination of the properties of the hydrochloric acid solution, characterized by the condition that + = 20.0, would be to calculate the composition of such a solution. This can be accomplished by means of the following empirical equation of Masson:' $,$
+ = k m!$
X +o
(2)
In this equation m is the molarity in mols per liter, and k and $0 are constants. These two constants for hydrochloric acid solutions at z j o have been found by Geffcken? to be 0.83 and 18.20,respectively. Introducing the above values of 4, k, and $o into equation z the molarity m of the solution is calculated to be 4.71. Hence the volume of the solution which contains one mol of HC1 is 213 cc. X o w from equation I , taking the volume of one mol of water to be 18.1, we find 11, the number of mols of water present in the solution, to be IO.j . This figure, however, can be only an approximate estimate because a very slight change in the value of $ produces n large variation in the calculated value of n. Thus, following the above procedure the following values of n have been calculated for different values o f $ : $ = 19.9,n = IZ.I;$ = 20.0, n = 10.7; 0 = 20.1,n = g.j. In view of this uncertainty we can only take 11 :is the approximate number of mols of water present in the limiting acid solution. Khile it is true that the foregoing calculations do not give any information regarding the state of the acid electrolyte when its apparent molal volume is 2 0 . 0 , we may reasonably suppose that this state is identified with a solution which contains I I mol6 of water for one mol of HC1. This supposition would lead to the conclusion that, so long as the q value of the acid is 2 0 . 0 , each mol of the added acid will have associated with it I I mols of water. In other words Masson: Phil. hag., ( 7 ) 8 , 218 I 1 9 2 ~ ) .The writer has discussed this equation in two previous papers of this series: J . Phgs. Chem., 35, 231 j , 3379 (1931J . Geffcken: Z. physik. Chem., 155, I (1931).
ARTHUR F. SCOTT
1028
we may look upon this figure I I as the number of mols of “fixed” water associated with or appropriated by each mol of acid when added to the saturated salt solutions. This interpretation of the calculated value of n makes it practically equivalent to what is generally termed the “hydration number” of the solute, and accordingly it may be designated as nh.
I
l
a
+ 3
b
.O
ai 0 2
X”,,
03 o+ 0 5 06 07 08
as
FIG.2 and (b) the Graphic representation of the Effect of HC1 on ( a ) the ne quantities of three Saturated Solutions.
a.
The salting-out effect] has frequently been investigated as a means of determining the hydration of the added electrolyte. The present value ( I I ) for hydrochloric acid is, with one exception, much higher* than the values obtained from the effect of the acid on the solubility of a given substance and is also higher than the values estimated from the results of the other methods which have been studied for this purpose. The exception noted above is, 1 For a summary and criticism of this method see Washburn: Jahrbuch der Radioaktivitat und Elektrotechnik: 5, 516 (1908). * For instance, Washburn cites 2.7as the maximum number of mols of water appropriated by HCI, as determined from its effect on the solubility of gases.
APPARENT VOLUMES O F SALTS IS SOLUTION
1029
however, of considerable interest. Bjerrum,’ in order to account for the variation in the activity coefficients of strong electrolytes with concentration, assumed that the ions of the completely dissociated electrolyte are hydrated and from the equation established on the basis of this assumption he estimated the hydration numbers of a number of electrolytes. Using the activityof HClas determined from freezing point measurements he estimated the hydration number of the acid to be 9, the figure also obtained from the electromotive force data of dilute acid solutions. On the other hand, employing activity values obtained from other electromotive force measurements nh for H+ was calculated to be 9 and nh for C1-, 2 , a total of 11. Because of the approximations involved in his calculations Bjerrum accepted I O as the approximate value of the hydration number of HCl but observed that if association of water were to be taken into account, slightly larger values would be obtained. Calculations of the nh values of HCl by Schreiner,* which were likewise based on Bjerrum’s equation, yielded essentially the same results as those we have already noted. The actual volume (&) of HCl when x = 1.00cannot be determined from Fig. 2b because of the fluctuations exhibited by the plotted points. However, when the @ 8 values of a given solution are plotted against the corresponding n, values, it is possible, by extrapolating over a very short range, to get the value of +a for the case where n, equals zero. This limiting quantity for the three solutions under consideration is approximately 23.5 cc., a minimum figure. Since n,, when x = I .oo, appears to be zero, the estimated value of bs may be the desired limiting value. In any case, because the quantity in question represents the volume of HC1 when it is in the solution state but with no water present, it may be compared with the volume of pure HC1 under various conditions. Some data of interest in this connection, which are based on measurements made or cited by Simon and SimsonI3are given below: Temp.
80’ Abs.
98’ Abs. 107’ Abs.
162’ Abs.
State
Volume
solid solid solid liquid
< 24.2 cc.
__
24.8 cc. 28.5
Structure
molecular lattice transition point face-centered cubic melting-point
I t is evident that the value 2 3 . 5 cc. approximates that of the solid rather than the liquid state. Some evidence that the limiting volume does not correspond to that of the polar lattice structure might be derived from the following considerations. A limiting value &, can be calculated from equation 2 by imposing the condition that m, = IOOO/&, and represents the solution state a t which the apparent volume of the solute is identical to the volume in which it is contained (n = o in equation I ) . For solutions of HCl this quantity is Bjerrum: 2. anorg. Chern., 109, 275 (1920). A more general derivation of Bjerrum’s equation and a discussion of it is to be f o m d in Taylor’s “Treatise of Physical Chemistry,” Vol. I1 (first edition), page 775. * 5chreiner:Z. anorg. Chem., 135,333 ( 1 9 2 4 ) ; 166,219 (1927). a Simon and Sirnson: 2. Physik, 21, 168 (1924).
ARTHUR F. SCOTT
1030
23.6 cc. andis practically the same as that found from the &-n. graph. However, in the second paper of this series reasons were advanced to show that for solutions of the polar alkali halide salts the 9, state was not the state a t which n equals zero. If HC1 solutions were assumed to conform to the same rule as that found to hold for the salt solutions, the limiting value of 4 can be calculated and the figure obtained is 22.4 cc. Since this figure is so much lower than the minimum 23.5 cc., it may be taken to indicate that solutions of HC1 are not analogous to those of the alkali halide salts. The general conclusions which the foregoing discussion suggests may be summarized briefly at this point. First, when hydrochloric acid is added to a saturated solution of the chloride salt, the acid appears to appropriate or require I I mols of water. Second, the pure acid when in thesolution state but not associated with water appears to have properties resembling those of the solid, possibly the modification with amolecular latticestructure. The nature of the change which takes place when the acid goes from one of the above -25 states to the other is, of course, unknown. -24 However, it may be observed that the -23 &-ns plot reveals two discontinuities the study of which with more precise data XN.CI I I I , I might throw some light on this question. 01 02 03 a4 0: o b 07 a8 09 We may next consider the salt pair FIG.3 KCI-NaCl. In Table I11 are the necessary Plot showing the Variation of and n, values of X, &, and n, calculated from the quantities with the mol fraction of XaC1 published measurements of Holluta and in the Solute, KC1 + NaCl Mautner.' The plots showing the relationships of these quantities are given in Fig. 3. Here again, despite the break in the &-x line at the eutectic point, it is obvious that the variation in the apparent volumes of the solutes is not directlyrelated to the amount of water present in the saturated solution. An analysis of the $8-x plot may be carried out in the manner described in the discussion of the preceding example. When NaCl is added to a saturated solution of KCl, it has, according to our argument, the properties of a solution whose 4 value is z 1.5 (x = 1.00). Using equations I and 2 the value of nh is computed to be 7.7 or 8. For the purpose of these calculations the constants k and $0 of equation 2 a t 18.5~ were determinkd from the measurements of Kohlrausch and HallwachsZ to be z . z 4 and 15.9,respectively. The value of $ which characterizes KCl as the added electrolyte is 32.3 cc. and, as in the case of NaC1, represents a concentration greater than that of
I:;,
,
ly
+?
a
Holluta and Mautner' Z. physik. Chem , 127,464 (1927). Kohlrausch and Hallwachs: Z. physik. Chem., 12. 538 (1893).
APPAREST VOLUMES O F SALTS I S SOLUTION
103 I
the saturated solution. N o data have been found by which to determine the constants k and +o which are necessary for the calculation of nh. The following method, however, appears practicable as a means of estimating the values of these constants. In the first paper of this series values of k and +o are given for both NaCl and KC1 solutions a t oo, 2 j o , and joo. Geffcken in his article gives in addition to these values, values of the same constants at 3 j o and 4 5'. ?;ow, when the k values of the KC1 solutions are plotted against those of the NaC1 solutions at the same temperatures, the T.4BLE
111
Values of x, & and n, for Two Mixtures a t 18.j"C KCI-KNO-
KCI-NaCI XNsCl
4s
0.000
30.8 30.5 30.0 29.5
0.043 0.086 0.127
"8
12.13 11.91
0.043
11.7.;
0.082
11.58
0.119 0.188 0.265
0.206 0.388 0.536 0.660
28. j
11.20
27.1
10.20
2j.8
9.28 8.36 7.80 8.07 8.36 8.62 8.75 8.93 9.08
24.8
0.727
24.0
0.772
23.4
0.84j
22.j
0.908 0.936 0.969
21.9 21.8 21.3 20.9
1.000
XIiSOa 0,000
0.288
0.368 0.497 0.708
0.814 0.874 0.934 I . 000
+s
n.?
30.8 31.4 32.1 32.5 33,5 34.4 34.8 35.4 36.3 38.1 39.3 40.0 40.5 41.3
12.13 11.68 11.18 10.79 9.99 9.16 9.82 IO.60 12.99 15.91 17.11
17.64 18.29 18. j 8
plotted points fall closely on a straight line, a fact which means that the ratio of the temperature coefficients of these constants is independent of temperature.' The point on this line corresponding to an abscissa value of z . z 4 is z.4* and may be accepted as the k value of KC1 solutions a t 18.5". A similar relationship appears to hold also for the +o constants, and the value of +o for KC1 solutions a t 18.5' estimated in this way is 26.0 cc. The above relationships cannot be established as a general rule without a more extensive test. In the present case, however, the estimated values of the constants can be checked indirectly. Thus, if for the saturated solution of KC1 &is taken to be 30.8 (Table 111),n, is calculated to be 12.3, afigure which agrees reasonably well with 12.1, the value given in the table. Employing these same constants and taking + % t obe 32.3, nh for the added KC1 is computed to be 6.4, or 6. These approximate nh values, 8 for NaCl and 6 for KCl, may be compared with other estimates. The corresponding values given by Washburn are For a discussion of a relationship of this character for the temperature coefficients of solubility see Scott. J. Phys. Chern., 33, 1000 (1929).
1032
ARTHUR F. SCOTT
10.5-9.5 and 9.0-8, as determined from the salting-out effect of these salts on the solubility of hydrogen, and in both cases they tend to decrease with increasing concentration of the added salt. Sugden' on the basis of distribution measurements estimated nh for NaCl to be 8 and that for KC1 to be 3.4.
FIQ.4 Plot showing the Variation of +s and n8 with the mol fraction of KNOa in the solute KCI KN03
+
Bjerrum from his theory calculated the hydration number for KC1 to be 2 . The order of magnitude of these comparison values is seen to be the same as the nh values calculated by our present method, a fact which strengthens the interpretation we have placed on the latter quantities. I n concluding this discussion of the KCI-NaCl mixture it should be pointed out that these salts as added electrolytes have different properties from what was found to be the case with the KCl-KBr and NaC1-NaI mixSugden: J. Chem. SOC., 129, 178 (1926).
APPARENT VOLUMES O F SALTS I N SOLUTION
I033
tures. I n the latter cases both KCl and NaCl on addition to saturated solutions were shown to be in the same state as in their own saturated solutions while in the present example both salts apparently are in a state which corresponds to a solution more concentrated than the saturated state. This difference in properties would seem, on the basis of the limited evidence at hand, to depend on whether the cation or anion of the added electrolyte is the same as that of the saturating salt. That no general rule regarding this condition can be formulated at this time will be evident from the results obtained with the following example. The last case of mixed electrolytes we shall consider is the combination KC1-KN03. The necessary data are included in Table I11 and are takenfrom the same source as the KCl-NaCl data. The usual plot of the x, b8, and n, values is shown in Fig. 4. Again it is evident that the values of bS bear no direct relationship to the number of mols of water present in the saturated solution. Although the salts of the present mixture have a common cation and therefore might be expected to resemble a mixture such as KC1-KBr, a comparison of the two &-x graphs shows that they are by no means similar. We may consider first K N 0 3 as the added electrolyte. Its limiting value is found to be 45.2 cc. Unfortunately, the constants of equation z for 18.5' are not known and consequently it is impossible to compute the composition of the solution corresponding to this value of 4. However, as an estimate based on the constants given by Masson for solutions of K N 0 3 a t 15' nh is calculated to be 4. Because of the small amount of water present in this hypothetical solution the calculated value of nh would not be greatly affected by small changes in temperature and is therefore approximately correct for 18.5'. A comparison of the present result with other estimates is only partially satisfactory. From the effect of KN03 on the solubility of gases the hydration number of this salt, as given by Washburn, is found to vary from 3 to 9. On the other hand Sugden on the basis of his measurements was forced to ascribe a negative value -2.7 to nh. In his article Sugden lists several examples where KN03 as an added electrolyte exerts an abnormal effect in that it tends to increase the solubility of the saturating salt. From our present standpoint, however, this salt appears abnormal only in its divergence from the general rule, which was noted with the first type of salt mixtures, that when the added electrolyte has a cation in common with the saturating salt its + value is the same as in its saturated solution. On the other hand when Kr\iOa is the saturating salt there is fairly definite evidence that the electrolyte has abnormal properties. I n Fig. 4 it can be seen that on the first addition of KCl the relationship between the two solutes is the same as what was found for the case where KCl is added to a saturated solution of KBr. I n short, over this range both solutes have properties in accord with the general rule. However, after the amount of KC1 relative to that of the saturating salt passes a certain value there appears to be a decided change in the properties of both solutes. Although the applicability of our present method of analysis to this range of the #s-x plot is uncertain, the con-
raj4
ARTHUR F. SCOTT
clusions to be derived from it may be pointed out. The nh value of the added electrolyte KCI is found to be 5-6 and is therefore similar to the value found from the KCl-NaC1 data. But the amount of water estimated to be required by the saturated solution of K N 0 3 is roughly 32 mols, a value which is almost twice the actual value. Hence, it would appear that the irregular variation of & on the addition of KCl to the saturated solution of KN03 is due primarily to some abnormal condition of the latter electrolyte. No conclusion can be drawn regarding the nature of the change which it is assumed KNO3 undergoes when sufficient KCl is added to its saturated solution. It may be observed, however, that with respect to many of its properties in solution K N 0 3 is regarded as an abnormal electrolyte. As an illustration of this fact Sugden, in the paper already quoted, cites the fact that solutions of this salt have “negative” viscosities. That the condition of this solute in the saturated state differs in some way from the conditions of the simpler alkali halides in the saturated state is indicated also by the following. It has been shown1 for saturated solutions of a number of alkali halide salts that the apparent molal volume is linearly related to the square of the number of molsof water present in the solutionat thesame temperature. It was found that saturated solutions of Ka1)\’03also conform to this rule. However, saturated solutions of KN03 and the heavier alkali nitrates are irregular in that the apparent molal volume varies not with the square of but directly with the number of mols of water. This exceptional property of the nitrates will be discussed in more detail in a subsequent article.
summary The present paper is a preliminary study of the apparent molal volumes of salts in saturated solutions of mixed electrolytes. A simple method is described for the analysis of the experimental data and is applied t o some typical mixtures. Because of the limited number of cases considered no definite generalization can be established, It appears, however, that the two following classes of added electrolytes can be distinguished, assuming that the apparent molal volume 6 of the saturating salt remains unchanged on the addition of the second electrolyte: (I) when the added electrolyte has a cation in common with the saturating salt, its apparent volume is the same as when it is the saturating salt; and (2), when the added electrolyte has an anion in common with the saturating salt, its apparent volume has a unique but constant value. Potassium nitrate was found to be an exception to these rules. The possibility of calculating the hydration number of the added electrolyte is discussed. 7 h e Rzce Inqtz!ute, Houqton, Texas. Scott and Durham: J. Phys. Chem., 34, 2035 (1930).
