FREDVASLOW
2286
(Fluka AG, Puriss) were used without further purification. Water was redistilled from alkaline permanganate and then from phosphoric acid, atmospheric carbon dioxide being excluded. Nitrous oxide (Matheson Co., Inc.) was purified by repeated freezing with liquid air and evacuation. Only fresh solutions were used, contained in glass-stoppered flasks, covered with plastic foil (to protect from carbon dioxide). In solutions of the concentrations used, 96-99% of the absorption of light a t 1849 A was due to the HP042- ion. The methanol, water, acetone, Hr PO4- ion, and nitrous oxide absorbed about 0.8, 0.8, 0.6, 0.1-1.5, and 0.1-0.2'35 of the light, respectively. Formation of nitrogen by the direct photochemical decomposition of nitrous oxide (by absorption of the 2537-A line of the lamp) could be shown to contribute
only 0.4% of the total quantum yield of nitrogen. The values of molar absorptivity at 1849 A of phosphate mono- and dianion,2bmethanol,3hacetone, lo and nitrous oxideaCtaken were 60, 420, 6.2, about 300, and 60 M-' cm-l, respectively. Water has an absorption coefficient of 1.45 cm-1 a t this wavelength.'l The correction Q for hydrogen yield resulting from the direct photolysis of methanol and water is estimated to be
0.008.6b Acknowledgment. This investigation was supported in part by Research Grant GX-05842 from the U. S. Public Health Service.
(10) E. Kosower, J . Am. Chem. SOC.,80, 3261 (1958). (11) M. Halmann and I. Platzner, J . Phys. Chem., 70, 580 (1966).
The Apparent Molal Volumes of the Alkali Metal Chlorides in Aqueous Solution and Evidence for Salt-Induced Structure Transitions by Fred Vaslow Chemistry Division, Oak Ridge National Laboratory,l Oak Ridge, Tennessee
37831
(Received January 31 1966)
High-precision, closely spaced measurements have been made of the apparent molal volumes (densities) of aqueous solutions of the alkali metal chlorides at 25" from 0.02 to 3.5 m. Above 0.1 m it is found that the results for LiCl are represented within experimental error as a linear function of cl/' in two sections of different slope with a narrow transition region a t about 1 N . For heavier salts the transition region becomes wider and the center moves to lower concentrations, the linear portions essentially disappearing for the RbCl curve. Comparing the volume curves with the behavior of the heat contents and viscosities of the solutions, it is concluded that the curve transitions actually do indicate some kind of physical transition of the solutions. It is tentatively suggested that the effect is due to a cooperative action of several ions on the solvent structure in the neighborhood of the ions.
Introduction In connection with studies on thermal effects in ionexchange resins, a number of graphs of literature values of the relative apparent molal heat contents of alkali metal halides and other salts were prepared. In many of the curves, where for convenience the independent variable had been taken as the log of the ratio moles of The Journal of Physical Chemistry
water to moles of salt, it appeared as if in the neighborhood of 1 m there were substantial, possibly abrupt changes in the slope or form of the curves. At lower concentrations the curves more or less paralleled the con(1) Research sponsored by the U. s. Atomic Energy Commission under contract with the Union Carbide Corp.
APPARENTMOLAL VOLUMES OF ALKALIMETALCHLORIDES
centration axis but in the neighborhood of 1 m they turned upward’ or downward depending on the salt. The interionic interaction energy is presumably slowly varying in this concentration region, and the concentration is well below the region where one might expect hydration shell effects, and the concentration dependence was wrong for an ion-pairing effect. Consequently, there did not seem to be any reasonable or simple explanation for a change in character of the curves, and since no quantitative or objective description of the “effect” could be given, it seemed sensible t80consider these “effects” as artifacts. About the time of these observations several new concepts of liquid structure were introduced: the “significant structure theory” of Eyring,2 the “statistical geometry” of Bernal, and the pentagonal tetrahedron suggested by Pauling4 as a basis for the structure of water. While different in purpose, a concept common to each of these theories was the idea of a L‘cryst~allite” or “pseudo nucleus” which contained a number of liquid molecules in some type of cluster large conipared to what might be expected in the first hydration shell of an ion. In particular, the type of cluster suggested by Pauling was a regular dodecahedron containing 20 water molecules. In the liquid there would probably be a small number of nonordered molecules associated with each of the dodecahedra so that perhaps a total of 25 molecules could be associated with each group which was about the ratio of water molecules to ions where the changes in the heat curve occurred. It has been pointed out5 that under certain conditions such groups need not be disrupted by the fields of neighboring ions and conceivably the effect might represent an interaction of the ions with an individual cluster of the Pauling or other type. With this rather speculative possibility in mind, the apparent molal heat content data as well as literature data on other properties such as volumes and viscosities were closely examined to see whether serious consideration of an effect was in fact warranted. Of particular interest were the apparent molal volume curves for KaCP and SaBr6J which showed that both above and below a short region around 1 N the curves were very accurately linear functions of cl/’ (c is the molar concentration).8 In a short region around 1 N , the proportionality confkant for the square-root law changed from one definite value to another slightly different value.g If there were an ideal physical situation where the true functional relationship between some property of the solution and the concentration were known and this relationship changed over a limited region to another
2287
and different relationship, then some sort of complex, nonlinear process would have to occur. For example, a component or a particular type of site could be exhausted or a cooperative change of structure could occur, not involving a first-order phase change, however. The essential point is not that there is a sharp angle or even an abrupt change in the curves but that the curves go asymptotically from one accurately defined functional form to another different form in a limited region. In a real experimental situation these considerations are still valid but the problem is to decide with any degree of assurance whether a given experimentally found relationship is physically significant and not simply a matter of inaccurate data or a fortuitous tangency over a limited range of the curve. In the case of the cl” relationship for the apparent molal volume, this function has been found applicable to a great many solutionslOjll over wide concentration ranges. For some of the most accurately measured ~ y s t e m s , ~ J > ~ ~ on either side of the transition region and on a highly expanded scale, the data show no obvious nonrandom deviation from the square-root relationship over extended concentration ranges. The concentration regions where the slope changes occur appear to be the same regions originally observed for the changes of the heat content curves, and the centers of these transition regions can be accurately and unambiguously defined. It is tempting, therefore, to consider that this behavior might be of physical significance and should be tested using whatever criteria that may be applicable or available. (2) H. Eyring, T. Ree, and N.Herai, Proc. AVutZ.Acad. Sei. U.S., 44, 683 (1958). (3) J. D. Bernal, Nuture, 185, 68 (1960). (4) L. Pauling, “The Nature of the Chemical Bond,” 3rd ed, Corne11 University Press, Ithaca, N. y., 1960, p 472. (5) F. Vaslow, J . Phys. Chem., 67, 2773 (1963). (6) W. Geffken and D. Price, 2. Physik. Chem., B26, 81 (1934). Figure 1. (7) TV. Geffken, A. Kruis, and L. Solana, ibid., B35, 317 (1937), Figure 3. (8) D. 0. Masson, Phil. Mag., [7] 8, 218 (1929). (9) It must be emphasized that only relatively high concentrations are being considered in this paper. At low concentrations the Debye-Htlckel universal limiting laws for each property are a p proached and neither the high concentration square-root relationship nor a linear and a c ’ / ~relationship used later in the paper are valid. While a t low concentrations, the data presented here are completely consistent with the theoretical limiting law, the agreement has been considered in the sense of a sensitive test for the data rather than a new confirmation of the theory. (10) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” 2nd ed, Reinhold Publishing Corp., New N.y., 1950, 253. (11) TV. Y. Wen and S.Saito, J . Phys. Chem., 68, 2639 (1964). (12) A. Kruis, 2.Physik. Chem., 134, 1 (1936).
Volume 70,Number 7 July 1966
FREDVASLOW
2288
In the work presented here very accurate and closely spaced measurements of the apparent molal volumes (densities) of the alkali metal chlorides have been made in order to define the functional relationships as clearly as possible. Statistical criteria are applied in order to test the validity of a mathematical description of the curves in terms of two segments and a transition region, and finally comparisons are made of the volume curves with thosr? of other properties. It is a t least tentatively concluded on the basis of the evidence presented that an effect or "transition" does occur. The transition occurs at different concentrations for different salts and hence is not indicative of any single type of solvent group. The degree of sharpness is found to be strongly dependent on the nature of the salt. A brief discussion is given of some possible interpretations of the effect although it is recognized that much more work in this area is necessary.
Experimental Section The apparatus used was a differential hydrostatic balance very similar to that described by Redlich and Bige1ei~en.l~Fused quartz bobs of 450-ml volume and mean density 1.2 were used with 0.002-in. tungsten wire suspensions. The small size of the support wires made corrections for changes in displacement or surface tension unnecessary; however, as with Pt wires a clean surface on the solution was essential. For rapid mixing of stock solution additions, identical motor-driven stirrers running in U tubes at the sides of the main containers were used. The system sensitivity was about two parts in lo7 in relative density. The salts used were specially purified LiCl and KC1 showing less than 0.03 and 0.01% by weight, respectively, of other alkalies and alkali earths by flame photometer analyses. All of the NaCl and the KCl used in run I11 were Harshaw single-crystal optical grade materials containing less than 10 ppm of other alkali metals and Ca. The RbCl and CsCl were from Penn Rare Chemical Co. and assayed about 99.9% by weight with the CsCl containing about 0.1% carbonate. The equivalent weights used were 42.40, 58.45, 74.55, 120.94, and 168.37 for LiCl, NaCl, KC1, RbCl, and CsC1, respectively. Water triply distilled from quartz was taken to have a density of 0.997071 g/ml at 25.000'. The temperature was controlled with a commercial regulator having drifts of a few thousandths of a degree per day which had no apparent effect on the runs. At the start of a run the weights of the individual suspensions and bobs were obtained as well as the system zero with both bobs in pure water. After determining the zero point of the balance, accurately weighed portions of stock solution were added to one of the chamThe Journal of Physical Chemistry
bers which contained about 850 ml of water known to about 0.1%. After each three or four additions of stock solution and the subsequent density measurements, a weight buret was used to withdraw and accurately weigh a sample of the solution for analysis. From the analyzed number of equivalents of salt added and removed and the measured concentrations, the exact amount of water in the system (to 0.01%) was calculated and used to interpolate concentrations between the analytical values. All of the analyses for LiC1, RbCl, and CsCl were by differential potentiometric titration of C1- with AgN03 solution with a procedure similar to that used by Kunze and F u o ~ s . ' ~Standardization of the AgN03 was against stock solutions of NaCl or KCl. The stock solutions as well as some of the more concentrated experimental solutions of KC1 and NaCl were analyzed by direct weighing of dried (at 400" for KC1 and 500" for NaC1) residues of the solutions with a minimum salt weight of 2 g. All weights were reduced to in vacuo values. Depending somewhat on the size of the sample, standard deviations of the sets of titration analyses ranged from 0.005 to 0.015% with the gravimetric analyses generally differing by less than 0.01%. The deviations in absolute standardization of the AgNO:, solutions from run to run were slightly larger than the average deviations within a run. Consequently, in a few runs small adjustments were made of the apparent AgN03 concentration in order to bring the data from different runs into better over-all coincidence. In the first run of this work NaC1-I the technique had not been fully developed and a slightly larger adjustment has been made. The adjustments to the Agn'O3 solutions normally about 0.13 mequiv/g of solution were multiplicative factors equal to 1.0005 for NaC1-I and a maximum of 1.0002 for any others. The effect of the adjustment is to change the concentration by a constant factor for each point of the particular run, lowering or raising the entire curve by a corresponding approximately constant amount. At least two independent runs were made for each salt with four runs for NaCl and three for KCl. Errors were considered on the basis of the equation given by Redlich and Bigeleisen13 64
=
--10006d doc
+ 1000(d - do)& C
(1)
64,6d, and
6c are the uncertainties in volume, density, and concentration, respectively, do is the density of pure water, and d is the solution density. (13) 0. Redlich and J. Bigeleisen, J. Am. Chem. Soc., 64, 758 (1942). (14) R. W. Kunze and R. M. Fuoss, J. Phys. Chem.. 66, 30 (1962).
APPARENTMOLALVOLUMES OF ALKALI METALCHLORIDES
Taking the chloride analyses as being accurate to i O . O l % , i.e., 6c/c = 0.0001, there is an uncertainty in volume of about 0.002, 0.003, 0.005, 0.010, and 0.015 for LiC1, NaC1, KCl, RbCl, and CsCl, respectively, with only a small dependence on concentration. The estimated error in the density measurements is based on an uncertainty of 0.1 mg on the balance which corresponds to about 0.002 ml at 0.1 m. Since this error decreases as l/m, above 0.1 m for all salts and for RbCl and CsCl at any concentration the errors are mainly due to concentration uncertainties. As shown in Table I1 of the Discussion, the error estimates shown here are consistent with statistical analyses of the data for LiCI, NaCl, and KC1 solutions but apparently too large for RbCl and CsCl. Since the numbers of points for RbCl and CsCl are lower, the statistical significance is less; however, the results might also indicate that the estimated error of analysis is conservative.
2289
4
39.5
Results The experimental results are shown graphically in Figure 1 where the theoretical limiting law, = 1.862/C,15 has been subtracted from the data. This subtraction allows a somewhat larger scale to be used than would be otherwise possible. The values of P were obtained by fitting the equation, = F20 1.862/C &,la to the data up to 0.1 N using a computer least-squares program to determine the parameters V20 and B. Points below 0.1 N were weighted according to the formula W = 10 N . The values of I'zo obtained are 16.991 f 0.01, 16.628 f 0.006, 26.886 i 0.01, 31.94 i 0.03, and 39.15 i 0.05 ml for LiCl, NaCl, KCI, RbCI, and CsC1, respectively. The errors given are based primarily on an estimated uncertainty in the absolute concentration which determines a larger error than that corresponding to statistical variations. No corrections have been made for impurities in the salts. Also shown in Figure 1 are points from previous work for KCl and NaCl. With the exception of the points for KC1 a t low concentration, the agreement seems generally very good. The differences for KC1 are larger than the expected errors, however, and run KCI-I11 was done as a check on the first two runs using an independent sample of high-purity KCI and a slightly different procedure. The new results were within experimental error of the first two runs. The approach of the curves to the limiting law should be a sensitive test of the quality of the data at low concentrations and the present data are completely consistent with this law. At the same time, the agreement at higher concentrations suggests that the ana-
rzo+
+
+
+
L
4 I
I
0.5
1.0
I
f.5
E-
I
2 .o
Figure l. Apparent molal volumes of alkali metal chlorides with limiting law subtracted from experimental points: 0, Kruis,lz magnetic float; 0, Wirth;ls X, Geffken and Price,* Kruis,lS dilatometer. magnetic float;
+,
lytical procedures are accurate and consequently it is difficult to account for the discrepancy. An accurate summary" of the data is contained in Table I, where the points have been read from very large-scale plots of all of the original data using splinedrawn smooth curves. For a more detailed examination of the original data, Table I1 gives one complete run for LiCl showing molality, apparent volume, and the change in density from that of pure water.
Discussion The principal purpose of these experiments has been to examine as critically as possible the validity of the description of the volume curves in terms of two dif(15) H. E.Wirth, J . Am. Chem. Soc., 6 2 , 1129 (1940),Figure 1. (16)0. Redlich and D. M. Meyer, Chem. Rev., 64,221 (1964). (17) The complete original data are available in Oak Ridge National Laboratory Report TM-1438.
Volume 70, Number 7 July 1966
FREDVASLOW
~
~~
Table I: The Apparent Molal Volumes of the Alkali Metal Chlorides in Aqueous Solution a t 25.00' (ml/mole) LiCl
NaCl
KCl
RbCl
CSCl
16.991 17.386 17.525 17.715 17.856 17.972 18.074 18.167 18.252 18.331 18.406 18.476 18.606 18.731 18.846 18.953 19.055 19.288 19.495 19.677
16.628 17.032 17.210 17.437 17.579 17.775 17.909 18.038 18.158 18.271 18.380 18.433 18.670 18.854 19.024 19.186 19.336 19.674 19.990 20.267
26.886 27.310 27.480 27.723 27.912 28.075 28.221 28.357 28.482 28.601 28.711 28.820 29.015 29.195 29.374 29.532 29.688 30.038
31.94 32.355 32.549 32.810 33.000 33.175 33.323 33.465 33.595 33.713 33.826 33.935 34.135 34.321 34.492 34.646 34.000
39.15 39.578 39.760 40.018 40.220 40.385 40.525 40.655 40.778 40.887 40.996 41.105 41.306 41.475 41.642
(3.8375 m) 19.788
(3.6602 m ) 20.353
(2.9343 m ) 30.322
(2.4487 m ) 35.115
(1.6977 m) 41.722
m
0 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5
Table 11: Apparent Molal Volumes and Change in Densities of LiCl Solutions *v, m
lOOOAD
ml/mole
0.028513 0.056754 0.084772 0.16984 0.26432 0.35556 0.44371 0.52891 0.62177 0.71126 0.79758 0,88090 0.96825 1.0524 1.1335 1.2118 1.2938 1.3727 1,4488 1.5222 1,6908 1.9129 2.0467 2.1974 2.5119 2.9179 3.2687
0.7146 1.4156 2.1064 4.1843 6.4643 8.6415 10.7247 12.7204 14.8758 16.9359 18.9074 20.7956 22.7623 24.6428 26.4432 28.1671 29.9608 31.6772 33.3213 34.8964 38.4863 43.1389 45.9043 49.0027 55.3356 63.3078 70.0109
17.297 17.403 17.488 17.665 17.806 17.920 18.016 18,099 18.185 18.260 18.329 18.392 18.453 18.511 18.564 18.614 18.667 18.714 18.760 18.803 18.895 19.014 19.082 19,150 19.292 19.462 19.601
The Journal of Physical Chemietry
ferent function segments and a transition region connecting the segments. If this description is valid and is consistent with other physical properties, then it is presumed that the transition represents a physically significant and interesting property of the solution. Examining the curves of Figure 1 it is seen that above about 0.1 N (cl/* = 0.4)the description for LiCl solutions is a very good one. For the heavier salts the width of the transition region increases until for RbCl most of the curve is transition and the description is not applicable. Comparing these curves with those for some other salt solutions where reasonable data are available and the above behavior seems clear, the NaBr curve6 appears to have a slightly sharper transition a t a slightly higher concentration than NaC1. In the tetraalkylammonium bromides measured by Wen and Saito," a sequence similar to that of the alkali chlorides is present in that the sharpness of the slope change (not the minimum in the curve) increases on going from the tetramethyl to the tetrapropyl salt. The tetrabutyl salt shows a slight dip just before the minimum and may indicate that the transition has been hidden by the minimum. It is of interest that the sequence of increasing sharpness of the transition parallels the sequence of iricreasing solvent ordering for both the alkali metal salts and the tetraalkylammonium salts.'*-21
APPARENT MOLAL VOLUMES OF ALKALIMETALCHLORIDES
Returning to the alkali chlorides, it is desirable, insofar as pbssible, to test mathematically the validity of the segmental concept of the curves. For this purpose an explicit description of the curves in terms of two slopes and a transition is derived and fitted to the data and this is compared with polynomials in cl/' (i.e., Q =A Bc1l2 Cc Dc112.. .) of from three to six parameters fitted to the data by a computer leastsquares procedure. The Gauss criterion22 is used to establish a statistically justifiable number of parameters and accuracy of fit ( i e . , standard deviation) of the equations. The explicit description of the curves requires two slopes, a zero intercept, an intersection point, and a parameter describing the relative sharpness of the transition. The transition itself can be described through the use of a function which rises from 0 to 1 in the appropriate region. The simplest function having this property and being a type common in chemical equilibrium expressions is of the form
+
2291
obtained from the power series expressions can be expected. The values of the standard deviations and Gauss criteria for the polynomials and eq 4 are shown in Table 111. Only points above 0.1 N were used and eq 4 was not applied to the RbCl and CsCl data.
+ +
K is very nearly the intersection point of the two slopes and n a parameter governing the width of the region. The parameter n has arbitrarily been limited to even integers. The slopes of the volume curves are then given by the expression (3) where S1is the initial slope and SZis the slope increment. The volume is given by
where Qo is a constant of integration not equal to V 2 0 0 Although the integral can be explicitly written, the expression is complicated for n > 2 and it is simpler to evaluate the integral at each concentration by a computer calculation. For values of cl/* sufficiently far from the transition, the function is either 0 or 1 and Q can be directly calculated using QO, SI, Sz, and K in a simple linear form. Above the lowest concentrations, the maximum deviation of two straight lines from the experimental points is about 0.04 ml for NaCl and 0.004 ml for LiCl. Initial parameters for eq 4 were obtained directly from the curves and these parameters refined by comparing the computed and experimental Values Of 4. since no explicit minimizing of the mean-square deviation was done, some increase in this quantity over that
Table 111: Gauss Criterion and Standard Deviations No. of parameters Salt
LiCl
R X lo8
x NaCl
103
n 0
KC1
n
RbCl CsCl
R
U
U
3
4
5
6
Eq4
14.4 3.7 44.2 6.5 23.8 4.7 4.7 9.6
13.4 3.5 15.5 3.8 24.1 4.7 4.5 7.1
4.2 1.9 10.2 3.1 21.5 4.4 4.2 6.9
4.3 1.9 7.7 2.7 21.0 4.2 4.1 6.6
4.4 2.0 8.4 2.8 22.8 4.5
The differences of points computed with eq 4 from the experimental values are shown in Figure 2 on a scale expanded on the original drawing approximately fifteen times that of Figure 1, along with the parameters used. The computed curves are almost indistinguishable from the points of Figure 1 on the scale of this figure. Returning to Table 111,it is seen that five parameters are justified for the LiCl curve and five or six for KaCl. The differences of the standard deviations of eq 4 from those of the five- or six-parameter power series are statistically insignificant and it can be concluded that eq 4 also represents the data within experimental error. While eq 4 cannot be justified for KC1, consistency with the LiCl and NaC1 curves might justify its use. It has not been possible to show that eq 4 has any more than a marginal statistical preference over fiveparameter polynomials and the question is: does the comparison support the segment concept? In this (18) R. IT. Gurney, "Ionic Processes in Solution," Dover Publications Inc., New Tork, N. T., 1962, p 258. (19) H. Yamntera, B. Fitzpatrick, and G. Gordon, J . M o l . Spectry., 14, 268 (1964). (20) S. Lindenbaum and G. E. Boyd, J . Phys. Chem., 68,911 (1964). (21) S. Lindenbaum, ibid., 70, 814 (1966). (22) A. G. Worthing and J. Geffner, "Treatment of Experimental Data," John Wiley and Sons, Inc., New York, N. Y., 1943, p 260. The Gauss criterion n is defined as
where yo - y is the difference of calculated and experimental values, n is the number of points, and m is the number of variable parameters. The function is minimized for the statistically justifiable number of parameters.
Volume 70, Number 7 July 1966
FRED VASLOW
2292
0 0.00 4 LL
.
- 0.01
0.02
0
0
5 .
.
2
.
-
t-
-
0 0.1
0.5
f .O
i.5
G Experimental
- Calculated
Apparent
Molal Volume.
Figure 2. Deviat,ions of apparent molal volumes from eq 4.
respect the justification of five or six parameters in itself requires data of a very high accuracy and polynomials of this complexity can accurately represent very involved curves. The conclusion that can be made under the circumstances is that eq 4 does represent the data within experimental accuracy and no simpler polynomial has been found which can equal this accuracy. If the transition observed in the volume curves does correspond to a real physical transition of the solution, then it should be observable in properties other than the volume. The presumed transition is small and diffuse, however, and detection is difficult unless it is possible to establish with some confidence that the property does obey a simple physical law. The criteria for the law are, for lack of a definitive theory, exactness and extent of fit, requiring again accurate, closely spaced data for the test. For two properties of LiCl and NaCl solutions, the relative apparent molal heat c ~ n t e n t * and ~ - ~the ~ relative v i ~ c o s i t y , ~reasonable ~-~~ data are available at moderate-to-high concentrations. Also, in some concentration regions it is empirically found that the The Journal of Physical Chemiatry
relative viscosity is linear in c and the heat content linear in cLia. Although these rules do not have a rigor~ ous theoretical foundation, the linear relationship may be related to the Einstein viscosity law and the c”’ relationship corresponds to the energy behavior of a regular ionic lattice and hence they are not wholly arbitrary functions. In order to show clearly the nature of the agreement of these functions with experiment, relative to the deviations, differences of experimental and calculated points are determined and plotted on a substantially enlarged scale. Parameters of the appropriate equation are obtained by a visual fit to the data and then used to calculate values of the property for each point. Figure 3 shows the LiCl heat curve, Figure 4 shows the NaCl heat curve, and Figure 5 shows both viscosity curves. The parameters are given in the figures and the arrows show the values of K obtained from the volume measurements. It is seen that in each of these curves as well as in the curve showing the slope of the apparent molal heat capacity given by Young and RIachinal there is a strong deviation of the data from the simple function as the transition region is approached. Anticipating the Conclusions section, the reason that SaCl heat contents do not follow the c”’ law below 1 N as does LiCl may be in a relative instability of the solvent structure in the neighborhood of the S a + ion. The volume and other properties can be plotted as functions of other variables, ie., m or lnl/’,rather than those used and in each case the graphs are curved with no apparent straight portion. The transition region can still be observed and hence is not an artifact of the equation or method of plotting. However, the appearance of the transition is that of a small change in curvature in the total curve. It is much less obviousand theobservation is much more criticallydependent on having accurate and closely spaced data. The existence of elementary relationships which do not show the transition property cannot be excluded (23)E. Lange and F. DUrr, 2. Physik. Chem., 121, 361 (1926). (24)S. G.Lipsett, F. bl. G. Johnson, and 0. Maass, J . Am. Chem. SOC.,50, 2701 (1928). (25) J. Wust and E. Lange, 2. Physik. Chem., 116, 161 (1925). (26) V. D. Laurence and J. H. Wolfenden, J . Chem. SOC., 1144 (1934). (27) L. Nickels and A. J. Allmand, J . Phys. Cham., 41, 861 (1937). (38) G. Jones and S. M. Christian, J. Am. Chem. Soc., 59, 484 (1937). (29) C. E.Ruby and F. Kawai, ibid., 48, 1119 (1926). (30) A. Chambers, Thesis data in R. H. Stokes and R. Mills, “Viscosity of Electrolytes and Related Properties,” Pergamon Press, Ltd., Oxford, 1965, p 118. (31) T. F. Young and J. S. Machin, J . Am. Chem. Soc., 58, 224 (1936).
APPARENTMOLAL VOLUMESOF ALKALIMETALCHLORIDES
160
I
I
I
e*
**
0 0.t
I
I
0.5
1.0
2293
I
3
o LiCl q/qo- 1 -(.0009 t . 1 4 8 ~ )
+x+NaCI
q/qo-l -(.OOOS t ,090C)
i
I 1.5
V5-i
Figure 3. Deviations of the relative apparent molal heat content of LiCl from m 1 1 3 law; data from Lange and Durr.23
300
-
I
I
I
1
t
-
v Figure 5. Deviations of the specific viscosities of LiCl and NaCl from a linear function of c: 0, Laurence and Wo1fenden;Ze 0 , Nickels and Allmand;" f, Jones and Christian;" x, Ruby and Kawai;Zg Chambers.30
*,
*+
0
I
NaCl
-(h- 647-
s e -
656n1"~)
I1
I
I
0 0.1
0.5
1.0
.
I 1. 5
J
K
Figure 4. Deviations of the relative apparent molal heat content of NaCl from m113law: Lipsett, Johnson, and Maass;2* 0 , Wust and Lange.16
+,
nor can it be proven that the relationships used are physically significant. The significance would appear to be in that, for each of these properties where it has been possible to find an elementary functional relationship, the data deviate sharply on approaching the transition region. In no case has it been possible to find such a relationship valid across the transition region.
Conclusions Accepting at least tentatively that a transition does take place over a limited concentration range, some consideration can be given to possible causes of the
effect. The evidence is limited and the discussion highly speculative; however, a few remarks can be made. The original incentive for this work was provided by the idea that the transitions in the curves might indicate the existence of a specific type of structure group in water. If the concentration at the intersection of the lines is taken as determining the size of the group, then apparently there is no obvious fixed group since the intersection point varies from 0.81 ( K 2 )in KCl to 1.14 in LiCl and about 0.5 in tetrapropylammonium bromide. The results are not inconsistent with theories proposing varying cluster sizes such as those of NBmethy and S ~ h e r a g or a ~Luck.38 ~ An explanation of the results involving a filling up of one type of site for the ions and the initiation of a different type at the transition would also appear to be ruled out. In order to obtain a sharp segregation into the different sites such as evidenced by the sharp (32) G. NBmethy and H. A. Scheraga, J . Chem. Phgs., 36, 3382
(1962). (33) W. Luck, Ber. Bunsenges., Physik. Chem., 69, 626 (1965).
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change of slope in the LiCl solutions, a large difference in the partial molal free energy per site would be necessary and this is not seen in the activity coefficient curve of LiC1. A similar argument would apply against any simple hydration shell picture based on the idea that the transition occurred when all of the water molecules were already in hydration shells and new ions had to penetrate these shells. In order to obtain a narrow transition region without a large partial molal free energy change, a cooperative effect among the ions appears necessary and this would seem borne out by the relatively high powers of the concentration found for eq 4. Whatever the nature of the solvent structure around an individual ion, as groups of ions approach one another, this structure is cooperatively changed. Those ions which initially had the most stable or ordered solvent structures in their neighborhood would require the largest number of cooperating ions to transform the structure. Ions with unstable neighboring solvent structures would
The Journal of Physaeol Chemistry
FRED VASLOW
show the most diffuse effect starting a t the lowest concentrations. It has been previously suggested by Samoilov34 and by the authol.5 that in a dilute solution the organization of solvent molecules in the neighborhood of an ion is largely determined by the normal water structure. Samoilov continues that in concentrated solutions the organization is determined by the combined ionic fields. The effects studied here might therefore be interpreted as a transition between the dilute and concentrated solution types of solvent organization.
Acknowledgment. The author is indebted to Mr. R. B. Quincy and Mr. D. E. Lavalle for preparation of some of the purified salts used and to Dr. T. F. Young for critical reviews and discussions of the manuscript. (34) 0. Ya. Samoilov, “The Structure of Aqueous Solutions and the Hydration of Ions,” English Translation, Consultants Bureau, New York, N. Y.,1965,p 134.
