J. H. STERNAND C. W. ANDERSON
2528
butane, 5 and 7.5, totally unreasonable, especially in view of the drastically different flash conditions. One would also expect a large yield of hydrogen in Thrush's exerp ments which may have escaped detection in his analytical system. This effect of mercury diethyl pressure may be attributed to the increased importance of reaction 11 over that of reactions 16-18 and the requirement of a third body for reaction 3 at low pressure. It should be noted that no reactions have been suggested here to account for the traces of butene and propylene observed in trace yields. Surface reactions have beenpostulated by others2s3to account for butene a t low intensity. Because of the relatively high extinction coefficient3 of mercury diethyl in the region 2000-2400 the absorption of actinic radiation results in a rather higher concentration of free radicals
near the walls of the cylindrical reaction cell than in its center. This tends to emphasize surface reactions. Indeed, because of the pronounced surface effects reported in Table 11, considerable uncertainty must be attached to the preceding interpretation and, indeed, to all mechanistic deductions which have been unable to distinguish quantitatively the extent to which a particular product is formed heterogeneously.
Acknowledgment. This research was supported by the Directorate of Chemical Sciences, Air Force Office of Scientific Research, Grant No. 513-64, and grateful acknowledgment is made thereto. The authors wish to thank Mr. S. Wrbican for determining the mass spectra of the product mixtures. Mr. Robert Cornel1 is thanked for preparing a sample of mercury diethyl.
w.,
Thermodynamic Properties of Aqueous Solutions of Mixed Electrolytes. The Potassium Chloride-Sodium Chloride and Lithium Chloride-Sodium Chloride Systems at 25"
by J. H. Stern and C. W. Anderson Department of Chemistry, California State College at Long Beach, Long Beach, California 90804 (Received Match SO, 1964)
-~
Heats of mixing a t constant total molality of aqueous KCl with YaC1 and LiCl with XaC1 over a wide concentration range (0.5 m to near saturation of the less soluble components) were determined calorimetrically a t 25' and fitted to an equation based on Harned's rule. The heats are discussed in relation to deviations from the Br@nsted-Guggenheim theory of specific interaction and are combined with excess free energies calculated from isopiestic vapor pressure data to yield excess entropies of mixing.
I. Introduction Mixed strong electrolytes in aqueous solution form an important part of many systems whose diversity ranges from sea water to physiological fluids. As a consequence of the complex interactions in such elecThe Journal of Physkal Chemistry
trolyte systems, their theoretical nature is not well understood and further advances are haiwered by 8. paucity of data. This paper is the second in a series reporting on the changes in thermodynamic properties when the
THERMODYNAMIC PROPERTIES OF AQUEOUS SOLUTIONS OF MIXEDELECTROLYTES
simplest type of ternary mixture is formed from two binary uni-univalent strong electrolytes with a common anion a t constant total molality. The first contribution describes heats of mixing and associated excess thermodynamic properties calculated from the heats and results of e.m.f. measurements for the system HC1-NaC1.I Excess thermodynamic properties are equal to the difference between the total and ideal property changes, respectively, when the mixture is formed from its coniponent solutions a t constant total molality, temperature, and pressure. The excess free energy of mixing AFmE is thus AFmE = AFm
- AFm
(1)
where AF, is the total free energy change and A F m is the free energy change anticipated if the mixing process takes place ideally. The excess heat of mixing AHmEis defined similarly, except that in this case AHmiis zero and AHmE= AHm. A F m E may be calculated from activity coefficient data of binary components in mixed ternary solutions. The activity coefficients obey Harned’s rule’ in many such systems log
7 2 =
log
72~0)
a ~ 3 [ m (l X2) I
-
P23[m(l - Xz)I2 ( 2 ) log
7 3
=
log
73(0)
- a3~[(mX2)1 - P32[(mX2)I2 (3)
where y z and y3 are the activity coefficients of electrolytes 2 and 3 in thLe presence of each other a t solute mole fractions X z and 1 - X 2 , respectively, and total molality m. yzc0)arid 7 3 ( 0 ) are the activity coefficients of the pure binary electrolytes a t niolality m. KCI-KaCl and LiC1-NaCl are two systems approximately obeying this rule. Values of individual Harned coefficients were obtained from isopiestic vapor pressure i i i e a 3 ~ r e n i e n t s . ~A~ subscript ~ 2 in all equations will refer to components KC1 and LiCl in their respective systems, while a subscript 3 will pertain to NaCl. For two uni-univalent electrolytes obeying Harned’s rule A F m E per mole of solute can be shown to take the form4
AFmE= -2.303RT(Xz)(l
- X 2 ) m [ ( a ~+ 3 a32) +
2529
A H , = 2.303RT2X2(l- X 2 ) m
at Xa
=
X3 = 0.50 eq. 5 reduces to
and eq. 4 becomes
AF,~
=
- 2.303RTm 4
[(a2a
+
a321
+ m ( ~ 2 3+
632)I
(7) AH, thus leads to the fixing of the temperature derivative function of the Harned coefficients which m(P23 P3dI/bT. For a t X = 0.5 is b[(a23 a321 brevity, this function will henceforth be called C. A F m E and AH, may be examined in relation to the Brqinsted-Guggenheim theory of mixed electrolytes based on Brqinsted’s principle of the specific interaction of ions.6 This principle assumes that specific short-range interaction in solutions of constant total molality is limited to ions of opposite charge only. Ions of like charge influence each other uniformly without regard to their species. The theory leads to a very simple result for mixing two electrolytes with a coiiinion ion a t constant total molality. No net changes in specific interaction are predicted and consequently A F , E and AH, are zero for such systems. Harned’s eq. 2 and 3 are consistent with the theory when a23 equals -a32 and all 0-coefficients are zero. n’onzero values of AFmE and AH, could be considered as a measure of the deviations from the Brgnsted-Guggenheim theory, and on this basis attributed to differences in interaction between like charged ions. It may be noted that the p-coefficients differ in magnitude for each system; for KC1-NaC1 p 2 3 = 0 and p 3 2 = -0.005, while for LiC1-KaC1 p 2 3 = 032 = -0.001. For the former system2 the term [ ( a 2 3 ~ ~ 3 2 ) m(pZ3 p 3 2 ) I of eq. 7 remains essentially constant (0.0136 measured a t m 2 l ) , while in the latter case3this
+
+
+
+
+
+
(1) J. H . Stern and A. A. Paaschier, J. Phua. Chem., 67, 2420 (1963).
Both electrolytes are initially at molality m and yield
(2) R. A. Robinson, ibid., 65, 662 (1961).
(3) R. A. Robinson and C. K. Lim. Trans. Faraday Soe., 49, 1144
a final solution of total molality m with solute mole fractions X z and 1 - Xp, respectively. AHnlper mole of solute may be obtained by combining eq. 4 and the
K. S. Pitzer and L. Brewer, McGraw-Hill Book Co., Inc., New York, N. Y., 1961, p. 572.
Gibbs-Hclmholtz equation
(5) See ref. 4, pp. 345, 569.
(1953). (4) G. N. Lewis and M. Randall, “Thermodynamics,” revised by
Volume 68, Number 9
September, 1984
2530
J. H. STERNAND C. W. AXDERSON
function increases from -0.010 a t 2 m to -0.003 a t 6 m. All isopiestic vapor pressure experiments were performed a t 25'. Calorinietric heats of mixing a t this temperature for the two systems a t unit total molality have been determined by Young and Smith.6 We have extended these measurements to concentrations ranging from 0.5 m to near saturation of the less soluble components in each of the two systems, respectively. These heats will show the nature of thermal interaction between such binary electrolytes and provide an accurate measure of deviations froni the BrgnstedGuggenheim theory over wide ranges of concentrations. In combination with AFmE excess entropies of mixing ASmE will be obtained via ASmE
=
AH, - A F , ~
T
(8)
IP. Experimental Calorimeter and Experimental Procedure. The calorimeter consisted of a 660-ml. cylindrical vacuum flask with a tightly fitting polystyrene cover whose interior portion reached into the flask to a depth of 7.5 cni. Passing through the cover were separate thin thermistor and heater probes, an off-center glass stirrer shaft with three tantalum propellers spaced a t equal intervals, a hollow Teflon shaft for mounting the mixing device, and an accessory port. A speed eontrolled motor drove the stirrer. Energy equivalents were plotted on a 1-mv. recorder (Bfown Electronik), utilizini the amplified (Leeds and Sorthrup pv. amplifier) off-balance potential from a Wheatstoiie bridge network. The bridge consisted of two six-dial resistances, a linear potentiometer, and the thermistor (Fenwal, 2.1 kohms a t 25'). Each of the three variable arms was set at a resistance approximately equal to that of the thermistor. The bridge was powered by two niercury batteries in parallel (Mallory WR142R, 1.35 v.) whose net e.m.f. was adjustable by a 10-kohni potentiometer. The calorimeter vessel was immersed to the level of the exterior of the styrofoani cap in a highly insulated enclosed 20-1. water bath, The temperature of the bath was regulated a t 25.000 + 0.001'by a proportional controller (Electron-0-therm 148) and loa--lag knife heater balanced against a submerged cooling coil. All runs were initiated a t 25.000 f 0.005' in a room controlled a t 24 i 1'. A heater coil (Karma, 404.2 ohms) immersed in Octoil and contained in a thin glass tube was used for calibration. The energy for the heater was furnished by a d.c. power supply (Power Designs 4005). The The Journal of Physical Chemistry
current was determined by measuring the potential drop across a standard 1-ohm resistance in series with the heater by means of a millivolt potentiometer (Rubicon 2702). The time of heating is given by an electric centisecond stopclock synchronized with the heater switch. Calibrations were performed after every measurement. The mixing device was fabricated from 0.5-mil polyethylene film. Two layers of film were sandwiched between molds and were heat-sealed along all edges except the top. A cylindrical tube with a sharply tapered bottom was formed (50-ml. capacity, approximately 0.1-g. weight). The tube mas filled with a weighed portion of one of the pure binary electrolytes and was tied with cotton thread to the end of the hollow Teflon shaft mounted in the cap. Passing through the shaft into the tube was a thin glass arrowshaped ramrod. Prior to a measurement the filled portion of the tube was submerged in the surrounding calorimeter liquid (400 ml.) consisting of an aqueous solution of the other electrolyte and was allowed to equilibrate; the end of the Teflon shaft remained above liquid level. A run was initiated by piercing the tube and withdrawing it from solution to facilitate compete mixing of the two electrolytes to produce a ternary solution. Details of subsequent mixing steps are described el~ewhero.~A very small volume of reactant solution was retained in the tube (ea. 0.3 cc.). Heat capacity corrections for the withdrawn tube were negligible. The calorimeter and mixing device were tested by measuring A H , for 1 m YaC1-LiC1 at 25'. The results are shown in Fig. 1 together with the data of Young and Smith. The agreement is excellent. The lowest heats per run determined with this apparatus were approximately 0.3 cal. corresponding to a temperature change of 6 x 10-4' with an over-all experimental error of =t0.570. The calorinieter was also checked for over-all accuracy by measurements of the heat of solution of KCl(s) in water. Glass ampoules were used to hold the small amounts of solid sample. These were attached to a glass rod by a Teflon coupling and were crushed against the bottom of the dewar. The mean of four determinations corrected to a molar ratio of 1:200 for KC1/HzO (4200 f 7 cal./niole) deviated 0.2% from the average based on the results of eight independent recent studies* (4191 f 14 cal./mole). (6) T. F. Young and Yi. E. Smith, J . P h y s . Chem., 5 8 , 716 (1954). (7) T. F. Young, Y . C. Wu, and A. A. Krawetz, Discussions Faraday Soc., 24, 37 (1957). (8) G . Somsen, J. Coops, and M. W. Tolk, Rec. trau. chim., 8 2 , 231 (1963).
THERMODYNAMIC PROPERTIES OF AQUEOUSSOLUTIONS OF MIXEDELECTROLYTES
A
b bT
+
= - [(a23
B
=
2531
+ 2/am(2P23+ P d l
cy&)
b bT
- [-2/3m(P23 - P d l
(10) (11)
While A is related to the magnitude of AH,,, the parameter B pertains to the asymmetry of the ckves in Fig. 1 and 2. When B = 0, the curves become symmetric about X = 0.5 and A becomes equal to the pararneter C. Thus
-lim A -
-O
c
=
1
and this ratio can be conveniently used as a relative measure of the asymmetry. Table I shows a summary of the parameters A , B, C, and A / C for both systems.*,
0
1.0
0.5
xrtci. Figure 1. Heats of mixing ( -AHm), KCI-NaC1, as a function of the solute mole fraction of KCI ( X R C ~ ) .
Materials. All salts, A.R. grade, were kept a t 150' 12 hr. prior to weighing and dissolved to the desired molalities with weighed quantities of triply distilled water. No difference in results was observed when the salts were recrystallized from aqueous solution prior to use. 111. Results and Discussion Observed values of AH," for NaCl-KCl as a function of the solute mole fraction X of KCl for 0.5, 2, 3, and 4.8 m solutions are represented by symbols in Fig. 1. Those for NaC1-LiCl a t 0.5, 1, 2, 3, and 6 m are shown in Fig. 2 as a function of X of LiCl. The data reported by Young and Smith a t 1 m are shown in both figures. The curves represent the fit of all data, by the method of least squares, arranged in analytical equations of the type
+ BXp)
AH,,, = 2.303RT2mXz(l- X Z ) ( A
0
0.5 XLiCi.
1.0
Figure 2. Heata of mixing ( A H , ) , LiCl-NaC1, as a function of the solute mole fraction of LiCl (XLIOI).
(9)
This equation is consistent with the requirement that A H , must become zero identically for both pure binary electrolytes. A and B are constants; these constants expressed in terms of eq. 5 are
(9) An error in ref. 1 may be corrected by multiplying the values of Table I and I1 by m, while AFmEof Table I11 should be divided by m before combining with AH,,, t o obtain AS,". This error arose when AHm in cal./mole was combined with equations of ref. 4 based on A H w in cal./kg. of solvent. Note that AH^ =mAH,. We are grateful t o Dr. R. H. Wood for bringing this t o our attention.
Volume 68, Number 9 September, 1.964
,J. H. STERNA N D C. W. ANDERSON
2532
Table I : Summary of Parameters A , B, C, and A / C KCI-NaCI
-A X 10’ - B X 106
-c x
106
AlC
9 0 9 0
10 2 -1 05 969 10
A /C a
106
5 98
8 31 0 750 869 0 96
7 66 1 09 821 0 93
7 71 0 298 786 0 98
-
_____ __________ 1
05
c x
32
LE-NaCI
A X 106 R x I06
3
20 5 1 45
19 0
3 I1 20 5 0 92
21 2
0 97
Values based on data
in
2
15 1 4 18 17 2
0 88
3
6
11 2
4 84
6 00 14 2
0 79
6 05 7 87 0 62
A similar asymmetry has bcen observed a t 25’ and lower ternperaturcs in the endothermic systrni HCIXaC1, with niaxiiiia displaced toward the HC1-rich side. In this case the proton is thought to bond water molcculrs to an extent comparable with the lithium ion.” Thc activity coefficient of pure HCI behaves similarly to that of pure I X 1 as a function of niolality. It is likely that thcrc is a correlation hrtween the observed asymmetry and the discusscd differcnccs in activity coefficients of the pure binary clectrolytcs. Figure 3 shows values of AH,,, at X = 0.50 for both systems plotted as a function of molality. These curves also differ in bchavior at higher concentrations. That for NaCI-KCI shows an approxiiriatcly linear variation with molality over the entire range. l’or NaCl-LiCl AH,,, tends to level out a t higher concentrations. Extrapolations below 0.3 ?n are shown with
ref. 6. 50
An examination of AHTnin Fig. 1 and 2 and data in Table I shows considerable differences bctween the two systems. All NaCI-KC1 curves in Fig. 1 are exothermic. They are nearly parabolic and are thus consistent with the quadratic dependence of A H , on the solute mole fraction X. Thcy exhibit little asymmetry as can be seen from values of the ratio A / C which do not deviate appreciably from unity a t all concentrations. Values of C show a regular trend in becoming less ncgative with increasing molality. All SaC1-LiC1 curves in Fig. 2 are endothermic. At low concentrations they show little asymmetry, but the maxima become progressively displaced from X = 0.50 toward the LiC1-rich side with increasing molality. AHm is always more endothermic in mixtures rich in LiCl than in SaC1-rich solutions of corresponding composition. The ratio A,’C ranges from 0.97 at, 0.5 m to 0.02 at 6 m. C decrcases rapidly as the conceritratiori increases. The differences in symmetry for both systems may in part be related to specific ion effects in the pure binary elrctrolytes. One niay examine the behavior of the activity coeficients for the pure binary electrolytes y o as a function of molality. As the concentrations increase the curves for yo begin to separate and to exhibit marked specific ion effects. The spread in yo between LiCl and SaCI becomes much larger than that between KC1 and SaCI.’”” This is thought to be mainly due to the stronger hydration of the lithium ion as a consequence of its high charge density. Thus, LiCl arid SaCl are two electrolytes which on this basis niay be considered “less alike” in nature than KCl and SaCl. The Journal of Physical Chemistry
1
40
30
.
IC
20
0
n
2
IO
i
s
-t E
> o
E
2 - 10
- 20 - 30
- 40 0
1
3
2
4
5
c,
m
) solute mole Figure 3. H e a b of mixing ( A H m L at fraction 0.5, KC1-XaCI a n d LEI-NaCI, as a function of the total molality (m).
S. Harned and B. €3. Owen, “The Physicul Chemistry of Electrolytic Solutions.” 3d Ed., Reinhdld Publishing Carp., S e w York, N.Y., 1958. p. 513. (11) 11. hl. Diamond, J . Am. Chrm. Soc., 80, 4808 (1958) (10) H.
1"EIZMOI)YNAMIC
2533
I'I1OPEKTIEY O F AQUEOUS SOLU'l'IONS O F AIIXED 14:LECTHOLYTES
Table 11: Summary of AFmn>AH,,,, and ASuE at X
=
0.50
KCI-NaC1
AP,,'", c.al./rnole AH,,, cd./rnole As,,,l';, (:d./rnole deg.
-
0.5
1
2
-4.93
-4.6 -9.62 -0.017
-9.3 -17.7 -0.028
3
- 14 -25.1 - 0 . 037
4.8
- 22 -:38.4 - 0 . 053
LiC1-NaC1 m0.5 @,,IC,
1
c:al./mole
AH,,,, c:al./rnole
10.8
20.9
cd./rride deg.
dashed lilies. It s(?cnis that in both systems thermal effccts, without changt in sign, may persist to very dilutct niixturcs. I t is recognized that such cxtrapolatioris are speculative, particularly in view of the frequently unpredictable behavior of thermodynamic propcrt,ies as iiifiriite dilution is approached. Tabltt IT givw valucs of all threc theriiiodynarnic excess propwtics AFn,'",AIZ",, and ASrnE a t X = 0.50. I t iiiay be iiotcd that for NaC1-KC1 all three properties iricrcaso ill absolutc iiiagriitude with increasing molality. Siriiilar trc:iids were observed for the HCl-NaCl system. 1 . 9 Icor SaCI-T,iCI AI^'^^'' remains essentially coristarit aiid orily and ASlnE increasc with concentration. It appears that adherence to the HrgnstedGnggcnhcini theory iniproves with decreasing coticcntration, that is, thc diffcrenccs bctween the short
2
6.8 35.0 0.09
.-
8
fi. I 43.3 0.12
6
6.I 48.0 0 . 14
rarigc rcpulsivc intcractions of hydrated likc-charged ions diminish. In each of the two systeiiis and at all niolalities all threc cxcess properties show the sanie algebraicssign. It iiiay also be iiotctd that, the (trror in calculated valucs of AF,nfi'is highw than that of AHm,especially a t higher niolalititts, partially bccause of the large uriccrtainty of the torlii m(& &) iii cq. 7. T h e absolute magnitude of AS,,," is siiiall in coniparisori to AS,' particularly for S a W K C l . Its quantitative significarice is riot firm sincc it is obtailictd by difference of two riunibcrs of similar tnagnitudc and varying accuracy.
+
Acknowledgment. The authors arc grateful t,o the United States Army Research Office (Durhani) for financial support.
Volume 68, IYumher 9
September, 101;4
