R. H. WOOD,J. D. PATTON, AND M. GHAMKHAR
346
Heats of Mixing Aqueous Electrolytes.
VI.
Magnesium Chloride
with Some Alkali Metal Chlorides1 by R. H. Wood, J. D. Patton,2and M. Ghamkhar Department of Chemistry, University of Delaware, Newark, Delaware
(Received July 18, 1968)
The heats of mixing aqueous solutions of magnesium chloride with the chlorides of lithium, sodium, potassium, and cesium at constant ionic strength have been measured a t 25' and ionic strengths of 0.5 to 3.0. The magnitudes of the heats of mixing are similar to the magnitudes of the heats of mixing two alkali chlorides. A t the lower concentrations RTho becomes more positive. -4trend to plus infinity for RTho is expected from the limiting law. If the contributioiis of oppositely charged ions are estimated and subtracted from the heat of mixing, the sign of the remainder correlates reasonably well with the properties of the water structure around the two cations. This observation extends the correlatioii to charge-asymmetrical mixtures.
Introduction Recent work on the heats of mixing electrolyte solutions has mostly been confined t o charge-symmetrical mixtures, that is, mixtures of salts of the same charge t ~ p e . ~ - For ' ~ these mixtures it has been shown that pairwise interactions of like-charged ions are generally more important than triplet and that a set of equations for predicting the heat content or free energy of many component mixtures can be derived using this informatio~i.~& The equations me accurate for mixtures of three s a l t ~ . ~ Further a work has shown that the structure of the water around the ions is the important factor in determining the sign of the heat oi m i ~ i n g . ~The purpose of the present investigation was to collect data on :L representative charge-asymmetrical mixture and to see in what ways the conclusions and theories developed on the basis of charge-symmetrical mixtures are affected by the charge asymmetry.
Experimental Section The details of the experimental procedure have been given elsewhere.'l Potassium, sodium, and magnesium chloride were Fisher Certified reagents and no impurity was greater than 0.01%. Cesium chloride (99.9%) was obtained from ICawecki Chemical Co. Lithium chloride (99.7%) vias furnished yratis by Foote Mineral Co. The LiCl and CsCl were analyzed for impurities by flame spectrophotometry and found to contain 0.01% or less alkali metal or alkaline earth impurities. Stock solutions mere prepared using deionized distilled water and the concentration determined gravimetrically with AgKO,. Operating solutions whose concentrations were accurate to 0.1% were prepared by weight dilution of the stock solutions. Heat of mixing was measured in a twin calorimeter which has been described previously.8J2 Errors in the measured heat of mixing due to hydrolysis and The Journal of Physical Chemistry
neutralization were reduced to a negligible level by adjusting the pH of all operating solutions to 4.0-5.0 prior to use. Heat of dilution errors due to slight differences in the concentrations of the solutions m-ere calculated to be no larger than the standard deviation of the data. Errors arising from impurities in the reagents are negligible.
Results and Discussion The experimental data were fitted by the method ol least squares to the equation A H , (callkg of solvent) =
where I is the molal ionic strength, y is the ionic strength fraction of magnesium chloride, hois a measure of the magnitude of the interaction, and hl is a measure of the skew of the interaction. The heats of mixing mere measured in the ranges y = 0-0.2 and y = 0.8-1.0. (1) Presented a t the Middle Atlhntic -Meeting of the American Chemical Society, Feb 2, 1968. (2) E. I. du Pont de Nemours and Co., Inc., Wilmington, Del. (3) T. F. Young and M. B. Smith, J . Phys. Chem., 58, 716 (1954). (4) T. F. Young, Y. C. Wu, and A. A . Krawetz, Discussions Faraday Soc., 24, 37, 77, 80 (1957). (6) J. H. Stern and A. A. Passchier, J . Phys. Chem., 67,2420 (1963). (6) J. H. Stern and C. W. Anderson, ibid., 68,2528 (1964). (7) Y . C. Wu, M.B. Smith, and T. F. Young, ibid., 69, 1868, 1973 (1965). (8) R. H. Wood and R. W.Smith, zbid., 69, 2974 (1965). (9) (a) It. €I. Wood and H. L. Anderson, ibid., 70, 992, 1877 (1966); (b) R. H. Wood and H. L. Anderson, ibid., 71, 1869, 1871 (1967). (10) M. S. Stakhanova, M. Kh. Karapetyants, I. V. Bazlova, and K. K. Vlasenko, Buss. J . Phys. Chem., 40, 553, 1000 (1966). (11) J. D. Patton, Ph.D. Thesis, University of Delaware, 1968. The results for the MgCla-KC1 mixture and all of the three salt mixtures containing sodium chloride are incorrect due t o errors in the concentrations of the solutions. (12) H. 8. Jongenburger and R. H. Wood, J . Phys. Chem., 69, 4231 (1965).
HEATSOF MIXINGAQUEOUSELECTROLYTES
347
-~
Table I: Heat of Mixing, 111gClz-MCl Ionia strength
RThoa
LiC1-MgC12
0.5 1 2 3
5 f 2 - 1 . 8 40 . 2 - 8 . 7 f0 . 2 -12.75 rf 0 . 0 4
NaC1-MgClz
0.5 1 2 3
189 42 172.5 f 0 . 9 138.8 rt 0 . 4 113.6rir 0.6
KCl-M@lz
0.5 1 2 3
108 f 2 86.7 rt 0.6 54.0 A 0 . 2 31.7 f 0 . 3
-8f4 - 4 f l - 3 . 1 f 0.4 -1.5 f0 . 6
15 8 7 6
CsC1-MgClz
0.5
73 f 2 19.0 f 0 . 4 -23.7 f 0 . 5 -49.6 f 0 . 1
-2.5 f4 2 1 1 2 . 7 A 0.8 9 . 6 f0 . 2
8 12 7 14
Salt pair
1 2 3 a
Units are calories per kilogram of solvent per ional squared.
The results together with the number of data points are given in Table I. Any points that differed from the least-squares fit by more than about twice the standard deviation were rejected. An examination of the results in Table I shows that RTho,which ranges from - 50 to 190, is of the same order of magnitude for these mixtures as for the mixtures of the alkali metal halides which range from 85 to - 195.' This is somewhat surprising since in these mixtures the concentration of chloride ion changes during the mixing so that oppositely charged pairwise interactions contribute to heat of mixing. The result is that Young's rule8 (which is equivalent to assuming RTho = 0) is about as good an approximation for these mixtures as for the alkali halides. One of the most striking things about the values of RTho plotted in Figure 1 is that they all turn toward more positive values a t low concentrations. This is in contrast to the results for charge-symmetrical m i x t ~ r e s ' ~ where J~ the curves are relatively flat. Friedman predicted that for charge-asymmetrical mixtures RTgo (the free-energy analog of RTho) would go to - 05 as In I when 1 approaches zero. This is n limiting law and is independent of the model. It depends only on the properties of the solvent arid the charge types of the electrolytes. The derivation of the limiting-law coefficient for both RTgo and RTho starts with eq 17.8 of Friedman13
Ge" - DHLL - = RT
--[3V1 -1 ns nz
In I
~ 2 1 2
.+ o p )
(2)
R Thi
Nb
-2.5 A 2 - 1 . 3 f0 . 2 -0.3 f0 . 2 -0.76 f 0.06
4 15 8 15
-6f2 -12 f 1 -15 A 1 -184 1
14 14 16 14
Number of experimental points.
160
c. 80
ca:
0
1
2
3
I.
Figure 1. IZTh vs. molal ionic strength for alkali metiil chloride-magnesium chloride mixtures. The limiting law is indicated by R dashed line.
applied to L: mixing experiment to give DHLL =
Am(S), &(F)
(13) H. L. Friedman, "Ionic Solution Theory," Interscience Publishers, New York, N. Y.,1962,p 244. (14) H.L.Friedman, J. Chem. Phys., 32, 1134 (1960). Volume 73,Number 8 Februaru 1968
348
R. H. WOOD,J. D. PATTON, AND M. GHAMKHAR
where the symbolism is Friedman’s. The change in the Debye-Hiickel limiting law (DHLL) is zero and for a mixture of a 1-1 electrolyte with a 2-1 electrolyte Am(n3’/nZ2) = y 2 , where y is the ionic strength fraction of 2-1 electrolyte. This gives
Gex/RT = - (A2/3V)y212 In I
+.
,
.
(4)
which is used to calculate AGex for the mixing
AmGex = (A2/3V)RT12y(l- y ) In I
(5)
but by definition AmGex = y(1 - y)12RTgo
(6)
so that go = (A2/3V)In I
(7)
and this is the limiting law for free energy. Using Friedman’s eq 18.5413
ho = - T [bgo/bT] gives
(’-d dad-T_ -D-bbD-T-
ho = - ( T A 2/3 V )
(8)
’) T
In I
cluster integrals, B(x,y,z), are integrals involving (x) magnesium ions, ( y ) sodium ions, and ( 2 ) chloride ions. Thus, for this kind of mixture, all possible pairs of ions contribute. For a charge-symmetric mixture x1 is equal to 22 and the last three terms in eq 11 cancel so that only cation-cation pair terms are left. It has been shown earlier that the sign of the heat of mixing could be correlated with the effect of the ions on the water structure for common-ion, charge-symmetric mixture^.^ The rule is that two structure-making ions or two structure-breaking ions give a positive value of RTho whereas mixing a structure-maker with a structure-breaker gives a negative RTho. Since the ion-pair interactions are the major contributors to these mixings, it is the heat effect of the cation-cation interactions which correlates with the water structure (the first three terms of eq 11). Thus, a similar correlation of the present results for charge-asymmetric mixtures is not expected. The results in Table I confirm this expectation. I n 1935 Guggenheiml* derived an equation for mixed electrolytes which, when applied to the present case,Iggives
(9)
RTho =
For water at 25” the numerical values are go = 1-05log I ; RTho
-633 log I
(10)
Thc limiting law is shown as a dashed line in Figure 1. An eventual trend toward 00 is predicted by the limiting law. The values of RTho do increase as the concentration decreases but there is no sign of quantitative approach to the limiting law. This is not surprising at ionic strengths of 0.5 and higher. The free energy measurements of alkaline earth chloridealkali metal chloride mixtures generally do not show the corresponding decrease in R Tgo as the concentration decreases, even a t 0.751.15316 Friedman has shown that HC1-AlCL mixtures do show the expected tre11d.l~ The interactions between two ions which contribute to a charge-asymmetric mixture with a common ion have been calculated by Friedman”
+
(X:zY?J
-
(21
- z2)B(0,0,2)
Zs(z1
- Za)(22 - 23)
(
where for a NaC1-MgCl2 mixture XI = z(Mg2+) = +2, 22 = z(Na+) = $1, and 23 = x(Cl-) = -1. The The Journal of Physical Chemistry
where the B terms are the interaction coefficients of the anion-cation pairs.lg Values of dB/bT at low concentration were taken from Lewis and Randalllg and the calculated values of RTho are given in Table 11. The values of RTho calculated from Guggenheim’s equation are not very close to the experimental values. This is expected because the like-charged ion interactions in eq 11 (B(l,l,O), B(2,0,0), B(0,2,0), and B(0,0,2))are ignored. The calculation is interesting because it gives a rough estimate2”of the cation-anion interaction terms (B(1,Ol) and B(O,l,l)) of eq 11. A comparison of the calculated and experimental values of RTho in Table I1 shows that the neglected terms are about as large as the catiowanion interactions. Guggenheim’s new equationz1 includes like-charged ion interactions but is not applicable to charge-asymmetric mixtures. It might be expected that the cation-cation inter(15) (a) R. A. Robinson and V. E. Bower, J . Res. Nat. Bur. Stand., 69A,19, 439 (1965); 70A, 313 (1966); (b) R. A. Robinson and A. K. Covington, ibid., 72A, 239 (1968). (16) J. ,N. Butler and R. Huston, J. Phys. Chem., 71, 4479 (1967). (17) H. L. Friedman, ref 13, eq 18.36. (18) E. A. Guggenheim, Phil. Mag., 19, 588 (1935). (19) G. N. Lewis and M. Randall, “Thermodynamics,” 2nd ed, revised by K. S. Pitzer and L. Brewer, McGraw-Hill Book Co., Inc., New York, N. Y., 1961, Chapter 26 and Appendix 4. (20) This is a rough estimate because the contributions of likecharged ion interactions to the properties of the pure electrolytes are ignored. (21) E. A. Guggenheim, Trans. Faraday Soc., 62, 3446 (1966).
HEATSOF MIXINGAQUEOUSELECTROLYTES
349
Table I1 : Comparison of Experimental and Calculated RTAo Using Guggenheim’s Equation
RTho, exptl
R Tho (exptl) RTho (oalcd)
5 -1.8 -8.7 -12.75
81 74 67 63 136 120 86 61
-
Salts
Ionic strength
R ThoDaI oalcd
-76 -76 -76 -76
LiC1-Mg Clz
0.5 1.0 2.0 3.0
NaCl-MgCd
0.5 1.0 2.0 3.0
53 53 53 53
189 172.5 138.8 113.6
KCl-MgC4
0.5 1.0 2.0 3.0
68 68 68 68
108
0.5 1.0 2.0 3.0
178 178 178 178
73 19.0 -23.7 -49.6
CsCI-h/IgCl*
86.7 54.0 31.7
40 19 14 36
- 105 - 159 -202
-228
a Guggenheim’s equation applied to heats of mixing predicts that 2Tho is independent of concentration. * These values are calculated from heats of dilution and should be accurate to about f10.
actions in a charge-asymmetric mixture would obey the water-structure correlation. These interactions can be estimated in the following manner to see if the
structure rule holds. The limiting law is neglected and the oppositely-charged ion interactions (B(l,O,l) and B(O,l,l)) are estimated from Guggenheim’s equation (eq 12). The difference between the experimental RTho and that calculated by eq 21 should then be equal to the like-charged pair interaction plus-any triplet interactions. If the triplet interactions are small, as they are for the alkali halides, and if the C1-, C1- interaction is small (B(0,0,2)) then the structural correlation should hold. I n Table I1 the last column shows the value of RTho when the oppositely charged pairwise interactions are subtracted. The rule predicts that the EiCl-MgC12 and NaCI-MgC12 mixings (structure-maker, structure-maker) should have a positive RThoand the KC1-MgC12 and CSCI-M~CIZ should have a negative RTho. The prediction is correct except for the I
