N. Islam and lsmail K
2180
Density, Viscosity, and Conductance of Molten Ca( N03)2*3.99H20-KCNS Systems N. Islam’ and lsmail K Department of Chemistry, Aligarh Muslim University,Aligarh. 20200 7, India (Received February 25, 1975)
Density, viscosity, and conductance measurements of molten Ca(N03)~3.99H20and its mixtures with KCNS were made as functions of temperature and composition. Densities were least-square fitted to an equation of the form, p = a - bt(”C). Fluidity, 4, and equivalent conductance, A, data were fitted to the ”~ - T o , ~ , Aand ) ] Y(4,A) = Am,,,’ exp[-Bm,A’l(V - V O , ~ , ,based ~)] equations, Y(4,A) = A ~ , A T - exp[-km,.dT on the free volume model. Am,.\, km.6, TO,^,.,, Ad,*’, Em,.,’, and V O , ~are , A empirical parameters. Almost identical values of Vo,@and VOJ, as well as those of TO,^ and To,* were found. Composition dependences of the empirical parameters have been discussed. The molal volume, Vm, and intrinsic volume, Vo, were found to be additive in nature. The glass transition temperature, To, has been found to increase linearly with composition. The ratio of the activation energies, EmIE.,, has been found as 1.26 f 0.03. The low values of the product of the ratio of critical void volume, u * , to average molecular (ionic) volume, D,, and a geometric factor, y, yu*/ir, viz., 0.31 and 0.25 obtained from fluidity and conductance data, respectively, both in the and its mixtures with KCNS ( a = 4.5 X cases of Ca(N03)~3.99H~O (a = 4.6 X indicate that a random distribution of free volume is apparently not obtained in molten salts.
Introduction Hydrated melts allow the exploration of their properties a t relatively lower temperatures than those in the corresponding anhydrous melts. A direct consequence of these low liquidus temperatures is that the temperature dependence of the transport properties of various hydrated e.g., Ca(N03)2*4H20, Mg(N03)~4H20,Na~S203* 5H20, Ca(N0&.4H20-Cd(N03)2.4H20, Ca(NOd2.4HzOKN03, is non-Arrhenius and is well described by an equation of the form where Y is equivalent conductance, A, or fluidity, 4; A and k are constants charxteristic of the transport process and the chemical system. To, on the other hand, is a constant of the chemical system alone provided the external pressure is held constant. Equation 1 may be derived from theories which take the free volume or the configurational entropy as the important quantity in setting the temperature dependence of the liquid transport properties. To has been called the “zero mobility” or “ideal glass transition” temperature a t the specified composition and interpreted as the temperature below which no further changes in internal energy by means of rearrangements of particles into configurations of lower potential energy are possible. In most cases where the glass transition can be observed as an experimental phenomenon the transition temperature, T,, is found to lie slightly above To. Empirically it is found that the non-Arrhenius behavior implicit in eq 1 is observed in the temperature interval To to 2To. Doolittle5 suggested empirically an exponential relation of the form
d = A1 exp[-Blqolufl
(2)
for the dependence of viscosities of normal alkanes on free volume. A1 and B1 are the empirical constants. The free volume was defined as uf = u - uo, where u is the specific volume of the liquid at any temperature and uo is the specific volume of liquid extrapolated to absolute zero without change of phase. Later Cohen and Turnbul16 derived theoThe Journal of Physical Chemistry, Vol. 79, No. 20, 1975
retically such an equation based on a “hard-sphere” model. Recently Doolittle’s expression was found to hold well in glass-forming anhydrous melts7 also. An attempt has been made here to apply Doolittle’s expression to aqueous melts of calcium nitrate tetrahydrate. However, in doing so the expression has been modified to
Y(4,A) = A ~ J ’exp[-Bm,A’l(V
- Vo)l
(3)
in which A’ and B’ are empirical parameters, V is the molal volume at any temperature, and VOis the intrinsic volume or the molal volume a t To. The hydrated cation of fixed stoichiometry with larger effective size is taken as a fundamental component in hydrated melts and also in their solutions with salts having cations of low chargelradius ratios as evidenced by spectral,s-g c o n d ~ c t a n c e , ~and , ~ density1° studies. However, many measurements,11J2 especially those in which the water concentration is an independent variable, show such an assumption to be untenable. For example, kinetically, there is no stoichiometry such that the transference number of water relative to calcium ion is zero. Similarly, the formation of associated species suggest a competition between hydration and ion association rather than a fixed stoichiometry. Density, viscosity, and conductance measurements of binary solutions of molten calcium nitrate tetrahydrate and potassium thiocyanate are made. The applicability of the above models (eq 1 and 3) has been examined, and the significance of the computed parameters emphasized.
Experimental Section Commercial calcium nitrate tetrahydrate (BDH) was used as solvent in the molten state. Potassium thiocyanate (BDH) was recrystallized twice from double-distilled water. Several samples of Ca(N0&4H20-KCNS were prepared at - 6 O O . Ca(N0&.4H20 was found to dissolve up to -65 mol % of KCNS. All measurements were performed in a manner as described earlier13 except for the differences in the dimen-
2181
Density, Viscosity, and Conductance Data for Binary Systems sions of the viscometer (6.26 cSt/sec) and conductivity cell (0.76027 cm-l). Results No reaction has been found t o occur between KCNS and molten calcium nitrate tetrahydrate unlike those in the molten KN03-NaN03 system.14 The measured densities of calcium nitrate tetrahydrate a t 2 5 O are found to be 0.012 and 0.14% higher than those reported by Ewing and Mikovsky16 and Moynihan? respectively. On the basis of the density comparison, the actual H20/Ca mole ratio has been corrected to 3.99 f 0.01. Density data for each melt were least-squares fitted to a linear function of the form p = a - bt(OC), and the molal volumes, V,, along with thermal expansivities, a,were computed (Table I). The measured viscosities and conductances of pure Ca(N03)~3.99HzOa t 40° differ by 43-10% when compared (Figure 1)16with those reported by Moynihan2 for Ca(N03)2*4.04Hz0. This may be attributed to a difference in the water content in the two cases. A 2% difference in our results for every 0.01 change in the H20/Ca ratio is consistent with those of Moynihan et al.3 The molal volume of pure KCNS a t 50° has been obtained as 57.5 cm3/mol by the extrapolation of molal volume isotherm and this almost coincides with that calculated from its density data,17 viz., 57.25 cm3/mol. The viscosity has been found to increase slightly from 0 to 20 mol % KCNS and then increases linearly with composition. However, no such regularity has been found in the case of the conductance isotherm. The additive nature of fluidity and conductance data could not be estimated accurately because it involves a 100°K extrapolation of literature datal7 for pure KCNS to lower temperatures. The conductance and fluidity data (Table II)I6 show non-Arrhenius behavior and are therefore least-squares fitted to eq 1. The empirical parameters along with the standard deviations in In A and In 4 are given in Table 111. The TABLE I: Densities. Molal Volumes, and Expansivities for Ca(NO3)2.3.99HzO-KSCN Meltsa Cation fraction
a
c a2'
a
103b
1.000 0.800 0.600 0.500 0.400
1.7694 1.7627 1.7592 1.7570 1.7543
0.80853 0.78832 0.78733 0.78662 0.78570
V, at 50°, 104a at cm3/mol 50°, deg-'
136.863 120.941 105.019 97.057 89.096
4.6763 4.5743 4.5778 4.5795 4.5811
The density equation isp(glcrn3) = a - bt("C).
linear plots (Figure 2) of log ATi12 and log (bT112vs. [1/(T To)]also signify the applicability of eq 1 based on the free volume model in explaining the transport behaviors in molten Ca(NOa)p3.99H20-KCNS systems. The conventional activation energies, E A and E+, were computed from the corresponding derivatives and their corrected values were obtained (Table IV)I6 as E,,,, = EA,+ (1/2)RT. Further, values of A and 4 plotted (Figure 3) against those of (V Vo) tend to be nonlinear signifying the inability of the Hildebrand18 equation, Y(A,4) = B(V Vo)/Vo, to explain the transport behavior in the present system. However, linear plots (Figure 4) of log A and log 4 vs. [1/(V - VO)]demonstrate a better fit of these data (Table V) to eq 3.
+
-
Discussion. The parameters A, k, and To do not vary significantly with composition unlike those expected. There are a number of A-k-To sets which may adequately describe the results. As an example, the fluidity data for XKCNS (mole fraction) = 0.2 may be fitted to eq 1with a standard deviation of 0.0165 in In 4, Le., twice that for the best fit for TO,+ anywhere in the range 206.6-209.0. The corresponding ranges in A+ and k+ are 8845-7917 and 676-648, respectively. It appears likewise, from this example, that the parameter TOis the one most precisely determined by the curve fitting procedure and that small variations in it will produce much larger variations in A and k. Consequently, one does not expect a large composition dependence of To while no meaningful trends are apparent in the composition dependences of A and k terms. Recently Angel1 and B r a s ~ e l ' considered ~ k as nearly constant multiples of To in aqueous melts of calcium nitrate tetrahydrate and substituted DTo for k in eq l where D is independent of composition. However, such a variation in k with composition has not been observed in the present case. This has been supported by an empirical rule1t4s20which states that the k term is composition independent for systems in which the composition changes do not alter the melt structure in too radical a fashion as found in a large variety of fused nitrates and chlorides and concentrated aqueous solutions. Therefore, the parameters A and To were computed by using almost constant values of k by the method adopted by Moynihan et al.3 The standard deviations for the fits with equal k terms are slightly larger than the best fit standard deviations (Table VI).16 However, such a fit gives TO,+ values approximately equal to To,* values within f 2 O as expected. A gradual increase in A and To values with composition has been observed (Table 111). A constant value for k is also expected in the light of
TABLE 111: Parameters for Eq 1 for the Fluidity and Electrical Conductance of Ca(N03h-3.99HzO-KSCN Melts Selected to Give Almost Constant k6 and kh Values Cation fraction 0 .o
0.2 0.4 0.5 0.6
Std dev 8579.9 86 84.4 9360.0 9430.2 9617.5
671.16 673.38 676.50 675.50 676.00
205.50 206.51 21 1.74 215.00 217.50
,o .009 19 0.00887 0.00817 0.01994 0.00709
Std dev 2120.1 2406.2 2912.1 3367.3 3583.9
542.53 547.69 545 .oo 544.30 542.00
203.40 206.98 210.60 214.31 216.44
0.0308 0.0163 0.0192 0.0159 0.0187
The Journal of Physical Chemistry, Vol. 79, No. 20, 1975
2182
N. Islam and lsmail
[lI(T-T,)] Figure 2. Plots of log
K
-
1.1 I1 IV
0.5
07
0.9
0.l
0.9
1.1
1.3 1,111,V
6.0
7.0
x102
Y(d,A)T"* vs. [ l / ( T - TO)]for molten Ca(N03)2-3.99H20-KCNS systems
3.0
L.0
5.0
8.0
(V-v, 1 Figure 3. Plots of &$,A) vs. ( V
-
V,) for molten Ca(N03)2-3.99H20-KCNS systems.
Cohen and Turnbull's "hard-sphere'' model6 in which k = yu*/aDm,where a is taken as the mean value of the expansion coefficient for a temperature change from TOto T and y is geometric factor to correct for the overlap of free volume in the calculation of the probability of occurrence of a critical void. On the basis of this model the diffusion coefficient of solutes, e.g., KCNS in this case, will be governed by the molecular size. If the solute molecule is smaller than The Journal of Physical Chemistry, Vol. 79. No. 20, 1975
the solvent molecule it will diffuse a t the same rate as that of solvent since the diffusive transport is completed only by the jumping of a neighboring solvent molecule into the vqid. In the case of conductance C ~ ( H Z O )may ~ ~ +act as a solvent cation of larger size. No doubt, the rate of diffusion will decrease by the addition of solutes due to a decrease in the average free volume per molecule. Consequently the critical void volume, u * , should remain the same both in
2183
Density, Viscosity, and Conductance Data for Binary Systems TABLE V: Best Fit Parameters for Eq 3 for the Fluidity and Equivalent Conductance of Ca(N03)2.3.99HzO-KSCN Meltsa Cation fraction
K' 0.0 0.2 0.4 0.5 0.6 a
Vo, e X t r R I )
1.Or
Am'
vo,m
BQ'
Std dev in In q5
0.0166 32.47 130.23 220.03 114.86 0,0110 271.43 31.42 99.90 0.0167 311.88 28.35 0.0147 92.02 474.85 30.90 0.0265 84.38 631.57 30.90 is obtained by extrapolating the plot of Vvs. T to TO.
.,
AA ' 52.656 84.210 123.040 177.500 224.18
B,'
0',
25.308 26.000 23.016 26 .OOO 24.357
A
130.04 114.79 99.98 91.79 84.42
Std dev in In A
VO,extrap
0.0502 0.0219 0.0408 0.0589 0.0359
129.25 114.30 99.50 92 .OO 84.75
1 independent of composition for the system under consider-
. 0.6
[llC v-vo i] Flgure 4. Plots of log Y(4,h)vs. [ 1/( V 3.99H20-KCNS systems.
- Vo)] for molten Ca(NO&
the cases of solvent and the molten mixture containing solutes of smaller molecular size. Since a varies by about 2% in the composition range studied, yv*/6, (or l z ) itself must be substantially independent of composition. The value of k+ = 676OK conforms with the value obtained by Moynihan2 for Ca(N03)~4.04H20and that of k A = 542OK is somewhat lower. The yv*& values are found to be 0.31 and 0.25 in the cases of fluidity and conductance, respectively, both for Ca(N0&3.99H20 ( a = 4.6 X and its mixtures with KCNS ( a = 4.5 X The value 0.25 seems to coincide with those for anhydrous melts2O obtained from conductance study. The ratio k + / k A = 1.24 is very close to those reported by others,2l viz., 1.18-1.2. The higher value of k + than k k appears to originate from the differences in E+ and E A which have actually been .observed here. The corrected activation energies for fluidity and conductance, E,,,,, are tested for linearity with the function [ T / ( T- To)]2for the most appropriate choice of To. The values of l z + , ~for different compositions have been calculated from the slopes of such plots: for example, k + ( X K C N S = 0.0) = 670.8, k+(XKcNs E 0.2) = 671.0, k+(XKcNs = 0.4) = 670.8, k m ( X K C N S = 0.5) = 676.1, and ~ + ( X K C N S= 0.6) = 679.2. Similar constancy in the values of k A has also been observed. This further signifies that k+,k remains almost
ation. From the activation energy isotherms (Figure 5)16 it is apparent that changes in E + and E A with composition are considerably less in the low concentrated region and become larger at higher concentrations. At low temperatures activation energies for fluidity and conductance are comparatively larger and the isotherms become more and more steep. According to the free volume model6 average free volume per molecule decreases with increasing composition and the molecules get closer and closer resulting in high intermolecular forces. consequently, in the concentrated region the flowing entities appear to involve clusters which evidently need higher energy to flow as compared to simple entities. As the temperature increases the free volume increases due to thermal expansion which causes a decrease in the intermolecular forces. This helps in bringing down the height of the potential energy barrier for viscous flow. Similar explanation also holds good for the conductance of ions. The ratios of the activation energies, E + / E A (Table VII), are found to be m1.26 f 0.03 which is close to those reported earlier13 in the cases of MC12 (M = Mn2+, C02+, Ni2+) -rich mixtures of BudNCl where E + / E A= 1.30 f 0.10. This ratio was found to be greater than unity in ionic melts also. Hence it is apparent that migration of molecular species requires higher activation energy to surmount the energy barriers for fluidity than those required for ionic conductance. The glass transition temperature, To, increases linearly with composition (Figure 6). This observation is similar to KN03 systems? A corthose in molten Ca(N0&4H20 relation has been found22 between T , (or To) and the characteristic Debye temperature, OD which, in turn, shows an rn-lI2 dependence on the effective masses of the component particles of the amorphous phase. Consequently, the increase in To observed here may be due to a decrease in the average molecular mass by the addition of KCNS. Qualitatively To of a particular system refers to the extent of cooling required to reach the glass transition region. Since the free volume decreases with increase in composition, less cooling is required for supercooling the material at higher concentrations than those at lower concentrations and accordingly this may result in an increase in To with composition. On extrapolation of the To isotherm one obtains To = 225OK for pure KCNS. However recently from electrical conductance data23the value of To for KCNS has been reported as equal to 203OK. This restricts such an extrapolation as was also the case in alkali metal divalent metal nitrate systems.24 Looking to the components embodied in A+,* terms it is clear that A+,Ais directly related to r n - l I 2 . Hence one can
+
+
The Journal of Physical Chemistry, Vol. 79, No. 20, 1975
2184
N. Islam and lsmail K
TABLE VII: The Ratio Ed/E.i a s a Function of Temperature for Ca(N03)2.3.99HzO-KSCN Melts
may be predicted presuming that VOremains independent of temperature for a hard-sphere model while it becomes temperature dependent for more complex and linear molecules such as normal alkanes. However, Vo has been found to decrease linearly with 0.0 mol % 20.0 mol 40.0 mol 50.0 mol 60.0 mol composition as apparent from Figure 6. On extrapolation of T,”K KSCN %KSCN O&KSCN %KSCN % K s C N this plot to 0 mol % Ca(N03)~.3.99HzOone obtains the VO for pure KCNS as 54 cm3/mol. VOis found to be additive 1.2663 1.2828 313.0 1.2963 1.2258 1.2778 XiV0,i where and can be given by the relation Vo,,, = 1.2660 1.2821 1.2268 1.2772 318.0 1.2949 VO,,~is the intrinsic volume of the melt with x i as the mole 1.2658 1.2815 323.0 1.2938 1.2280 1.2767 fraction of the ith component. This additive nature of VO 1.2810 1.2763 1.2658 328.0 1.2927 1.2291 may also be due to the ideal behavior of the system with re1.2761 1.2659 1.2807 333.0 1.2917 1.2302 spect to the molal volume. Vo appears to show a direct de1.2758 1.2662 1.2806 1.2902 1,2324 343.0 pendence on m unlike To (Figure 6). It is important to note here that, even though the free volume model seems to be a useful and successful representation of the present data, the empirical parameters may not be quantitatively interpreted in terms of the structure of the system. Especially during the study26-28of the effect of pressure on viscosity or T,and on electrical conductivity the free volume theory fails badly. The Rice-Allnatt theory,29,30based upon Kirkwood’s hypothesis31 in which the dissipative forces are divided into components arising from the long- and short-range parts of the intermolecular pair 220.0 potential, was extended to molten salts by Berne et al.32 7 0 . 0 p and Rice33 and has been found to be a more promising quantitative theory of transport in ionic melts. Recent ex200.0 50.0 amination of some fundamental simplifying approxima0.0 20.0 40.0 60.0 tions made in the Rice-Allnatt t h e ~ r yby~ Smedley ~ , ~ ~ and Mole % of KCNS Woodcock34 using Monte Carlo and molecular dynamics Figure 6. Variation of (a) T o , 4 , and ~ (b) V 0 . 4 , ~with composition for computational result^^^-^^ has indicated the cooperative molten Ca(N03)2.3.99H20-KCNS systems. nature of transport and the distribution of relaxation times. Moreover such an analysis reflects that cross correlapredict that the increase in A$,,\ with increasing XKCNS is tions between hard and soft forces are important which due to the lower molecular mass of KCNS. However, such a implies that the simple two-event mechanisms for momenprediction fails in the case of Ca(N03)~-4.09HzO-Cd(N03)~tum transfer is not suitable to real liquids. Secondly, cou4.07HzO melts3 where A increases with increasing mole lombic forces are found to make an appreciable contribufraction of Cd2+ having larger mass. Moynihan et al.3 pretion to the dissipation of energy in ionic liquids largely sumed that this discrepancy may be due to the fact that the through cross correlations with the short-range repulsions composition dependence of A is also related to differences and, therefore, the transport properties of the melt are in the lability of water or nitrate ions in the coordination largely determined by short-range forces. Lastly, the relaxshells of Ca2+ and Cd2+. ation time characteristic of the dispersion (soft) forces is A comparison of the plots (Figures 2 and 4) suggests a distinctly less than that due to the repulsive (hard) forces similarity in the “hard-sphere” and the Doolittle models. in ionic melts. Higher standard deviations in In C#I and In A in Doolittle’s From the molal volume and equivalent conductance isofit may apparently be due to the absence of T-I12 in the therms (Figure 8)16it is apparent that AVE = 0, but A n E # preexponential term although its effects are insignificant 0. This reflects that the system is not strictly ideal in thereven in Cohen and Turnbull’s expression. Furthermore, B’ modynamic properties and the additivity of molal volumes in the exponential term is related to yu* per mole and reis not a very rigorous test of ideal mixing. Such behaviors AgBr and PbClz PbBr2 mains composition independent like that of Cohen and are also observed in AgCl melts.39 A appears to decrease with composition over the Turnbull’s h as supported by the least-squares fit and the slopes of the linear plots (Figure 4) of log C#I and log A vs. temperature range 298-308OK, even though, the decrease is [l/(V - Vo)]. Similarly, A’ is expected to depend on com= 0.2 to XKCNS = 0.4. It seems that negligible from XKCNS the isotherm passes through a maximum at XKCNS= 0.4 position as is the case with A . V O ,is~ found to be nearly over the range 313-328OK and, further, this maximum apequal to V ~ , as A To,$and To,,,. pears to shift to XKCNS= 0.5 in the range 333-343OK. It is interesting to note that the VOobtained from the exThroughout the temperature scan there is a decrease in A trapolation of the V-T plots (Figure 7)16 to To are almost from XKCNS = 0.0 to XKCNS = 0.2. Here the substitution of similar to those obtained from the least-squares fit (Table the more highly conducting K+ for %Ca2+ causes a deV). This emphasizes the vie^^,^^ that the origin of free volcrease in conductance instead of the anticipated increase. ume is not at OOK but To. This phenomenon is found to be common to many binary In order to account for the deviation in normal alkanes systems, e.g., MgClz KCl, CdClz KC1, AlF3 NaF. At from Doolittle’s expression at low temperatures Millerz5 the moment we are not able to explain why conductance reasoned that the intrinsic volume, Vo, is dependent on isotherms show such behaviors. However, in the region temperature. No such deviation within the experimental 0.0-0.2 mole fraction of KCNS the decrease in conductance range of temperature is observed in the present case. This
1
+
+
The Journal of Physical Chemistry, Vol. 79, No. 20, 1975
+
+
+
Heats of Mixing of
2185
PolystyrenesulfonicAcid
may be due to the suppression of the mobility of K+ ions by the steric hindrance of hydrated cations of the solvent which are in excess. Consequently the decrease in the average free volume per ion by the addition of solute causes a decrease in the conductance. As cited earlier, the rate of diffusion of the smaller solute cation becomes similar to that of the solvent cation and the lower value of E@/EAfor XKCNS = 0.2 provide further support for the above view. Acknowledgment. The authors are indebted to Professor W. Rahman, Head of the Department of Chemistry. One of us (I.K.) is also thankful to the CSIR (New Delhi) for the financial help. Supplementary Material Available. Tables 11, IV, and VI and Figures 1, 5, 7, and 8 will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Business Office, Books and Journal Division, American Chemical Society, 1155 16th St., N.W., Washington, D.C. 20036. Remit check or money order for $4.00 for photocopy or $2.50 for microfiche, referring to code number JPC-75-2180.
References and Notes (1) C. A. Angell, J. Phys. Chem., 70,3988 (1966). (2) C. T. Moynihan, J. Phys. Chem., 70, 3399 (1966) (3) C. T. Moynihan, C. R. Smalley, C. A. Angell, and E. J. Sare, J. Phys. Chem.. 73, 2287 (1969). (4) C. A. Angell, J. Electrochem. Soc., 112, 1225 (1965). (5) A. K. Doolittie, J. Appl. Phys., 22, 1471 (1951). (6)M. H. Cohen and D. Turnbull, J. Chem. Phys., 31, 1164 (1959).
(7) N. Islam, M.R. Islam, S. Ahmad, and B. Waris, Appl. Spectrosc., 29, 66 (1975). (8) C. T. Moynihan and A. Fratieilo, J. Am. Chem. Soc., 69, 5546 (1967). (9) E. J. Sare, C. T. Moynihan, and C. A. Angell, J. Phys. Chem., 77, 1869 (1973). (10) J. Braunstein, L. Orr, and W. Macdonald, J. Chem. fng. Data, 12, 415 (1967). (11) e. W. Laity et al., Electrochemical Society Symposium, Chicago, Extended Abstracts, Vol. 73-1, 1973. (12) H. Braunstein, J. Braunstein, and P. T. Hardesty, J. Phys. Chem., 77, 1907 (1973). (13) N. Islam, M. R. Islam, S. Ahmad, and B. Waris, J. Am. Chem. SOC.,97, 3026 (1975). (14) M. E. Martins, A. J. Calendra, and A. J Arvia, J. lnorg. Nucl. Chem., 36, 1705 (1974). (15) W. W. Ewing and R. J. Mikovsky, J. Am. Chem. Soc., 72, 1390 (1950). (16) See paragraph at end of text regarding supplementary material. (17) G. J. Janz, F. W. Dampier, G. R. Lakshminarayanan, P. K. Lorenz, and R. P. T. Tornklns, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 15, 105 (1968). (18) J. H. Hlldebrand and R. H. Lamoreaux, J. Phys. Chem., 77, 1471 (1973). (19) C. A. Angell and R. D. Brassel. J. Phys. Chem., 76, 3244 (1972). (20) C. A. Angeli, J. Phys. Chem., 68, 1917 (1964). (21) C. A. Angell and C. T. Moynihan, "Transport Processes in Low-Melting Molten Salt Systems" in "Molten Salts", G. Mamantov, Ed., Marcel Dekker, New York, N.Y., 1969, pp 315-375. (22) C. A. Angell, J. Am. Ceram. SOC.,51, 117 (1968). (23) P. Dulieu and P. Ciaes, Bull. SOC.Chim. Belg., 82, 639 (1973). (24) 0. J. Kleppa and L. S. Hersh, Discuss. Faraday Soc..32, 99 (1962). (25) A. A. Mlller, J. Phys. Chem., 67, 1031 (1963). (26) M. Goldsteln, J. Chem. Phys., 39, 3369 (1963). (27) J. M. O'Reilly, J. Polym. Sci., 57, 429 (1962). (28) B. Cleaver, S. I. Smedley, and P. N. Spencer, J. Chem. SOC., Faraday Trans. 1, 68, 1720 (1972). (29) S. A. Rice and A. R. Alinatt, J. Chem. Phys., 34, 2144 (1961). (30) A. R. Allnatt and S. A. Rice, J. Chem. Phys., 34, 2156 (1961). (31) J. 0. Kirkwood, J. Chem. Phys., 14, 180 (1956). (32) B. Berne and S.A. Rice, J. Chem. Phys., 40, 1347 (1964). (33) S. A. Rice, Trans. Faraday Soc., 56, 499 (1962). (34) S. I. Srnedley and L. V. Woodcock, J. Chem. Soc., Faraday Trans. 2, 70, 955 (1974). (35) K. Singer and L. V. Woodcock, Trans. Faraday SOC.,67, 12 (1971). (36) L. V. Woodcock, Chem. Phys. Lett., 10, 257 (1971). (37) L. V. Woodcock, Adv. Molten Salt Chem., 3, 1 (1974). (38) L. V. Woodcock, J. Chem. Soc.,Faraday Trans. 2, 71, 41 (1975). (39) H. Bloom, "The chemistry of Molten Salts", W. A. Benjamin, New York, N.Y., 1967, p 61.
Heats of Mixing of Polyelectrolyte Solutions Having a Common Polyion. 1. Polystyrenesulfonic Acid with Its Magnesium Salt J. Skerjanc Department of Chemistry, University of Ljubljana, 6 1000 Ljubljana, Yugoslavia (Received April 14, 1975) Publication costs assisted by the Department of Chemistry, University of Ljubljana
The heats of mixing of aqueous solutions of polystyrenesulfonic acid with solutions of its magnesium salt of the same concentration have been measured at 25' a t two polyelectrolyte concentrations, 0.0600 and 0.00811 monoM. The heat effects are endothermic; the maxima of the curves, AH, vs. equivalent fraction of the acid, decrease with increasing polyelectrolyte concentration. The experimental values have been compared with those predicted by the cell model with cylindrical symmetry. Reasonable agreement between theory and experiment has been found.
Introduction Most of the research work in the field of synthetic polyelectrolytes has thus far been concerned with the properties of a single polyelectrolyte in a pure solution or in a solution containing an excess of simple electrolyte. Studies of
such properties are essential to an understanding of the interionic forces which distinguish polyelectrolyte solutions from ordinary polymer solutions. Usually only one counterionic species has been present in pure polyelectrolyte solutions. However, few studies have been reported on solutions containing mono- as well as divalent counterions. The Journal of Physical Chemistry, Vol. 79, No. 20, 1975
