J. Phys. Chem. 1983, 87, 1242-1255
1242
Thermodynamic Properties of Aqueous Solutlons of the Alkall Metal Chlorides to 250 OC H. F.
Holmes' and R. E. Mesmer
Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 (Received August 26, 1982; In Final Form: November 1. 1982)
Osmotic Coefficients of LiCNaq), KCl(aq),and CsCUaq) have been determined, at 225 and 250 "C, by isopiestic comparison with NaCl(aq). Equilibrium molalities ranged up to 8 mol kg-'. Isothermal osmotic data can be precisely described by the ion interaction model of Pitzer. The osmotic, and activity, coefficients continue to decrease with increasing temperature with LiCl(aq) retaining a measure of individuality when compared to the other alkali metal chlorides. Our present results have been compared and combined with previously reported thermodynamic data (isopiestic and vapor pressure measurements, electrochemicalcell potentials, freezing temperature determinations, enthalpies of solution and dilution, and heat capacities) within the framework of the ion interaction model. The resulting set of equations provides a thermodynamic description, essentially within the accuracy of the reported experimental results, of LiCl(aq), KCl(aq), and CsCKaq) as a function of temperature (from 0 to 250 "C) and molality (up to about 6 mol kg-'1. The ion interaction parameter P ( O ) was in the order LiCl > NaCl > KC1 > CsCl at all temperatures. The same trend was observed for the excess thermodynamic properties 4, y, and 4L. Contributions of the short-range interactions to the activity coefficient (In y - f f ) are shown to be linearly related to the reciprocal radius of the cation. Excess free energy data for the alkali metal chlorides to 250 "C can be modeled surprisingly well with a single parameter-the hard-core diameter-using the theoretical form of the ion interaction model.
Introduction The alkali metal chlorides, in addition to being the most common family of metal salts, are widely used as models in both experimental and theoretical studies of aqueous solutions of strong electrolytes. However, at elevated temperatures, there is a deficiency of thermodynamic information concerning these systems, particularly of experimental results that are both reliable and extensive. In two previous papers'V2 we have presented results of isopiestic studies of LiCl(aq), KCl(aq), and CsCl(aq) over the temperature range of 110-200 "C. We have now extended the measurements on these three salts to 250 "C and the results are reported in the present paper. During the past several years there has been a significant and welcome increase in the amount of experimental thermodynamic results for aqueous solutions of the alkali metal chlorides at temperatures above 25 "C. This increase has not been limited to free energy studies as there are now some enthalpy and heat capacity results. Basic thermodynamic relationships can be used for an intercomparison of the different types of data available for a given electrolyte solution. The available results for NaCl(aq) at temperatures to 300 "C have been analyzed by Silvester and Pitzer3 within the framework of the ion interaction modeL4 A similar comparison for Na2S04(aq),but more restricted in data content and temperature range (to 200 "C), has recently appeareda5 A much more limited analysis (to 1mol kg-' and about 75 "C) for the alkali metal halides has previously been published by Fortier and Desnoyers? Our present results for LiCl(aq), KCl(aq), and CsCl(aq) have been combined with our previous studies',2 and the available literature data (free energy, enthalpy, and heat capacity) for these three electrolytes. The analysis and (1) H. F. Holmes, C. F. Baes, Jr., and R. E. Mesmer, J.Chem. Thermodyn., 10, 983 (1978). (2) H. F. Holmes and R. E. Mesmer. J. Chem. Thermodyn., 13, 1035 (1981). (3) L. F. Silvester and K. S. Pitzer, J. Phys. Chem., 81, 1822 (1977). (4) K. S. Pitzer, J. Phys. Chem., 77, 268 (1973). (5) P. S. Z. Rogers and K. S. Pitzer, J. Phys. Chem., 85, 2886 (1981). (6) J.-L. Fortier and J. E. Desnoyers, J. Solution Chem., 5, 297 (1976). 0022-3654183/2087-1242$01.5010
the resulting equations for the thermodynamic properties as a function of temperature and molality are given in the present article.
Experimental Section Salts used in the present study were the same lots of "ultrapure" compounds (Alfa Products) that were used in our previous work with these The alkali metal chlorides were used as received, without additional purification. In the case of LiCl (because of the strong hygroscopicity involved) a stock solution was prepared and analyzed by precipitation of the chloride as AgC1, with triplicate analyses agreeing to within 0.02%. Mass aliquots of the LiCl stock solution, contained in titanium cups, were allowed to evaporate to the solid hydrate by using anhydrous CaSO., as a desiccant. This latter step was necessary to avoid difficulties during removal of air from the apparatus prior to the start of an experiment. Mass aliquots of NaC1, KCl, and CsCl were weighed (using a semimircobalance) directly into titanium cups after drying the salts overnight at 130 OC. Duplicate samples of all four salts were used in the experiments. Brief descriptions of the current high-temperature isopiestic facility have appeared in previous publications from this laboratory.',* For the present series of experiments it was found necessary to replace the optical window (quartz) and its associated seal (a Viton O-ring) in order to operate successfully at temperature above 200 "C. At 225 "C, the quartz, Viton, and water reacted to produce SiF4 and HF (at least partly by hydrolysis of the SiF,). This reaction was inferred from the presence of insoluble fluorides (identified by X-ray) in the sample cups plus an etched groove in the quartz window where it was in contact with the Viton O-ring, all occurring during an attempted experimental sequence with the alkaline earth chlorides. Replacing the quartz with sapphire and the Viton with Teflon proved to be a simple and effective remedy. (7) H. Braunstein and J. Braunstein, J. Chem. Thermodyn., 3, 419 (1971). (8) H. F. Holmes, C. F. Baes, Jr., and R. E. Mesmer, J. Chem. Thermodyn., 11, 1035 (1979).
0 1983 American Chemical Society
The Journal of Physlcal Chemlsrry, Vol. 87,
Thermodynamic Properties of Alkali Metal Chlorides
TABLE I: Isopiestic Molalities, m (m/mol kg-I) NaCl LiCl KC1 ~~
~
No. 7, 1983 1243
~
CSCl
NaCl
LiCl
KC1
CSCl
2.0309 2.04 86 2.5966 3.2475 3.8864 0.7022 0.7016 0.7022 0.7068 0.7066 0.7075 0.9224 0.9221 1.3438 1.9468 2.6785 3.5364 4.0768 4.7325 5.7288 6.8259 7.8526
1.9089 1.9205 2.4016 2.9526 3.4741 0.6848 0.6841 0.6848 0.6886 0.6884 0.6891 0.8938 0.8933 1.2862 1.8328 2.4724 3.1918 3.6222 4.1365 4.8776 5.6455 6.3173
2.1232 2.1387 2.7324 3.4431 4.4166 0.7185 0.7180 0.71 86 0.7332 0.7222 0.7230 0.9470 0.9475 1.3908 2.0313 2.821 2 3.7620 4.3534 5.0797 6.1874 7.3964 8.5152
225.34 2.1719 2.1908 2.7975 3.5245 4.23 23 0.7312 0.7303 0.7307 0.7347 0.7347 0.7356 0.9628 0.9640 1.4187 2.0784 2.8881 3.8426 4.4386 5.1570 6.2468 7.4180 8.4767
"C 2.0480 2.0485 2.5973 3.2520 3.8909 0.7028 0.7018 0.7021 0.7072 0.7066 0.9233 0.9217 1.3435 1.9443 2.6780 3.5403 4.0765 4.7327 5.7249 6.8199 7.8547
1.9214 1.9243 2.4025 2.9559 3.4788 0.6849 0.6841 0.6853 0.6887 0.6881 0.8939 0.8931 1.2862 1.8308 2.4700 3.1942 3.6244 4.1366 4.8730 5.6397 6.3164
2.1385 2.1420 2.7336 3.4454 4.1490 0.7189 0.7184 0.7193 0.7226 0.7221 0.9486 0.9470 1.3894 2.0293 2.8209 3.7634 4.3540 5.0766 6.1736 7.3870 8.5070
2.1934 2.1914 2.8014 3.5252 4.2359 0.7311 0.7305 0.7311 0.7343 0.7344 0.9634 0.9638 1.4185 2.0760 2.8869 3.8441 4.4379 5.1629 6.2398 7.4069 8.4760
4.3536 5.0062 5.8823 6.8853 7.8588 3.9506 3.5172 3.0969 2.5928 2.3842 1.4114 1.8299
3.8429 4.3446 4.9942 5.6918 6.3343 3.5250 3.1761 2.8266 2.3992 2.2192 1.3478 1.7300
4.6074 5.3143 6.2682 7.3426 8.3682 4.1756 3.7058 3.2516 2.7092 2.4867 1.4554 1.8962
250.43 "C 4.3613 4.6648 5.0006 5.3 584 6.2879 5.8828 7.3196 6.8702 8.2900 7.8628 4.2341 3.9512 3.7623 3.5157 3.3068 3.1080 2.7573 2.6387 2.4158 2.5321 1.4828 1.4162 1.9292 1.8827
3.8484 4.3419 4.9925 5.6861 6.3404 3.5268 3.1751 2.8364 2.4379 2.2472 1.3531 1.7774
4.6182 5.3170 6.2642 7.3327 8.3748 4.1767 3.7049 3.2632 2.7584 2.5200 1.4597 1.9525
4.6745 5.3602 6.2875 7.3124 8.2896 4.2364 3.7634 3.3189 2.81 04 2.56 76 1.4850 1.9870
The essence of our isopiestic experiments consists of allowing solutions (contained in titanium cups) to attain equilibrium with a common vapor phase while sitting on a massive copper block inside a sealed pressure vessel at constant temperature and pressure. At equilibrium the concentrations of the solutions are determined by in situ weighing with an electromagnetic torsion balance to a precision of 0.2 mg. For each set of measurements a calibration of the balance is obtained by weighing standard weights that are interspersed with the solution cups. Solution compositions can be changed by adding or removing water through a capillary tube.
Experimental Results and Discussion Equilibrium isopiestic molalities of the three experimental solutions and the reference solution, NaCl(aq), are listed in Table I. In most cases, for the sake of consistency and to avoid any round-off error, the last digit is not significant. From the reproducibility of the results and calibrations, we estimate that the molalities given in Table I are accurate to 0.2% or better, especially for the middle of the molality range. Precision of the measurements is somewhat better as the molalities listed in Table I are the averages of duplicate samples whose molalities rarely differed by more than 0.1 % . The osmotic coefficients, 4, for LiCl(aq), KCl(aq), and CsCl(aq) were calculated from the molalities of Table I with 4x= (mr/mx)4r= (1) where m is the molality, R is the isopiestic ratio, and the subscripts x and r refer to the experimental and reference salt, respectively. Equation 1 is valid when the reference and experimental salts are the same charge type. Osmotic
r I
I
I
I
I
1
'P
'
o
I
1
110
+
100
090
080 076 0
1
2
3
4 m / m l kg-'
5
6
7
Flgure 1. Osmotic Coefficients 4 for LiCl(aq), KCl(aq), and CsCl(aq) as a function of molality m at 225 and 250 OC. The lines are leastsquares fits of the Ion interaction model to the experimental results.
coefficients of the reference solution were calculated from the ion interaction model4 in its semiempirical form by using the parameters derived by Silvester and Pitzer3 in their analysis of thermodynamic results for NaCl(aq). Above 100 "C these parameters are determined primarily by the experimental vapor pressure measurements of Liu and L i n d ~ a y . ~ Osmotic coefficients computed from the molalities of Table I with eq 1 are shown in Figure 1 (approximately half of the experimental points are plotted in Figure 1). The lines drawn through the points in Figure 1 are least-squares fits of the ion interaction model4which will (9) C. Liu and W. T. Lindsay, Jr., J. Solution Chem., 1, 45 (1972).
1244
Holmes and Mesmer
The Journal of Physical Chemistty, Vol. 87, No. 7, 1983
TABLE 11: Isothermal Ion Interaction Parameters for LiCl(aq),KCl(aq),and CsCl(aq) p(O)/(kg mol-') p(')/(kg mol-') C@/(kg'mol-') 4@) 225.34 "C LiCl 0.1141 0.4697 -0.00186 0.001, KCI 0.0691 0.4182 -0.003 33 0.001, CSCl 0.0613 0.3590 -0.00231 0.001, 250.43 "C LiCl 0.1102 0.4576 -0.0024 5 0.001, -0.00306 0.000 ., KCl 0.0664 0.4711 CSCl 0.0613 0.4083 -0.00228 0.000,
be discussed below. It is clear that the absolute accuracy of the results in Figure 1 can be no better than that of the reference osmotic coefficients for NaCl(aq). Silvester and Pitzer3 state that their parameters reproduce the experimental results for NaCl(aq) with a standard deviation of fit of 0.005 in the osmotic coefficient. However, the results shown in Figure 1 are considerably more precise than i0.005 so that, in the present case, the uncertainty in the reference osmotic coefficients is the limiting factor for overall accuracy. A cursory comparison of Figure 1 with previous results for these three electrolytes'$ clearly shows that the osmotic coefficients are continuing to decrease with increasing temperature. The osmotic coefficients of KCl(aq) and CsCl(aq) are nearly equal and not very dependent on molality after the initial sharp decline in dilute solutions. The osmotic behavior of NaCl(aq) at these temperatures3p9 is very similar to that of KCl(aq) and CsCl(aq). Certainly the outstanding feature of the results in Figure 1 is that LiCl(aq) continues, at these temperatures, to be unique among the alkali metal chlorides. The ion interaction model of Pitzer4 has been very successful in describing osmotic results, both at 25 OCl0 and at elevated temperatures (e.g., see ref 2). From this model the equation for the osmotic coefficient of a 1:l electrolyte is
4 = 1 + f+ + mB@+ m2C@
(2)
where f @ is defined as f# = -Am'/2/(1
+ bm'iz)
(3)
and B@is given by
B+ = @(O)
+ @(I)exp(-am'/2)
(4)
(For the present class of electrolytes the ionic strength and the molality are, of course, equivalent if one assumes complete dissociation of the electrolyte.) A is osmotic Debye-Huckel coefficient (calculated as in ref 3 and listed in Table 11), and a and b are constants which have been conveniently set, by trial and error,4,l0at 2.0 and 1.2 kg1i2 respectively, for all electrolytes in which at least one of the ions is univalent. @(O), fll), and C+are parameters which are specific for each individual electrolyte. These three parameters are fixed, for each electrolyte and each temperature, by a least-squares fit of eq 2-4 to isothermal experimental results. A general least-squares computer program" was used to determine @(O), @'), and C@from the osmotic coefficients calculated from the isopiestic molalities of Table I by using eq 1. These parameters, for each of the three electrolytes at each temperature, are listed in Table I1 with the corresponding standard deviation of fit, ~ ( 4 ) As . a matter of convenience the Debye-Huckel cofficients used in the (10) K. S. Pitzer and G. Mayorga, J. Phys. Chem., 77, 2300 (1973). (11) W. R. Busing and H. A. Levy, Oak Ridge National Laboratory Report ORNL-TM-271, 1962.
Al(mo1-l'' kg'',) 0.6804
0.7514
calculations are also given in Table 11. It is obvious that the ion interaction model gives an excellent representation of our experimental osmotic coefficients. Since the molality dependence of the osmotic coefficient is largely controlled by P(O), it is not surprising that @(O) is largest for LiCl(aq) and comparable in the case of KCl(aq) and CsCl(aq). A brief comparison of Table I1 with previous results1,2J0(also see Figures 3-5) shows that, with the exception of LiCl(aq), most of the temperature dependence of and C@occws below 100 OC while @(l)is temperature dependent over the temperature range of 25-250 OC. A quantitative description of the temperature dependence will be given in a later section of this paper. The ion interaction model gives the mean activity coefficients, y, of a 1:l electrolyte as In y = p mBY m2CY (5)
+
+
where the long-range electrostatic term,
p B y BY
= -A[m1l2/(1 is defined as = 2@(0)+ 2@(')[1- (1 +
+ bm1/2)+ (2/b)
In (1
p , is given by
+ bm1/2)]
(6)
- a2m/2) e ~ p ( - a m ' / ~ ) ] / a ~(7) m
and CY is related to C@by CY = 3C"2
(8)
with the symbols and constants having the same definitions and values as in eq 2-4. Since eq 5 results from a Gibbs-Duhem integration (from 0 to m)of eq 2 the validity of the calculated activity coefficients depends on how well eq 2 describes the osmotic coefficient in the dilute region where there are no experimental results. This procedure is quite adequate at 25 "C and there is some experimental justification for the use of eq 5 at elevated temperatures.2 Activity coefficients calculated from eq 5 are shown in Figure 2 for temperatures of 225 and 250 "C. The parameters of Table I1 were adjusted very slightly for the small temperature difference between Table I1 and Figure 2 with the adjustment being undetectable on the scale of Figure 2. In general, the trends of y in Figure 2 are, as expected, quite similar to those of 4 in Figure 1with the dependence on molality being distinctly different in the case of LiCl(aq) as compared to KCl(aq) and CsCl(aq). The difference between the activity coefficients of KCl(aq) and CsCl(aq) is larger than the corresponding difference in the osmotic coefficients. However, even in this case the activity coefficients of KCl(aq) and CsCl(aq) differ by only about 6% in the concentrated solutions. From 2 , 4 , 5 , and 7 the contributions of P ( O ) and P(l)are magnified in the case of In y as compared to 4. The contribution of is twice as large for In y and fi(') makes a substantial contribution to In y in concentrated solutions, having a broad maximum at 4 mol kg-'. In contrast, the contribution of P(l) to 4 in concentrated solutions is very small. The only comparable experimental results for these electrolytes in the present temperature range are the vapor
The Journal of Physical Chemistry, Vol. 87,
Thermodynamic Properties of Alkali Metal Chlorides I
I
I
I
0.7
225'C 0
A 0
I
I
A
/ /I
250°C LlCl AKCI CSCl
0.6
I
these relationships to aqueous electrolyte solutions at various temperatures has been detailed in two previous publications by Pitzer and co-workers dealing with NaCl(aq)3and Na2S04(aq).5 We will describe the thermodynamic basis and mathematical manipulations only in sufficient detail to permit the informed reader to follow the treatment without reference to earlier work. The principal free energy function involved is the excess Gibbs energy, GEx,given in terms of the osmotic and activity coefficients by
GEx= n,vmRT(l
0.5
Y
No. 7, 1983 1245
-4
+ In y)
where the undefined symbols are as follows: n, is the number of kilograms of solvent; v is the number of ions in one molecule of solute; R is the gas constant; and Tis temperature in Kelvins. A useful thermodynamic function for electrolyte solutions is the relative enthalpy, L , which is related to GEx by
0.4
L = -7WGEX/T)/dT)pJn 0.3
0
4
2
3 4 m/mol kg-'
5
6
7
Flgure 2. Calculated activity coefficients y for LiCi(aq), KCi(aq), and CsCi(aq) at 225 and 250 OC. Points are for identification only.
TABLE 111: Comparison of Isopiestic and Vapor Pressure Measurements salt m/(mol kg-') @a Gb LiCl CsCl
(9)
1.0121 1.0267
225 "C 0.867, 0.798,
0.861 0.798
AC
0.75 0.04
250 "C 1.0233 0.829, 0.825 0.54 LiCl CsCl 1.0369 0.772, 0.771 0.19 a Calculated from eq 2 by using slightly adjusted parameters from Table 11. From ref 12. Difference in percent.
pressure measurements of Lindsay and Lid2 for LiCl(aq) and CsCl(aq) at a nominal molality of 1 mol kg-l. Table III is a comparison of the osmotic coefficientsfrom Lindsay and L i d 2 and those calculated from eq 2 with the parameters used for Figure 2. (The difference in using the adjusted parameters over those of Table I1 is insignificant, amounting to 0.0005, or less, for the osmotic coefficient.) In the case LiCl(aq) the agreement between the two sets of results is not quite as good as we observed in the temperature range of 110-200 OC2but is slightly better in the case of CsCl(aq). In any event, the agreement is sufficient to generate a great deal of confidence in both sets of measurements.
Analysis in Combination with Previous Results Thermodynamic Basis. Regardless of the specific model used to describe individual thermodynamic properties as a function of such factors as temperature, pressure, and concentration, relationships between the various functions must be thermodynamically consistent. In the present paper we wish to combine and compare experimental free energy, enthalpy, and heat capacity results from various types of physiochemical measurements. Fundamental relationships involving these three thermodynamic quantities can be found in standard texts.13 Application of (12) W. T. Lindsay, Jr., and C. Liu, J.Phys. Chem., 75, 3723 (1971).
(10)
Experimental enthalpy measurements on electrolyte solutions are usually tabulated in terms of the apparent relative molal enthalpy, @L,which is simply related to L by @L= L / n 2 (11) with n2 being the number of moles of solute. For aqueous electrolyte solutions the two enthalpy quantities most commonly obtained from calorimetric measurements are the enthalpy of dilution, A(@L), and the integral enthalpy of solution, AH0. The enthalpy change on diluting a solution from molality ml to molality m2 is given by
A(@L)= "L2 - @Li
(12)
For real concentrations, the integral enthalpy of solution, is related to @Lthrough the enper mole of solute, MO, thalpy of solution at infinite dilution, ARso,by
M0= ARO"+ @L
(13)
It is also useful to work in terms of relative and apparent quantities when dealing with heat capacities of aqueous electrolyte solutions. We will be working with the apparent molal heat capacity, @Cp,which is easily shown to be related to 4L through
@cp = C P 2+~ ( d @ L / d T ) , ,
,
(14)
where C P 2 O is the partial molal heat capacity of the solute at infinite dilution. If the experimental results are known as a function of temperature a useful equation relating Meo and CPz0is
CppZ0= cpZo(s) + (aARso/anp (15) where C,20(s) is the heat capacity of the pure solid solute. WorkingEquations. In order to compare and relate the various types of thermodynamic results which are available for an electrolyte it is necessary to have mathematical descriptions of the thermodynamic functions in terms of temperature and concentration. In previous papers we have used the ion interaction model,4 under isothermal conditions, to describe our experimental osmotic coefficients and calculate activity coefficients for the solute. This model's usefulness at elevated temperatures has been further enhanced by its success in correlating several kinds of thermodynamic data for NaCl(aq)3 and Na2S04(aq)5 (13) K. S. Pitzer and L. Brewer, revised edition of 'Thermodynamics" by G. N. Lewis and M. Randall, McGraw-Hill, New York, 1961.
1246
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
over an extended temperature range in both cases. With a few exceptions we have followed the treatment used by Silvester and Pitzer3 in their analysis of the NaCl(aq) data. Although this is an arbitrary choice, a consistent treatment should make intracomparison of the alkali metal chlorides more meaningful. For the operations expressed in eq 10 and 14 it is convenient to use a function B , defined by Pitzer and Kim14 as
Holmes and Mesmer
Mso = q1 + qPT+ q3P+ q4P+ q5 In ( T - 270) (26) CP2" = Cp2"(s)+ q2 + 2q3T + 3 q 4 P + q 5 / ( T- 270) (27) cpzo(S)
=
Q6
+ q,T
(28)
These equations, without the terms involving q5 are also identical with those used by Silvester and Pitzere3A term similar to that containing qs was used by Rogers and Pitzer5 in their description of CP2"for Na2S04(aq)as a B = B y - B4 (16) function of temperature. The quantities 260 and 270 K where B4 and BT are defined by eq 4 and 7 , respectively. were selected to give a rapidly changing term in the vicinity of 0 "C. It should be pointed out that any of the p and In terms of the parameters p(O) and p(l) B is given by q parameters can, and will be, set equal to zero if they are B = p(O) + 2p(')[l- ( 1 + exp(-~um'/~)]/a~m (17) not needed for an adequate description of the experimental results. (We reemphasize that the equations given in this paper Debye-Huckel Limiting Law Parameters. In describing are specific for 1:l electrolytes. For general equations see the osmotic and activity coefficients of these three elecref 3.) For the present purpose we need expressions for trolytes we have used the long-range interaction (Debyethe various thermodynamic quantities in terms of the ion Huckel) parameter as calculated by Silvester and P i t ~ e r . ~ interaction parameters p(l),and 0. Equations 2 and This was a convenient procedure to follow as the osmotic 5 serve this need in the case of the osmotic and activity coefficients for the NaCl(aq) standard were calculated in coefficients,respectively. In the ion interaction model the the same manner. Bradley and Pitzer15 have calculated total excess free energy is given by a new set of Debye-Huckel limiting slopes based on a GE' = revised equation for the dielectric constant of water. Their 2 n w R T m [ - ( 2 A / b )In ( 1 bm1i2)+ B m + m 2 C / 2 ] (18) claim is that the revised equation gives more realistic derivatives of the dielectric constant of water with respect Application of (10) and (11) to (18)gives an expression for to temperature and pressure. For the present purposes the apparent relative molal enthalpy we have adopted their revised equation for the dielectric constant of water along with their redefinition of the en4L = ( 2 / b ) A HIn (1 + bm'/2) - 2RP(mB'-t m2C') (19) thalpy and heat capacity limiting law slopes. The difwhere AH is the Debye-Huckel coefficient for enthalpy (see ference between these Debye-Huckel parameters and those section on Debye-Huckel parameters for explanation) of ref 3 amounts to 0.0023,0.0108, 0.003, 420 J mol-', and 28.7 J mol-' K-' for 4, In y,y, 4L, and @Cp,respectively, B!= (aB/aomP (20) for a 1:l electrolyte at 6 mol kg-l and 250 "C-the maxic' = (ac4/aom,/2 (21) mum difference for this work. In the arbitrary expression 25, these differences are easily compensated in the adFurther differentiation of (19) according to (14) gives the justable parameters. apparent molal heat capacity as Thermodynamic Data Base. The selected experimental results included in the least-squares analysis are listed in @Cp= CP2" + ( A , / b ) In ( 1 + bm1i2)Table IV for LiCl(aq), KCl(aq), and CsCl(aq). These ta2 R T [ m ( 2 B r+ TB") + m2(2Cr+ TC")] ( 2 2 ) bles are not exhaustive listings of all the available literature data. This particular set of experimental results was AJ is the Debye-Huckel coefficient for heat capacity (see chosen to include a variety of data types, a wide range of section on Debye-Huckel parameters) and B" and C"are temperature and molalities, compatible data sets, and the given by data of greatest estimated precision and accuracy. Where B" = (a%/aP),, (23) necessary and possible the following refinements were applied to the literature results: thermochemical data were c" = ( a 2 c + / a ~ ) , , / 2 (24) converted by using 4.184 J cal-l; osmotic coefficients were calculated from freezing temperatures by using the equaEquations 2 , 5 , 1 8 , 1 9 , and 22 deal with the dependence tion of Scatchard, Vonnegurt, and Beaumont;16 and isoof a particular thermodynamic function on molality but piestic results were recalculated by using the parameters at a constant temperature. In the absence of theoretical of Silvester and Pitzer3 in those cases where NaCl(aq) was guidelines we will assume that the parameters Po, p(l),and used as the reference. In order to properly weight the C@'can all be described by arbitrary functions of tempervarious types of experimental results, we assigned an esature, f(7'),of the form timated standard error to each data set, or in many cases, f(?3 = p1 + p z ( l / T - 1 / T d + p3 In ( T / T R ) + to individual experimental points. The three factors p 4 ( T- T R ) + p 5 ( P - T R ~+) p6 In ( T - 260) (25) considered in making the error assignment were the reported experimental uncertainty, internal consistency of where the p's are determined by a least-squares fit of eq the particular data set as measured by an isothermal fit 25 to experimental results and TRis conveniently set at to the ion interaction model, and compatibiity with the 298.15 K. With the exception of the term involvingp,, (25) remainder of the data base. These assigned standard eris identical with ihe form used by Silvester and P i t ~ e r . ~ rors are listed in the fifth column of Table V. One can mS", C P 2 O , and Cpzo(s) are also temperaiure-dependent reasonably question the inclusion of the smoothed values and CpZoare related quantities. If we recall that mg0 listed in Robinson and Stokes17 with the experimental through (15) these three quantities can be described by the following set of empirical equations:
+
(14) K.
S.Pitzer and J. J. Kim, J . Am. Chem. SOC.,96, 5701 (1974).
(15) D. J. Bradley and K. S. Pitzer, J . Phys. Chem., 83, 1599 (1979). (16) G. Scatchard, B. Vonnegut, and D. W. Beaumont, J. Chem. Phys., 33, 1292 (1960).
Thermodynamlc Properties of Alkali Metal Chlorides
results given in Table V. However, the values tabulated by these two workers represents the majority of the ex-
(17)R. A. Robinson and R. M. Stokea, "Electrolyte Solutions"; 2nd ed., revised, Butterworths, London, 1965. (18)K. L. Hellams, C. S. Paterson, B. H. Prentice, 111, and M. T. Taylor, J. Chem. Eng. Data, 10,323 (1965). (19)J. T. Moore, W. T. Humphries, and C. S. Patterson, J. Chem. Eng. Data, 17, 180 (1972). (20)R. Caramazza, Ann. Chim. (Rome),53,472 (1963). (21)A. N. Kirgintaev and A. V. Luk'yanov, Russ.J.Phys. Chem., 37, 1501 (1963). (22)H.F. Gibbard, Jr., and G. Scatchard, J. Chem. Eng. Data, 18,293 (1973). (23)G. Scatchard and S. S. Prentiss, J. Am. Ch'em. SOC.,56, 4355 (1933). (24)F. Monicchioli, 0.Denoto, G. Grandi, and G. Cocco, Ber. Bunsenges. Phys. Chem., 74,59 (1970). (25)H. F. Gibbard, Jr., and A. Fawaz, J. Solution Chem., 3,745(1974). (26)J.-L. Fortier, P.-A. Leduc, and J. E. Desnoyers, J.Solution Chem., 3,323 (1974). (27)J. E. Desnoyers, C. de Visser, G. Perron, and P. Picker, J. Solution Chem., 5,605 (1976). (28)H. Ruterjans, F. Schreiner, U. Sage, and Th. Ackermann, J.Phys. Chem., 73,986 (1969). (29)Y. C. Wu and T. F. Young, J. Res. Natl. Bur. Stand., 85, 11 (1980). (30)W.H.Leung and F. J. Millero, J. Solution Chem.,4,145 (1975). (31)W.T. Lindsay, Jr., and C. Liu, J. Phys. Chem., 75,3723 (1971). (32)A. F. Kapustinskii, M. S. Stakhanova, and V. A. Vasilev, Izu. Akad. Nauk SSSR, Otd. Khim. Nauk, 2082 (1960). (33)R. H. Wood, R. A. Rooney, and J. N. Braddock, J. Phys. Chem., 73,1673 (1969). (34)J. E. Mayrath, Ph.D. Dissertation, University of Delaware, Newark, DE, 1980;J. E. Mayrath and R. H. Wood, J. Chem. Thermodyn., 14, 563 (1982). (35)S. J. Drakin and C. Yu-min, Russ. J. Phys. Chem., 38,1526(1964). (36)E. Lange and F. Durr, Z. Phys. Chem. (Leipig), 121,361(1926). (37)C. S. Patterson, L. 0. Gilpatrick, and B. A. Soldano, J. Chem. Soc., 2730 (1960). (38)B. A. Soldano and C. S. Patterson, J. Chem. SOC., 937 (1962). (39)W. T. Humphries, C. F. Kohrt, and C. S. Patterson, J.Chem. Eng. Data, 13,327 (1968). (40)R. F. Platford, J. Chem. Eng. Data, 18,215 (1973). (41)C. W. Childs and R. F. Platford, Aust. J. Chem., 24,2487(1971). (42)V. I. Lebed and V. V. Aleksandrov, Russ.J. Phys. Chem.,38,1414 (1964). (43)T. M. Herrington and R. J. Jackson, J. Chem. SOC.,Faraday Trans. 1,69,1635 (1973). (44)H. P. Snipes, C. Manly, and D. D. Ensor, J. Chem. Erg. Data, 20, 287 (1975). (45)G. M. Giordano, P. Longhi, T. Mussini, and S. Rondinini, J. Chem. Thermodyn., 9,997 (1977). (46)H. S. Harned and M. A. Cook, J.Am. Chem. Soc., 59,1290(1937). (47)J. E. Tanner and F. W. Lamb, J. Solution Chem., 7,303 (1978). (48)V. I. Borodenko and I. S. Galinker, Izu. Vyssh. Ucheb. Zaued, Khim.Khim. Teknhol., 19,1908 (1976). (49)Q.D.Craft and W. A. Van Hook, J. Solution Chem., 4,901(1975). (50)A. Dadgar and M. R. Taherian, J. Chem. Thermodyn., 9,711 (1977). (51)M. V. Kilday, J. Res. Natl. Bur. Stand., 85,467 (1980). (52)G. Olafsson, S. Sunner, N. Efimov, and J. Laynez, J. Chem. Thermodyn., 5, 199 (1973). (53)V. P. Vasil'ev and G. A. Lobanov, Russ.J. Phys. Chem., 11,383 (1966). (54)S., Likke and L. A. Bromley, J. Chem. Eng. Data,18,189 (1973). (55)R. Caramazza, Ann. Chim.(Rome),53,481 (1963). (56)T. Mussini, P.Longhi, and G. Rive, J.Chem. Thermodyn., 4,591 (1972). (57)T. H. Lilley and R. P. Scott, J. Chem. Thermodyn., 6,1015(1974). (58)W. H. Leung and F. J. Millero, J. Chem. Thermodyn., 7, 1067 (1975). (59)M. S.Stakhanova and V. A. Vasilev, Russ.J. Phys. Chem., 37,839 (1963).
The Journal of Physlcal Chemistry, Vol. 87, No. 7, 7983
1247
perimental results prior to publication of their book and inclusion of both 6 and In y from their tables along with more recent results at 25 "C has the desirable effect of increasing the statistical weight of the data at 25 "C where results are far more numerous and experimentation is less difficult. Constant Pressure Requirements. Several of the thermodynamic relationships in previous sections are, from a strictly rigorous viewpoint, not valid except for constant pressure results as they contain partial derivatives at constant pressure. The results listed in Table V are nominally at atmospheric pressure for temperatures of 100 "C and below and at saturation pressure or slightly greater for temperatures above 100 "C and therefore do not meet the strict requirement of constant pressure. In principle the experimental free energy (G), enthalpy (H), and heat capacity (C,) results can be corrected to a constant pressure by means of thermodynamic relationship^'^ using an appropriate volume (V) (dG/dP)T = V
(29)
(~H/w= ) ~v - T(av/ar),
(30)
(dC,/dP)T = -T(d2V/dP)p
(31)
The practical application of (29)-(31) at the temperatures involved in the present work requires data which are almost nonexistent. Only in the case of NaCl(aq) are the requisite PVT data available in sufficient quantity to make calculations of the required corrections. Rogersffihas made these calculations for NaCl(aq). It is encouraging that the calculated and experimental pressure coefficients are in reasonable agreement for the apparent enthalpy6' and apparent heat capacity68 of NaCl(aq). In the absence of more applicable data, we will assume that the corrections for NaCl(aq) approximate those for LiCl(aq), KCl(aq), and CsCl(aq). For the thermodynamic functions used in the present paper the pressure corrections are most important for enthalpies and heat capacities. Assuming that one elects the expedient route and corrects the low temperature results to the saturation pressure of water at 250 "C (39.73 bar), the approximate corrections are either about equal to (in a few cases), or less than, the assigned error of the experimental value. Because of their relative size, we have chosen to consider the pressure corrections as insignificant. Ignoring the pressure effects will not be possible at temperatures much above 250 "C, especially so for enthalpies and heat capacities. Least-Squares Fit of the Experimental Data. The parameters of eq 25-27 were determined by a simultaneous least-squares fit to the data of Table IV for LiCl(aq), KCl(aq), and CsCl(aq) with the same computer program1' utilized for the isothermal fits. Parameters q6 and q, of (60)M. S. Stakhanova, K. K. Vlasenko, M. Kh. Karapet'yanta, and I. V. Bazlova, Russ. J. Phys. Chem., 42,274 (1968). (61)A. S.Levine and R. H. Wood, J. Chem. Eng. Data, 15,33 (1970). (62)A. M. Bahia, T. H. Lilly, and I. R. Tasker, J. Chem. Thermodyn., 10,683 (1978). (63)A. F. Borob'ev, N. A. Jhragim, and S. M. Skuratov, RUSS.J . Inorg. Chem., 11, 13 (1966). (64)A. N. Kirgintaev and A. V. Luk'yanov, Russ. J.Phys. Chem., 40, 686 (1966). (65)J. A. Rard and D. G. Miller, J. Chem. Eng. Data, 27,169 (1982). (66)P. S. Z.Rogers, Ph.D. Dissertation, University of California, Berkeley, CA, 1981. P. S. Z.Rogers and K. S. Pitzer, J.Phys. Chem. Ref. Data, 11, 15 (1982). (67)R. H.Busey, unpublished results. (68)D. Smith-Magowan, Ph.D. Dissertation, University of Delaware, Newark, DE, 1980; D. Smith-Magowan and R. H. Wood, J. Chem. Thermodyn., 13, 1047 (1981).
1248
The Journal of Physical Chemistry, Vol. 87,No. 7, 1983
Holmes and Mesmer
TABLE IV: Thermodynamic Data Base for LiCl(aq), KCl(aq), and CsCl(aq) exptl property" methodb tablesd tablesd is0 is0
temp range/"(=
molality rangel (mol kg-') USC LiCl( aq) 0.1-6.0 0.0025 0.003 0.1-6.0 0.003 0.6-5.6 0.003 0.6-6.3 0.7-1.5 0.003 0.00 5 1.3-4.8 0.1-6.0 0.05 2.3-4.8 0.01 1.0-6.4 0.003f 0.004-1.25 0.003 0.01 6-3.9 0.003 0.04-1.3 0.003 1.0 J mol-' K-' 0.04-0.96 0.05-1.8 3.0 J mol-' K-' 3.0 J mol-' 0.03-0.96 0.03-6.75 (3.0 J mol-')h 0.24-1.15 7.0 J mol-' 0.003 1.0 3.0 J mol-' K-' 1.O-4.5 0.14-3.0 10.0 J mol-' 0.016-9.4 25.0 J mol-' 365 J mol-' 0.08-0.24 3 50 J mol'' 0.14-6.1
cal cal cal cal ca1
25 25 110-200 225-250 45 80 0-50 25 25-100 (-4.9)-0 (-21.5)-0 (-5.1 5)-(-0.15) 25 30-130 25 25 30 125-250 25 25 100 25 25
tablesd tablesd is0 is0 is0 is0 is0 is0 ft ft emf VP cal Cal cal Cal emf emf cal cal Cal Cal cal Cal cal cal cal cal c a1
25 25 110-200 225-250 100-121 45 60-80 0-15 (-4.0)-0 (-9.9)-(-7.8) 25-90 50-70 30-130 40-80 25 30 10-70 040 5-85 220-250 25 10-75 100-200 25 10-75 23-85 25-117 18-70 140-200
0.1-4.8 0.1-4.8 1.0-8.0 0.7-8.5 0.7-5.0 0.5-3.5 0.8-6.7 0.1-4.0 0.01-1.25 2.4-3.0 0.005-0.1 0.7-3.25 0.5-1.8 0.12-4.4 0.02-1.0 0.2-1.0 0.05-0.5 0.1-4.0 0.1-4.7 2.0-12.8 0.12-3.0 0.15-3.4 0.01 5-4.5 0.01-0.03 0.104 0.04 -0.11 0.12 0.12 0.3-1.5
tablesd ta blesd is0 is0 is0
25 25 110-200 225-250 45 100
is0
121
emf emf
0-50 25-90 25 (-9.3)-( 0.05) 10-70 (-1.6)-0 30-130 25 30
0.1-6.0 0.1-6.0 0.7-7.5 0.73-8.3 1.O-3.5 1.0-4.9 0.7-5.0 0.1-5.0 0.005-0.1 3.0-5.7 0.01-3.1 0.05-0.7 0.01-0.5 0.5-1.6 0.01-0.8 0.26-0.96
125-250 25 25 25
0.5-5.0 1.0-5.0 0.2-3.0
is0
is0 emf is0 VP
ft ft ft cal cal Cal cal cal VP
is0
is0 ft
emf ft c a1 cal cal VP
cal cal Cal
1.0
KCl(aq) 0.002 0.004 0.003 0.003 0.0035 0.005 0.003 0.003 0.002 0.002 0.01 0,003' 3.0 J mol-' K-,' (20.0 J mol-')' 3.0 J mol-' K-' 14.0 J mol-' 0.01 5 0.005-0.01 3.0 J mol-' K-* k 25 J mol-' k
(5-30 J k
1% 100 J mol-' 100 J mol-' 100 J mol-' (5-20 J mol-' K-')k CsCl(aq) 0.005" 0.004" 0.003 0.003 0.003 0.005 0.01 0.04 0.01
0.005 0.003 0.015 0.005 2.5 J mol-' K-' 2.5 J mol-' K-' 1 5 J mol-' 0.003 6.0 J mol-' K-' 20 J mol-' 65 J mol-'
UP
ref 17 17 2 e 18 19 20 21 22 23 24 25 26 28 26 29 30 31 32 33 34 35 36
0.0021 0.0024 0.0020 0.0029 0.0021 0.0059 0.044 0.011 0.00458 0.0031 0.0036 0.0028 0.90 J mol-' K-' 3.07 J mol-' K-l 2.0 J mol'' 11.5 J mol-' 5.9 J mol'' 0.0025 3.7 J mol-' K-' 9.8 J mol" 32.5 J mol-' 75 J mol-' 30 J mol-'
17 17 1 e 37,38 18 19,39 40,41 23 24 42 43 28 44 26 30 45 46 47 48 33 49 34 50 49 51 52 53 54m
0.0012 0.0023 0.0030 0.001 7 0.0037 0.0048 0.0017 0.0023 0.001 2 0.0016 0.0084 0.003 8' 1.9 J mol'' K-' (19 Jmol-')s 0.8 J mol-' K-' 8.4 J mol'' 0.015 0.0066 2.1 J mol-' K-' t 38 J mol-' 63 J mol-'
17 17 2 e
0.0036 0.0041 0.0015 0.0019 0.0029 0.0037 0.0064 0.040 0.0097 0.0046 0.0031
18
37 38 55 42 21 24 56 57 28 26 58 31 59 60 61
U
460 J mol-' 1 1 2 J mol'' 47 J mol-' (51 J mol-')" 4 2 J mol- I 21.7 J mol-' K-'
0.011
0.0041 2.1 J mol-' K" 3.0 J mol-' K-' 6.9 J mol'' 0.0018 (1.9 J mol-' K-' I' 37 J mol-' 92 J mol-'
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Thermodynamic Properties of Alkali Metal Chlorides
1249
TABLE IV (Continued) ~~
~
exptl property methodb
molality range/ (mol kg-') 0.005-11.0 1.0-4.4 0.017-0.07 2.1-4.9 0.74-7.4
ref "ip 34 ( 6 9 J mol-')X 0.002 62 0.0017 @ AH, 180 J mol-' 63 75 J mol-' 0.003 64 0.0015 @ @J 0.002 65 0.0016 is0 = isopiestic, emf = electrochemical cell potential, vp = vapor a Function explicitly used in the least-squares routine. Assigned standard error (see text). Tables of smoothed pressure, ft = freezing temperature, and cal = calorimetry. us for the values (see text). e This work. f us = 0.01 for 6.4 mol kg-'. g C, has been corrected according to ref 27. concentrated and dilute solutions is larger by a factor of 10. us = 0.007 for most concentrated solution. j At 80 "C us increases with increasing molality reaching 125 J mol-' at 4 . 1 mol kg-'. k Standard error assigned on a point by point basis. Three points have U, larger than 30 J mol". Results at 80-120 "C are not included in the least-squares routine. From 5-6 mol kg-' us = 0.01. O Most of the experimental points have us less than 1 0 J mol-'. P Standard deviation of fit using Excluding the data at 6.4 mol kg-'. Deviation larger for the most concentrated solution. the parameters of Table V. Deviations of the individual points ranged from 6 5 to 3100 J mol". For 4 0 and 6 0 "C. At 80 'C, ui = 67 J mol". ui is 1 2 J mol'' at 100 "C, 37 J mol" at 150 OC, and 4 1 J mol'' at 200 "C. " Does not include points at 117 "C where ui = 299 J mol". Does not include most dilute solution. Includes all points. If seven points are omitted u i is 5.5 J mol-' at 100 'C, 26 J mol-' at 150 'C, and 29 J mol-' at 200 "C. A@L
cal is0 cal is0 is0
temp range/"(= 100-200 25 25 25 25
USC
k,o
Q
TABLE V : Parameters from Least-Squares Fit of the Ion Interaction Model t o the Data of Table IV Using Eq 25 temp dependence quantity
CsCl(aq) KCl(aq) 0.03352 0.04808 ($0) PI -758.48 ($0) Pz -1 290.0 -4.7062 p(0) P3 -8.4279 0.01 8502 0.01007 2 p P4 -3.7599 x -6.7942 X lo-' p(0) P5 p(0) P6 0 0 0.04 76 0.04 29 p(') PI 303.9 p(') P2 -38.0 p(') P3 1.066 0 0") P4 0 0.001306 0 0 p(') P5 0.0470 0 p(') P6 -7.88 x 10-4 -2.62 x 1 0 - 4 C@ PI C@ P2 91.270 157.13 0.58643 1.0860 C@ P3 C@J P4 -0.0012980 -0.0025242 4.9567 X lo-' 9.840 x lo-' C@ PS P b 0 0 0 7.927 x i o 4 1.5774 X l o 5 2.2559 x l o 5 A g o 41 -1037.86 -1 519.99 A g o and q2 -88.61 A&" and C,,' q3 2.3991 2.7739 3.8313 A&" and 2° q 4 -0.00 24 63 21 -0.00284332 -0.00360769 AH,' and C p l o q5 0 -686 0 c, 2 O q h 40.65 46.35 45.86 q7 0.02514 0.016 7 2 0.02208 CPi 0.920 0.834 0.84 8 0 0 Overall standard deviation of fit calculated as u o = (rW(yq- y c ) 2 / ( N o- Np))'" where y o is the obServed (experimental) value, y c is the calculated value, N o is the number of observations, N , is the number of parameters, and W is the weight of each observation taken as l / u s Z .
cL
parameter
LiCl(aq) 0.14847 0 0 -1.546 X lo-' 0 0 0.307 0 0 6.36 x 10-4 0 0 0.003710 4.115 0 0 -3.71 x 10-9
cpt
cp
(28) were fixed with a simple least-squares calculation by forcing the heat capacity data for the three solids69 t o follow a simple linear dependence on temperature over the range of interest. These values of 46 and q7 were then used t o compute C P 2 O ( s ) for use in t h e general least-squares routine for determining t h e remaining parameters. T h e resulting parameters for the three electrolytes are assembled in Table V. By a trial and error procedure it was determined t h a t several of t h e parameters were not necessary t o reproduce the data and these have been set t o zero in Table V. T h e term in (25) involving In (T - 260) is absent in all cases for /3C0) and C4. Other combinations of terms might work equally as well but we felt t h a t a n exhaustive optimization was not warranted. T h e number of digits given for each parameter is sufficient to reproduce the calculations t o about 0,0001 for C$ and In y, 10 J mol-' (69) JANAF Thermochemical Tables, 2nd ed.,Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 37 (1971).
for enthalpies, and 0.01 J K-' mol-' for heat capacities. Discussion of the Fit. Based on the standard deviation of fit (last row in Table V) the parameters of Table V give an excellent description of the experimental results listed in Table IV. It is somewhat ironic that LiCl(aq), the most individualistic member of this family, is by far the simplest t o describe mathematically. All of the free energy and apparent enthalpy results for LiCl(aq) can be adequately described, as a function of temperature and molality, by using only seven adjustable parameters while a minimum of 13 (12 in the case of NaCl(aq)3) are required for the same task in the case of KCl(aq) and CsCl(aq). In the instance of KCl(aq) parameters pll and q5 would not be necessary except for fitting heat capacity data below 298.15 K. A similar situation was apparent for NaCl(aq).3 This requirement is more probably a characteristic of water than of the particular electrolyte involved. T h e p 1 parameters can be compared directly with the corresponding parameters obtained by Pitzer and Mayorga
1250
The Journal of Physical Chemistty, Vol. 87,
No. 7, 1983
Holmes and Mesmer
fortunate that the enthalpy of dilution measurements of from isothermally fitting the ion interaction model to data MayrathU are totally inconsistent with the remaining data at 298.15 K for LiCl(aq), KCl(aq), and CsCl(aq).lo (For as they are the only enthalpy results for LiCl(aq) above KCl(aq) it is the sum of the terms involving p 6 and pll 100 "C. His results at 150 and 200 "C are only about half which must be compared to @(I)for KCl(aq) from ref 10.) as exothermic as they should be to agree with the free For LiCl(aq) and KCl(aq) the agreement between the two energy data. The disagreement is somewhat surprising as sets of parameters is excellent. In the case of CsCl(aq) the his measurements at 100 "C are in reasonable accord with agreement is not so good with the two values of C+actually the other thermodynamic data for LiCl(aq) (with the exhaving opposite signs. Perhaps a better way to compare ception of the most concentrated solution, they are, howthe two sets of parameters is by differences in calculated ever, consistently more endothermic than the calculated osmotic coefficients. For LiCl(aq) and KCl(aq) the maxvalues). The standard error for the two sets of enthalpy imum difference in C#I is 0.0016 and 0.0009, respectively, of solution for LiCl(aq) appears too large but it did not but is 0.0038 for CsCl(aq). Our parameters for CsCl(aq) seem reasonable to use a value much less than 1% for this reflect (see discussion below) the input of recent isopiestic type of measurement. work at 298.15 K62p65that has appeared since the work of Most of the fits obtained with the KCl(aq) thermodyPitzer and Mayorga.'O It should also be pointed out that namic data are quite acceptable and require no comment. we have allowed pl, p67 and p12to be influenced by all of The early work of Soldano et al.37>38 mesh reasonably well the experimental results in contrast to the work on with the other results but, as we have noted before,' the NaCl(aq)3where the parameters were fixed at the values later work at higher temperature^'^^^^ is clearly not comdetermined by Pitzer and Mayorga'O from data at 298.15 patible with the remaining data and have been omitted K only. In any event we are confident that the parameters from the least-squares calculation. Electrochemical results of Table V are entirely adequate to represent all of the of Mussini et al.* are in fair agreement at low temperatures thermodynamic data (except, of course, the volumetric but are consistently more negative (in In y) than the properties) for these solutions at 298.15 K. calculated values at the higher temperatures. Through an In nearly all cases the fit as a function of temperature oversight, the activity coefficients of Lietzke and Stoughwas about as good as that obtained in the isothermal apton73for KCl(aq) were not included in the data base. This plication of the ion interaction model. This close correomission has no effect on the final values of the parameters spondence can be seen in Table IV by comparing the asfor KCl(aq) because the data of ref 73 are in excellent signed standard error (the isothermal fit was an input for agreement wit the more extensive results of Harned and this quantity) with the standard deviation (column seven) Cook.46 With the exception of the work of Likke and by using the parameters of Table V. A notable exception Bromely," which covers the very important temperature is our high-temperature isopiestic results where the isorange of 80-200 "C, the heat capacity results for KCl(aq) thermal fit is better than the temperature-dependent fit are in satisfactory agreement, both among themselves and by a factor of about two (this can be seen by comparing also with other types of data. Not only is there considthe corresponding entries of Table IV with Table I1 and erable scatter in the results of Likke and B r ~ m l e ybut ,~~ ref 1and 2). However, this exception is probably a matter also in the region where overlap exists their data give very of precision rather than overall uncertainty. The goodness different standard state properties (CP2")than those obof fit generally deteriorates somewhat for temperatures tained from Tanner and Lamb47or Ackermann and coremoved from 25 "C with two noteworthy exceptions being workdem2* Nevertheless, we have used (at reduced our isopiestic data and all of the freezing temperature weight) Likke and Bromley's results from 140 to 200 "C results. As is generally the case, the enthalpies and heat in the least-squares routine because theirs is the only set capacities are not as precise, on a percentage basis, as the of heat capacities for KCl(aq) in this temperature range. free energy results, being particularly noticeable for some The poor agreement is evident from the standard deviation of the enthalpy of solution measurements. With few exof fit of their data (Table IV). Enthalpies of dilution and ceptions, deviations of the individual points from the solution (one concentration at each temperature) of calculated values were random for all types of data. KCl(aq) from Craft and Van were included only With two exceptions, the free energy results for LiCUaq) because of the temperature involved in their work, a reare reproduced quite well with the seven parameters of mark also applicable to the results of Borodenko and Table V. The vapor pressure results of Gibbard and Galinker48which must be regarded as no more than a ScatchardZ2at 6.4 mol kg-l (their measurements for more rough estimate. In contrast to his work with LiCl(aq), the concentrated solutions were not included in the present enthalpy of dilution measurements for KCl(aq) by Mayanalysis) were lower than the calculated values by amounts rath%are a valuable addition to the thermodynamic data ranging from 0.6 to 1.6%. Electrochemical cell results of base for KCl(aq) in the temperature range of 100-200 "C. Caramazza20scattered badly (about 5%) about the calcuThere are numerous sets of enthalpy of solution mealated values and were included primarily because of the surements for KCl(aq) in the literature. The six sets setemperature range covered by the measurements. Isopiestic results of Soldano and c o - w ~ r k e r s and ~ ~ the ~ ~ ~ ~ lected ~ ~ ~ 'for ~ inclusion in Table IV are fairly recent and all but one set cover a range of temperature with the work vapor pressure measurements of Campbell and Bhatnagof KildaP1 being particularly detailed and extensive. For er72were not included in the LiCl(aq) data package because the most part, the results are limited to dilute solutions, of excessive scatter and/or inconsistency with the other an important factor in fixing the infinitely dilute value results. Enthalpy of dilution measurements for LiCl(aq) It should be pointed out that the heat capacity at 25 "C are in substantial agreement with the exception and enthalpy of solution data for KCl(aq) below 25 "C noted in Table IV (footnote h). Millero's enthalpies of require the terms involving p 6 (for @(I))and q5 (these are dilution at 30 "C are consistently high (more exothermic) absent in the cases of LiCl(aq) and CsCl(aq) where no such but are well within the expected uncertainty. It is unfor KCl(aq) data exist). As a matter of comparison, aso at 25 "C calculated from Table V is 17236 J mol-l and the (70) B. A. Soldano and M. Meek, J. Chem. SOC.,4424 (1963). (71) B. A. Soldano and P. B. Bien, J. Chem. SOC.A , 1825 (1966). (72) A. N. Campbell and 0. N. Bhatnager, Can. J. Chem., 57, 2452 (1979).
(73) M. H. Lietzke and R. W. Stoughton, J. Tenn. Acad. Sci., 42, 26 (1967).
I
160
I
1
k
140 l5O
30
I
I
p/f
21) I .o
.;/
0 0
05
1
i I 50
I 100
1251
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Thermodynamic Properties of Alkali Metal Chlorides
I
I
150
200
,
I
I
0
50
100
I
I
I
150
m
250
tpc Flgure 4. Ion Interaction parameter pi)as a function of temperature. Lines are calculated from Table V and ref 3.
250
tPC Flgwre 3. Ion interaction parameter
Po)
as a function of temperature. Lines are calculated from Table V and ref 3.
value given by Kilday5l is 17241 f 18 J mol-'. Free energy data for CsCl(aq) from the cell potential measurements of C a r a m a z ~ aand ~ ~ Mussini et al.56are no more certain than was the case with LiCl(aq)20and KC1(as)&and the same comments are equally applicable. In the case of the isopiestic measurements on CsCl(aq) by Soldano and ~ ~ - ~ ~ rtheksituation e r is s the ~ same ~ ~ as with KCl(aq)-the lower t e m p e r a t u r e ~are ~ ~included ,~ in Table IV while the higher temperature^^^^" are rejected. From the present analysis it appears that tables of osmotic and activity coefficients for CsCl(aq) in Robinson and Stoked7are in need of some minor revision. A t molalities above 0.5 mol kg-' the osmotic coefficients of Robinson and Stokes are consistently low by amounts ranging from 0.002 to 0.007 units. These low values were previously pointed out by Rard and Miller.B5 Osmotic coefficients from the isopiestic measurements of ref 62,64, and 65 mesh together quite well in the present work with the extensive results of Rard and Miller65being, in all probability, the most reliable available for CsCl(aq) at 25 "C. In the case of CsCl(aq)-also LiCl(aq)-a noticeable feature of Table IV is the lack of thermal data at elevated temperatures with the only two sets available being the heat capacity measurements of Ackermann and co-workers28and the enthalpies of dilution by Mayrath.% It is indeed pleasing that these two sets of thermal data agree reasonably well with the free energy results which, at elevated temperatures, consist mostly of our own isopiestic measurements. Ion Interaction Parameters of the Alkali Metal Chlorides The temperature dependence of the empirical ion interaction parameters @(O), @('), and CQis depicted in Figures 3-5, respectively. For completeness the parameters for NaCl(aq) as a function of temperature, as determined by Silvester and Pitzer? are included. Points shown in Figures 3-5 are from isothermal fitting of the ion interaction model to individual data sets which, with few exceptions, represent osmotic coefficients derived from isopiestic measurements. Parameters derived from electrochemical cell potential results were much more erratic, primarily
40
30
5 .a
20
N
10
0
0
x
t
~
~
-10 -20
~
~
~
~
~
~
-30 L -4 0
NoCl -5 0 0
I 50
1
100
150
200
250
t /T
Flgure 5. Ion interaction parameter d as a function of temperature. Lines are calculated from Table V and ref 3.
because of the limited molality range covered in most of these cases. An obvious exception to this limitation is the work of Harned and Cook&on KCl(aq). In a sense the ion interaction model is quite forgiving in this respect because of the covariance of the parameters, particularly between Pc0)and CQ. The individuality of LiCl(aq) is apparent in Figures 3 (especially so) and 5 but not in Figure 4. Since @(O) is normally the dominant parameter the different temperature dependence exhibited by LiCl(aq) in Figure 3 becomes increasingly significant as the temperature decreases, particularly so below about 100 OC. A t all temperatures the @(O) parameter for the alkali metal chlorides is in the order of LiCl(aq) > NaCl(aq) > KCl(aq) > CsCl(aq) which is the inverse order of their ionic size. However, there is probably not a simple quantitative relationship with size because of, as pointed out by Pitzer,'" the numerous other factors involved in @(O) (and @(')), The @(') parameter for these salts also follows the inverse size order except for the highest temperatures where the only certainty is that @(l) for CsCl(aq) is the smallest. In contrast to @(O), @(l)uniformly increases with increasing temperature. Third virial coefficients-for triple ion interactions in the model-for these four electrolytes decrease sharply with temperature up to about 100 "C (Figure 5) and then, with the exception of C+ for LiCl(aq), remain relatively independent of tem-
1252
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Holmes and Mesmer I I W C ! W C 250°C -
B
1.2
0 0
a
0
I
I
1
1
LiClfool
0
150 "C
1.0
+-
150 O C 0.8 ,
L - - 1
0
I
2
,
1
3
4
5
I
I
!
- _ L a -
6 0 1 m/mol kq-'
2
3
4
5
6
Figure 6. Osmotic Coefficients 9 for aqueous solutions of the alkali metal chlorides. Calculated from Table V and ref 3. ,
I
/
4
, 7 -
-
0.6
1 1.0
_-
c
I
250 "C
I
I
I
400 O
I
2
3
4
5
6
0
1
2
3
4
5
6
m/mol kg-'
Activity Coefficients y for aqueous solutions of the alkali metal chlorides. Calculated from Table V and ref 3.
300
Figure 7.
perature. Obviously there is no correlation of C@with smoothly varying properties such as ion size. One should remember that the contribution of C@to the thermodynamic properties is negligible at low concentrations and is still small at the highest molalities. It is perhaps more appropriate to treat C@as an arbritary fitting parameter rather than as having physical significance. The behavior of aqueous electrolyte solutions is apparently less complicated at elevated temperatures. One facet of the simplified behavior can be seen in the decreased temperature dependence of the ion interaction parameters at temperatures above 100 OC (Figures 3-5). Mathematically it is possible to describe the osmotic coefficients of KCl(aq) and CsCl(aq) in the range of 100-250 "C with a a(4) of less than 0.005 by treating @(O) and C@as temperature-independent constants with @(l) depending on temperature in a logarithmic or linear manner. Thermodynamically, this is not a very realistic description as it is not possible to fit the enthalpy and heat capacity data for KCl(aq) and CsCl(aq) within such a simple framework.
Trends for the Excess Thermodynamic Quantities Osmotic coefficients, activity coefficients, apparent enthalpies, and excess heat capacities are displayed in Figures 6-9, respectively, for the four most common alkali metal chlorides at temperatures of 50, 150, and 250 "C. For NaCl(aq) these properties were calculated from parameters given by Silvester and Pitzer3 while calculations for the other three salts are based on the results listed in Table
+
LiCl (aq)
NaCl (oq)
I
200 L
300
200
100
n 0
100
200
0 tpc
100
200
Figure 9. Excess heat capacities per mole of solute (CPEXIm) for aqueous solutions of the alkali metal chiorkles. Calculated from Table V and ref 3. Dashed lines are outslde the experimental results: 0 , ref 68;W, ref 74; +, ref 47.
V. (Complete results of the calculations for LiCl(aq), KCl(aq), and CsCl(aq) are available as supplementary material. See paragraph at end of paper concerning supplementary material.) In the case of enthalpies and heat
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Thermodynamic Properties of Aikaii Metal Chlorides
capacities for LiCl(aq), KCl(aq), and CsCl(aq), many of the calculated resulta are outaide the range of experimental data (this situation also existed for NaCl(aq) when Silvester and Pitzer3 did their analysis) and, as a precautionary measure, should be regarded as tentative until confirmed by experimental work. These regions are indicated by dashed lines in Figures 8 and 9. Further discussion on this point is given in a succeeding paragraph. One prominent feature of the results shown in Figures 6-9 is the similarity of all four salts at all temperatures. LiCl(aq) does tend to be somewhat different, particularly so in the case of the osmotic and activity coefficients but the distinction is not so apparent for the enthalpy and heat capacity. The uniformity of the trends is another notable feature of the results displayed in Figures 6-9. With the exception of the excess heat capacity, the thermodynamic properties of these four electrolytes are in the order LiCl(aq) > NaCl(aq) > KCl(aq) > CsCl(aq). An additional uniform trait is that these quantities become more temperature dependent as the temperature increases, i.e., there is more change between 150 and 250 "C than between 50 and 150 "C. The work of Silvester and Pitzer3 indicates that, with the exception of the activity coefficient at high molalities, the trait of increasing temperature dependence continues above 250 "C in the case of NaCl(aq). One should be reminded that, strictly speaking, the thermodynamic relationships between these various properties require a constant pressure. Neither the present work nor that of Silvester and Pitzer3 meets the strict requirement of constant pressure (see earlier discussion). Above 250 "C the corrections to a constant pressure became increasingly more important while the volumetric properties necessary to make the corrections are not availablecertainly not in sufficient detail and accuracy. The osmotic and activity coefficients for LiCl(aq), KCl(aq), and CsCl(aq) listed in the supplementary material and shown in Figures 6 and 7 are considered to be as reliable as the reference data, i.e., as reliable as those for NaCl(aq). In the case of the enthalpies and heat capacities the situation is not so clear when one considers the lack of reliable experimental results for LiCl(aq), KCl(aq), and CsCl(aq) at the higher temperatures. Although there are basic thermodynamic relations between these quantities and the excess free energy, the process of differentiation always introduces additional uncertainty into the derived quantity. However, the uniformity of the trends within the series, both with regard to molality and temperature, generates a measure of confidence in the derived properties outside the range of experimental results in the case of +L and CpEx. In this respect it should be noted that 'L values for NaCl(aq) tabulated by Silvester and Piker3 (and shown in Figure 8) are in reasonable agreement with the recent calorimetric measurements by B ~ s e y . ~ ~ Excess heat capacities (per mole of solute) shown in Figure 9 are more reliable than apparent heat capacities, particularly so outside the range of experimental results. These two quantities are related by CpEx/m = +ep - CP2" (32)
c
Since " is not constrained by the excess free energy, extrapofltions using (27) outside the experimental range are more uncertain than the second derivative of the excess free energy (CpEx). Such extrapolations are especially hazardous at low and high temperatures where Cpzo is changing rapidly.Q@J4 Some recent experimental results covering the high- and low-temperature ranges are shown (74) G. Perron, J.-L. Fortier, and J. E. Desnoyers, J. Chem. Thermodyn., 7, 1177 (1975).
2'4
r----l
i -
t 0
I
it -
I
'
I
I
II
,
1253
1
1
i 1
,
I
I
I
I
2 mol kg-'
0.4
-
-
0 0
100
200
0
I00
200
tPC Flgure 10. Contribution of short-range interactions (In y - f 7 ) to the activity coefficients of aqueous solutions of the alkali metal chlorides. Calculated from Table V and ref 3.
in Figure 9 for NaCl(aq)@J5and KCl(aq).47 Silvester and Pitzer3 were aware of ref 74 but did not include it in their NaCl(aq) work because it would have required a more complex expression for ( f p z o . Smith-Magowanand Wood@ made their measurements at a constant pressure of 177 bar while the calculated values in Figure 9 are for saturation pressure. The pressure difference accounts for about 70 J mol-' K-' (estimated from ref 66) of the discrepancy between ref 3 and 68 at 3 mol kg-' and 250 "C. The results of Tanner and Lamb4' for KCl(aq) define the curve below 25 "C and have been included to show the fit obtained in this region. We consider the shapes of the Cpb curves for the alkali metal chlorides as functions of temperature and , molality to be experimentally verified and that, where measured values exist, the agreement between calculation and experiment is acceptable. Since in its empirical form the ion interaction model does not provide a variable ion size parameter in the expression for the long-range interactions, this part of the thermodynamic functions (the Debye-Huckel (DH) contribution) is the same for all of the alkali metal chlorides (actually it is invariant for a given charge type). Differences between members of the same family are thus restricted to the contributions of short-range interactions (non-DH part) to a particular property. In Figure 10 the quantity (In y - p),where p is defined by (6), is plotted as a function of temperature at three molalities for each of the alkali metal chlorides. The quantity (In y - p ) ,when multiplied by the appropriate factors, is just the non-DH part of the excess partial molal free energy of the solute (see eq 9). When viewed in this manner there are indeed some stricking differences among the alkali metal chlorides-not only in the size of (In y - p)but also in the temperature dependence of this factor. On going from LiCl(aq) to CsCl(aq) the temperature dependence of (In y - p)changes, in a smooth manner, from decreasing with to increasing, with increasing temperature. In the case of NaCl(aq), KCl(aq), and CsCl(aq) the increase, with increasing temperature, of the non-DH contribution to the activity coefficient is particularly marked below about 50 "C, a temperature range where rapid changes in other (75) K. S. Pitzer, Acc. Chem. Res., 10, 371 (1977).
1254
--
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983 2 .O
TABLE VI: Fit of the Theoretical Model (Ea 33)
1.6
1.2
0.8 0.4 A
u-
0.8
2m
n
7
0.4
0
t
06
A 08
10
l 12
14 06
i
1
l
I
08
10
12
,
.
,
14
rip-1
Figure 11. Short-range contributions (In y - f') to the activity coefficients as a function of the reciprocal cation radius for aqueous solutions of the alkali metal chlorides. Lines are linear least-squares fits.
properties, e.g., CP2,are frequently observed. In all fairness a positive temperature coefficient for (In y - f y ) is observed at low molalities (below about 0.7 mol kg-' in the case of LiCl(aq)) for all four salts. The behavior under discussion could have been inferred, of course, from the temperature dependence of /?(O), /?('), and C@ (Figures 3-5, respectively), but Figure 10 is a quantitative description of a particular property, the activity coefficient in this case. In this respect, the type of plot shown in Figure 10 should be quite useful for extrapolating to higher temperatures when estimated activity coefficients are necessary. At all temperatures involved, (In y - p ) is in the inverse order of the cation size (crystal). The dependence on size is demonstrated in a semiquantitative manner in Figure 11 which shows the non-DH portion as a linear function of the reciprocal of the cationic radius for three molalities at four temperatures. Results for RbCl(aq) at 25 "C were calculated from Pitzer and Mayorga.lo The straight lines in Figure 11 are least-squares fits of the data with the maximum standard deviation amounting to about 5% in the activity coefficient (the maximum standard deviation is at 25 "C and 6 mol kg-'). For the cases shown in Figure 11 the average standard deviation is 2.2%. Two trends are evident in Figure 11. Dependence of (In y - f y ) on the cation radius decreases with increasing temperature and decreasing molality. A similar dependence (In y - p ) on the cation radius exists for the alkali metal bromides and iodides at 25 "C although in those cases the relationships are not as quantitative as for the alkali metal chlorides.
Theoretical Ion Interaction Model In the development of useful equations from the ion interaction model a three-term Debye-Huckel expression results from consideration of the pressure equation of statistical mechanic^.^^'^ For the osmotic coefficient the three-term equation is 4-1 = - ~ 1 ~ / ( 6+( 1KU)) + c[2*a3/3 + aaw212/(3(1+ KU)2)] (33)
1 = e 2 / D k T ,and where w = C,Z,~(C,/C),
K~
Holmes and Mesmer
= 4dwc with
z, and c, being the charge and concentration, respectively,
m(max)/ (maxlb (mol kg-')C
t "C
alA
.(@I"
50 150 250
3.931 3.632 3.277
LiCl 0.0242 0.0098 0.0046
0.0613 0.0251 0.0097
6 6 6
50 150 250
3.205 3.120 2.848
NaCl 0.0071 0.0180 0.0200
0.0112 0.0373 0.0382
0.4 6 6
50 150 250
2.742 2.815 2.689
KCl 0.0140 0.0204 0.0210
0.0188 0.0317 0.0286
0.6 6 6
50 150 250
2.530 2.684 2.652
CSCl 0.0026
0.0044 0.4 0.0135 0.5 0.0125 0.0176 0.6 a Standard deviation of f i t calculated as in Table V except by using unit weights for each point. Maximum deviation of the theoretical ion interaction model. Molality at which the maximum deviation occurs.
0.0101
of the ith ion, e is the charge on the electron, D is the dielectric constant, c is the total concentration (in ions ~ m - ~k )is, the Boltzmann's constant, and a is the hard-core diameter. The first term of (33) contains the DebyeHuckel limiting law while the second and third terms are contributions resulting from the finite size of the hard-core diameter, a. In the semiempirical form of (33), which was set up for convenience in dealing with mixture^,^ coefficients for the second and third terms (a total of three in the semiempirical form) are evaluated from osmotic or activity data while a fixed size parameter, for all electrolytes, is used in the first term. For this reason, the physical meaning of the parameters is clouded. When used as a fitting function, eq 33 contains only one adjustable parameter, a, the hard-core diameter. P i t ~ e r ~ , ' ~ has shown that the three-term Debye-Huckel expression (33) does an excellent job of fitting the osmotic coefficient of HBr(aq) up to 1 mol kg-' at 25 "C. Table VI contains the results of least-squares fitting of eq 33 to the osmotic coefficients of the alkali metal chlorides at 50,100, and 250 "C up to molalities of 6 mol kg-l. The standard deviation of fit ranges from acceptable (-2.5%) to excellent (-0.3%). Differences between (33) with the hard-core diameters of Table VI and the semiempirical expression using the parameters of Table V would not be discernible on the scale used in Figure 6. It is clear that the obskrved behavior of the alkali metal chlorides is quite consistent with this theoretical model. It should be mentioned that if the molality is restricted to 1mole kg-', or less, excellent fits are obtained for all four salts at all temperatures. The hard-core diameters listed in Table VI are in the inverse order of the crystallographic cation size at all temperatures and are temperature dependent-quite strongly so in the case of LiCl(aq) and reverse at about 150 "C for KCl(aq) and CsCl(aq). The mean spherical approximation (MSA)'6 is also a relatively recent theoretical description of electrolyte solutions in which the ionic size can be treated as an adjustable parameter. It is interesting that ionic sizes obtained by application of the MSA theory to data for the alkali metal chlorides7' are comparable to, and have the same trend with crystallographic size as, the hard core (76) S. Watanasiri, M. R. Brule', and L. L. Lee, J. Phys. Chem., 86, 292 (1982), also earlier work cited in this reference. (77) R. Triolo, J. R. Grigera, and L. Blum, J.Phys. Chem., 80, 1858 (1976).
J. Phys. Chem. 1983, 87, 1255-1263
diameters given in Table VI. A further similarity is that improved fits were obtained with the MSA model if the ionic size was temperature dependent. It is clear that the hard-core diameters of Table VI (or the ionic sizes from the MSA model) are physically realistic only if they refer to the solvated ions. In this respect they are consistent with generally accepted trends in hydration. In conchsion we mention additional experimental results which would be highly desirable. These include enthalpies of dilution for KCl(aq) and CsCl(aq) above 200 “C and the same for LiCl(aq) above 100 “C, heat capacity measurements for all three electrolytes above 130 “C (existing data” are not in very good agreement with other thermodynamic results), and, in an interesting region, the
1255
heat capacities of LiCl(aq) and CsCl(aq) below 25 “C.
Acknowledgment, This research was sponsored by the Division of Chemical Sciences, Office of Basic Energy Sciences of the U.S. Department of Energy under Contract W-7405-eng-26 with the Union Carbide Corporation. Registry No. LiCl, 7447-41-8;KC1,7447-40-7; CsCl, 7647-17-8.
Supplementary Material Available: Tables VII-XVIII (24 pages) contain osmotic and activity coefficients, apparent molal enthalpies, and excess heat capacities at rounded molalities and temperatures for LiCl(aq), KCl(aq), and CsCl(aq). Ordering information is given on any current masthead page.
-+
Theoretical Analysis of the Quantum Contributions to the Reactions H,(v = 1) H H 2 ( v ’ = 0, 1) and H,(v = 1) D H H D ( v ’ = 0, 1)
+
+
+H
-
Robert B. Walker’ Theoretical Dlvision, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
and Edward
F. Hayes
Dlvlslon of Chemistty, National Science FoundaNon, Washlngton, D.C. 20550 (Received: August 20, 1982)
Detailed quantum-dynamicalcalculations on the Siegbahn-Liu-TruhlaHorowitz (SLTH) surface are reported for a rotating linear model (RLM)approximation with and without corrections for bending zero-point energy. These dynamical results predict that there are substantial prethreshold quantum contributions to state-selected cross sections and rate constants for both of the title reactions. However, the mechanisms for these prethreshold quantum effects are not the same. For Hz(v = 1) + H, a threshold resonance is responsible for the large prethreshold quantum contribution: 65% of the total rate of 300 K. For Hz(v = 1) + D, tunneling is found to be large, leading to a 66% prethreshold quantum contribution at 300 K. These large quantum corrections are not large enough to provide an explanation for the previously identified discrepancybetween the experimental and classical theoretical rate constants for these reactions.
I. Introduction The main purpose of this paper is to examine the quantum contributions to the reactions H + H2(v = 1) Hz(u’ = 0, 1) + H and D + Hz(v = 0) HD(v’ = 0, 1) + H. We became interested in this reaction after reading the Mayne and Toennies paper’ in which they identified a major discrepancy between the experimentally determined2“ and theoretically predicted rate constants. The theoretical predictions were derived from quasi-classical trajectory studies using the Siegbahn-Liu-Truhlar-Horowitz (SLTH) potential energy s ~ r f a c e . ~In J view of the excellent agreement between experiment and theory for
-
-
(1)H.R.Mayne and J. P. Toennies, J . Chem. Phys., 75,1794 (1981). (2)R. F. Heidner, 111, and J. V. V. Kasper, Chem. Phys. Lett., 15,179 (1972). - .. -,. (3) Y. M. Gershenzon and V. B. Rozenshtein, Dokl. Phys. Chem. (Engl. Transl.),221,664 (1975). (4)E. B.Gordon, B. I. Ivanov, A. P. Perminov, V. E. Balalaev, A. N. Ponomarev, and V. V. Filatov, Chem. Phys. Lett., 58,425 (1978). (5) M. Kneba, U. Wellhausen, and J. Wolfrum, Ber. Bunsenges. Phys. Chem., 83,940(1979). (6)P.Siegbahn and B. Liu, J. Chem. Phys., 68, 2457 (1978);B. Liu, ibid.,58, 1925 (1973). (7)D.G.TNhlar and C. J. Horowitz, J . Chem. Phys., 68,2466(1978); 71,1514 (E) (1979).
.
0022-3654/83/2087-1255$01.50/0
the H + Hz(v = 0) reaction, this reported discrepancy between experiment and the identical theoretical approach for the H H2(v = 1) reaction is particularly surprising. A short review of the status of both the theoretical and experimental efforts on this system has been recently given by Schatz.8 Very recently, Glass and Chaturvedig have completed a new measurement of the D + H2(u = 1) reaction rate using a discharge flow apparatus coupled with EPR detection of H atoms produced by the reactions. They obtain a rate constant which is over 1order of magnitude lower than that measured previ~usly.~ These new measurements substantially reduce the discrepancy between theory and experiment for the D Hz(u = 1) reaction and, by implication, cast doubt on the accuracy of the measurements of the H + H2(v = 1)rate. A possible contributing factor to the lack of agreement between the experimental and theoretical rate constants is that quantum-dynamical effects not included in the
+
+
(8)G. C . Schatz in “Potential Energy Surfaces and Dynamics Calculations”, D. G. Truhlar, Ed., Plenum Press, New York, 1981,p 287-310. (9)G.P. Glass and B. K. Chaturvedi, J. Chem. Phys., 78,3478(1982).
0 1983 American Chemical Society
