Oct 10, 1994 - culated from the measured densities by using the relation. 1000(do - d) ... where y is the mole fraction of LiOH in the electrolyte mixture and the.
Journal of Solution Chemistry, Vol. 24, No. 2, 1995
Volumetric Properties of Aqueous Electrolytes at High Temperature: Mixtures of LiOH and KOH up to 523 K Horacio R. Corti 1,2 and Federico E. Svaro 1 Received October 10, 1994; Revised November 1, 1994 The densities of mixtures of aqueous lithium and potassium hydroxides were measured up to 3 molal, at 373, 423 and 523 K at pressures close to saturation. The partial molar volumes were calculated and the coefficients of the Pitzer equation for the mixtures were obtained. The mixing volume is positive at 373 K while at higher temperatures the mixture is ideal within experimental error, probably as a result of association of the lithium hydroxide.
KEY WORDS: Alkali metal hydroxides; densities; partial molar volumes; high temperature; ionic association.
1. INTRODUCTION Natural or industrial process waters and geothermal brines are examples of concentrated aqueous electrolytes mixtures whose thermodynamic properties are of considerable importance in chemical engineering. The ion-interaction theory (1) provides parameters for binary solution mixtures that have been useful to predict properties of ternary systems. The method can be applied over a wide range of temperature, provided the parameters have been determined over the same ranges. The effect of pressure on properties such as activity or osmotic coefficients, dilution enthalpies, heat capacities, could be estimated from the pressure dependence of the Pitzer coefficients for the electrolytes. lInsfituto de Qufmica Ffsica de Materiales, Universidad de Buenos Aires, PabeUdn 2, Ciudad Universitaria, CP 1428, Capital Federal, Argentina. 2Departmento Qufmiea de Reactores, Comisidn Nacional de Energffa Atdmica, Av. Libertador 8250, CP 1429, Capital Federal, Argentina. 121 0095-9782/95/0200-0121507.50/0 9 1995 Plenum Publishing Corporation
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Corti and Svarc
These coefficients can be obtained from the volumetric properties of the binary solutions. At room temperature it is customary to approximate the volumetric properties of the mixture by the parameters obtained for the binary solutions, the ternary or higher order interaction coefficients being neglected. At high temperature there is not enough information on mixtures to decide whether or not this is a reasonable assumption. The volumetric properties of the mixtures also give an insight into the intermolecular interactions in solution, involving ions, ion-pairs and solvent molecules. Important effects on the electrostriction of water molecules by ions are expected at high temperature, not only due to changes in the structure of water, but also because of changes in ion speciation. It is well known that ionic association increases with temperature in aqueous solutions.~2~ The volumetric properties of aqueous electrolyte solutions at high temperature have been studied by several authors. (3"~~ The available information extends over a wide range of temperature and pressure but, only binary systems (salt-water) have been studied beyond room conditions. The only exceptions are the works by Millero and coworkers, (xa'v'~ where the volume changes of mixing of the major components of sea water were studied in the range 273-373 K. As the authors know, there is a complete lack of data for the volumetric properties of multicomponent electrolyte solutions at temperatures higher than 373 K. This prevents us from testing the applicability of mixture rules formulated for ternary or more complex systems, (~3xs) under hydrothermal conditions. In this work we have extended a previous work (~~ on volumetric properties of alkali metal hydroxides at high temperature. We report the densities of mixtures of lithium and potassium hydroxides in aqueous solutions at 373,423 and 523 K, at molalities between 0.5 and 3 mol-kg-1.
2. EXPERIMENTAL Stock solutions of LiOH and KOH were prepared with carbonatefree AR grade reagents and demineralized water of conductivity less than 0.1 m~tS-cm-1. The solutions were standardized with potassium hydrogen phthalate and stored in plastic bottles under nitrogen until used. The mixtures, having lithium mole ratios 0.25, 0.50 and 0.75, were prepared by weight and corrected for buoyancy in air. The total molalities were accurate to 0.01 percent. The vibrating tube densimeter used to measure the density of the ternary mixtures is the same one used for the binary solutions; its operation and calibration has been described in detail elsewhere. (~~ In order to
Volumetric Properties of LiOH and KOH
123
eliminate systematic errors the density of the mixtures were measured at the same temperature and pressure as the binary solutions (1~ (373.15 K and 0.4 MPa, 423.15 K and 1.5 MPa, 523.15 K and 4.8 MPa). Water and anhydrous ethylene glycol were used for calibration below 423 K. The density of ethylene glycol was calculated using the equation given in a former work, (x0) valid in the range 298-423 K and 1 bar and corrected to the working pressure using compressibility data. (16) Above 423 K water and deuterium oxide were used as reference fluids. The densities of heavy water were taken from Hill et al. ( ~ and corrected for hydrogen content (less than 0.5 percent) using an ideal mixture rule. The water densities were taken from steam tables. (~8~The constant of the densimeter at the working temperatures and pressures agreed within experimental error with those reported in the study of the pure alkaline hydroxides. Moreover, the density of one pure KOH and one pure LiOH solution (around 1 molal) were measured at each temperature and pressure, and the values obtained agreed within experimental error with those calculated using the Pitzer equation with the coefficients reported in our previous study. (1~ The resonance period of the vibrating tube was measured with a precision of 1 ppm, with a counting time of 20 seconds. The densities of the solutions were calculated from the measured resonance periods of the solution z and water Zo and the constant K of the densimeter d - do = K (z - %). Because the water baseline period shifts slightly (0.02-0.05 Us) during densimeter operation, it was necessary to determine Zo after each two samples measured. Since it is not easy to adjust the temperature and pressure of the system at round values, and small drifts in these parameters are unavoidable, it was necessary to correct measured densities to refer them to the chosen round values. The use of the thermal expansion coefficient and isothermal compressibility coefficient of pure water was sufficient to allow for such corrections. (1~
3. RESULTS The apparent molar volume of the electrolyte mixture can be cap culated from the measured densities by using the relation
v, =
1000(do - d)
Mmix
ddom
-'3-"
(1)
where Mmix is the mean molecular weight of the electrolyte, defined by, Mmix = yMuoH + (1-y)MKon
(2)
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Corti and Svarc
Table I. Densities and Apparent Partial Molar Volumes of LiOH + KOH Mixtures at 373,423 and 523 K 373 K
423 K
523 K
m
YLi
d
Vr
d
Vr
d
Vr
0.4718 0.4811 0.4906 0.7543 0.7698 0.8709 0.7858 1.2064 1.2240 1.2418 1.6965 2.0969 2.1596 2.3898 3.0376 2.8479 2.8502
0.75 0.50 0.25 0.75 0.50 0.50 0.25 0.75 0.50 0.25 0.75 0.75 0.50 0.25 0.75 0.50 0.25
0.97532 0.97716 0.97910 0.98355
(-0.82) 0.37 4.42 -2.66
0.93511 0.93739 0.94034 0.94380
-8.59 -5.03 (-2.50) -6.16
0.82242 0.82468 0.82795 0.83420 0.83839
(-33.20) (-29.10) -27.84 -29.51 -26.52
0.99030 0.99093 0.99570 1.00179 1.01036 1.01026
2.95 5.11 -0.15 3.15 (4.49) 0.18
0.95098 0.95306 0.9585 0.96340 0.97014 0.97333
-1.78 -1.10 -5.13 -0.74 1.37 -3.88
0.84342 0.85021 0.85706 0.86589
-24.81 -23.51 -21.24 -21.02
1.03247 1.05102 1.04601 1.05375 1.06763
4.17 7.32 1.86 4.89 7.62
0.99659 1.01749 1.01167 1.01899 1.03539
0.20 2.50 -1.72 1.23 2.94
0.88080 0.89441 0.91539 0.90957 0.91705 0.93523
-18.34 -16.31 -13.40 -14.38 -12.35 -11.99
Units: m, mol-kg'l; d, g-cm3; V$ cm3-mo1-1.
where y is the mole fraction of LiOH in the electrolyte mixture and the molecular weights are given by MLiOH = 23.946 and MKOH = 56.11 g-mol1. Table I summarizes the densities and apparent molar volumes of LiOH-KOH mixtures at the compositions and temperatures studied in this work. 3.1. Limiting Partial Molar Volumes
Since the concentrations used in this work are far from the dilute region, we preferred to calculate Wmix,the partial molar volume of the electrolytes in the mixture at infinite dilution, by means of the additivity relationship r~mix = yV~LiOH+ (1--y)~MOH
(3)
where r~Moa is the partial molar volume of the corresponding binary alkaline hydroxide solution at infinite dilution. This procedure avoids errors associated with the extrapolation of the apparent molar volumes of the mixtures to zero concentration.
Volumetric Properties of LiOH and KOH
125
Table II. Partial Molar Volumes at Infinite Dilution for Aqueous Alkali Metal Hydroxide Solutions at Different Temperatures LiOH
KOH
~
P (MPa)
~22(cm3-m~
e (MPa)
100 150 250
0.4 1.5 4.8
-8.5• -16.0• -54.0•
0.4 1.5 4.8
V~2(cm3-mo1-1) 4.4• -1.7• -43.6•
The values of the partial molar volumes at infinite dilution for KOH and LiOH up to 523 K determined in a previous work (10)are summarized in Table II. It was concluded that LiOH is strongly associated at high temperature and the ion-pair association constants were calculated by assuming that the solution of stoichometric molality m is composed of a m moles of the ion pair and (1-a)m moles of dissociated electrolyte.(19)The apparent partial molar volume of the ion pair was assumed to be equal to the experimental partial molar volume at the higher concentration (m = 3 mol-kgl), since under this condition most of the ions are associated as ion pairs. A similar approach was used (2~ in the study of volume changes upon ion-pairing. The values obtained for the association constant Ka at 477 and 523 K were 90 and 160 respectively, in good agreement with those reported by Wright e t al. (2~) from electrical conductivity measurements. The values of Ka at low temperatures were determined by electrical conductivity. (22) It can be seen in Fig. 1 that Ka is approximately linear in T -1 over the range 298 - 523 K. The interpolated values for the association constant at 373 and 423 K obtained from Fig. 1 are 10.6 and 33.1, respectively. Thus, association is important even at 373 K for the concentrations used in this work, and we would expect larger negative values for ~ for LiOH than those previously reported. In order to test this assumption, we calculate the partial molar volume of LiOH at infinite dilution by using
rI~LOH = r~LiCX- ~MCl+ I'~MOH
(4)
where M = Na, K. Table III shows the averaged results obtained for r~LiOa using Eq. (4) with the values reported by Ellis (23) for LiC1-KC1 and LiC1-NaC1. The last column shows the averaged results obtained with the data by
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Corti and Svarc
6
I
I
I
I
r Y
2
c"
-2 1.5
I
I
I
2.0
2.5
3.0
3.5
4.0
I/T (I O 0 0 / K ) Fig. 1. The temperature dependence of the association constant for LiOH in aqueous solutions: D, data from density measurements, Ref. (10); o, data from high temperature, Ref. (21); =, data from conductivity at low temperature, Ref. (22).
Wood e t al. (24) for LiC1 (extrapolated at 4.8 MPa), by Pabalan and Pitzer (25)for KC1 and by Rogers and Pitzer e t al. (2~ for NaCI. Our results for NaOH and KOH (1~ were used in the calculations. Since W~cl was obtained by extrapolating the Wood e t al. (24) data from 16 and 32 MPa at saturation pressure, the uncertainties associated to these values could be larger than those reported in Table III, which correspond to the difference between the individual values of Wuor~calculated with the sodium and potassium salts and the mean value. For comparison we also include in Table III the values reported previously for LiOH and the values calculated using the Tanger and Helgeson (27) semiempirical equation. We concluded that the values of r~oa previously reported at 373 and 423 K agree within the experimental uncertainty with the values calculated with the additivity relationship using the Ellis data and with the values calculated with the Tanger and Helgeson approach. It is clear that the crude value previously reported for Wuor~ at higher temperatures is less negative than the correct values by several cm3-mol1. At 523 K, the true value of WLiOHis about 11 cm3-mo1-1 more negative than the uncorrected value. It is surprising that such good agreement is obtained between the mean experimental value resulting from the use of the additivity principle and that calculated with the semiempirical approach. We finally adopted the value of -65.2 cm3-mo1-1 for the infinite dilution value of W~on at this temperature.
Volumetric Properties of LiOH and KOH
127
Table III. Partial Molar Volumes of Aqueous LiOH at Infinite Dilution a ~ 100 150 250
Experimental b
Calculatedc
Eq.(9) a
Eq.(9) e
-8.5_+0.5 -16.0__+0.5 -54.0_+0.7
-7.6 -15.3 -65.1
-8.4_+0.7 -17.0+1.3
-6.1 _+1.1 -12.8-+0.9 -65o2_+0.8
a Units: em3-mo1-1, b Ref. 10. c Ref. 27. dReL 23. e Refs. 24-26.
3.2. Apparent Molar Volume and Excess Volume
The experimental results are better represented by the reduced apparent molar volume, defined as A,,
v; = v,--b-In(1 + b4-mm)
(5)
where Av is the Debye-Hfickel limiting slope for the apparent molar volume, m is the total molality of electrolyte and b = 1.2 for 1:1 electrolytes. Figs. 2a-c show the results obtained for V** at the temperatures studied. The concentration dependence of the reduced apparent molar volume can be described in terms of the ion interaction model developed by Pitzer. o) In the particular case of a mixture of two electrolytes having a common ion (MX+NX) the following equation is derived for the reduced apparent molar volume of the mixture (2~
V; = WOO+ 2RTm[yB[iori + (1-y)B~:oH + m[yC[ioH + (1-y)C~oH]] + 2RTy(1-y)mO[iK + RTy(1-y)mZ~[~ou
(6)
where B" and C v are the usual vifial coefficients for the pure electrolytes, 0 v and ~v are the binary and ternary mixture parameters. Due to the limited precision of our data, the B v coefficient can be approximated by the independent concentration parameter [~o v. Our experimental values for the reduced apparent molar volume of the mixtures and those obtained previously for the pure electrolytes were fitted to Eq. (6). The values of V~, = V~ for the mixtures were calculated from Eq. (3) with the data reported in Table II, except for WLiOHat 523 K, where we used the value corrected by ion association. Thus, the fitting equation has six parameters which were adjusted by a
128
Corti and Svarc 5
I
i ....
-42
I
~0
a -44 ! 0 0
-46
E -5
E 0
b
-48
/
-10 -50
-15
I , 0
I 1 m
I 2
(moI/kg)
I 3
-52 0
c I 1
....
I 2
...... I 3
m (mel/kg)
Fig. 2. Reduced apparent molar volume of the KOH-LiOH mixtures at three different mole ratios as a function of the total molality. (a) 373 K; (b) 423 K; (c) 523 K: m, y=0.50; -, y=0.25; V, y=0.75.
least squares procedure of the entire data set at each temperature. Those points which deviate more than twice the standard deviation were eliminated (the data in parenthesis in Table I). The values obtained for the Pitzer coefficients are summarized in Table IV. N is the number of experimental points considered and c is the standard deviation of the fit. At 373 K we found that the standard deviation of the fitting is similar to that obtained for the pure binary electrolytes when we include the binary mixture parameter. If the ternary mixture parameter is also considered in the fit, the standard deviation does not improve. A similar situation was found at 423 K, although the standard deviation is about 50 percent larger than for the pure binary electrolytes. The binary mixture parameter is small in this case and its inclusion has a negligible effect on the fit. It was reported in Table IV only for comparison.
Volumetric Properties of LiOH and KOH
129
Table IV. Pitzer's Parameters for LiOH + K 0 H Aqueous Mixtures at Different Temperatures ~ 100 150 250
p (MPa)
N
0.4 1.5 4.8
25 26 24
tr~5oV a 1135•V a lt~ Po,KOH *~ VO,LiOH 3.45 0.0897 1.53
1N6t,.,v b *~ ~KOH
tC~6w,vb *" "-'LiOH
1N5I~va *~ ~IO_.i
~c
-8.49 1.72 -2.94
-2.29 -9.55 -40.76
1.47 0.333 -
0.43 0.56 1.25
2.56 4.93 18.96
a Units: kg-mol-XbarL b Units: k g 2 - m o l - a b a r L c Units: cm3-mol q.
At 523 K the fit does not improve if a binary mixing parameter is used, and the standard deviation was larger than that found for other temperatures. It is probable that ion association effects, which were taken into account in our estimation of the partial molar volume at infinite dilution, could not be well represented by the simplified Pitzer Eq. (6) for the reduced apparent partial volume. The inclusion of a concentration dependent coefficient 13~ in the Pitzer equation, which is usually related to ionic association, is not useful in this case because of the lack of accuracy in the data. To evaluate this coefficient by fitting the concentration dependence of the partial molar volumes it is necessary to perform precise measurements in the dilute region.
4. DISCUSSION The volume of mixing ZXmVper kilogram of water is defined as the volume change when an amount of LiOH binary solution at molality m containing y m mole of electrolyte is mixed with the amount of KOH binary solution at molality m containing (1-y)m mole of electrolyte, in such a way that a ternary solution of total molality m and LiOH mole fraction y is formed. For such a mix process, the volume change is AmW -- ~mX'tx- [ Y r ~ O H +
(1-y)~u]
(7)
where ~ x is the excess volume per kilogram of water at total molality m, defined as: gx = m(V,,i-
=
m(V,,i-
(8)
where i = mix, L i 0 H or KOH. The volume of mixing becomes AmV = mV 0 - ymV~,(LiOH) - (1-y)mV,(KOH)
(9)
From Eqs. (5, 6) for the apparent molar volume of the binary solutions and Eq. (9) we obtain
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Corti and Svarc
AmV = 2y(1-y)0~z + y( 1-y)m~gi~oH*
(10)
RTm 2
Thus, 0 v is a measure of the magnitude of the binary like-ion interactions occuring after mixing, while ~g" is related to the asymmetry of the mixing volume due to ternary interactions. According to the values of 0[a~ reported in Table IV, the mixture effect is only appreciable at 373 K. At this temperature the volume of mixing has a maximum at y = 0.5 at a given molality and its value is 0.23 m2(cm~-kg-1). At the highest concentrations used in this work (ca. 3 molal) the volume of mixing is around 2 cm3-kgx at the maximum, while the estimated error is close to 0.5 cm3-kg-1. Despite the limited precision of our data, it is clear that at 373 K there is a mixture effect for the system LiOH-KOH. It is worthy to compare the volume of mixing measured for this system with that reported for the system LiBr-KBr. (29~ At 298 K, the volume of mixing for the bromide solutions is 0.1 cm3-kg-1 at m = 1 at the maximum (y = 0.6). This value is approximately 50 percent of the volume of mixing measured at 373 K in the hydroxide solutions. At 423 K the maximum volume of mixing (y = 0.5, m = 3) is 0.55 cm3-kg-~, which is approximately the experimental error of the measurement. Finally, at 523 K, the volume of mixing is zero within the standard deviation of the fit, that is, AmV never exceeds 1.25 cm3-kg-1 over the concentration range studied. Conaughton and Millero~11> have found the temperature dependence for the mixing volumes of Na + and Mg 2+ mixtures with a common anion (C1- or SO~-). At constant ionic strength (3 molal) the mixing volume is negative at low temperatures (278-298 K) and it tends to zero as the temperature increases to 368 K. The volume of mixing for these systems are low (0.1-0.4 cm3-kg-1) and were attributed to ion-specific interactions between cations and water. This effect was explained by Desnoyers et al. (~~ in terms of the Gumey co-sphere model. The reorienration of water molecules during the interaction of two structure makers cations, such as Na § and Mge+, leads to negative mixing volumes. In mixtures of structure maker and breaker ions (such as Li § - K § the volume is positive. On the other hand, ionic association could be responsible for modulating the mixing volume at high temperature and depleting its value as the system becomes more ideal than expected in view of the temperature effect on the degree of formation of ion-pairs. Nevertheless, the accuracy of the data reported in this work prevents us from per-
Volumetric Properties of UOH and KOH
131
forming a quantitative assessment of the association effect on the measured partial molar volumes. It must be emphasized that ternary systems with a common ion where two of the ions have strong specific interactions leading to ionic association should be treated as a quaternary systems containing three ions and the ion-pair. Precise density measurements performed on systems with strong ion-pair formation at room and moderate temperatures could help to understand the effect of ion-ion and ion-solvent interactions on the pVT properties of ionic systems.
ACKNOWLEDGMENT The partial support of this work by the Consejo Nacional de Investigaciones Cientificas and Tecnicas (CONICET) is gratefully acknowledged. REFERENCES 1. K. S. Pitzer, J. Phys. Chem. 77, 268 (1973). 2. R. Fernandez Prini, H. R. Corti, and M. L. Japas, High Temperature Aqueous Solutions, Thermodynamic Properties (CRC Press, Boca Raton, 1992). 3. A. J. Ellis and I. M. McFadden, Geochim. Cosmochim. Acta 36, 413 (1968). 4. D. F. Grant-Taylor, J. Solution Chem. 10, 621 (1981). 5. R. Hilbert, Doctoral Dissertation, Univ. of Karlsruhe, Germany, (1979). 6. R. C. Phutela and K. S. Pitzer, J. Chem. Eng. Data 31, 320 (1986). 7. L A. Gates and R. H. Wood, J. Chem. Eng. Data 34, 53 (1989). 8. I. A. Dibrov, V. P. Mashovets, and R. P. Matveeva, Zh. Prikl. Khim. 37, 29 (1964). 9. S. Kerschbaum, Thesis, University of Karlsruhe, (1988). 10. H. R. Corti, R. Fernandez Prini, and F. E. Svarc, J. Solution Chem. 19, 793 (1990). 11. L. M. Connaughton and F. J. Millero. J. Solution Chem. 16, 491 (1987). 12. L. M. Connaughton, F. J. Millero, and K. S. Pitzer, J. Solution Chem. 18, 1007 (1989). 13. T. F. Young andM. B. Smith, J. Phys. Chem. 58, 716 (1954). 14. V. S. Patwardhan and A. Kurnar, AIChE Journal 32, 1429 (1986). 15. A. A. Humffray, Can. J. Chem. 65, 833 (1987). 16. R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 63, 898 (1941). 17. P. G. Hill, R. D. MacMillan, and V. Lee, J. Phys. Chem. Ref. Data 11, 1 (1982). 18. L. Haar, J. S. Gallagher, and G. S. Kell, NBS/NRS Steam Tables. (Hemisphere Publishing, Washington D.C., 1984). 19. L. Barta and D. J. Bradley, J. Solution Chem. 12, 631 (1983). 20. Y. Marcus, Z. Naturforsch. 38, 247 (1983). 21. J. M. Wright, W. T. Lindsay, and T. R. Druga, Report WAPD-TM-204 Bettis Atomic Power Lab., Pittsburgh PA, (1961). 22. H. R. Corti, R. Crovetto, and R. J. Fernandez Prini. J. Solution Chem. 8, 897 (1979).
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23. A. ]. Ellis. J. Chem. Soc. 1579, (1966). 24. V. Majer, A. Inglese, and R. H. Wood, J. Chem. Thermodyn. 21, 321 (1989). 25. R. T. Pabalan and K. S. Pitzer, J. Chem. Eng. Data 33,354 (1988). 26. S. Z. Rogers and K. S. Pitzer, J. Chem. Phys. Ref. Data 11, 15 (1981). 27. J. C. Tanger and H. C. Helgeson, Amer. J. Sci. 288, 19 (1988). 28. K. S. Pitzer, Rev. Mineral. 17, 97 (1987). 29. K. Patil and G. Metha, J. Chem. Soc. Faraday Trans. 1 84, 2297 (1988). 30. J. E. Desnoyers, M. Arel, G. Pernon, and C. Jolicoeur, J. Phys. Chem. 73, 3346 (1969).
