J. Chem. Thermodynamics 1975, I, 655-660
Solubility and argon
of carbon in molten
A. BORODZIfiSKI,”
dioxide, nitrogen, zinc chloride
A. SOKOLOWSKI,a and L. SUSKI b
Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw 01-224 and Cracow 30-059, Poland (Received 4 June 1974; in revised form 28 December 1974) A volumetric method for measuring the solubility of gases in molten salts has been elaborated, and solubilities of CO1 over the range 709 to 778 K, NS at 720 K, and Ar at 720 K have been determined. The results are discussed in terms of Blander’s model.
1. Introduction Solubility of gases in molten salts is an important quantity from both practical and theoretical points of view. Recently the literature has been reviewed by Flengas and Block-Bolten.“’ The correlation of existing solubilities with the surface tension of the ionic solvent is common. The investigation of a similar dependence for molten salts with a strongly associated structure and low surface tension is of great interest. In this work the solubilities of some gases in molten zinc chloride were determined by a modified volumetric method. Some experimental aspects of this work will be described. The experimental techniques used in determination of solubility of gases in molten salts are not satisfactory. Some methods have been critically described in a review by Battino and Clever. (‘) The methods may be classified as follows: (1) the direct methods: manometric, gravimetric and volumetric, (2) the method consisting in desorption of gases from the salts, previously saturated with gases: stripping by another gas or chilling, and (3) the indirect methods: cryometry, transpiration, electrochemical measurements. Each of the methods has its drawbacks. The determination of the amount of gas dissolved by measuring its volume appears to be the simplest method. So far it has been applied to gas + molten salt solutions only by Bratland et aZ.(3) The accuracy obtained by these authors is, however, lower than that reported for the chilling method. Literature values of Henry’s constants for gases dissolved in molten salts differ widely. For example table 1 presents the values of Henry’s constants for two solutions determined by different methods. A detailed investigation of experimental techniques for the determination of solubilities is needed. Nor can the results shown in table 1 be used as reference values for testing a new experimental method. o 01-224, Warszawa, Poland. b 30-059, Krak6w, Poland.
A. BORODZINSKI,
656 TABLE
A. SOKOLOWSICI,
AND
L. SUSKI
1. Literature values of Henry’s law constants Kfl and enthalpies of solution m mixtures of gas + molten salt, determined by different methods
for two
System
Method
lo6 K,/Pa-’
AH/kJ mol-1
Ref.
He + NaN03 637 K
stripping chiling manometric stripping chiling
1.06 f 0.01 2.16 f 0.01 17.2 f 1.7n 2.24 5 0.03 0.58 f 0.07
13.5 f 0.8 13.7 f 0.5
4 5 6 4 5
Nz + NaN03 637 K
11.5 f 3.5 16.6 f 9.2
*At 642K.
2. Experimental A schematic drawing of the measuring device is presented in figure 1. A Pyrex vessel 1 filled with 50 cm3 of the melt under investigation is connected to a capillary 3 mm in diamater 2. The position of a mercury drop 3 determines the change of volume of the gas due to its dissolution in the melt. The container (1 dm3) of the gas 4 stabilises the gas pressure. The position of the mercury drop is measured by an optical device with an accuracy of kO.01 mm. The saturation of the melt is helped by a stirrer 5, consisting of an iron ring sealed in Pyrex glass which moves up and down by means
6 \ 13 ‘C
FIGURE 1. Schematic drawing of measuring device: 1, 50 cm3 Pyrex vessel; 2, glass capillary; 3, mercury drop; 4, pressurestabilizing container; 5, magnetic stirrer (internal part); 6, magnetic stirrer (external part); 7, molten alkaline nitrate bath; 8, electric furnace; 9, thermocouple; 10, vacuum distillation apparatus; 11, gas-storage container; 12, temperature-stabilizing water; 13, pressure-measuring manometer; A, B, C, D, E, F, valves.
SOLUBILI’IY
OF Con, Na, AND Ar IN ZnCldl)
657
of an external magnetic device 6. The vessel with the melt is immersed in the thermostat bath 7 containing a eutectic mixture of alkaline nitrates, the temperature of which is stabilized within f 1 K. The vessel 1 was f3led with the salt by distillation under vacuum (low4 Torr) from the container 10 directly before the experiment, and then the container 10 was cutoff by sealing.? After reaching the set temperature the gas was introduced from the container 11 through the valve F. The initial position of the mercury drop was fixed by closing the tap A and then the mixing of the molten salt was commenced. Figure 2 presents a typical plot of the position of the mercury drop against time t after introducing a new portion of a gas. The moment of switching on the stirrer is marked by point a on the curve in figure 2. The determination of the mercury position
t/h FIGURE 2. Rise h of mercury drop plotted against time t after introducing a new portion of gas to the measuring vessel. Point a is the beginning of stirring. Point b is when equilibrium is reached.
at t = 0 was carried out by extrapolation to 0 of the first part of this curve, obtained before the stirrer was switched on. Point b corresponds to saturation of the solution by the gas. The change of the gas volume above the melt, measured as the rise of the mercury drop from the initial position, obtained by extrapolation, to the final equilibrium position at b, gives the amount of the gas dissolved at a given pressure and temperature. When equilibrium has been reached, a new measurement at a different pressure begins. The pressure of the gas is changed by introducing an additional portion of the gas from the container or by decreasing its amount by pumping through valve E. In the latter case the equilibrium between the gas and melt was obtained by desorption of the gas and was measured by the determination of the lowering of the position of the mercury drop. t Torr = (101.325/760) kPa.
658
A. BORODZIfiSKI,
A. SOKOLOWSKI,
AND L. SUSKI
In all the isothermal experiments the solubility was measured at three different increasing pressures and at three decreasing pressures. The largest error of a single measurement of the solubility was 4 to 5 per cent for values of Henry’s constants of about 10” Pa-‘. The accuracy of the determination of this constant is given by the standard deviation of the slope of the curve of solubility plotted against pressure calculated for six different pressures. For illustration, the standard deviation of Henry’s constant for the solubility of argon in ZnCl,, calculated in three independent experiments, was f 1.5 per cent. Zinc chloride p.a. was distilled under vacuum prior to its distillation directly to the apparatus. The gases used were 99.99 moles per cent pure. 3, Results The dependence of the amount of gas dissolved in molten ZnC1, on pressure is given in figure 3. As can be seen, for the three gases studied, three different linear dependences were obtained. From the sIope of the lines the Henry’s law constants were calculated as &,
= X/P,
(0
where x is the mole fraction of the gas in the melt andp is its pressure above the melt. The Henry’s law constants calculated from the slope of the lines in figure 3 by the least-squares method are reported in table 2. The temperature dependence of Kn of
p/lo4 Pa FIGURE 3. Results of measurements of mole fraction x solubilities of COa, Nz, and Ar in molten ZnC& at 720 K as dependent on the pressure p of gas. The points correspond to experimental results obtained in three independent experiments for each gas. Lines represent the least-squares equations. A, COa; 0, Ar; w, Ns.
SOLUBILITY TABLE
OF COz, Nz, AND Ar IN ZnCL(1)
2. Henry’s law constants KS of COa, Ar, and NQ dissolved in molten ZnCla in the pressure range lo4 to lo5 Pa
Gas
T/K
lOlo KS/Pa-l
CO2
778 753 723 721
7.46 7.40 7.27 7.04
co2 co2 co2
659
f f f f
Gas
0.50 0.30 0.50 0.21
co2 co2 Ar N
T/K
lOlo KdPa-l
719 709 720 720
6.41 6.52 4.77 3.33
f & f &
0.20 0.06 0.03 0.10
COz in ZnCl, can be described by the equation: log,,(lO1OK,/Pa-l) = -(457 + 193) K/T-(8.504 f 0.263). (2) The standard enthalpy and entropy of solution of the gas at 720 K are, respectively: AH” = -Ra(ln K,)ja(l/T) = (8.74 + 3.68) kJ mol-‘; (3) AS” = AH”/T+R ln(c,/c,) = -(9.58 -t 5.02) J K-’ mol-‘; (4) where c, and cg are concentrations of the gas in the liquid and gaseous phases, respectively. In these calculations, a reference concentration of 1 mol dmp3 was used.(3) 4. Discnssioll The logarithm of the solubility of a gas, dissolved without any chemical interaction with the liquid solvent, usually decreases linearly with the increasing surface tension of the solvents.“) An interpretation of this correlation was given by Uhlig.‘g) Blander et aZ.(“) applied Uhlig’s model to the solubility of an inert gas in a molten salt, neglecting the interaction between the particles of the gas and liquid. According to Blander’s model the gas produces its own holes in the liquid, exerting the work against the surface tension of the liquid. The formula given by Blander is In L = NAa,i,,,/RT, (5) where L is the Ostwald coefficient, A the surface area of the hole, and ~micro the micro surface tension. The Oswald coefficient is defined as: L = K,R T/ V,, (6) where KH is the Henry’s law constant and V, the molar volume of the solvent. The simple equation (5) is in good agreement with experiments, as proved by several authors.(31 5*l”-13) Assuming that the radii of the holes are the same as the crystallographic radii of the gases dissolved and that the micro surface tension is the same as the bulk surface tension, one obtains solubilities which are of about the same size as the experimental values. This conclusion is also shown here for Nz, Ar, and CO2 in ZnCl,. In table 3 the values of Henry’s law constants measured for the three systems at 720 K are compared with the respective values calculated from equation (5). The surface area of the holes was calculated for argon from the van der Waals atomic radius of the gas, and for nitrogen and carbon dioxide in two ways: (a) for spherical holes assuming full rotation of the gas molecule; and (b) for minimal surface area 45
660
A. BORODZINSKI,
A. SOKOLOWSKI,
AND L. SUSKI
of the hole containing the gas molecule, excluding any rotation of this molecule. In the latter case we assume the hole to be a cylinder to which two hemispheres are attached. The length of the cylinder was assumed to be equal to the N-N and O-C-O bond lengths and the hemispherical radii were calculated from van der Waals’ radii of N or 0 atoms.(4) The mean surface area of the real holes are probably higher due to some translation and oscillation of the molecule in the hole. TABLE 3. Comparison of experimental Henry’s law constants Ka for Nat Ar, and CO1in molten Z&l2 at 720K with respectivevaluescalculatedfrom Blander’sequation
lOlo Kn/Pa-l (experimental) lOloK&-l (calculatedfor sphericalholes) lOloKn/Paml(calculatedfor cylindricalholes) {KH(expt)/K&alc.)} (sphericalholes) (K&xpt)/K&alc.)} cylindricalholes)
N!d
Ar
3.33* 0.10 5.78 11.64 0.58 0.29
4.17& 0.03 7.71 0.54 -
co, 6.90f 0.27 1.12 8.25 6.16 0.84
As can be seen from table 3, in the case of CO2 better agreement between experimental and calculated values of the Henry’s constant was obtained for the spherocylindrical holes. The ratio of experimental to calculated values is (0.84/0.80) and is practically constant in the temperature range 710 to 780 K. On the other hand the standard entropy of solution of COz in ZnCl,, -(9.58 + 5.02) J K-’ mol-‘, when compared with corresponding values for CO2 in NaNO,, - (62.5 + 0.9) J K-’ mol-’ ; Ar in NaNO,, -(23.4 f 5.4) J K-’ mol-‘; and N, in NaNO,, -(22.2 ) 1.2) J K-’ mol-‘, seems to prove the existence of rotation of CO, molecules dissolved in molten ZnCl,. This could be possible only in the spherical holes. Taking into account the entropy changes the agreement between experimental and calculated “cylindrical” solubility constants in table 3 may be explained as being due to some cancellation of inaccuracies made by neglecting the interaction between the gas and the solvent on one side, and by the assumption of the micro surface tension being equal to the bulk value on the other. REFERENCES 1. Flengas,S. N.; Block-Bolten,A. Solubilitiesof reactivegasesin moltensalts.In Advances in Molten Salt Chemistry, Vol. 2, Braunstein.J.; Mamantov,G.; Smith,G. P. editors.Plenum Press:New York. 1973. 2. Battino, R.; clever, H. L. Chem. Rev. 1966,66,315. 3. Bratland,D.; Grjotheim,K.; Krohn, C.; Motzfeldt, C. Acta Chem. Stand. l!X%,20, 1811. 4. Field, P.; Green,W. J. Phys. Chem. 1971, 75, 821. 5. Cleaver,B.; Mather, D. E. Trans. Faraday Sot. 1970, 66, 2469. 6. Copeland,J. L.; Zybko, W. C. J. Phys. Chem. X%5,69, 3631. 7. Saylor,J. H.; Battino, R. J. J. Phys. Chem. 19S8, 62, 1334. 8. Janz,G. J. ; Dampier,F. E.; Lakshminarayan, G. R. ; Lorenz, P. K.; Ton&ins, R. P. T. Nat. Stand. Ref. Data Ser.N.B.S. 15.1968,October.Janz,G. J. ; Lakshminarayan, G. R. ; Ton&ins, R. P. T. ; Wang, J. Nat. Stand. Ref: Data Ser. N.B.S. 28, 1969, August. 9. Uhlig, H. H. J. Phys. Chem. 1937,41, 1215. 10. Blander,M.; Grimes,W. R.; Smith,N. V.; Watson,G. M. J. Phys Chem. 1958,62, 862. 11. Grimes,W. R.; Smith,N. V.; Watson,G. M. J. Phys. Chem. 1958,62, 862. 12. Watson,M.; Evans,R. B.; Grimes,W. R.; Smith,N. V. J. Chem. Eng. Data. 1962, 7, 285. 13. Pan&a, F.; Zambonin,P. G. J. Chem. Sot., Faraday 7kans. 1972, I 65, 2083.