MIXINGIN
THE
I,IQUID CADMIUM-CADMIUM CHLORIDE SYSTEM
44 1
Radiometric Determination of the Volume Change on Mixing in the Liquid Cadmium-Cadmium Chloride System by J. Moicihski Institute of Nuclear Technique ACH, Cracow, Poland
and L. Suski Institute of Physical Chemistry of the Polish Academy o j Science, Cracow, Poland Accepted and Transmitted by The Faraday Society
(March 10, 1967)
A relative method for the determination of molar volume in the Cd-CdClz solution with respect to molar volume of pure CdC1, by measurement of y-ray absorption is described. The isotope zoaHgwas used as a radiation source. Absorption coefficients of pure components of the solution and dependence of absorption of y rays on the composition of the solution have been determined for this source and a given geometry of the experimental setup. The molar volumes of the Cd-CdClz solutions determined by this method for three different temperatures are in good agreement with the data available in the literature obtained by classical methods. Accuracy of the method and sources of errors are discussed. The volume effect of mixing, positive for these solutions, is derived.
Introduction One of the interesting physicochemical properties of the metal-molten salt solutions is the molar volume of these systems. Determination of its value makes it possible to calculate the volume effect of mixing which is of great interest in studies on thermodynamic properties of these solutions. Knowledge of molar volume is also necessary in interpretation of measurements of electrical conductivity and viscosity of these systems. Owing, however, to the experimental difficulties, the data concerning the molar volume of the metal-molten salt systems are far from being complete. Measurements of this kind were carried out by Keneshea and Cubicciotti for the systems Bi-BiC13,1 Bi-BiBr3,z and Bi-Bi13,3 supplementing earlier results of Atenq4 Measurements of molar volume were also done for a Cd-CdClz system which has been a subject of the most extensive studies yet. The density of the Cd-CdClz solution a t 873°K: was measured as early as 1910 by Aten.6 These measurements have been repeated recently by Tomlinson and oo-workers6J a t temperatures of 873 and 973°K and a t the same temperatures by Vetyukhov, et aL8 Other measurements of molar volume in the metalmolten salt systems comprise studies on the Ce-CeCla system carried out by Mellors and Senderoff.0 It appears, however, that these results were affected by the corrosion of the measurement vessels.1° The measurements of density a t high temperatures
have been carried out by four classical m e t h o d ~ : l ~ - ’ ~ hydrostatic, pycnometric, dilatometric, and the pressure method. The experiments on the metal-salt systems were performed with the h y d r o s t a t i ~ ~ ~ ~ ~ ~ and the p y c n o m e t r i ~ ’ - ~methods. *~,~ The most accurate results are obtained with the pycnometric method, which, however, in the medium of molten salt, encounters serious experimental difficulties. The hydrostatic method contains an error caused by condensation of evaporating salt on a wire which holds a sinker.’lJZ This method seems particularly (1) F. J. Keneshea and D. Cubicciotti, J. Phys. Chem., 62, 843 (1958). (2) F.J. Keneshea and D. Cubicciotti, ibid., 63, 1112 (1959). (3) F. J. Keneshea and D. Cubicciotti, ibid., 63, 1472 (1959). (4) A. H.W. Aten, Z . Physik. Chem. (Frankfurt), 66, 641 (1909). (5) A. H.W. Aten, ibid., 73, 578 (1910). (6) C. A. Angel1 and J. W. Tomlinson, Discussions Faraday SOC.,32, 237 (1962). (7) G. A. Crawford and J. W. Tomlinson, Trans. Faraday Soc., 62, 3046 (1966). (8) M. M. Vetyukhow, A. Asylbayev, and Yu. W. Plotnikow, Tr. Leningr. Politekhn. Inst., 223, 35 (1963). (9) G.W. Mellors and 8. Senderoff,J. Phys. Chem., 64, 294 (1960). (10) M. Bredig in “Molten Salt Chemistry,” M. Blander, Ed., Interscience Publishers, Inc., New York, N. Y., 1964,p 367. (11) J. L. White in “Physico-Chemical .Measurements at High Temperatures,’’ J. O’M. Bockris, J. L. White, and J. D. Maokenzie, Ed., Butterworth and Co. Ltd., London, 1959,p 193. (12) W. D. Kingery, “Property Measurements at High Temperatures,” John Wiley and Sons, Inc., New York, N. Y., 1959. (13) A. A. Vertman and E. S. Philippov, Issled. Metal. vzhidkmni Tverd. Sostoyaniyakh Akad. hrauk SSSR, 100 (1964).
Volume 79,Number d
February 1968
442
J. MOSCIX~SKI AND L. SUSKI
inappropriate for measurements with the metal-molten salt systems, which, owing to their susceptibility to oxidation, require a closed apparatus. It appears that measurements of the density of these systems should be carried out in a closed system applying high vacuum or pure inert atmosphere. The possibility of measurements in a closed system is realized by radiometric m e t h ~ d s . ' ~ JThese ~ methods make it possible to determine a relative density as a function of the variable parameters of state with respect to the density in arbitrary initial conditions. They are, in fact, methods for measurements of changes of molar volume and in our opinion may find wide applications in determinations of the volume effect of mixing in various kinds of solutions. In continuation of our investigations on application of the radiometric methods for studies of physicochemical properties of the metal-molten salt systems,16 the present work is an attempt to determine the volume effect of mixing in the Cd-CdClz system by measurements of the y-ray absorption. Principles of Method. In the preceding paperl6 a well-known equation describing absorption of radiation by a solution of metal in its molten salt has been given
Ne N,
In - = XpBpsT- XpnpcT where N , and N , are the counting rates for pure salt and a metal solution, p , and p , are the mass absorption coefficients, pcT and paT are densities of the solution of metal in its salt (c) and pure salt (s), respectively, and X is the thickness of the absorption layer. It can be readily shown that the ratio N , / N , determined in a given absorption cell does not depend on the absorption in the walls of cell. From the additivity law of mass absorption coefficients, the following relation between the mass absorption coefficient of the solution and the mass absorption coefficients of its components can be written pc
= Wmpm
+ (1 - W m ) L
(2)
where p m denotes the mass absorption coefficient for pure metal and W , is the weight fraction of the metal in the solution. From eq 1 and 2 the density of metal solution in pure salt can be expressed as
From eq 3 a density of solution a t a given temperature as dependent on weight fraction of metal can be determined by measuring N , and N , if psT and constant values X , p,, and pm are known. The molar volume of metal solution in its salt is then The Journal of Physical Chemistry
VnT = XmMm
+ xsil.le -
P oT
kmMm
+ xaMs) [WmPm + (1 - Wm)~alX (4) Nn XpSpaT- In N,
where VoTis the molar volume of solution a t temperature T , X m and x, are the molar fractions of metal and salt, respectively, in the solution, and M m and M , are the molecular weights of the metal and its salt, respectively. As known, the mass absorption coefficients depend on radiation energy, showing a constant value for only a monochromatic radiation. For a monochromatic radiation the mass absorption coefficients are practically independent of the thickness of the absorption layer in a certain range of changes of this thickness. Values of the mass absorption coefficients depend also to a certain extent on the geometry of the experimental setup and hence have to be determined experimentally for given experimental conditions.
Experimental Section The apparatus employed in the present study was the same as that described in the preceding paper.I6 The methods of preparation of the materials and experimental procedure were also the same. The essential difference was application of a different source of radiation-isotope 20aHg-of the activity of about 30 mcuries, which emits p radiation of maximal energy of 0.214 mev, y rays of energy of 0.279 mev, and also bremsstrahlung rays of the continuous spectrum and maximal energy equal to that of 0 particles. Owing to such a characteristic of the y-ray spectrum, it is possible by discrimination in the measurement setup to eliminate impulses of the energy lower than 0.279 mev and hence to obtain a monochromatic radiation. With the use of 203Hgas a radiation source, the thickness of the absorption cells had to be increased to 1.4 cm. The number of impulses counted in the 5-min measurements was about 2 X lo6,which corresponded to a statistical standard deviation of about 0.22%. I n all the measurements, an allowance for decay of the source in time was made. Determination of the Mass Absorption Coefficients The Mass Absorption Coeficient of Cadmium. The measurements of the absorption coefficient of metallic cadmium were performed at room temperature in the apparatus described previously.16 The counting rate of the radiation traversing various numbers of cadmium plates of thickness of about 0.045 cm was measured. The thickness of the plates was measured separately for each plate with the accuracy of 0.0001 cm. Deter(14) I. G. Dillon, P. A. Nelson, and B.
s. Swanson, Rev. Sci. Instr.
37, 614 (1966). (16) J. Mos'cirkki and L. Suski, J . Phys. Chem., 70, 1727 (1966).
MIXINGIN
THE LIQUID
CADMIUM-CADMIUM CHLORIDE SYSTEM
mination of the radiation intensity for 13 sets of different numbers of plates was equivalent to the application of 13 absorption layers of different thicknesses. For each thickness of the absorption layer, the counting rate of the radiation passing through the layer of absorbent in 5 min was measured fourfold and the mean counting rate was calculated. The radiation intensity in the absence of the absorbent, i e . , at X = 0, was also measured, :Figure 1 shows relative mean values of the radiation counting rate in a logarithmic scale as dependent on the thickness of the absorption layer of cadmium (lime A). The slope of the straight line A in Figure 1 is equal to a linear absorption coefficient of cadmium for 203Hg radiation in a given geometry of the experimental setup and a t a given temperature. The value of this coefficient calculated with the leastsquares method was 1.545 & 0.008 cm-’. For calculation of the mass absorption coefficient, which is independent of temperature, the obtained value is divided by a cadmium density at the temperature a t which this coefficient was determined. The density of cadmium was taken from the literature datal6 as equal to 8.64 g/ cc. The quoted monograph16does not give the error in determination of this value. Assuming even a very large standard deviation in the value of density given in this monograph, of f0.04 g/cc, the value of the mass absorption coefficient of cadmium, ,%d, is 0.1788 0.0012 cm2/g. The M a s s .Absorption Coeficient of Cadmium Chloride. The absorption coefficient of cadmium chloride was measured in the apparatus described a t the temperature of 903°K. Counting rate of the radiation traversing three cells of different thickness X = 0.317 f 0.003, 0.966 f 0.006, and 1.408 f 0.014 cm was measured. The thickness of the cells was measured by an optical method with the use of a microscope. Counting rate of the radiation traversing a layer of liquid cadmium chloride was measured in two independent experiments with X = 0.317 cm, in one experiment with X = 0.966 cm, and in three experiments with X = 1.408 cm. In each experiment, the number of pulses passing through the absorption layer in 5 min was measured several times and the mean values were calculated. After each experiment a number of pulses in the absence of the absorbent, i.e., a t X = 0, were also measured several times. Moreover absorption of radiation in the walls of the absorption cells was measured, which made possible a standardization of the results obtained, making them independent of the difference in thickness of the walls of cells. In Figure 1 (line B), the relative, mean values of the radiation counting rates are plotted in a logarithmic scale as a function of the thickness of the absorption layer. The value of the linear absorption coefficient of cadmium chloride a t 903°K calculated with the least-squares method is 0.500 f 0.007 cm-’. The value of density of CdClz a t 903”K, needed for
*
443
O --r
-40
h
t
t
1 1 0
\
I
04
c
06’
62
X cm Figure 1. Determination of absorption coefficients of cadmium and cadmium chloride. Logarithm of the relative mean values of the y-radiation counting rate N ( X ) / N ( X = 0) as a function of the thickness of the absorption layer X for cadmium (line A) and liquid cadmium chloride (line B).
calculation of the mass absorption coefficient, was taken from the literature data. Table presents temperature dependence of density of CdClz as given by various authors. The equations shown in this table
Table I: Dependence of Density of Liquid Cadmium Chloride (g/cc) on Temperature Expressed by the Equations pcdcizT = b( T 873), Calculated from the Experimental Results of Various Authors
a
-
-
a
3 * 355 3.336 3.320 3.366 3.345 3.359
Ref
b
7.45 x 7.60 x 6.85 x 8.40 x 8.60 x
8.00 x
10-4 10-4 10-4 10-4 10-4 10-4
6,7
8 17
18 19 20
(16) J. R. De Voe, “The Radiochemistry of Cadmium,” National Academy of Sciences, National Research Council, Nuclear Science Series, NAS-NS-3001, Jan 1960. (17) R. Loren?;,H. Frei, and A. Jabs, 2.Physik. Chem. (Frankfurt), 61, 468 (1908).
(18) N. K. Boardman, F. H. Dorman, and E. Heymann, J . Phys. Colloid. Chem., 53, 375 (1949). (19) M. F. Lantratov and T. N. Shevlyakova, Fiz. Khim. Rasplavlen. Solei i Shlakov, T r . &go Vses. Soveshch., 13 (1965). (20) H. Bloom, I. W. Knaggs, J. J. Molloy, and D. Welch, Trans. Faraday SOC.,49, 1458 (1953).
Volume 72, Number 2 February 1968
J. M O ~ C I ~ AND ~ S KL.I SUSKI
444
io73 'K
P
f f
P
-i6
-/6 -14 0.04
0
a !2
0.08
0.5.!
020
xu
,
-4
.
-6
.
-8
'
-io
'
-i2
.
-i4
. 0
*
'
"
I
'
0.04
a f2
0.06
4 020.
0./6
xu
Figure 2. Logarithm of the mean relative values of the counting rate of radiation traversing the Cd-CdClz solution as dependent on molar fraction of cadmium at 903°K for three independent experiments.
O K -2 .
t
0
"
"
Figure 4. Logarithm of the mean relative values of the counting rate of radiation traversing the Cd-CdClz solution as dependent on molar fraction of cadmium at 1073°K for four independent experiments.
''I 0
Aten'
873 'K
0.04
0.08 XGi
0.u
0.!6
02a
Figure 3. Logarithm of the mean relative values of the counting rate of radiation traversing the Cd-CdClz solution as dependent on molar fraction of cadmium at 1003°K for three independent experiments.
are quoted after the original papers or have been calculated by us from the data found in the literature. The mean density of cadmium chloride at 903"K, calculated taking into account all the data of Table I, is 3.323 f 0.007 g/cc. The mass absorption coefficient of cadmium chloride, pCdCll, calculated employing the above given value for the CdCl2 density, is 0.1506 f 0.0022 cm2/g.
Results and Discussion Figures 2-4 show dependence of the logarithm of the relative radiation counting rate traversing the Cd-CdClz solution on the molar fraction of cadmium in the solution XOd a t the temperatures of 903, 1003, and 1073"K, respectively. The statistical deviation The Journal of physical Chemistry
0.06
0.08
0112
Of6
a20
xu Figure 5. Dependence of the molar volume of the Cd-CdClz solution on the molar fraction of cadmium for three different temperatures. The crossed areas denote the error in determination of this dependence. The dashed lines correspond to the additive volumes of the Cd-CdClz solutions. Results of the other authors are given by points.
of the radiation counting rate and errors caused by the detecting device are taken into account. As seen from Figures 2-4, these errors do not exceed the scattering of the experimental points resulting from the total error of the method. The lines given in the figures were calculated with the least-squares
MIXINGIN
THE
method as corresponding to the empirical equation of the type (5)
Calculations of the empirical functions (eq 5) were done with the assumption that these lines pass through the origin of the coordinate system; Le., constant A in eq 5 is equal to zero. Such an assumption is substantiated by the fact that the result did not contain an error caused by deviation in composition of the solution which could affect values of the other experimental points. For calculation of the constants in eq 5, only these experimental points were taken, which correspond to the molar fractions of cadmium below the miscibility limit in the Cd-CdC12 system. The latter was determined for the same temperatures in our previous work.15 In Table I1 the constants of eq 5 for three temperatures of the measurement are given. The calculations have shown that using a polynomial (eq 5) of an order higher than 2 does not increase the accuracy of the approximation of the experimental results. Table I1 : Constants of the Empirical Equations (Eq 5) Calculated from the Results Plotted in Figures 2-4 for Three Different, Temperatures T,OK
B
C
903 1003 I073
0.0703 dz 0.0116 0.0524f0.0051 0.0354 f 0.0046
0.161 & 0.088 0.135f0.032 0.211dz0.028
The empirical equations describing the experimental results in particular temperatures can be substituted into eq 4
[XCdMCd
445
LIQUIDCADMIUM-CADMIUM CHLORIDE SYSTEM
+ (1 - xCd)MCdClil x
WCd (weight fraction of cadmium in the solution) is related to XCd (molar fraction of cadmium) by the expression
For calculations of VcT from eq 6, the values of density of pure CdCl2 a t three temperatures were used. These values were derived from the data of Table I in the same manner as density of CdClz a t 903°K. The values of PCdClT calculated are 3.245 f 0.005 g/cc a t 1003°K and 3.190 f 0.005 g/cc at 1073°K. I n the present work special attention has been paid to the method of determination of molar volume of CdCl2 solution when molar volume of pure CdCll
at a given temperature is known. It seems appropriate, therefore, to discuss the errors of this kind of measurements and to indicate the parameters, the errors of which determine the accuracy of the method. An error in determination of the molar volume VcT derived from eq 6 for a given XCd is expressed by
where a(VcT)is the standard deviation of the calculated value of V,* and u ( P J is the standard deviation of the measured parameters P,. Table I11 gives values of the components of the sum (eq 8) at three temperatures and for three arbitrarily taken compositions of the solution. As seen from Table 111,the error in determination of the molar volume from eq 6 is caused practically only by errors in determination of three parameters PCdCl?, B, and C. Moreover, the contribution of the error made in measurements of density of pure CdClz is particularly large a t low values of XCd whereas at higher concentrations the total error of the method is determined by constants of empirical eq 5. It should be pointed out that the discussion of the error does not comprise an error in the assumed values of the variable XCd. The accuracy of weighing of cadmium and cadmium chloride is sufficient to neglect the error made in it. However the radiation traverses a solution, the concentration of which may differ from the equilibrium value owing t o incomplete mixing of the two solution components. The error resulting from this is shown by scattering of the results and is contained in the error of constants B and C. As can be seen from Figures 2-4, this source of the experimental errors is particularly distinct at the lowest temperature used, Le., a t 903°K. The discussion of errors has shown that measurements of the parameters PCd, pCdC1z) and X were made with a sufficient accuracy. Dependences of the molar volume of the Cd-CdClz solution on the molar fraction of metal in the solution a t three different temperatures are presented in Figure 5 . The crossed area in this figure denotes the region of the standard deviation calculated from eq 8. The results of the other authors5-* obtained at 873°K with the classical methods are also given in this figure. The different measurement temperature makes difficult a full comparison; one can, however, see that the dependence of VOTon the molar fraction XCd determined in this work is in general similar to that observed by the other authors. The data obtained by classical methods by different authors show, however, considerable differences. Moreover, papers5-' report a linear dependence of VCTon XCd) whereas according to our results this dependence deviates from linearity, particularly a t 1073°K. Volume 73, Number
W February 1968
J. MOSCIASKI AND L. SUSKI
446
Table 111: Values of [(dV,T/dPi)~(Pi)]a X 104 of E q 8 Calculated from the Experimental Parameters of Eq 6 for Three Different Values of XCd and Three Temperatures Parameter Pi CCd
T,
-XCd-
0.04 0.10 0.16 0.04 0.10
O K
903 1003 1073
1 1 1
7 7 8
1
X
ECdClz Y X C d -
17 18 19
2 3 5
0.16
0.04
29 40 44
0
13 17 20
I
I
1
0 0
I
X -Cd-
X -Cd-
0.100.16 0.04
2 1 1
6 4 4
C
B
PCdClaT
-XCd-
127 72 78
Y X C d -
0.10
0.16
0.04
0.10
0.16
0.04
0.10
0.16
114 66 71
101 59 64
66 14 12
370 81 71
843 186 164:
6 1 1
213 33 25
1239 193 150
1
67
5.5
* vc‘
53
w 8-50
950
rzn
io50
*K
Figure 6. The temperature dependence of the molar volume of the Cd-CdClz solutions of the cadmium content XCd = 0.04 and 0.10 according to the results obtained in this work and by other authors.
XGi
Figure 7. The volume effect of mixing in the Cd-CdClz solutions as dependent on XCd at three different temperatures, calculated from the results of the present work. The crossed areas give the error in determination of this value.
Figure 6 shows a dependence of VaTon temperature for two values of the molar fraction XCd, observed in this work and reported in the previous The temperature dependences of the molar volume presented in Figure 6 show some difference between the results of this work and those obtained by other authors. It should, however, be pointed out that the temperature range in this work was considerably larger than in the other studies. The molar volumes determined a t three temperatures obey a linear temperature dependence. The results presented in Figures 5 and 6 show that a radiometric method in application to the determination of the relationship between the molar volume of the Cd-CdClz solution and the composition of this solution gives results essentially in agreement with the results obtained with the other methods and has a sufficient accuracy. Measurements of the molar volume of solution are employed in the first place in determination of the volume effect of mixing. The method presented in the present work aimed also at that. The volume effect of mixing in the Cd-CdClz solution is defined as AvoT = VcT The Journal of Physical Chemistry
- VadT
(9)
Table IV : Dependence of Density of Liquid Cadmium (g/cc) on Temperature, Expressed by the Equations pCdT = a b( T - 873), Calculated from the Experimental Results of Various Authors
-
a
b
Ref
7.673 7.727 7.690 7.719 7.702
12.08 X 10.57 X 10-4 12.28 X 10.69 X 11.16 X
a
b C
d e
‘F. Sauerwald, 2. Anorg. Allgem. Chem., 163, 319 (1926). A. Jouniaux, Bull. SOC.Chim. Belges, 47, 524 (1930). H. F. Greenway, J . Znst. Metats, 74, 133 (1948). F. G. McCutcheon and J. R. Musgrave in “Rare Metals Handbook,” C. A. Hampel, Ed., Reinhold Publishing Corp., New York, N. Y., 1954, p 87. e W. C. Tshirkhin, “Teplofisicheskiye svoistva materialov,” Moscow, 1959.
where AVOTis a volume effect of mixing for the CdCdClz solution of a given concentration a t tamperature T and the molar volume for the additive volumes of the solution components Vad‘ is
MIXINGI N THE LIQUIDCADIUM-CADIUM CHLORIDE SYSTEM VedT
'= XCdVCdT
+ (1 -
XCd)VCdClaT
(10)
Such defined volume effect of mixing in this system corresponds to a solution of metallic cadmium in its molten salt and does not take into account the real species existing in the solution.21 For calculation of the volume effect of mixing from the experimental results of the present work, the temperature dependence of the density of liquid cadmium has to be taken into account. These dependences derived from the data available in the literature are shown in Table IV. For calculations, the mean values of the cadmium density calculated from the data of Table IV were used. They are, respectively, pcdeoa = 7.668 0.011, pcdloo3= 7.555 *0.014, and pcd10'3= 7.475 i 0.016 g/cc. It should be mentioned that standard deviations of (densities give an additional error in the volume effect of mixing which is, however, negligible
447
in comparison with the error in determination of the value of VoT. Figure 7 shows volume effects of mixing in the CdCdClz solution for three temperatures. The results shown in the present work show once again a positive sign of the volume effect of mixing found by other authors.6-8 The Cd-CdClz solution thus exhibits a behavior different from that of solutions of bismuth in its liquid halides.lw4 This fact has been recently discussed by Crawford and Tomlinson
.'
Acknowledgments. The authors want to express their thanks to Dr. A. Briickmann for the valuable discussion. (21) M.A. Bredig, H. A. Levy, F. J. Keneshea, and D. Cubicciotti, J. Phys. Chem., 64, 191 (1960).
Volume 78, Number 8 February 1968
