Krypton Diffusion in Granular Charcoal F. F. Castellani, G. G. Curzio," and A. F. Gentili lstituto di lmpianti Nucleari, 'Universita di Pisa, Pisa, Italy
The diffusion coefficient of krypton in an activated charcoal is determined by measuring the amount of krypton that leaves a cell as a result of diffusion and by analyzing the elution rate. The obtained values of the molecular diffusion coefficient in the porous medium are well fitted by the linear function D = Do KT. The values of the coefficients are in good agreement with the values we previously found by an indirect method.
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A good knowledge of the effective diffusion coefficient of noble gases in porous media can be useful for determining the characteristics of treatment devices for fission produced noble gases in nuclear plants (1). We have studied the diffusion of krypton in granular charcoal with the above aim in mind and, besides this, with a view towards confirming the dependence of the effective diffusion coefficient on temperahre, which we previously had found by an indirect method ( 2 ) . The experimental method here adopted is the classical one, employed at first, for example, for measuring thermal conductivity or ion diffusion in liquids ( 3 , 4 ) . This method involves the measurement of the amount of krypton that leaves a cell as a result of simple diffusion: the diffusion cell is a cylinder (i.d. 54 mm, height 120 mm), the lower part of which (95 mm high) is filled with charcoal (Barnebey-Cheney Type 592, coconut shell activated charcoal 8-14 mesh); the cell is filled with dry air a t atmospheric pressure, with a weak amount of Kr traced with 85Kr. After a suitable time (necessary for the adsorption and homogeneous diffusion of krypton in the charcoal), the air in the top part of the cell is swept off by a continuous stream of pure dry air. The s5Kr concentrations in the outlet stream are measured and recorded by nuclear detectors. Krypton distribution, as a function of time, in the charcoal and krypton flow from its top surface can be calculated by Fick's law ( 5 ) ;the krypton concentration in the outlet stream can be expressed as
8i io3 2 2 0
0
~
:: -
../.
where t is the time, T = 412/.rr2X I/D', 1 is the height of charcoal in the cell, and D' is the effective diffusion coefficient of krypton. Therefore, after a period of time approximately equal to T , krypton concentration in the outlet stream decreases according to a simple exponential law, as is also shown by the experimental trend (see Figure 1). Figure 2 shows the experimental values of the half time T ~ = D T In 2 , from which it is possible to calculate the effective diffusion coefficient D' as a function of temperature. The effective diffusion coefficient can be expressed as D' =Dy/p~ ( 6 ) ,where D is the molecular diffusion coefficient in the porous medium, y is the tortuosity factor, p is the charcoal bulk density, and K is the adsorption coefficient of krypton in charcoal. This coefficient is an exponential function of inverse temperature ( 7 ) , K = KO exp (@/e), where 8 is the absolute temperature and KO and cy are constants: the results of fitting our previous experimental data obtained with the same charcoal ( 8 ) give KO = 0.0353 g/cm3 and cy = 2095 K-l. For simplicity's sake, let us assume a linear dependence of D on temperature, D = DO + K T . The constants DO and K , as well as y,can be evaluated by the least squares method; the values obtained are DO = 0.085 cm2/sec, K = 0.00055 cm2/sec "C, and 7 = 0.43. In the temperature range here explored, these evaluations very closely match with our earlier ones ( D O = 0.09 cm2/sec, K = 0.00016 cm2/sec "C, and 7 = 0.45). The agreement is evident on the two curves drawn in Figure 2: they represent the ~ 1 1 2values calculated using first one and then the other set of values for DO,K , and y; both of which f i t the experimental data in a satisfactory way.
.... I..,
-
..: '.. .
' ....... 0
5 10 TIME ( h
,
15
Figure 1. Kr concentration at the outlet of the diffusion cell vs. time ( T = 3 8 "C)
Figure 2. Experimental values of T , , ~vs. temperature. Continuous and broken lines represent, respectively, the theoretical values of T I U calculated using 00,K, and y values here obtained and the Do, K, and y values obtained in (2)
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
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LITERATURE CITED (1) (2) (3) (4)
D. W. Underhill, Nucl. Appl., 6, 544 (1969). G. G. Curzio and A. F. Gentili, Anal. Chem., 44, 1544 (1972). L. R. lngersoll and 0. A. Koepp, fhys. Rev., 24, 92 (1924). J. S. Anderson and K. Saddington. J. Chem. SOC., 1949, 5381-6. (5) H. S. Carslaw and J. C. Jaeger, "Conduction of Heat in Solids", 2nd ed., Oxford University Press, 1959. (6) W. E. Bolch, R. E. Seileck, and W. J. Kaufman, "Gas Dispersion in Porous Media", SERL Rep. 67-10 (1967).
(7) S. Kitani. S. Uno, J. Takada, H. Takada, and T. Segawa, Recovery of Krypton by Adsorption Process, JA€R/, 1167 (1968). ( 8 ) G. G. Curzio and A. F. Gentili, Liberation de gaz nobles par les centres nucleaires: quelques remarques sur le functionnement des filtres de charbon de bois, VIe Congres international de la SOC.Francaise de Radioprotection, VI, SFRP/21, 233 (1972).
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RECEIVEDfor review July 30, 1975; Accepted August 29, 1975. This work was supported by CNR Contract No. 73.01279.07.
Determination of Diffusion Coefficients by Diffusion from Tubes N. C. Fawcett' and Roy D. Caton, Jr." Department of Chemistry, University of New Mexico, Albuquerque, N.M. 87 13 1
A new approach for the determination of diffusion coefficients is presented. Since the method employs open tubes containing 0.6-1.4 ml of diffusant solution, ultrasensitive analytical methods need not be used to determine solute concentrations during experiments as in the capillary method. The apparatus consists of stationary glass tubes, filled with a solution of diffusant, in a bath of stirred pure solvent. Results for Pb(ll) in 0.1 M KCV0.005 M HCI and anthracene in acetonitrile are in excellent agreement with those obtained using the capillary method and electrochemical methods. New values for p-nitrobenzene and 4,4'-dinitrozobenzene in acetonitrile are given.
The diffusion coefficient ( D ) for an electroactive species in solution represents an important datum in electroanalytical chemistry. D values may be determined by electrochemical means in many cases. Often, however, the complexity of the system precludes easy evaluation. Even when the diffusion coefficient can be obtained from electrolysis data, confirmstion by a determination independent of electrochemistry is highly desirable. This problem has been addressed by Adams and coworkers ( I , 2) who have had considerable success measuring diffusion rates using the capillary method of Anderson and Saddington ( 3 ) . This appears to be an especially suitable method for determining D values to be applied in electroanalytical chemistry because Bearman ( 4 ) has shown that the identity of the so-called capillary diffusion coefficient corresponds closely to that of the polarographic diffusion coefficient. The capillary method possesses a rather unique set of attributes compared with alternative methods. For example, diffusion rates of both ionic and molecular species may be measured in a variety of solvents, only simple apparatus is required, and the method is absolute in the sense that calibration with a substance of known D is not required. Despite these advantages, application has been somewhat limited by the small total amount of material that can be diffused from a capillary, which is of necessarily small internal volume. This is an especially important restriction to the electroanalytical chemist who desires to measure diffusion rates in very dilute solutions. Because of the small amount of material that can be diffused, past application has been limited to those substances for which very sensitive analysis is available, e.g., radioassay or fluorimetry. Present address, D e p a r t m e n t of Chemistry, Southwest Texas State University, San Marcos, Texas 78666.
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ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
Another reason for limited use of the capillary procedure is perhaps the possibility of high results arising from partial convective loss of diffusant. Wang et al. (51, and Mills (6) in particular, have thoroughly criticized the capillary method, with special attention being given to convective loss. A differential error analysis of the method has been published (7). In this paper, a new method for determining diffusion coefficients is proposed and tested by the determination of several diffusion coefficients in both aqueous and nonaqueous solutions. The new method is closely related to the capillary procedure, but tubes, several millimeters in diameter, are substituted for capillaries. Although the use of tubes results in much greater convective loss, this loss is accounted for by the method used to calculate D . The greater internal volume of a tube permits more substance to be diffused in the course of an experiment. Since the amount of substance diffused is greater, it is possible to use standard methods of analysis such as titration or spectrophotometry to follow changes in diffusant concentration. This, in turn, should make the new method more widely applicable than the classical capillary procedure, while at the same time retaining the useful attributes of the older method.
OBSERVATION OF BOUNDARY FORMATION IN TUBES A glass tube, several centimeters long and a few millimeters in diameter, may be sealed a t one end, filled with dye solution, and immersed vertically in a large container of pure solvent. If the solvent is stirred in a uniform, nonturbulent manner and if the solution in the tube is not less dense than the solvent, the following phenomenon is observed. Convection caused within the mouth of the tube by the stirring motion of the solvent causes dye solution to be swept from the tube. Upon continued observation, the loss of dye subsides and a sharp boundary forms between a column of stationary dye solution in the lower part of the tube and a moving column of solvent in the upper part. Figure 1 illustrates this phenomenon. Also included in Figure 1 is an illustration of what is observed if the outer fluid is more dense than the fluid in the tube. In that case, the boundary is not stable, and the tube's entire content is swept into the surrounding fluid. How much of the bore will be swept by convection depends in part on tube diameter, as shown in Figure 2. For a very small diameter tube, Le., a capillary, only a very small portion of the bore is swept out. For example, about 1 mm of the bore is swept from a 1-mm i.d. capillary under conditions given for Figure 2.
