DIFFUSION COEFFICIENTS IS LIQUIDSBY
A
POROUS-FRIT METHOD
proposed model. The sharp increase in transition temperature lowering with chain length, indicated in Figure 4a, appears, therefore, to be the result of increasingly strong hydrophobic bonding to the denatured protein. -4 similar model pertains to the branched-chain alcohols, but here the concept of eff ective chain length in~roduced in ref. 2 must be included in the calculation of hydrophobic bond free energies. It may be supposed, from the fact that the branched alcohols do not give as large molar lowerings as their straight-chain counterparts, that only some fraction of the carbons are capable of interacting with the nonpolar residues of the protein to form hydrophobic bonds. A quantitative I hcory for interaction of the branched
Diffusion Studies. I.
303
chains could be developed in the manner described above by estimating these fractions. While denaturation of proteins by various agents is still not completely understood, iiiuch of the general picture has emerged within the past few years. The study reported here lends weight to the supposition that the exposure of the nonpolar groups of the native structure to the solvent is one important feature of the denaturation process. Acknowledgment. The excellent technical assistance of Nrs. Alary Thomas, -1lrs. llarcia Pottie, and -1Irs. Barbara Toupin is gratefully acknowledg?d, as is the help in the purification of ribonuclease given us by Dr. Tatsuo Ooi.
Diffusion Coefficients in Liquids by a Radiometric
Porous-Frit Method'
by Arthur E. Marcinkowsky, Frederick Nelson, and Kurt A. Kraus Chemistry Division, Oak Ridge 2V\Tational Laboratory, Oak Ridge, Tennessee
(Received A u g u s t 24, 1964)
A porous-frit method for measuring self-diff usion coefficients and tracer diffusion coefficients of solutes in liquid systems has been investigated. A thin slab of porous material ( e . g . , porcelain) is saturated with a solution containing a radioisotope of the eleiiierit of interest. A solution of the same composition, but not containing tracer, is rapidly pumped past the frit. From the counting rate of the frit as a function of time, the diffusion coe5icient (6)) is obtained after calibrating the frit with a solute of known a. Through use of yenergy discrimination techniques and appropriate recording equipment, the method may be applied to siniultaneous measurement of diffusion coefficients of several radioisotopes, The method is rapid and yields values of 6)accurate to a few per cent. Typical examples of diffusion coefficient measurements in aqueous solutions are presented.
The porous-frit method,2- particularly when con-ibined with radiometric technique^,^ is a simple, rapid, method capable of yielding diffusion coefficients with reasonable precision. The present paper describes further tests and applications of the method to measurements of self-diffusion and tracer diffusion coefficients in aqueous electrolyte solutions.
Experimental Frits approximately 0.3 X 0.7 X 1.5 cm. were cut from bulk material (unglazed porcelain plate) with a (1) Research sponsored by the Office of Saline Water, IT. S. Department of the Interior, under Union Carbide Corporation's ctontract with the U. S. Atomic Energy Commission.
V o l u m e 65%S u m h e r 1 J a n u a r y 1965
304
glass saw and ground by hand to various uniform thicknesses on a glass plate with a mixture of coarse carborunduni (So. 320) and glycerol. Final polishing was carried out with fine carborunduin (So. 600) in glycerol. The edges and corners of the frits were rounded to minimize danger of chipping. The frits were was’led with water to reiiiove glycerol, and then with hot 6 111HC1-1 AI S a C l to remove other impurities and with distilled water. Thicknesses of the frits, as measured with a niicroineter, ranged from 0.033 to 0.174 i 0.002 cm. Several iiieasurements were taken over the surface of each frit and an average value was calculated. The pore size of the frits was measured microscopically and ranged from 0.025 to 4 p ; the average pore size was less than 1 I.(. For diffusion nieasureiiients, a frit was equilibrated with a solutiori containing an appropriate tracer. Excess solution was removed by wiping. The frit was supported vertically in a tapered glass tube in front of a counter and, after establishing the initial counting rate, was rapidly “eluted” by puiiiping solution not coiitairiirig tracer past it while measuring the counting rate as a function of time. In most experiments, about 200-300 nil. of eluting solution was circulated past the fri t in a loop arrangeiiient described earlier.4a The pump a variable speed type, permitted a large range of linear flow rates past the frit. Temperature of the solutions was maintained at 25.0 f 0.1’. The counting equipment consisted of a flat, 3.8-cm. TI-activated sodiuni iodide crystal detector, associated amplifiers. a multichannel analyzer (niodified Packard, llodel l5), arid a tinie-base generator (Radiation Inst runient s Development Laboratories, Model 54-6). The analyzer was used in the niultiscaler mode to collect counts over preset time intervals. Counts accuniulated in each time interval were stored in successive channels; the time-base generator was used to set the period of the counting intervals and, at the end of each interval, to advance to the next channel. For single tracer nieasureiiients, 400 channels were available. At the end of a ~ u i i ,data were pririted out with an IBM typewriter. The equipment also periiiits siniultaneous iiieasurenieiit of counting rates of two tracers provided they have sigriijicaritly different y-spectra. A scheiiiatic diagrani of the equipiiieut is given in Figure 1. Pulses froiii thc detector are routed to two single-channel analyzers u.hich are set to span characteristic y-energy regions for XJach tracer; pulses froiii both single-channel analyzers itre mixed and fed into the analog-digital converter. These pulses, through 4-wsec. delay lines, are used to routr thc counting data to the appropriate The Journal o f Physical Chemistry
A. E. MARCINKOWSKY, F. NELSON,AND K. A. KRAUS
DIGITAL
CHANNEL
NUMBER
Figure 1. Simultaneous counting of two tracers with a multichannel analyzer.
iiieiiiory unit of the analyzer. Counts of the individual tracers are stored in separate halves of the nieiiiory of the iiiultichannel analyzer. With two crystals, counting rates of four different tracers may be nieasured simultaneously and, in these cases, the data are stored in separate quarters of the iiieniory unit. The radioisotopes 421< = 12.4 hr.), 82Br(Tllz = 35.5 hr.), 6 5 Z ~ 1(TI,, = 246 days), arid I 3 l I = 8 days) were obtained from the Radioisotopes Divisioii of ORNL. The 22Na (TI,* = 2.6 years) was obtained from Nuclear Science and Engineering Corp. Tracer solutions for diffusion measurements were prepared by evaporating aliquots of “stock” tracer solutions to dryness and taking up the residue with appropriate electrolyte solutions. Reagent grade cheiiiicals were used throughout. For solutions for which viscosity data were not available, viscosities were measured relative to water with a Cannon-Ubbelohde viscometer a t 25 f 0.02°.5
Results and Discussion 1. Method. The porous-frit niethod apparently was first used by Wall, Grieger, and Childers2. for deterniiriirig diffusion rates of slowly diffusing polymers. They suspended a porcelain disk, saturated with the solution of interest, in a bath from the arm of an analytical balance and determined the weight change of the frit as a function of time. The bath liquid was vigorously stirred except when weighings were made. From the weight-time data, relative diffusion rates (2) (a) F. T. Wall, P. F. Grieger, and C. W. Childers, J . Am. Chem. Soc., 74, 3562 (1952); (b) F. T. Wall and R. C. Wendt, J . Phys. Chem., 6 2 , 1581 (1958).
(3) F. Grun and C. Blatter, J . Am. Chem. Soc., 80, 3838 (1958). (4) (a) F. Nelson and K. A. Kraus in “Production and Use of ShortLived Isotopes from Reactors,” 5’01. I, IAEA, Vienna, 1962-1963, p. 191; (b) F. Nelson, J . Polymer Sci., 40, 563 (1959). (5) We are indebted to Dr. R. J. Raridon and Mr. C. G . Westmoreland of the ORNL Chemistry Division for carrying out these viscosity measurements.
DIFFCSION COEFFICIENTS I N LIQUIDS BY
A
POROUS-FRIT METHOD
were determined from which diffusion coefficients were obtained by calibrating the frits with material of known diffusion coefficients. In the radiometric porous frit n i e t h ~ d ,which ~ is similar to the method of Wall, et al., a porous frit is saturated with a solution containing a radioisotope and a solution o i the same conipositiori but not containing tracer is pumped past the frit; the counting rate, C, of the frit is determined as a function of time. These nieasurei:ients are inade continuously, in contrast with the weighing method where stirring must be interrupted or the frit removed from the bath during the time a measurenient is made. Diffusion coefficients may be evaluated from the counting ratetime data if the flow rate past the frit is sufficiently rapid so that bhe tracer concentration a t the fritsolution interface can be set substantially equal to zero. With these boundary conditions and the additional does not vary with concentration restriction that of tracer, the diffusion equation has a simple solution6: after an initial transient, the counting rate of the frit decreases as e-Xst where X, = A D and A is a constant which is characteristic for each frit. This asymptotic exponential relation has been shown to hold even for irregularly shaped frits.3 When 9 varies with concentration of the diffusing substance, interpretation of concentration-time functions is difficult. As pointed out by Wall and Wendt,2b the functional relationship between concentration and diffusion must be available (or assumed) in order to evaluate 5 from the data. The present study is restricted to tracer and self-diffusion systems in which % can reasonably be assumed independent of concentration of tracer. The (diffusional) “decay constant” Xs is readily evaluated from the linear portion of a plot of In C (or log C) us. time. The frit constant A is determined by a calibration experiment with a standard, i.e., a material for which $, is known; 5 for a tracer of interest may then be obtained from the relationship, D = %dXs/Xs(atd) = X,/A, where B s t d and Xs(std) are the diffusion coefficimt and observed slope for the standard. As in Wall’s method, the assumption is niade throughout that t,hPre are no significant or specific interactions between the frit iiiaterial and the solute whose D is to be determined. With pores as large as those of unglazed porcelain and solutes of size small compared with the size of the pores (as is the case here) there should be no serious problems at reasonable concentrations of the solute of interest. However, at high dilution and in carrier-free tracer experiments, adsorptive properties of the frit material may cause errors, if the
305
frit material has significant adsorptive capacity or reasonable selectivity €or the tracer. I n this case, reliability of the method may be tested by determining the distribution coefficient D of the tracer between frit and solution; D should be unity if expressed in terms of amount of tracer in the frit per gram of imbibed solution and amount of tracer per gram of contacting solution. It is also desirable to check separately for the absence of radioactive impurities in the tracer which might be selectively adsorbed by the frit material. When short-lived tracers are used, significant radioactive decay of the tracer may occur during the experiment. The (asymptotic) diffusional decay constant may then be obtained from the observed slope, Xobsd = -d In Cldt through the relation A, = Xobsd - X, where X is the radioactive decay constant. 2 . Calibration. For callloration of the frits, diffusion of S a + in 1 M NaCl solution was chosen as standard. Not only has self-diffusion of Na+ in NaCl solutions been extensively studied by diaphragm cell and capillary tube methods but convenient y-emitting tracers of Na (22Na and 24Na) are also available. While for 1 M S a C l values of asaranging from 1.20 to 1.30 X 10-5 cm.2 sec.-’ have been reported,’-ll it appears from the most recent study by Slillsll that precise values for the self-diffusion coefficients of S a have now been established for a fairly wide range of SaCl concentrations. Mills carefully corrected for, or avoided, sources of error in the capillary tube and diaphragm methods he used and was able to obtain agreement (within 1%) between the two methods; for 1 M SaC1, D N =~ 1.234 X loe5c m 2sec.-’was found and we have used this value for calibrations. To obtain meaningful calibration results and nieasurements of 9, -d In C/dt = XoIJsd should be independent of flow rate. In a series of tests with the 0.33and 0.53-nun. frits in 1 and 5 M S a C l solutions, X, was measured as a function of flow rate in the range ca. 0.1-115 cni. ’sec. A broad plateau was observed in the region 1 to 50 cni./sec. where A, remained constant within limits of experimental error. At lower flow rates, A, was lower than the plateau value, while a t flow rates above 50 ciii. ’sec., A, was significantly greater than the plateau value, particularly +
(6) W. Yost, “Diffusion in Solids, Liquids, Gases,” Academic Press, Inc.. New York, N. T.. 1952, Chapter 8, p . 37. (7) J. M . Neilson, A. W. Adamson, and J. W. Cobble, J . Am. Chem. Soe., 74, 446 (1952). (8) J. H. Wang and S. Miller, ibid., 74, 1611 (1952). (9) R. Mills and J. W. Kennedy, ibid.. 75, 5696 (1953). (10) R. 1Mills and A. W. Adamson, ibid., 77, 3454 (1955). (11) R. Mills, ibid., 77, 6116 (1955).
Volume 65. ,%-umber 1
January 1966
A. E. MARCINKOWSKY, F. SELSOX, A N D K. A. KRAUS
306
Table I : Calibration of Porous Frits with NaCl Solution.
-
As
.
Material
X 103,
d , mm.
aec. -1
0.616 ,752 ,981
2.38 1.51 0.933 0.942 0.938 0.944 0.933 0.938 0.549 0.301 12 0 4.66
A X 10-2, cm. - 2
Ad
1.93 1.22
0.732 0.690
0.760 0.445 0.244 9.72 3.78
0.731 0.729 0.739 1,058 1.062
0”
Porcelain I
0
w
+ a lx
W
zt-
z
3 0 V
Av. 0.01
0
\I 30
I 60
90
I 120
I t50
I 180
2tO
TIME, minutes
Figure 2. Cdibration of porous frits of various thicknesses ( 22Na 1 M NaC1, 25’)
+
if the frits were placed in the supporting holder a t a slight angle to the direction of flow. On the basis of these experiments, all calibration and diffusion nieasurements were carried out at flow rates of ca. 10-20 cni./sec. and precautions were taken to align the frits parallel with the direction of flow. Typical calibration experiments are shown in Figure 2. For these experiments, 0.616-, 0,981-, and 1.74mm. frits were saturated with 1 M KaC1 containing 22Ya and then eluted with 1 M NaC1. The initial counting rates of the frits were about 5 X lo4 counts/ min. Counting intervals were 25, 50, and 100 sec., respectively. The data plotted represent suinniatioiis over several counting intervals. After an initial transient, log C/Co decreases linearly with time, with A, ranging from 2.38 X l o v 3 to 3.01 X set.-', which corresponds to diffusion “half-times” of 4.84 to 38.3 min. Calibration data for frits of various thickness and from two different samples of porcelain are summarized in Table I ; values of A, represent an average of a t least two determinations. To illustrate reproducibility, five individual values are listed for the 0.981-mni. frit along with the average value. Reproducibility s e e m better than *2%. The constant, A = X S p I & ) / a ) ~ &which , should be independent of the electrolyte used to calibrate the frit, was computed for each frit. Considering the frit as an “infinite slab,” A should be6 inversely proportional to the square of the thickness d and as shown in Table I , the product, A d Z , is essentially constant for a given frit material as expected. However, for two different porcelain samples, Ad2 shows significant differences presumably because of differences in structure and porosity of 1 he materials. 3. Diffusionof K + and I- in KI Solutions. DifThe Journal of Physical Chemistry
1.28 1.74 0.33 0.53
Porcelain I1
’ 1 M NaCl
+ W a , 25”, a x ,
=
1.234 X 10-j cm.2 set.-'.
fusion coefficients of K + and I- in 0.5 and 1 M K I solutions were determined and the results are compared in Table I1 with measurements of Mills and Kennedy9 obtained by the capillary tube method. Agreement between the two methods seems satisfactory; the frit method yields diffusion coefficients which are lower but within experimental error (2-3%) of corresponding measurements by the capillary tube method. Table I1 : Self-Diffusion Coefficients of K and I - in KI +
Solutions a t 25’ -9 iM KI
Ion
0.5
K+
0.5 1.0
I-
1 .o
’ Data
x
105, cm.2 sec.-l-Capillary tube Frit method methoda
1.96 1.99 1.91
1.88
2.03 2.03 1.96 1.94
Difference,
70
3.6 3.0 2.0 2.6
of Mills and Kennedy, ref. 9.
4. Z n ( l l ) in KCZ Solutions. In preliminary experiments, tracer Zn(I1) (ca. lo-’ M ) in neutral KCl solutions was found to adsorb appreciably on porcelain; 110 adsorption occurred, however, if a small amount of acid (ca. to M HCl) was present. Hence, to avoid adsorption difficulties, diffusion nieasurements were carried out with KC1 solutions containing M HC1. Diffusion coefficients of tracer Zn(I1) in 0.25-4.0 M KC1 M HC1) are coinpared in Table I11 with data of WanglZobtained by the capillary tube method. For the latter, KCl solutions containing 5 X lo-* (12) J. H. Wang. J . Am. Chem. Soc.. 76, 1528 (1954)
DIFFUSION COEFFICIENTS IN LIQUIDS BY
A
POROUS-FRIT METHOD
M HC1 were used; in addition, possible adsorption of 66Zntracer on the walls of the capillary was avoided through use of 5 X M Zn(I1) solutions. While diffusion coefficients of Zn(I1) obtained by the frit method are generally slightly lower than those obtained by the capillary tube method, agreement between the two methods is within experimental error.
Table V : Self-Diffusion Coefficients of Br- in HBr, NaBr, and KBr Solutions a t 25""
Electrolyte
HBr
Table 111: Diffusion Coefficients of Tracer Zn(I1 j in KC1 Solutions (10-2 -3.1 HC1) at 25"
M KCI
0.25 1.00 2.00 3.00 4.00 a
NaBr
x
,-D
105, cm.2 sec.-lCapillary tube Frit method methoda
0.71 0.81 0.93 0.97 0.94
Di5erenoe, %
0.73 0.82 0.94 0.97 0.95
2.8 1.2 1.1 0.0 1.1
KBr
Data of Wang. ref. 12. a
5 . Difusion of K + in KCl Solutions. Diffusion coefficients of K + in 0.25-4.0 M KC1 solutions (containing 5 X M HC1) were determined and the product D* = :T)q/go, where q/qo is the viscosity of the medium relative to water, was computed. As seen in Table IV, while 3~ decreases significantly with increasing KC1 concentration, D*K shows only minor variations with increasing ionic strength.
Table IV : Self-Diff usion Coefficients of K in KC1 +
Solutions a t 25"
DK x
a
lo6,
M KC1
cm.2 Beo. - 1
0.00 0.25 1.00 2.00 3.00 4.00
1.96" 1.91 1.85 1.84 1 84 1.75
D*K x
105, om.%s e c . - ~
1.96 1.92 1.86 1.86 1.91 1.90
Nernst limiting value (DO) computed from conductivity data.
6. D i f u s i o n of Br- in H B r , N a B r , and KBr Solutions. Diffusion coefficients D and D* of Br- in 0.1-8.8 M HBr, 0.05-2.5 M XaBr, and 0.1-4.0 M KBr were determined and are given in Table V. For all three electrolytes, 9~~decreases appreciably with increasing ionic strength while D*B, varies only slightly. A similar invariance of D*B?with ionic strength was observed earlier4 with tracer Br- in HCl, LiCl, and
307
WB* = 2.079 X
M
x 105, cm.2 8ec. - 1
0 174 0 702 1 36 2 46 4 91 8 78 0 050 0 50 1 00 1 50 2 00 2 50 0 100 0 500 1 00 2 00 3 00 4 00
2 00 1 90 1 81 1 73 1 53 1 13 1 94 1 90 1 78 1 75 1 67 1 58 1 95 1 96 1 93 1 92 1 86 1 77
x lo6, cm.2 sec. -I
D*Br
2.02 1.95 1.88 1.87 1.87 1.86 1.95 1.96 1.90 1.93 1.93 1.91 1.95 1.93 1.87 1.84 1.81 1.78
cm.2 sec-1.
benzyltrimethylanimonium chloride solutions. Although for the latter electrolyte the influence of viscosity on diffusion is particularly large at high concentrations, D*B, is remarkably constant over a wide range of ionic strength. 7 . Dij'usion of Z n ( I I ) in HCl and HC104 Solutions. As pointed out by Wang,12 the rapid increase of Dzn with increasing KCl concentration implies that Zn(I1) diffuses considerably more rapidly in the form of chloride complexes than in uncomplexed forms. Since solutions of higher chloride concentration can be prepared with HC1 than with KC1, it appeared of interest to measure diffusion coefficients of Zn(I1) over a wider range of chloride concentration through use of HCl solutions. The results are shown in Table VI for 0.1 to 10 M HCl solutions along with corresponding data for the diffusion of Zn(I1) in essentially nonconiplcxing media, 0.2 to 10 A4 HClO,. The observed values for %, may be compared with the diffusion coefficient of Zn+2 at infiiiite dilution (Dozn) computed from conductivity data and the Kernst equation, Do, = RTXol/z,F2,where R is the gas constant, F is the Faraday, T is absolute temperature, Xol is the equivalent conductance of diffusing species i, and z , is its valence. Using Xozn = 52.813 and z 1 = 2, DOZ, = 0.71 X ~ 1 1 1set.-' .~ was computed. At low acid concentrations (0.1 M HC1 or HCI04) (13) B. B. Owen and R. W. Gurry, J . Am. Chem. SOC.,6 0 , 3074 (1938).
Volume 69, S u m b e r 1 January 1966
A. E. MARCINKOWSKY, F. YELSON, AND K. A. KRAUS
308
Tracer Diffusion of Zn(I1) in HClO, and HCI Solutions at 25”
Table VI:
a)zn x 106, M
Electrolyte
HClOi
om.’ eec. - 1
0.100 1.oo 5.97 9.04 0.100
HCI
1.00 1.50 2.02 4.00 6.04 10.0
D*zn x cm.3
0.72 0.72 0.56 0.37 0.71 0.76 0.80 0.85 0.82 0.75 0.59
108,
MC. -1
0.72 0.73 0.88 1.01 0.71 0.81 0.87 0.95 1.02 1.06 1.09
the observed values for %, are the same, within experimental error, as the computed value for So%,. In HC104, a)zn decreases with increasing He104 concentration, particularly at high HC1O4 concentrations where viscosity effects are large. In HC1, however, 92, increases with increasing M HCl to a slight maximum, Dzn = 0.85 X cm.2 sec.-’, near 2 M HC1 and then decreases with further increase of HC1 concentration. More revealing of differences in diffusion of the Zn(I1) species in HC1 and HC1O4 solutions are the variations of %*z, (Figure 3). For HC104 solutions, B*z, rises gradually with increasing acid concentration; in HCl, ~ * a ,rises very rapidly with increasing HC1 concentration and levels out near 4 M HCl. The rapid increase of 9 * z n between 0.1 and 2 M HC1 may be attributed to chloride complexing reactions which occur particularly in this region of chloride concentrati0n.1~ I n the region 4 to 10 M HC1, where Zn(I1) presumably exists principally as negatively charged
chloride complexes, B * z n increases only slightly with increasing M HC1. 8. Discrimination Techniques; Diflusion of Tracer Z n ( I I ) and K + in KCl Solutions. To test the method for simultaneously measuring diffusion rates of two radioisotopes, diffusion coefficients of 65Zn and 42K in KC1 solutions were determined. This system appeared particularly suitable for testing purposes since the results could be compared with the diffusion coefficients of Zn(I1) and K + in KC1 solutions established by integral counting techniques (Tables I11 and IV). In addition, the principal y-energies of 65Znand 42K, 1.12 and 1.52 Rfev., respectively, are easily discriminated. The experiments were carried out with the 0.98mm. frit; the frit was equilibrated with slightly acidified 0.254.0 M KCl solutions containing 42Kand 65Zn and then eluted. Diffusion rates were measured by counting pulses in the regions 1.9-1.2 and 1.4-1.6 MeV. ; these energy regions conveniently span the principal y-energy peaks of 42Kand 65Zn, respectively. The results of a typical experiment are shown in Figure 4, a seniilog plot of counting rate, corrected for “background,” us. time. After an initial transient, the counting rates of the two tracers decrease with time in the expected exponential manner. The “background” corrections for the 65Zn counting data include rooni background and also a correction for scattered radiation from the higher energy 42K. For the latter, the counting rate of 42K in the 65Zn ’E
0
20
40 60 TIME, minutes
80
too
Figure 4. Simultaneous measurement of diffusion rates, K + and Zn(I1) in 1 M KC1 (0.981-mm. frit, 2 5 ” ) . 5.2
0
2
4 6 M O L A R I T Y OF ACID
Figure 3. Diffusion of tracer Zn(I1) in HC1 and HCIOl solutions.
The Journal of Physical Chemistry
8
10
(14) K. A. Kraus and F. Nelson, “Symposium on the Structure of Electrolytes,” Electrochemical Society Meeting, Spring, 1957, Walter J. Hamer, Ed., John Wiley and Sons, Inc., New York, N. Y . , 1959.
DIFFUSIONCOEFFICIENTS IN LIQUIDS BY
A
POROUS-FRIT METHOD
region (1.0-1.2 MeV.) was established relative to its “normal” counting rate a t 1.4-1.6 Mev., and from these data appropriate “background” corrections were computed. Diffusion coefficients of K + and Zn(I1) obtained by the 7-discrimination method were in excellent agreement with corresponding values from Tables I11 and IV determined by integral counting. The extent to which the methods agree is illustrated in Table VII, where the Table VI1 : Ratio of Diffusion Coefficients hleasured by 7-Discrimination and Integral Counting Methods: K + and Zn(I1) in KC1 Solutions a t 25” M KC1
--Ratio K+
0.25 1.00
1.02
3.00
1.01
4.00
1.03
1.01
of diffusion coeffioientrr, R-Zn(I1)
1 .oo 0.99 0.99 1.01
ratio, R, of diffusion coefficients obtained by 7-discriminat>ionmethods to those obtained by integral counting
309
are given for K + and Zn(I1) in 0.25-4.0 M KC1. was Within experimental error, the same value of obtained by the two methods and hence R is seen to be essentially unity for the various experiments. 9. Summary. We have endeavored in these studies to illustrate the general applicability of the radiometric porous-frit method. The speed and simplicity of the technique are especially advantageous. The method also has broad applicability since convenient tracers for most elements are now available and hence systematic and comparative diffusion studies may be carried out in a reasonably short time. With the thin frits we have used, usually 0.3 to 1.0 mm. in thickness, a diffusion experiment can usually be completed in less than 1 hr. In systems where diffusion rates are slow, more time is required; however, in principle a t least, time requirements may be minimized by use of even thinner frits.
Acknowledgment. The authors are indebted to nlr. J. W. Woody, Jr., and Mr. J. A. Keathley of the ORNL Instrument Division for assembling the counting equipment and for helpful advice concerning its use.
Volume 65, .Vumber 1
January 1565
