T H E
J O U R N A L
OF
PHYSICAL CHEMISTRY Registered in
U.S. Patent Ofice 0 Copyright, 1966, by the American Chemical Society
VOLUME 69, NUMBER 5 MAY 14, 1965
Effect of Pressure on Conductance.
I.
Tetraisoamylammonium
Picrate in Diethyl Ether and in Benzene'
by James F. Skinner2and Raymond M. Fuoss Contribution Yo. 1770 from the Sterling Chemistry Laboratory, Yale University, New Haven, Connecticut (Received February 1 , 1966)
The conductance of tetraisoaniylammonium picrate (TIAPi) has been measured in diethy to 3 X lo-' M a t 30" to 5000 kg./cm.* and in ether at five concentrations from 3 X to 3 X M at 25" to 750 kg./cm.2. The benzene at four concentrations from 3 X change in conductance with increasing pressure in both solvents has been explained in ternis of decreased ionic mobility owing to increased solvent viscosity and shifts in the ion pair and triple ion association equilibria as a result of increased dielectric constant of the solvent. In the highly compressible ether, a t concentrations below the conductance minimum, the conductance increased by about one order of magnitude while in benzene, at concentrations above the niiniiiiuni, a small decrease in conductance appeared as predicted. A value of A. = 190 for TIAPi in ether and values of the center-to-center contact distances for ion pairs (4.9 b.)and triple ions (15 b.)were obtained from the data. The corresponding Walden product for TIAPi in diethyl ether is 0.39, in good agreement with values of 0.42 in water, 0.47 in nitrobenzene, and 0.43 in ethylene dichloride.
The equivalent conductance of an electrolytic solution is a function of the solute concentration and of the following solvent properties: density, dielectric constant, and viscosity, which in turn are pressure dependent. By varying the pressure on an electrolytic solution, the dependence of conductance on these properties can be observed without changing the chemical nature of the solvent. The effect of pressure on the conductance of aqueous solutions has been fairly well investigated. In water, where ionic association is low or negligible, the change in conductance depends primarily on the variation of the viscosity of the solvent with pressure. Only a small amount of work, however, has been done on the effects
of pressure in nonaqueous solutions. Schmidt3 measured the pressure dependence of conductance for tetraniethylaiiiiiioriiuiii iodide in a series of organic solvents. Strauss4 measured the conductance of sodium chloride in methanol at elevated pressures. Recently, Fuoss and co-workers5 have measured the conductance of (1) This work was partially supported by the Directorate of Chemical Sciences, Air Force Office of Scientific Research, Grant No. AFAFOSlt-244-63. (2) This paper is based on part of a thesis submitted by J. F. Skinner to the Graduate School of Yale University in June 1964, in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (3) E. W. Schmidt, 2.physik. Chem., 7 5 , 305 (1911). (4) W. Strauss, Australian J. Chem., 10, 277 (1957).
1437
1438
JAMES F. SKINNER AND RAYMOXD 11. Fuoss
tetrabutylammonium picrate in toluene to 6000 kg./ cm.2 and proposed that the observed decrease in conductance with pressure was the net result of increases in the dielectric constant and viscosity of the solvent. The purpose of the present investigation was to determine the relative importance of the hydrodynamic and electrostatic factors in nonaqueous solvents. In solvents of dielectric constant less than about 10, an electrolyte is associated to ion pairs, triple ions, and higher clusters to an extent which depends on concentration. The corresponding association constants depend exponentially on the dielectric constant of the medium. The concentrations of the various ionic species should therefore be affected exponentially by an increase in dielectric constant with pressure, while their mobilities should be affected multiplicatively by an increase in solvent viscosity with pressure. The results of this study verify this hypothesis.
Experimental The pressure-generating system (Autoclave Engineers) consisted of three principal components: a hand-operated pump, a 10: 1 pressure intensifier, and a pressure bomb. The bomb is a gun steel cylinder, 55.88 X 15 cm. o.d., with a central cylindrical cavity, 30.48 X 3.81 cm. Three insulated electrical leads (Coors Go.) came through the bottom closure of-the bomb, each lead supporting a small mercury-filled steel cup. Pressurizing oil (Hercoflex 600, Hercules Powder Go.) was pumped through the top closure. The bomb was made liquid-tight by pressure of the threaded top and bottom closures on O-rings. The system has a blow-out patch rated a t 80,000 p.s.i. Pressure was measured with two calibrated Ashcroft Bourdon gauges, one to 50,000 p.s.i. connected to the low pressure side of the intensifier, the other to 100,000 p.s.i. connected directly to the bomb. By means of the hand pump, the system can be pressurized to 30,000 p.s.i.; to reach 75,000 p.s.i., the intensifier was used. About 15.3 m. of 0.635-cm. 0.d. copper tubing were wound tightly around the bomb, the turns about 1.27 cm. apart; the tubing was cemented to the bomb with a 0.95-cm. layer of Thermon T-85 heat transfer cement. Oil from a thermostat (k0.02") was pumped through the tubing at 300 nil./min. An iron-copnic thermocouple in a thermowell in the top of the bomb cavity indicated the temperature inside the bomb (30.0 f 0.1"). The cell, shown in Figure 1, was designed for dielectric constant measurements (Schering bridge) on low-loss pure liquids and for conductance measurements (Wheatstone bridge) on solutions. TWOCOThe Journal of Physical Chemistry
Figure 1. High pressure conductance cell.
axial, concentric platinum electrodes are separated at one end by a Teflon washer and are fastened at the other end by platinum rods (2.3 mm.) in a threaded Supramica plug (Nycalex Gorp.). The platinum rods are epoxied through the Supramica arid serve as electrical leads, dipping into the mercury cups in the bottom of the pressure bomb. The Supramica plug screws into a Teflon cylinder (19.05 cm. long) against an O-ring. A Teflon piston slides on two O-rings (Viton) into the other end of the cylinder, separating the electrolyte from the pump oil. A 0.157-cm. hole through the piston allows air to escape; after the cell is filled and all air is expelled, the hole is closed by a machine screw. The cell rests on a Teflon support, which has three clearance holes through which the leads carrying the mercury cups pass. For dielectric constant measurements, the cell was (5) C. M. Apt, F. F. Margosian, I. Simon, J. H. Vreeland, and R. M . Fuoss, J . Phys. Chem., 66, 1210 (1962).
EFFECT OF PRESSURE ON CONDUCTANCE
calibrated by measuring its capacitance in the thermostated pressure bomb at 1 atm. with air, toluene, npropyl ether, and diethyl ether. This gave a corrected C, of 11.43 pf., corresponding to a cell constant of cni.-'. For conductance measurements 7.74 X the cell was also calibrated by measuring the conductance of solutions of TIAPi in benzene of known conductance6 on the Wheatstone bridge. The conductance calibration gave a value of 7.77 X low3cm.-', in good agreement with the value obtained from the capacitance measurements. The Supraniica undergoes negligible compression to 5000 kg./cni.2 giving no variation in cell constant with pressure. The change in cell constant owing to compression of the Teflon spacer resulting in eccentricity in the centering of the electrodes would amount to a maximum of 0.2y0,which is within the other experimental errors. Capacitance measurements were assumed to be good to 0.50j, and resistance measurements t o 1%. TIAPi was prepared by neutralization of the corresponding hydroxide with picric acid in ethanol. The salt was recrystallized four times from isopropyl alcohol (13 g./5B nil.) and dried at 80" and 5 p pressure for conductance runs. TIAPi is soluble in diethyl ether only to about lop3M , limiting the range of the conductance measurements. In order to eliminate the hazards of peroxide formation, a fresh can of diethyl ether (Mallinckrodt anhydrous) was opened for each run. The density a t 30" is 0.7018 g./nil.; solvent conductance, 6.3 X lo-" mho. The benzene (Fisher Certified reagent) was used as received. The density at 25" is 0.8737 g./nil.; the solvent conductance was negligible. At 25" benzene freezes at about 800 kg./cm.2, limiting the pressure range on conductance measurements. Solutions were prepared by weight, a vapor correction being applied for the diethyl ether solutions. The solvent density corresponding to the relevant pressure was used to convert weight concentration to molarity. Capacitances and resistances were measured on the high voltage Schering-Wheatstone bridge already described.' The detector was replaced by a General Radio Type 1232-A tuned amplifier and null detector. The General Electric power amplifier was teiiiporarily replaced by a Dynaco Mark I11 60-w. amplifier coupled to a Triad high fidelity output transformer, Type S-152 A. Capacitance nieasurements were made on the Schering bridge a t 500 c. and 400 v., and resistance measurenients on the Wheatstone circuit were made a t 500 c. and 80 v.
1439
The density values for diethyl ether a t 30" were those of ChangBas calculated from the data of BridgThe viscosity values for ether were graphically interpolated from Bridgnian's'O values a t 30" and a t 1, 1000, 4000, and 8000 kg./cni.2. The dielectric constant values for ether were determined by the authors." There are no literature values for the density of benzene at 30". It was assumed that the relative volunies for benzene would be the same as those for toluene at 30" and the same pressures. Table I gives the solvent properties.
Table I : Solvent Properties P, kgJcm.2
d, g./ml.
71
CP.
Diethyl ether at 30" 0.7018 0.7801 0.8249 0 . a577 0.8841 0.9065
1 1000 2000 3000 4000 5000
0.211 0.447 0.690 0.970 1.31 1.79
4.17 4.87 5.30 5.65 5.94 6.19
Benzene -------At
--At
25-'
30'--
P
d
P
d
1 457
0.8737 0.913
1 154 295 429 577 745
0.8685 0.882 0,890 0,897 0.904 0.912
The conductance data are given in Tables I1 and 111. Pressures are given in kg./cin2 and concentrations in equiv./l.; A is equivalent conductance. It should be noted that in both solvents the one 1-atni. values before and after pressurizing usually agree within 1% (2y0in the iiiost dilute ether run) although the conductance changes under pressure by as much as a factor of 8, indicating very little hysteresis.
Discussion As the dielectric constant of an electrolytic solution is decreased, the Coulombic interactions of the ions (6) K. M . Fuoss and C. A. Kraus, J . A m . Chem. SOC.,5 5 , 3614 (1933). (7) .D. Edelson, W. N . Maclay, and R. M. Fuoss, J . Chem. Educ., 2 7 , 644 (1950). (8) Z . T. Chang, Chinese J . Phya.. 1 , No. 2, 1 (1933). (9) P. W. Bridgman, Proc. Am. Acad. Arts Sei., 49, 62 (1913). (10) P. W. Bridgman, "The Physics of High Pressure," G. Bell and Sons, Ltd., London, 1958, p. 343. ( 1 1 ) Work t o he published.
Volume 69, Number 6
M a y 1965
JAMES F. SKINNER AND RAYMOND M.Fuoss
1440
Table 11: Conductance of TIAPi in Diethyl Ether a t 30’ P
10%
1 998 2011 3094 4148 4908 3881 1533 1
1 928 1969 3101 4134 4851 3867 2686 1406 1 1 998 2039 3108 4092 4795 3726 2587 1547 1
294.3 327.1 346.1 360 8 372.2 379.3 369.5 338.0 294.3 28.32 31.31 33.23 34.72 35.80 36.45 35.54 34.22 32.29 28.32 2.911 3.236 3.428 3.571 3.677 3.742 3,639 3.506 3.347 2.911
P
A
0 0 0 0 0 0 0 0 0
0892 188 266 332 379 398 365 208 0888
0 152 0 425 0 698 0 937 1 07 1 14 1 04 0 851 0 552 0 152
1 907 2039 3129 4148 4887 3930 2672 1828 1
1 92 1 2039 3234 4148 4922 3600 2658 1617 1
10%
A
0.101 0.240 0.394 0.515 0.590 0.634 0.577 0.468 0.371 0.102
105.8 116.8 124.9 129,9 133.8 136.3 133.0 127.8 123.4 105.8 13.51 14.93 15.90 16.64 17.08 17.41 16.82 16.31 15.58 13.51
0.202 0,587 0.994 1.34 1.53 1.63 1 .4Q 1.18 0.868 0.204
411 32 18 81 22 37 05 52 1 80 0 419 0 1 2 2 3 3 3 2
k3-1
Table 111: Conductances of TIAPi in Benzene
- P~ _ _ -
25’ 104~
104~
1 457
9.847 10.29
3.189 2.741
1 457
6.723 7.026
2.343 2.079
1 457
3.083 3.222
1.525 1.450
30’-
,
P
1 154 295 429 577 745 1
104~
21.0 21.3 21.5 21.7 21.9 22.0 21.0
104~
8.13 7.73 7.33 7.08 6.64 6.27 8.17
become more intense, resulting in ionic association to pairs, triples, and larger clusters. For solutions with a dielectric constant of 10 or less, for the concentration range where only ion pairs and triple ions need be considered, the following equation12 describes the conductance h = &/(KAC)~” h$1i2/K~1iak3 The Journal of Phyaical Chembtry
where A. and Xo are the limiting equivalent conductances for the solute species (A+.B-) and the triple ions (AzB+.ABz-), respectively, K A is the ion pair association constant, and k3 is the triple ion dissociation constant. In the very dilute region, only free ions and ion pairs are present; here, the formation of ion pairs causes a decrease in conductance, given by the first term in ( 1 ) . A plot of log A against log c in this region will have a slope approaching -l/z with decreasing concentration. As the concentration is increased, triple ions will become stable, and their formation causes a net increase in the number of charge carriers and an increase in conductance, represented by the second term in ( 1 ) . These two opposing effects will produce the well-known conductance minimum. At concentrations above the minimum, the predominant ionic species in solution will be the triple ions. It can readily be shown that as the dielectric constant is increased the concentration a t which the minimum occurs increases. The equilibrium constants for ion pair and triple ion association depend exponentially on dielectric constant and are given e ~ p l i c i t l yas ’~~~~
(1)
= ( ~ N a ~ ~ e - ~ / 1exp(b3/2) 000)
(3)
where b = e2/aekT and b8 = ez/a3ekTare the Bjerrum parameters for ion pairs and triple ions, respectively, e is the electronic charge, N , Avogadro’s number, e, the dielectric constant, k , the Boltzmann constant, T , the absolute temperature, and a and a3 are the contact distances for ion pairs and triple ions. An increase in dielectric constant of the solvent would decrease association to both ion pairs and to triple ions. A decrease in ion pair association will increase the conductance while a decrease in triple ion association will decrease the conductance. The net resultant change in conductance is determined by the relative concentrations of ion pairs and triple ions in solution. Below the conductance minimum, where ion pairs are predominant , an increase in dielectric constant should strongly increase conductance. As the niinimuin is approached, the increase in conductance with increasing dielectric constant should become less as triple ions become important. Above the niininiuni, there should be a decrease in conductance with increasing dielectric constant because triple ions are now the predominant species in solution. (12) R. M. Fuoss and F. Accascina, “Electrolytic Conductance,’’ Interscience Publishers, Inc., New York, N. Y., 1959, p. 253. (13) R. M. Fuoss, J. Am. Chem. Soc., 80, 5059 (1958). (14) See ref. 7, p. 260.
EFFECT OF PRESSURE ON CONDUCTANCE
1441
The results in the present study confirm this hypothesis. By applying hydrostatic pressure to the solution, the solvent density, dielectric constant, arid viscosity are all increased without changing the chemical nature of the solvent. The magnitudes of these changes are shown in Table I. As the solution is compressed, the specific conductance increases, of course, owing to increased volume concentration. This effect is compensated by calculating equivalent conductances, using concentrations determined from the densities a t the given pressures. Any change in equivalent conductance with pressure will therefore be due to changes in dielectric constant and viscosity. The coricentrations of free ions and triple ions will depend exponentially on dielectric constant through the equilibrium constants. Diethyl ether was chosen for the present investigation because its high compressibility gives a large variation in dielectric constant, arid this should result in a strong pressure dependence of conductance. Figure 2 shows the relative change in
Figure 3. ?,A as a furiction of pressure for TIAPi in diethyl ether. Bottom to top: 2.943 X 1.058 X 2.832 X 10-5, 1.351 X 10-8, and 2.911 X 1 0 F M.
--
0
2 a
1.2 1.1 I.o
0
I
2
Io-sP
4
5
Fiyrire 2 . Pressure dependence of dielectric constant: upper curve, diethyl ether; open circles, this work; solid circles, Danforth. Lower curve, toluene; open circles, this work; closed circles, Chang.
dielectric constant with pressure for diethyl ether and toluene measured by the authors and by Danforth15 and Chang.8 At 4000 kg./cm.2 and 30°, the dielectric coristarits of diethyl ether arid toluene are increased by The mobilities of about 42 and 1 5 ~ o respectively. , the free ions and triple ions will be decreased niultiplicatively by the decrease in fluidity with increasing pressure. The viscosities of diethyl ether and toluene at 4000 kg./cni.2 and 30" are increased by factors of 6.2 and 7.9, respectively. The densities of the two liquids increase by 26 atid 17y0, respectively. We
Figure 4. Log A again.;t log c TIAPi in diethyl ether. to top: 1, 1000, 2000, 3000, 4000, and 5000 kg./cm.*.
Bottom
note that, while dielectric constant, viscosity, and density increase with pressure, the relative increases are specific for a given liquid and that there is no obvious correlation between de/bP, bq/bP, and the compressibility. Table I1 shows the variation in A with pressure for TIAPi in ether at five concentrations. It should be noted that despite the sixfold increase in solvent viscosity, the conductance increases at all concentrations studied. If the equivalent conductances are multiplied by v(P)/v(l)= qr, the relative viscosities at the corresponding pressures, the variation in ?,A with pressure must be due to the variation in the dielectric constant. Figure 3 shows that AT, increases for all concentrations (15) W.
E. Danforth. Phys. Rev., 38, 1224 (1931).
Volume 69,.Vtimber 5
May 1965
1442
JAMESF. SKINNER AND RAYMOND 11. Fuoss
9.o
8.0.‘ (I
0 ‘0
-4
0
“E! 0
-.
‘.0.3
0 0
?.O. 0
‘
o
o
I.
0
250
P
500
I
7LJ
0.16
I 0.18
I
I/€
I
0.22
J
0.24
Figure 6. TIAPi in diethyl ether: upper curve, log A against l / e ; lower curve, log B against 1 / ~ .
Figure 5. A as a function of pressure for TIAPi in benzene. Top to bottom: 2.099 X 10-3 ( 3 0 ” ) , 0.9847 X (25”), 0.6723 X (25”),and 0.3083 X M (25’).
-
where studied and that the increase is greatest a t the lowest concentrations, as expected. The concave upward nature of the curves comes from the exponential increase in viscosity with pressure. The conductances at integral pressures in Figure 3 were obtained by graphical interpolation from the data in Table 11. Figure 4 shows isobars of log A against log c. The 1 kg./cm.2 isobar shows considerable curvature. The most concentrated solution measured lies just below the minimum. The dashed line on Figure 4 is drawn The solubility limit prohibited with a slope of - 1 / 2 . working a t higher concentrations in ether. The 5000 kg./cm.2 isobar is nearly linear, indicating that the minimum has been shifted to higher concentration for the higher dielectric constant. To test the dependence of the triple ion association on dielectric constant, runs were made with TIAPi in benzene at four concentrations above the minimum. Figure 5 shows the results; as expected, the decrease in conductance owing to decreased triple ion association becomes more pronounced with increasing concentration. This is in agreement with the results of a recent investigation5 on the pressure dependence of the conductance of Bu4NPi in toluene a t concentrations above the minimum. If (1) is multiplied by C”’vr and the explicit functions for K A and kt are substituted, the following equation results vrAc‘I2= A
The Journal of Physical Chemistry
+ BC
(4)
A
=
1.99 X 10-llAo~r exp(-b/2)/a3’/’
(5)
and
B
=
3.77 X 1O1OX0ql,exp(-bb/2
+ b3/2 -
(6)
~ ) Q ~ ~ / U ” ~
Plots of the left-hand side of (4) against concentration are linear a t all pressures, and A and B may be evaluated from the slopes and intercepts, respectively. Taking logarithms of both sides of ( 5 ) , rearranging, and substituting in the known constants log A
=
log (1.99 X 10-11Aoq7/a”z)- 119.4/de (7)
If it is assumed that the first term on the right-hand side of (7) is independent of pressure, then a plot of log A against 1 / ~for the pressures studied should evaluate d from the slope. The plot is shown in Figure 6 ; a value of 4.9 8. is obtained. If this value for d is substituted into the value of the intercept, 190 is obtained for Aov,. Since vr is unity a t 1 atm., this gives 190 for the limiting conductance of TIAPi in diethyl ether. The corresponding Walden product is 0.39, in good agreement with values of 0.42 in water,16 0.47 in-nitrobenzene,” and 0.43 in ethylene dichloride.18 (16) H . M.Daggett, E. J. Bair. and C. A. Kraus, J. Am. Chem. Soc., 7 3 , 799 (1951). (17) E. G. Taylor and C . A. Kraus, ibid., 69, 1731 (1947). (18) L. M. Tucker and C . A. Kraus, ibid., 69, 454 (1947).
SURFACE TENSION IN THE RECIPROCAL SYSTEM K+, Cd+2-C1-, Br-
If logarithms are taken on both sides of (6) and numerical values of the universal constants are substituted, the following equation results log B
=
log (3.77
x
1010~~q, e ~ p ( - 3 ) a ~ 3 / a " ~-) 119'4(1/d - 1/d3)/E (8)
A 'lot
Of log against for the pressures studied should evaluate d3 from the slope, using the value of d
1443
obtained from A . Figure 6 shows this plot; a value of 15 b. is obtained for d3. This is larger than might be expected, but previous s t u d i e ~have ~ ~ ~found ~~ considerably larger values for d3 than for &. (19) N. L. Cox, C. A. Kraus, and R. M.Fuoss, Trans. Faraday Soc., 31, 749 (1935). (20) R. M. Fuoss and C. A. Kraus, J . Am. Chem. Soc., 5 5 , 3614 (1933).
Surface Tension in the Reciprocal System' K + , Cd+'-Cl-, Br-
by R. B. Ellis and A. C. Freeman Southern Research Institute, Birmingham, Alabama
(Receioed March 7 , 1964)
The variation in surface tension with composition and temperature for the reciprocal system K+, Cdf2-C1-, Br- has been studied from the standpoint of observing the presence of complex species in molten salts. Contour lines of constant surface tension were drawn a t 500, 600, and 700". Profiles of sections taken a t constant C1:Br ratios show stepwise changes in slope that indicate the presence of complexes, probably CdX3- and CdX4-2. There is some evidence for the existence of mixed-halogen complexes.
Introduction The presence of complex ions in molten salts is an interesting part of the study of the structure of ionic liquids. Various degrees of association into complex species2have been postulated for a number of individual compounds arid mixtures on the basis of evidence from several lines of i n ~ e s t i g a t i o n . ~Jan2 and RlcIntyre4 have demonstrated clearly an extensive association in molten mercuric halides arid their mixtures with alkali metal halides. Similar but less extensive associations have been reported for molten zinc and cadniium halides. One of the techniques for detecting the presence of complex species is to look for nonideal behavior in mixtures. There are iiunierous examples in the literature of investigations on mixtures containing three different ions, two cations arid oiie anion or two anions and one cation, but, until recently,6 none on mixtures of four ions. As an example likely to show rionideal behavior,
we chose the reciprocal system K+, Cd+2-C1-, Br-. As the experimental technique for detecting coniplexes, we have measured the surface terisioris of mixtures over a wide range of temperatures. As a result of Gibbs adsorption, the surface terision of a liquid is insensitive (1) This work was performed under the sponsorship of the U. S. Atomic Energy Commission, Contract No. AT-(40-1)-2073.
(2) I n this paper, the term "complex" may refer to any of several species, including cations, anions, and neutral molecules. (3) (a) H. Bloom and J . O'M. Bockris in " Modern Aspects of Electrochemistry, No. 2," ed. by J . O'M. Bockris, Academic Press, New York, N. Y.,1959; (b) E. R. Van Artsdalen in "Structure of Electrolytic Solutions," ed. by W. J . Hamer, John Wiley and Sons, Inc., New York, N . Y.,1959; (c) G. E . Blomgren and E . R. Van Artsdalen in "Annual Reviews of Physical Chemistry," Val. 1 1 , Annunl Reviews, Inc., Palo Alto, Calif., 1960; (d) F. R. Duke in"Advances in Chemistry of Coordination Compounds," ed. by S. Kirschner, The Macmillan Co., Inc., New York, N . Y.,1961; also U. S. Atomic Energy Commission Report No. IS-317; (e) G . J. Jnnz, J . Chem. Edtcc., 3 9 , 59 (1962). (4) G. J . Janz and J. D. McIntyre, Ann. S . Y . Acad. Sci., 7 9 , 790 (1960); J . Electrochem. Soc., 109, 842 (1962). (5) H . Bloom and B. J. Welch, Trans. Faraday Soc., 59, 410 (1963).
Volume 69, Sumber 5
.)fay 1965
