43 14
NOTES
Table I : Comparison of Experimental Critical Temperatures with Literature Values Compd
Exptla
Lit.b
Ethyl ether Acetone Cyclohexane n-Hexane n-Heptane Ethyl acetate Benzene
192.5 & 0 . 5 234.5 f 0 . 5 281.5 f 0 . 5 235.6 f 0 . 5 267.0 f 0 . 5 248.6 5= 0 . 5 289.4 f 0 . 5
193.8 235.0 281.0 234.8 267.1 250.1 288.9
a Corrected for thermal lag using the melting point of p-chlorocinnamic acid as a standard. b “Handbook of Chemistry and Physics,” Chemical Rubber Publishing Co., Cleveland, Ohio, 41st ed, 1959-1960.
form allows for a rapid and reasonably precise determination of critical temperature for those substances whose critical pressures do not exceed approximately 45 atm.
Acknowledgment. We are indebted to the Research Foundation of the City University of New York for funds which made the above work possible.
A Rapid Method for the Determination of Electrical Conductance of
Ion-Exchange Membranes by V. Subrahmanyan and N. Lakshminarayanaiah Department of Pharmacology, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 19104 (Received March 85, 1968)
I n a recent paper, Steymansl has discussed the measurements of electrical conductance of ion-exchange membranes by both direct and indirect methods. I n the direct method, the electrical resistance of a membrane strip held between two suitable electrodes is measured. Meares and ~ o w o r k e r shave ~ ~ ~ measured the membrane resistance by both ac and dc methods. Arnold and Koch4 and Steymans’ have used a “hanging-strip” cell in which the membrane, in the form of a ribbon, was clamped between platinized platinum electrodes at one end and the other end was held in the electrolyte solution in which the membrane had been previously equilibrated. We tried these procedures and found them to be much involved, in that we never realized the optimum conditions for getting reproducible results in the measurements. Further, they were time , ~ consuming. The direct method of Hills, et ~ l . although applicable to stiff ion-exchange rods, could not be used with strips of membrane, as the strip would buckle during measurement although initially it was The Journal of Physical Chemistry
held tight. The membrane resistance by the indirect methoda,’ was measured as the difference between the resistances of a conductivity cell containing the electrolyte solution with and without the membrane. With dilute solutions (0.01 N ) and highly conducting membranes, this becomes a negligible difference between two large quantities. Estimation of this small difference with certainty becomes difficult without the use of a well-machined cell and a conductance bridge which can be read correct to 1 ohm in the 200-300-ohm range. However, in this note a modification of the method has been described. This has enabled us to measure the resistances of membranes directly using equipment ordinarily available. In very early work connected with the measurement of the electrical resistance of glass membranes, mercury has been used to establish contact with the membrane surfaces.* Similar procedure is employed in the method described here. A cell of the type shown in Figure 1 was used. Ionexchange membrane in the required ionic form was equilibrated in the appropriate metal chloride solution (always 0.01 N ) and then clamped between two halfcells using rubber gaskets, G, as shown in the figure. The half-cells were filled with pure mercury previously equilibrated with the same metal chloride solution as the membrane. Trapped air bubbles were removed by tilting the cell back and forth. Platinum-wire electrodes dipping in mercury established electrical contact. The cell was enclosed jn a plastic bag and kept in a constant-temperature bath maintained at 25 0.01’. The resistance of the membrane was measured directly on a General Radio Z-Y bridge provided with a HewlettPackard wide-range oscillator (Model ZOOCD) and a General Radio null detector (Type 1212-A). Generally, a frequency of 1000 cps was used in the nieasurements. The resistance of the cell without the membrane was negligjble. Constant and reproducible resistance values were realized when the cell attained temperature equilibrium. This took about 30-40 min. This short time required to reach a steady value, we believe, was due to the wet membrane attaining equilibrium with its surroundings. I n which position the six-way measurement switch on the bridge was held (ie,, either on “Z measure” or on “Z initial balance
*
(1) C1. Steymans, Ber. Bunsenges. Phys. Chem., 71, 818 (1967). (2) P. Meares and H. H. Ussing, Trans. Faraday Soc., 5 5 , 244 (1959). (3) D. Mackay and P. Meares, ibid., 5 5 , 1221 (1959). (4) R. Arnold and D. F. A. Koch, Aust. J . Chem., 19, 1299 (1966). (5) G. J. Hills, A. 0. Jakubovic, and J. A. Kitchener, J . Polym. Sci., 19, 382 (1956). (6) H. P. Gregor, Research and Development Report No. 193, Office of Saline Water, U. 8. Department of the Interior, Washington, D . C., May 1966. (7) J. H. B. George and R. A. Courant, J . Phys. Chem., 71, 246 (1967). (8) J. T. Littleton and G. W.Morey, “The Electrical Properties of Glass,” John Wiley & Sons, Inc., New York, N. Y., 1933, pp 61-64.
4315
NOTES
Table I : Conductance of the AMF C-103 Membrane in the Na Form as a Function of External XaC1 Concentration
Y G
Figure 1 Membrane conductance cell. M is the membrane held in rubber gaskets, G, and clamped between the two half-cells.
reversed”) from the start of the experiment had no effect on the constant value of the membrane resistance. This meant to vis that the ac current (not measured) put out by the oscillator and going through the membrane had no control over the final resistance value of the membrane. All measurements were made only a t the ac current normally put out by the oscillator. The effects of various factors influencing the resistance of the membrane were also investigated. It was found that the value of the membrane resistance noted at the start of the experiment changed with time. However, in a short time (about 30-40 min and in some cases in about 15 min) it became constant and changed little thereafter when it was followed for a period of more than 6 hr. The change in resistance in the course of this period was also insignificant when the membrane was continuously subject to the ac current put out by the oscillator. This pointed to the fact that there was negligible polarization at the mercury-membrane interfaces. The constant value obtained for the membrane resistance was sometimes higher but often lower than the value observed a t the beginning of the experiment. Membranes equilibrated with the desired electrolyte concentration were used always wet without removing the adhering surface liquid. Some experiments were also carried out with membranes whose surface liquid had been removed by blotting between the folds of a filter paper. Even in this procedure, the values realized for the resistance of the membrane were not significantly different from the values obtained with wet membranes. Blotted membrane and dry mercury were also used. I n these experiments, it was found that the resistance was about 5% higher than the other values. The spread of results obtained using different pieces of the same AMF C-103 membrane (supplied by the American Machine and Foundry Co.) was also k50/0.
A,
[NaCIl, N
lOC, ohm -1 om -1
ohm-‘ om2 equiv-1
0.001 0.01 0.10
1.14 & 0.07 1.45 0.08 2 . 2 2 i:0.11
0.50
2 . 5 6 i:0 . 0 6
1.30 1.51 2.22 2.40
This spread which determined the accuracy of the results was probably due to the nonuniformity of the membrane. However, in the case of more homogeneous cross-linked polymethacrylic acid and phenosulfonate membranes which were prepared by us, the reproducibility was better than h2%. The results reported in this note were all derived using wet membranes and wet mercury. Experiments were also carried out with equilibrated membranes in the concentration range 0.001-0.5 N . At least six pieces of membrane were used in these measurements at each concentration. The mean specific conductance values along with their average deviations are given in Table I. I n these concentration ranges, no anomalous behavior was noted. However, the average deviations are high in the concentration range 0.0010.1 N and low at 0.5 N . This is in agreement with the fact that as the membrane became more conducting owing to Donnan absorption of the electrolyte in the high-concentration region, it became more uniform in its conducting capacity. The effect of frequency on the membrane resistance was also investigated in the limited range 500-10,000 cps. At 500 cps the resistance was higher than the value obtained a t 1000 cps by about 5%. I n the frequency range 1000-10,000 cps, the value of the membrane resistance did not change significantly from the value observed at 1000 cps, which was therefore the ac frequency used in the measurements reported here. Since the area, thickness, and equivalent concentration of the membrane were known by independent measurements, the specific (8) and equivalent (X) conductances were calculated in the usual way, and these values are given in Table I1 for the AMF C-103 membrane in different ionic forms. The X values given here are all slightly lower than the values obtained by Gregor6 and his coworkers9 for the same C-103 membrane. This difference may be attributed again to the membrane variability. However, the activation energy for the Na ion determined by the present method was 4 kcal/mol, agreeing with the value given by Gregor. The membrane conductance (X) sequence for the (9) K. Kawabe, H. Jacobson, I. F. Miller, and H. P.Gregor, J . Colloid Interfac. Sci., 21, 79 (1966).
Volume 72, Number 12 November 1968
4316
NOTES
Table 11: Conductances of the AMF C-103 Membrane in Different Ionic Forms A, Ionic form
lOG, ohm-1 om-1
ohm-1 oms equiv-1
Li + Na +
1.20 1.45 1.77 1.93 1.95 0.48 0.43 0.09
1.33 1.51 2.03 2.17 2.60 0.49 0.55 0.09
K+ Rb + c5+
CaZ + Mg2+ La3 +
alkali metal ions is Li+ < Na+ < E(+ < R b + < Cs+, the normal sequence observed in their aqueous solutions. The X values obtained for mono-, bi-, and trivalent ions are in close agreement with the findings of George and Courant.’ The values of X vary for monovalent ions from 1.33 to 2.6, for bivalent ions from 0.5 to 0.55, while the value for the trivalent lanthanum is as low as 0.09. Because the membrane is held in equilibrium with sufficiently dilute solutions (0.01 N ) , there are very few coions in the membrane phase, and so in all the cases considered (Table 11), the current-carrying species are the cations. The charge on the ion has a very big effect on the mobility of the ions in the membrane. This is in contrast to what is observed in aqueous solutions, in which the limiting ionic conductances are not related to charge type as most of the conductance values fall in the range from 38.7 for lithium to 77.8 for rubidium. As the charge on the counterion is increased, the membrane conductance decreases. This may be ascribed to increased ion association with the membrane exchange groups.
Acknowledgments. The work was supported by a grant from the Office of Saline Water, U. S. Department of the Interior.
Thermal Conductivity and Diffusion Parameter : Critical-Point Behavior by L. Seigel Department of Physics, Columbia Unicersity, N e w York, N e w York 10027 (Received February 26, 1968)
I. Thermal Conductivity : Critical-Point Behavior Classical measurements of the thermal conductivity, A, near the critical point are beset by numerous technical difficulties. Recently, it has become possible to circumvent these difficulties by using the half-width Rayleigh scattered light as a probe for A (this requires The Journal of Physical Chemistry
independent determination of the thermal diff usivity and the isothermal compressibility). In this section, we make two observations concerning the Rayleigh “line” which suggest a more direct optical approach for determining the critical-point behavior of the thermal conductivity. In 1934, Landau and Placzek3 predicted that the spectrum of light scattered from entropy fluctuations in a fluid would be Lorentzian in shape with a halfwidth, WL-P, given by
where 2 is the momentum-transfer vector, p is the density, and C, is the specific heat at constant pressure More recently, Fix(the thermal diff usivity =h/CPp). man and others4J proposed that the effects of longrange correlation would modify the Landau-Placzek result so that
Here
K,
the inverse correlation length, is given by /
1
\I/,
(3) where ICB is the Boltzmann constant, T i s the temperature, @T is the isothermal compressibility, and R is a short-range parameter, typically the order of the intermolecular distance. Our first observation is that the Fixman term, O L - P K ~ /isK ~proportional , to the thermal conductivity. To see this, we employ the wellknown thermodynamic relation
(4) In the critical region, C, is more weakly divergent than C, and hence may, we assume, be neglected in eq 4. If factors (eq 3 and 4) are combined and if it is assumed that R and (dP/bT)v are nearly independent of temperature, our first observation is readily verified. Currently a number of research groups are engaged in a search for the Fixman term; if successful, the temperature dependence of the thermal conductivity can be extracted from these studies. A parallel attack on the measurement of A may be (1) This work was supported in part by the Joint Services Electronics Program under Contract DA-28-043-AMC-O0099(E) and in part by the U.S. Army Research Office (Durham) under Contract DA31-124-ARO-D-296. (2) (a) J. V. Sengers, Ph.D. Thesis, van der Waals Laboratory, Amsterdam, The Netherlands, 1962; (b) J. V. Sengers and A. Michels, Papers Symp. Thermophys. Properties, Rnd, Princeton, N . J., i962, 434 (1962). (3) L. Landau and G. Placzek, Physik. 2.Sowjetunion, 5,172 (1934). (4) M. Fixman, J . Chem. Phys., 33, 1363 (1960). ( 5 ) W. D. Botch, Ph.D. Dissertation, University of Oregon, 1963, p 63.
