May, 1956
A MODIFIED DIEE~T C m m CONDUCTANCE METHOD
apparept from the studies reported here on the ternary system Ge-Cu-Pb, that the Ge-Cu melts are not ideal but exhibit negative departures from ideality. That is, equation 7 gives an upper limit to the activity coefficient f;" referred to pure solid copper. If referred to pure supercooled liquid copper, the reference state used for the ideal solutions just mentioned, the upper limit to the activity co&cient would even be smaller, namely, 0.4 rather than 0.62. 4.5. The Binding Energy of Copper in Germanium Solid Solutions.-The binding energy of copper can be defined as the difference in molar heat content between copper in the ideal vapor
595
state and in the dilute solid solution, ie., HE- Hs. Since = - H,*and the heat of sublimation of copper is HE - H,", the binding energy can be obtained. From Brewer'slo compilation we obtain 81 kcal. for the heat of sublimation of copper around 700°,which gives a value of 47 kcal. for the binding energy. 5. Acknowledgments.-We wish to thank F. Trumbore for helpful discussions and M. Kowalchik for experimental assistance. (19) Leo Brewer, "Chemistry and Metallurgy of Miscellaneous Materials: Thermodynamics." National Nuclear Energy Series IV-19B. Ed. L. L. Quill, paper 3, 1st Ed., McGraw-Hill Book Co., New Yor k, N. Y.,1950.
A MODIFIED DIRECT CURRENT CONDUCTANCE METHOD FOR GENERAL APPLICATION BY L. ELIAS AND H . I. SCHIFF Department of Chemistry, McGill University, Montreal, Canada Received October 81, 1966
The relatively simple direct current method developed by Gunning and Gordon for measuring electrolytic conductance has been modified to extend its application t o electrolytes for which reversible electrodes are unavailable. Silver-silver halide electrodes were immersed in a suitable halide solution and contact made with the cell solution through liquid junctions. Differences in liquid junction potentials were small and remained constant during the measurements. No contamination of the cell solution by diffusion was observed over a period of at least two hours. The conductance was indey d e n t of the current passed through the main body of the cell over the same range as reported by Gunning and Gordon. he method has been applied to several electrolytes in aqueous, methanol and nitromethane solutions, with a precision of fO.O1 conductance unit.
I. Introduction The direct current conductance method, as developed by Gordon and his associates, has been applied to aqueous' and methanol2 solutions with an accuracy comparable to that obtained with the most refined alternating current techniques. The inherent simplicity of the method and its freedom from most of the difficulties encountered in high precision ax. work recommend its use wherever practicable. Briefly, the method consists of passing a known current through the solution and measuring the potential difference between two probe electrodes; the conductance is then calculated from Ohm's law. Since no current is passed through the probe electrodes other than the small momentary one before potentiometer balance is obtained, reproducible readings are assured if the probes are reversible with respect t o the solution. This, however, limits the method t o solutions for which reversible electrodes can be found, which is a rather serious restriction, particularly for non-aqueous solutions. Thus, for example, silver halides were found to be soluble in nitromethane solutions of alkyl ammonium halides. It is the purpose of this paper t o describe a modification of the Gordon conductivity cell which removes this restriction. 3 (1) H. E. Gunning and A. R . Gordon, J . Chern. P h y s . , 10, 126 (1942): G. C. Benson and A. R . Gordon, ibid., 19, 470 (1945); R.E. Jervis, D. R. Muir, J. P . Butler and A. R. Gordon, J . A m . Chem. Soc., 16, 2855 (1953). (2) J. P. Butler, H. I. Schiff and A. R. Gordon, J . Chem. Phys., 19, 752 (1951). (3) D. J. G. Ives and S. Swaroopa (Trans. Faraday SOC.,49, 367 (1953)) have attenipted to extend the applicability of the d.c. riiethod
11. Experimental Method.-Although the probe electrodes must be reversible with respect to the solution with which they are in contact, this solution need not be the one whose conductance is being measured. In this modification a liquid junction is formed between the cell solution and a suitable halide solution in which each reversible silver-silver halide electrode is immersed. The cell is identical with that described by Gunning and Gordon, l and is shown diagrammatically in Fig. l. The liquid junctions were effected by means of the probe chambers represented in the lower portion of the figure. Type A chambers were used when the probe solution was less dense, and type B when the probe solution was more dense than the cell solution. Type A chamber was made of 12 mm. Pyrex tubing which was tapered to a 4 mm. opening a t its lower end. The 19/38 standard taper inner joint fitted the outer joint of the probe side arm of the cell, and the 12/30 outer joint matched the inner member of the probe electrode. The probe chamber was blocked at the lower end and filled with halide solution to a level just below the rubber bulb. The probe electrode was inserted in the chamber and the 12/30 ground joint wetted with the solution to ensure an air-tight seal. The lower end of the chamber was unblocked and the rubber bulb was depressed to expel about 2 cmeaof solution. An equaI volume of cell solution was drawn up, by releasing the bulb while the tip of the chamber was immersed in a sample of the cell solution. The position of the boundary is shown as a dotted line in Fig. 1. Type B chamber was made of 13 mm. Pyrex tubing; the by the uae of quinhydrone electrodes in potassium hydrogen phthalate stabilizer. However, the precision reported was an order of magnitude lower than that achieved with the Gordon cell. We have constructed a cell similar to the one they describe and found that the long probe path seriously decreased the sensitivity of the mcasure~nents.
L. ELIASAND H. I. SCHIFF
596
FRONT
GORDON
I
CELL
i
SIDE
LIQUID J U N C T I O N
P R O B E CHAMBERS
Fig. 1.-Above the original Gordon cell and probes; below, the liquid junction probe chambers and probe electrodes. inner tube was 8 mm. in diameter and 3 cm. long. To form the boundary in this chamber, cell solution was first run into the side opening while the top of the chamber was blocked, so that only the inner tube was filled. A clean rubber finger cot was pressed against the side opening while the robe solution was run into the chamber from the top; the goundary formed just above the tip of the inner tube Finally the robe electrode was inserted and the finger cot removed. Eontamination of the cell solution by mechanical mixing was successfully avoided by this procedure. The filled probe chambers were wiped clean on the outside with filter paper and placed in the probe side arms of the cell. All ground glass joints were aligned by etch marks on the inner and‘outer members although this did not seem to be at all critical. Rotation of the probea by as much as 90” had no effect on the measured potential differences. Apparatus and Materials.-The electrical measurements were made in the manner described by Gunning and Gordon’; the “constant current” circuit was modified slightly to accommodate a 6SJ7 rather than a 1B4P pentode. The probe electrodes were made of thin platinum strips 1 mm. wide and 6 mm. long sealed into Nonex glass in such a manner that no edges were exposed; they were silver plated and anodized in an appropriate halide solution after the method of Brown .4 The main, current-carrying electrodes were made of heavily silver-plated platinum. Cell constants were determined using the Jones and Bradshaw 0.01 demal standard.6 The oil-bath was regulated to better than 0.005” and set a t 25.000’ with a mercury-in- lass thermometer which was piodically calibrated by the %hermometry Division of the ational Research Council a t Ottawa. Water of specific conductance 0.7 X ohm-’ cm.-l was used in preparing the aqueous solut,ions. These solutions were degassed by application of water-aspirator vacuum for three minutes and returned to normal pressure with purified air. All solutions were prepared gravimetrically, final weighing8 being made after the degassing proce(4) A . 8. Brown, J . Am. Chem. Soc., 56, 646 (1934). (5) G.Jones and B. B. Bradshaw, ibid., 55, 1780 (1933).
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dure. All solutions and solvents were transferred by pressure of purified nitroeen. Methanol was distilled from magnesium turnings; the distillate was found to contain less than 0.006 weight per cent. water by Karl Fischer titration. The nitromethane had a specific conductance of 1 X 10-8 ohm-’ cm.-l; details of the purification of this solvent and the preparation of the quaternary ammonium halides will be given in a future pa er. geagent grade potassium chloride, twice recrystallized from conductivity water, was fused under a purified, dry nitrogen stream for the preparation of the aqueous solutions, and heated a t 600” in a nitrogen atmosphere for the preparation of the methanol solutions. Sodium nitrate was precipitated from a concentrated aqueous solution by the addition of methanol and dried in vacuo a t 150’ for 12 hours. No attempt was made to obtain this salt in ultra-pure form since i t was not required for absolute conductance measurements.
111. Results The most sensitive criterion for a satisfactory probe arrangement is that the calculated resistance must be independent of the current that is passed through the solution. This condition will not be satisfied if the probes perturb the potential gradient in the main body of the cell. Table I shows a typical set of readings for a 0.002 N aqueous NaNOa solution, with Ag,AgBr probe electrodes in a 0.002 N methanol solution of KBr in type A probe chambers. E, is the potential drop across a 1000 ohm standard resistor in series with the cell. E, is the potential difference between the probes, taken with the current flowing first in one direction (+), and then in the other (-). The ratio EJEs (and consequently the calculated conductance) is invariant within the limits of error of the measurements (0.01%) for at least a fivefold change in current. TABLE I DEPENDENCE OF MEASURED RESISTANCE ON CURRENT E.,
Eo, V.
Eo/Es
1.12492
+O ,78711
0.69913
0.69068
+
V.
0.55036 0.23990 0.20632
+ + -
+ -
,78583 .48352 .48225 ,38545 .38414 .16837 .16706 .14491 .14361
.69914 .69917 .6991i .69920
Static bias 0.00066 v.
Effect of Concentration of Probe Solutions.-The probe electrodes were made narrow to minimize the effect of “shorting out” the solution across the probe surface. With the liquid junction arrangement there should be no danger of any “shorting” effect arising from the probe solution if it has a lower specific conductance than the cell solution. To test the stringency of this requirement the resistance of a 0.001 N nitromethane solution of Me4NC1 was measured with a series of aqueous KC1 solutions in type A probe chambers. Table I1 shows that an error of not more than 0.01% is introduced when the concentration (or in this case, the specific conductance) is as much as 100 times that of the cell solution. On the other hand, the probe solution cannot be made too dilute without seriously decreasing the sensitivity of the measure-
May, 1956
A MODIFIEDDIRECTCURRENT CONDUCTANCE METHOD
ments as well as altering the effective cell factor. The general practice has been to use a probe solution having a specific conductance comparable with that of the cell solution. TABLE I1 DEPENDENCE OF MEASURED RESISTANCE ON CONCENTRATION OF PROBE SOLUTION Concn. of probe s o h , N
Measured resistance of cell soh., ohm
0.001 0.01 0.1
1643.24 1643.20 1643.1s
The Effect of the Liquid Junction Potentials.There is no completely satisfactory method of estimating the magnitude of liquid junction potentials, particularly if both solvent and solute differ in the two solutions. However, since the method involves the measurement of the potential difference between a pair of electrodes, only the difference between the two liquid junction potentials is of importance. This difference will, of course, be in addition to the usual bias potentials between the two silver-silver halide probe electrodes. It will be seen from Table I that the difference between any pair of E, readings is independent of the current and is equal to twice the “static bias” measured with no current flowing through the cell. The “bias” was never found to be more than a few millivolts, and, what is more important, did not change with time during the course of the measurements. I t therefore appears that any difference in liquid junction potentials can be eliminated along with the usual electrode bias by averaging pairs of E, readings. The Effect of Diffusion.-Although diffusion did not seem to affect the difference in liquid junction potentials, there remained the possibility that diffusion of the probe solution might contaminate the cell solution. Consequently the resistance of an aqueous 0.002 N NaN03 solution was measured over a period of time, with 0.002 N KCl in methanol in the type A probe chambers. Table 111 shows the readings obtained a t 15-minute intervals after the cell had been in the oil-bath for one hour. Similar results were obtained with both types of probe chambers for at least two hours after the junction had been formed. As long as there is an appreciable density difference between probe and cell solutions there appears to be ample time to make the measurements without danger of contamination. TESTFOR
TABLE I11 CONTAMINATION BY PROBE SOLUTION
Time, min.
Resistance, ohms
0 15 30 45
459.53 459.53 459.50 459.51
results; the radii of the circles correspond to 0.01 conductance units. The open circles were obtained with Ag,AgCl probe electrodes and methanolic KC1 in type A probe chambers; the filled circles were obtained with Ag,AgBr probe electrodes and methanolic MerNBr in the same probe chambers. The solid curve is drawn from the OnsagerShedlovsky equation A’ = A’ BC DC log C using the values of the constants given by Benson and Gordon.’
+
150.75
150.50
+
I t
149.80 I 0
I I I I 40 60 80 100 104 c. Fig. 2.-Shedlovsky plot for KCl in water at 25”.
I
20
The solvent conductance was measured with the unmodified Gordon cell using Ag,AgBr electrodes. Although a few experiments indicated that the solvent conductance could also be measured with the required accuracy using a liquid junction arrangement there appeared to be no advantage in doing so. The solvent conductance measured with a small alternating current cell always seemed to give values which were about 3% too high. The liquid junction method was also compared with the original method of Gordon by measuring identical methanol solutions of KC1 by both techniques; aqueous KC1 was used in type (B) probe chambers. Table I V shows the agreement obtained. These results also illustrate the absence TABLE IV COMPARISON OF THE LIQUIDJUNCTION AND GORDON METHODS Concn. of KCI in MeOH,
N
Accuracy and Precision of the Method.-The accuracy of the method was tested by measuring the conductance of aqueous KC1 solutions. Figure 2 shows the sensitive Shedlovsky A i plot of the
597
0.01 .005 .002 .0005
Measured resistance, ohms Lj. Gordon probes cell
446.85 765.38 1775. Is 6187.2
446.83 765.35 1775.19 6186.9
L. ELIASAND H. I. SCHIFF
598
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of diffusion of probe solution into cell solution, since type A probe chambers, Details of these measureconductances of methanol solutions are very sensi- ments along with those of other nitromethane solutive to traces of water. tions will be published shortly. Figure 3 illustrates the precision obtainable when the liquid-junction method is applied to solutions for which suitable reversible electrodes cannot be found. The curve is a Shedlovsky plot for aqueous NaNO8 solutions measured with methanol solutions of KBr in type A probe chambers. The solutions 99.00 were made by dilution of different stock solutions, and were measured in random order. It should be emphasized that since no attempt was made to obtain this salt in a high state of purity these results are not intended to represent accurate conductance data, but merely to serve as an example of the precision possible with this method. '
