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J. L. R . MORGAN A N D 0. M. 1,AMMERT
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[CONTRIBUTION FROM THE CHEMICAL LABORATORIES OF COLUMBIA UNIVERSITY (NO.
510) A N D
O F VASSAR COLLEGE]
FACTORS INFLUENCING THE ACCURACY OF MEASUREMENTS OF THE ELECTRICAL CONDUCTANCE OF LIQUIDS AND SOLUTIONS. 111 A DISCUSSION OF THE BRIDGE ASSEMBLY FOR THE MEASUREMENT OF ELECTRICAL CONDUCTANCE WITH PARTICULAR REFERENCE TO THE VREELAND OSCILLATOR AS
ASOURCEOFCURRENTOFCONSTANTFREQUENCY BY J. LIVINGSTON R. MORGAN AND OLIVEM. LAMMERT RECSIVED J A N U A R Y 22, 1926
PUBLISHED MAY5, 1926
Introduction The present status of our knowledge of methods for measuring the electrolytic conductance of solutions and liquids is such that it is quite necessary for a conscientious investigator, who wishes to make even a small number of determinations with any degree of precision, to have a t his disposal a generous supply of both time and equipment. One reason for this state of affairs is that since the work of Kohlrausch2 enough improvements in apparatus have been made and sources of error discovered to disturb the complacency of investigators as to the accuracy of results possible with the apparatus then used, but not enough to give them any confidence in the results obtainable with the newer assemblies now recommended since, in every instance, either for lack of time or equipment, workers in this field have had to abandon the problem after the publication of a few papers. Washburn3 made some noteworthy improvements in the bridge assembly as a whole but was obliged to give up the work before its completion. Taylor and Acree4 also attacked the problem as a whole and from another point of view, but it is ten years since their set of papers was published. Aside from these more extensive investigations, there have been isolated publications on more specific parts of the general problem. Curtis and Grover5 1 A preceding paper, to which reference will be made as Part I, was published by us [THISJOURNAL, 45, 1692 (1923)] under the title “The Design and use of Conductance
Cells for Non-Aqueous Solutions.” As the general scope of the work has been broadened to include a study of the cause, magnitude, correction and possible elimination of the errors affecting not only the precision of relative results, but finally the absolute accuracy of the values for the electrical conductance of all types of liquids and solutions, the series is continued under the changed title given above. See Kohlrausch and Holborn, “Leitvermogen der Elektrolyte,” B. G. Teubner, Leipzig, 1898, and the references given there. Washburn and Bell, THIS JOURNAL, 35, 177 (1913). Washburn and Parker, ibid., 39, 235 (1917) Washburn, ibid., 38, 2431 (1916). 4 Taylor and Acree, (a) ibid., 38,2396; (b) 2403; (c) 2415 (1916), and referencesgiven there. 5 Curtis and Grover, Bur. Standards Bull., Vol. 8, No. 3 (1911).
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published a paper on resistance coils which has resulted in the fairly general use of Curtis coils for resistances over 1000 ohms. Schlesinger and Reed6 have pointed out some likely errors. Hibbard and Chapman' have made a general resume of the method in an attempt to find a simplified apparatus for botanists. Percy8 in surveying the work done up to 1922 makes a distinction between the resistance of the solution alone and of the solution with the electrode effects. Kraus and Parkerg have discovered some of the errors current in the determination of cell constants, and Parker and ParkerlO have made a redetermination of the specific conductance of 0.1 N potassium chloride solutions. We, ourselves,11 have pointed out some special precautions which must be taken when nonplatinized or dried cells are used. Aside from these researches, which in most cases are based on the Kohlrausch method of using alternating current, we have a number of isolated researches dealing with the use for conductance measurements of special methods such as the direct current method of Eastman.'2 Nevertheless the determination of electrical conductivity is one of the most important, generally applicable and, once the apparatus is installed, quickly determined measurements we have. Its application to botanical, physiological, and industrial problems, as well as its application to the theory of aqueous and non-aqueous solutions and to the problem of fused salts is well known. Conductance data abound, notwithstanding the fact that we have no adequate method for what should be a very simple determination. There are practically as many equations relating conductance to other properties of a solution as there are investigators of conductance, and yet the most definite thing we can say about the accuracy of the results in the literature is that very few of them can have, for one reason or another, as much as a precision of 0.1%. What the absolute accuracy can be in view of the fact that practically all values are based upon some other value used as a standard had best be left unpredicted! The difficulties involved in the absolute measurement of the conductance of solutions and liquids by the Kohlrausch alternating current method may be grouped into three classes ;the first comprises those difficulties attendant upon the measurement of the resistance of a metallic conductor in a Wheatstone bridge circuit with an alternating current of definite frequency as the source of current; the second includes those difficulties peculiar to the Schlesinger and Reed, THISJOURNAL, 41, 1727 (1919).
' Hibbard and Chapman, Michigan Agr. Coll. Expt. Sta. Tech. Bull., 23 (1915). Percy, Inaugural Dissertation, Basel, 1922. (a) Kraus and Parker, THISJOURNAL, 44, 2422 (1922). (b) Parker, ibid., 45,
1366 (1923). lo l1 l2
Parker and Parker, ibid., 46,312 (1924). Morgan and Lammert, (a) ibid., 45,1692 (1923);(b) 46, 1117 (1924). Eastman, ibid., 42, 1648 (1920).
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measurement of the relative resistance of the solutions and liquids themselves, which is to say those errors inherent in the conductance cell; and the third embraces all of those difficulties arising in the absolute measurement of the specific conductance of a standard solution. The first part of the problem has been worked out with greater success than the second; the situation a t present is that whereas, with good judgment as to the selection and use of apparatus, the resistance of metallic conductors can be measured with an absolute accuracy approaching O.OOl%, the absolute accuracy of the values for the resistance of electrolytes is unknown. I n the first case, there is always the possibility of checking up the results against direct current values, while in the second case we have neither an adequate design for a cell with which consistent relative results can be obtained throughout all ranges of resistance, nor a standard solution, the infallibility of whose resistance is assured, since all values for the so-called standard solutions have been obtained either with an inferior bridge assembly or with cells, the design of which leads us personally to be pessimistic as to the value of the results. It is our object, therefore, to make an experimental review of the instruments now recommended for alternating current work, in order to determine in the first place the limit of precision of each part of the bridge circuit as assembled for measuring a metallic conductor; second, to develop furtherlla the technique of using the conductance cell and if necessary the design so that the limit of precision of the cell and its contents will be not less than the rest of the assembly; and third, after we know more of the so-called “electrode effects” and the magnitude and correction of the errors dependent upon them, to determine the absolute specific conductance of some liquid suitable as a standard. In this paper we are presenting some experimental details which, it is hoped, will bring together much that is useful to those working in the field and for the lack of which the present investigators wasted much time. Furthermore, it would seem wise to define a t the outset just what is the precision of the various instruments, since among workers there is great divergence, dependent upon the uses to which the results are put and upon the attitude of the investigator, as to what constitutes precision in conductance measurements.
Experimental Part Source of Current; Type A Vreeland Oscillator.-In the course of an investigation to develop methods for conductance measurements with an accuracy of O.OOl%, Taylor and Acree4*considered the various sources of alternating current and came to the conclusion that the various types of Vreeland oscillators were by far the best suited to conductance work. In the first place, they give the pure sine wave necessary for the prevention of unsymmetrical polarization a t the electrodes and for the elimination of
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the influence of harmonics and in the second place they were found to give sources of current of the most constant frequency, which frequency could be changed at will by changing the capacitance in the circuit. Of the induction coil, used so generally until recently, they report that it does not give an alternating but a pulsating current, with a large number of overtones and inconstant frequency and that the range of frequencies possible is small, while of the various types of motor generators they say that either a pure sine wave is possible only when the output is purified by inductance and capacitance in the circuit, or that the frequency is inconstant and not easily regulated. Our experience corroborates Taylor and Acree’s, in that we have found that it was necessary to give considerably more attention to the motor generator than to the Vreeland oscillator in order to obtain the very short range of complete silence in the telephone possible with the latter and, furthermore, that the special regulating device attached to give a constant frequency was continually out of order. Much to our amazement, however, we found these authors too optimistic about the constancy of the frequency of the oscillator under all conditions, which fact led us to make a systematic study of the laboratory Type A Vreeland oscillator in order to determine to what extent the frequency remains constant under varying conditions. Whereas Taylor and Acree state that the frequency can be “kept conTable I shows the typical action of our stant for weeks to within O.lO%.” Type A oscillator during a day’s run; in the first column is given the time in hours during which the oscillator has been operating; in the second column, the capacitance setting necessary to maintain the frequency a t 1024 oscillations per second as tested by a standard tuning fork giving that TABLE I THE VARIATION OF FREQUENCY OF THE TYPEA VREELAND OSCILLATOR DATASHOWING WITH THE TIMEOF OPERATION-FREQUENCY 1024 --CONSTANT LOADON SECONDARYAND INPUTIN PRIMARY Frequency Capacitance with Te,mp. in constant in primary initial condenser Time, circuit capacitance chamber, hours Microfarads OC. 0.00 3.82 1024 28 -25 3.835 1022 .50 3.84 1021 .75 3.84 1021 1.00 3.845 1021 30 1.25 3.85 1020 30 1.50 3.855 1020 30 1.75 3.86 1019 31 2.00 3.87 1017 32.5 2.25 3.88 1016 32 2.50 3.88 1018 32 2.75 3.885 1016 32.5 3.00 3.89 1015 32.6
-
.. .. ..
Time hour: 3.25 3.50 3.75 4.00 4.25 4.50 7.25 9.00 10.00 11.00 12.00 13.00
Frequency Capacitance with Temp. in constant in primary initial condenser circuit capacitance chamber Microfarads N OC. 3.89 1015 33 3.88 1015 32.3 3.89 1015 32.6 3.895 1015 32.6 3.895 1015 32.6 3.90 1014 33.0 3.90 1014 33.9 3.90 1014 36 3.90 1014 34.6 3.90 1014 37 3.90 1014 35 3.90 1014 33.6
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number of vibrations per second; in the third column, the frequency which the oscillator would furnish a t any one time had the capacitance in the oscillating circuit been kept a t the same initial value; and in the fourth column, the temperature of the air surrounding the condensers, The values in column three were calculated from the equation, used to express in such a circuit, the relation of the frequency to the capacitance and inductance] namely: f = A d r C , where f is the frequency, C the and L the inductance capacitance, A a constant equal to (1/27r
