Even now, however, the uncertainty of the faraday is about one order of magnitude smaller than that of chemical standards commonly used. ACKNOWLEDGMENT
The authors wish to express their gratitude to the following colleagues at the National Bureau of Standards: to Delmo
Enagonio for providing the benzoic acid; to John L. Torgesen for oxalic acid dihydrate; to Virginia C. Stewart for spectrographic analysis of the benzoic acid; to Joseph P. Cameron, for valuable discussions in the preparation of the manuscript. RECEIVED for review May 24, 1968. Accepted June 19, 1968.
A Sensitive and Versatile Differential Vapor Pressure Apparatus R. J. Farm' and Stanley Bruckenstein2 Department of Chemistry, University of Minnesota, Minneapolis, Minn. 55455
A thermistor differential vapor pressure apparatus (vapor pressure osmometer) capable of being used over a wide temperature range is described. Solvent and solution contact only glass and platinum, and the cell is gas tight so that any desired atmosphere can be maintained in the cell. By means of a double waterjacket, the random temperature fluctuations between the solvent and solution thermistors are held to +1 x At relatively high solute concentrations, >O.OlM 10-5'. in suitable solvents, an accuracy of about 0.25% is attainable. In higher vapor pressure solvents, 1% precision is obtained in solutions as dilute as 1mM.
IN connection with acid-base equilibrium studies in solvents such as benzene ( I ) , chlorobenzene ( I ) , acetic acid, and hexane ( 2 ) , it became necessary to design a differential vapor pressure apparatus to determine the total concentration of all dissolved species in various mixtures of acids and bases. Several such devices, which have been misnamed vapor pressure osmometers, are available commercially for the determination of molecular weights. All these instruments are based upon the principle first used by A. V. Hill (3) in 1930 and applied by others (4-10) since then. However, these devices did not meet the necessary requirements for a truly versatile research tool. We believe a differential vapor pressure (DVP) apparatus designed for application in chemical research should possess the following properties: it should be usable with corrosive solvents such as sulfuric and acetic acid or ethylenediamine; electrical conductivity arising from dissolved solutes should Present address, Central Research, 3M Co., Hudson Road, St. Paul, Minn. Present address, Department of Chemistry, State University of New York, Buffalo, N. Y . 14214 (1) S. Bruckenstein and A. Saito, J . Amer. Chem. SOC.,87, 698 (1965). (2) D. E. Untereker and S. Bruckenstein, unpublished work, 1966. (3) A. V. Hill, Proc. Roy. SOC.,Ser. A, 127,9 (1930). (4) E. J. Baldes, Biodynamics, 2, No. 46 (1939). ( 5 ) A. P. Brady, H. Huff, and J. W. McBain, J . Phys. Colloid Chem., 55, 304 (1951). (6) R. J. Muller and H. J. Stolten, ANAL.CHEM., 25, 1103 (1953). (7) M. Davies and D. K. Thomas, J. Phys. Chem., 60,763 (1956). ( 8 ) W. I. Higuchi, M. A. Schwartz, E. G . Rippie, and T. Higuchi, ibid., 63,996 (1959). (9) J. J. Neumayer, Anal. Chim. Acta, 20, 519 (1959). (10) W. Simon, C. Tomlinson, and Ch. Chylewski, Proceedings,
International Symposium on Microchemical Techniques, Pennsylvania State University, University Park, Pa., 1961, Part 111.
have no effect; it should have high sensitivity and accuracy, i.e., be capable of giving results accurate to 1 or 2% at total concentrations of 1 millimolar; it should be capable of being used over a wide temperature range, both above and below room temperature; it should be possible to completely control the atmosphere inside the instrument so that hygroscopic and easily oxidized solutions could be studied; it should be possible to change solvents rapidly; the entire apparatus should reach equilibrium rapidly; and the data should be obtained without tedious manual adjustments requiring the continuous attention of the operator, i.e., the data presentation should be in a digital or analog form. A description of a DVP apparatus meeting the above prescribed requirements is given below. This instrument has been used in the temperature range 10 to 40 OC in helium, nitrogen, and argon atmospheres in addition to air. Solvents such as methylene chloride, chloroform, benzene, hexane, acetic acid, and water have been employed, as could any solvent which does not attack glass. Re-equilibration of the apparatus after changing solvent takes approximately 30 to 40 minutes. The experimental results are obtained as an analog signal display using a potentiometric strip chart recorder. Temperature control is achieved using a commercially available thermostated bath with an adjustable temperature range. THEORETICAL
A DVP apparatus consists of a chamber whose walls are maintained at constant temperature and filled with a gas at atmospheric pressure. Generally, two thermistors of low heat capacity are suspended in the center of this chamber by supports of high thermal resistance. The chamber contains some pure solvent, and the entire chamber is in a vapor pressure equilibrium with this pure solvent. A drop of pure solvent containing some solute is placed on the other (solution) thermistor; the solvent will condense on the solution drop, and the heat of condensation increases the temperature of the solution drop until the vapor pressure of the solution drop equals the vapor pressure of the pure solvent at temperature To. The temperature difference between the solution drop and the solvent drop produces a resistance difference between the solution and solvent thermistors, which can be measured with a Wheatstone bridge circuit, Figure 1. We shall relate the unbalanced emf, AE, to the concentration of solute, assumVOL. 40, NO. 1 1 , SEPTEMBER 1968
e
1651
I I
I 1
I
I
I
I
I
1 1 I I I
I 1
I I I
I I
I I 1
I
I
I
I
I
I
I
I I
I 1
I
I I
I
I I
I
I
I
I 1
I
I I
I
I I
I
I I
I
I
I
I I
1
I
I
Figure 1. Simplified DVP Wheatstone bridge circuit
I
I
I I
I I
V
1
I I
I I I
I
I I I
I
.' -
I I
11.2"
I
I
- - - --' !--
V = bridge voltage, AE = unbalanced bridge potential, R1 =
RP, both fixed resistors. Rv and Ra are adjustable. Trl and Trz are matched thermistors of resistance p 1 and p Z , re-
spectively. Ideally, p~
= p~
7-
at the same temperature.
5.7
Figure 2. DVP cell bottom ing that there is no heat transfer between the solution or solvent drops and the cell chamber wall, and further that dilution of the solution drop by condensation is negligible. Initially, we shall consider an experimentally unrealizable situation, in which we assume that the resistance and temperature coefficient of each thermistor is exactly the same. In Figure 1, R1 = R z , R a
