426
E. CHARLESEVERSAND FREDERICK R. LONGO
They write Fick's equation for diffusion with the additional term -kcc, where c, is the concentration of the solvated electron and k and c are defined above. They assume that solvated electrons diffuse toward the solution from a plane a t the fixed distance 6 from the electrode and obtain for the steady-state photocurrent
Pc,"(kcD)"' (5) where F is the faraday, c, is the value of c, in the plane at the distance 6, and D is the diffusion coefficient of
i
the solvated electron.
in arriving a t eq 5 are mentioned in connection with eq 4. The concept of saturation current is, i.e., the current for kc -+ a ,is then introduced, and ce is calculated as a function of is by the same approach as in polarography. Thus
c,"
=
The main simplifications made
=
s
-(2*
FD
- i)
Since eq 5 and 6 correspond to steady-state conditions, Q and Qs of eq 4 are proportional to i and is, respectively, and eq 4 follows immediately.
The Conductance of Dilute Solutions of Lithium in Liquid Ammonia at -71°',2
by E. Charles Evers and Frederick R. Longo The John Harrison Laboratory of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania (Received July 86, 1966)
The conductance of solutions of lithium in liquid ammonia at -71" has been measured from 0.000309 to 0.14 N . The results are compared with the data for sodium in liquid ammonia at -34" and for lithiunz in methylamine at -78". A mechanism for conduction based on the inversional motion of the ammonia molecule is proposed for dilute metal solutions.
The properties of metal-amine solutions have been investigated extensively for many years. Unfortunately, because these systems are metastable and the reaction between metal and ammonia is subject to catalysis, it has been difficult to obtain precise data in very dilute solutions; however, such data are essential since these solutions represent a region in which the systems exhibit quasi-electrolytic properties that gradually transform into those representing a metallic system as the metal concenbration is increased. If we may assume that the metal solutions a t low concentrations do conform to laws which govern the behavior of normal electrolytes, then, by measurement of various physical properties, it should be possible to establish some mode of the electrical interactions which occur among the species. One method of approaching this The Journal of Physical Chemistry
problem is to study the conductance of these systems as a function of solute concentration, for, in the case of electrolytes, we have a fairly comprehensive theory of the interaction of ions subject to various parameters such as temperature and dielectric constant. Precise conductance data have been reported for very dilute sodium in ammonia solutions by Kraus3 and lithium in methylamine solutions by Berns, Evers, and Frank.4 These data have been analyzed4J using a (1) Taken in part from a thesis by F, R. Longo, presented in partial fulfillment of the requirements of the Ph.D. degree, Dec 1962. (2) Sponsored in the main by the Office of Ordnance Research, U. S. Army, and partially by the Advanced Research Project Agency, Contract SD-69. (3) C. A. Kraus, J . Am. Chem. SOC.,43, 749 (1921). (4) D. S. Berns, E. C. Evers, and P. H. Frank, Jr., ibid., 82, 310 (1960).
CONDUCTANCE 01" DILUTESOLUTIONS OF Li
IN
LIQUIDNHa
conductance function based upon a modified form of the Shedlovskya equation for conductance and a mass action model proposed by Becker, Lindquist, and Alder.? An equation relating the conductance to the two equilibrium constants for the reactions proposed by Becker, et al., is
where A is the equivalent conductance, A,, is the equivalent conductance at infinite dilution, S ( 2 ) includes mobility corrections as defined by Shedlovsky, f is the mean ionic activity coefficient for the ionized metal, N is the normality, kl is the equilibrium constant for the ionization, RI = M + e-, and k2 is the equilibrium constant for the dimerization, 14 = 0.5 ill,. More recently, Dewald and Dyes have reported a conductance study of dilute solutions of alkali metals in ethylenediamine at room temperature. They noted that solutions in this solvent are less stable than those in ammonia or methylamine. The data were treated by the Shedlovsky analysis, and values for A. and the ionization constant were obtained for solutions of cesium, potassium, and rubidium. These values were compared with those calculated by Evers, et al., for Na in NH3 and Li in Dewald and Dyeg augmented their conductance studies with a spectral investigation and, on the basis of this work, have concluded that amine solutions differ essentially from ammonia solutions.1° They postulate the existence of "gaslike covalent dimers and electrons trapped by oneelectron bonded ;\I2+ ions," in addition to the species which are generally accepted as being present in ammonia solutions. In order to obtain further, precise data for dilute solutions it was decided to measure the conductance of solutions of lithium in liquid ammonia. At -34' decomposition was so rapid in dilute solutions that it was not possible to obtain reproducible results; hence, The the measurements were finally made at -71'. data obtained are compared with the data for sodium in liquid ammonia at -34' and for lithium in methylamine at -78'.
+
Experimental Section At -71.0' the rate of decomposition was negligible provided that extreme care was taken to guarantee the cleanliness of the equipment, but even a t this low temperature it was noted that the shiny platinum electrodes became blackened during some experiments. The black material could not be removed by strong mineral acids or by alcoholic KOH. However, it
427
-
was found that the electrodes could be cleaned by elec trolysis in concentrated HC1 solutions. The conductance cells used in this investigation were large enough to accommodate 1 1. of solution. The bright platinum ball electrodes, previously described by Hnizda and Kraus," were small in area, and the cell constants varied from 1 to 2 cm-'. The cell was filled with a 50 vol yo mixture of concentrated sulfuric acid and fuming red nitric acid and steamed out before using. The cell constants are determined by established procedures.12 A thermocouple well was sealed through the body of the cell in such a way that the temperature could be measured close to the electrodes. A 23-mm Pyrex tube rose vertically from the top of the cell and communicated with a "doser" stopcock assembly which was used to provide the cell with weighed samples of lithium. The cell also communicated with the vacuum system through this tube. The entire cell, including electrodes, was sealed through a desiccator-like lid. The lid was then cemented with black Apiezon wax to a large jar which served as a bath for temperature control. Details concerning construction may be found in the thesis by Longo.' Xeasurements were made at -71.00 0.03'. This temperature was maintained by controlling the vapor pressure of CHF2Cl (Freon 22), which was distilled into the bath around the conductance cell. The bath was stirred by permitting a stream of Freon vapor to pass through the liquid at all times. The vapor pressure of this liquid was controlled at approximately 145 f 0.05 mm with the use of a R4icro-Set Manostat (Catalog No. 63273, Precision Scientific Co.). A copper-constantan thermocouple was 'used for temperature measurements in conjunction with a Leeds and Northrup portable precision potentiometer, Model No. 8662. Lithium was obtained from the Lithium Corp. of America, (analysis: Li, 99.95; Na, 0.005; K, 0.01; Cu, 0.002; N, 0.01; Fe, 0.01; Si, 0.002; C1, 0.001%). Metal samples were cut under argon-saturated mineral oil in a heavy petri dish. The cut samples were taken from the mineral oil with forceps and placed in a
*
(5) E.C.Evers and P. H. Frank, Jr., J . Chem. Phys., 30, 61 (1959). (6) T. Shedlovsky, J. Franklin Inst., 2 2 5 , 739 (1938). (7) E.Becker, R.H. Lindquist, and B. J. Alder, J . Chem. Phys., 2 5 , 971 (1956). (8) R. R. Dewald and J. L. Dye, J . Phys. Chem., 6 8 , 128 (1964). (9) R. R.Dewald and J. L. Dye, ibid., 68, 121 (1964). (10) R. R. Dewald and J. L. Dye, ibid., 68, 135 (1964). (11) V. F. Hnizda and C. A. Kraus, J . Am. Chem. Soc., 71, 1956 (1949). (12) E.C. Evers and A. G . Knox, Jr., ibid., 73, 1739 (1951).
volume 70, Number 8 February 1966
428
bottle, where the mineral oil was washed away with dry toluene by a procedure described by Longo.1 After being washed, the lithium samples were transferred under argon into weighing bottles which were designed to fit on a vacuum system. The toluene was pumped off, the samples were weighed under vacuum, and transferred into the four doser stopcocks under an argon atmosphere. For solutions of higher concentration, a large metal sample was sealed in a side a m above the cell. It was pushed into the cell with a glasscovered magnet. Ammonia was obtained from the National Ammonia Co. (The company furnished the following analysis: HzO, 50 to 100-ppm; hydrocarbon oils, 3 ppm; nonvolatiles, 1 ppm.) It was purified in a manner which was previously found successful for monomethylamine. The bath was filled with Freon 22 by distillation from a commercial cylinder. Ammonia was condensed in the cell from a weighed storage can and was stirred by an externally driven glass-covered magnet. The vapor pressure of the Freon was adjusted, and the ammonia came to temperature equilibrium within 1 hr after the distillations. The lithium samples were dropped individually from the four doser stopcocks. The resistances of the resulting solutions were measured a$ 2000 cps with a Leeds and Northrup Jones bridge using earphones as a null detector. The concentration of metal is reported in g-atoms of metal per liter of solvent. For the calculation of solvent volume, the density data of Cragoe and Harper13 were used. I n order to apply the method of Evers and Frank5 it was necessary to know the dielectric constant and viscosity coefficient of the solvent. The dielectric constant was obtained by a graphical interpolation of data in the lit,erature covering the temperature range from -77.70 to 35O.14 At -71.0°, the dielectric constant, D, is 25.1. Using the method of Nissan,I5 we calculated the viscosity a t -71’ by extrapolation of the data of Fredenhagan16; a t -71.0°, 7 = 0.00500 poise.
Discussion
fl~ for the conductance of ~i~~~ 1 is a plot of Li in liquid ammonia at -71’. At the lowest concentration measured, 0.000309 N , the value of A is 445 Kohlrsusch units. The equivalent conductance decreases sharply with increasing metal concentration Until it reaches a minimum value Of about 220 a t approximately 0.025 N . F~~~ this point it rises to a value of 304 at 0.14 N , the concentration a t which a The Journal of Physieal Chemistry
E. CHARLESEVERS AND FREDERICK R. LONGO
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