NOTES
3048
The apparent molecular weight of T N T P in chloroform and the less polar 1,2-dichloroethane was also dependent on concentration. If the compound dimerizes to a small extent, it is easily shown that the relation l/nn= (l/Mm) - (K(M)o/M,) should be followed, where ATn is the apparent number average molecular weight, M , is the molecular weight of the monomer, ( M ) ois the concentration of monomer added, and K is the equilibrium constant for dimerization. The test of' this relation is shown in Figure 1. The molecular weights were obtained by vapor phase osmometry Results in chloroform at 51" and in dichloroethane at 29" were less precise, but the effect of temperature on the slope seems to be small, indicating that the heat of dimerization is near zero. The equilibrium constant calculated from the slope of the line is 0.6 ]./mole which means that about 8% of the molecules are dimerized a t a concentration of 0.1 M. The molecular weight of p-terphenyl under the same conditions was independent of concentration, but a cursory examination of 4-nitro-p-terphenyl indicated a molecular weight variation similar to TNTP. The wavelength a t which the intermolecular chargetransfer band occurs as well as the magnitude of the equilibrium constant and its small temperature dependence signifies that the interaction between the molecules in the complex is very weak. A recent calculation has shown that purely random contacts between the molecules in a solution can give rise to a measured equilibrium constant of about 0.2 l./mole.13 Thus, T Y T P exhibits characteristics which one would expect for a contact complex rather than a stable, discrete dimer. Crystalline TSTP is dimorphic; a metastable orange form with eight molecules per unit cell is converted endothermically at 150" to a stable yellow form with two molecules per unit cell. Both crystals are monoclinic. We were unable to examine the spectrum of the orange form since the yellow was produced on grinding with potassium bromide. There is no evidence that either form contains complexed TNTP, however, since the calculated densities of the two forms are identical (1.44 g/cc> and both forms are very good electrical insulators with conductivities of about lo-'* ohm-' em-' at 25" (polycrystalline compacts).
T' Acknow'edgment* We wish to thank Dr* Gorres for the X-ray data and Dr. G. V. D. Tiers for helpful discussions. (11) J. van Dam, Rec. Trav. Chim., 83, 129 (1964). (12) J. J. Neumayer, Anal. Chim. Acta, 20, 519 (1959). (13) J. E.Prue, J . Chem. SOC.,7534 (1965).
The Journal of Physical Chemistry
Adsorption Equilibrium at a Mercury Drop Electrode
by Donald W. Imhoff and Justin W. Collatl Department of Chemistry, The Ohio State University, Columbus, Ohio 45210 (Received February 20, 1967)
Diffusion is well recognized as the rate-limiting step in reaching equilibrium between an adsorbable species in a dilute solution and the phase adsorbed on a mercury surface. Notable recent references to the subject are those of Lorenz and i\Iocke1,2R e i n m ~ t hDelahay ,~ and T r a ~ h t e n b e r g ,and ~ Nemec.5 In connection with a study of the electrochemical behavior of cyanocobalamin, we have measured the differential capacitance of mercury electrodes in dilute solutions of this compound and some of its homologs. The measurements have been made as a function of time to observe the establishment of equilibrium and have yielded data which demonstrate a distinct two-step rate process which leads finally to an equilibrated interface. This may have significance for future studies on large adsorbable molecules. Experimental results and possible processes which might lead to this observation are reported herein. Experimental Section Cyanocobalamin (vitamin Biz) was purchased from Sigma Chemical Co. ; hydroxocobalamin samples were donated by Glaxo Ltd. and Squibb Institute for Medical Research. Sodium nitrate and potassium chloride for supporting electrolytes were purified by recrystallization, and triply distilled water was used to prepare all test solutions. The capacitance bridge employed was essentially the same as those described by Grahame,6 Delahay and T r a ~ h t e n b e r g ,Hansen, ~ Kelsh, and Grantham,' and Biegler and Laitinen.* Bridge balance was detected by means of a General Radio Corp. Type 1232-A null detector and its output was displayed on a Tektronix Model 502 oscilloscope. (1) T o whom all correspondence should be addressed at The Petroleum Research Fund, American Chemical Society, 1155 Sixteenth Street, N. W., Washington, D. C. 20036. (2) W.Lorenz and F. Mockel, Z . Elekfrochem., 60, 507 (1956). (3) W. H. Reinmuth, J . Phys. Chem., 65, 473 (1961). (4) P. Delahay and I. Trachtenberg, J . A m , Chem. Soc., 79, 2355
(1957). . . (5) L. Nemec, Collection Czech. Chem. Commun., 31, 1162 (1966). (6) D. C. Grahame, J . Am. Chem. Soc., 63, 1207 (1941); ibid., 71, 2975 (1949). (7) R. S. Hansen, D. J. Kelsh, and D. H. Grantham, J . Phys. Chem., 67, 2316 (1963). (8) T. Biegler and H . A. Laitinen, ibid., 68, 2374 (1964).
NOTES
The cell consisted of a water-jacketed beaker of about 150-ml capacity fitted with a cylindrical platinum gauze electrode with an area of about 12 cm2 and either a dropping mercury electrode or a hanging drop electrode. The dme was made by drawing to a fine tip ordinary 0.5-mm capillary tubing. A capillary electrode with a 0.20-mm 0.d. and 0.025-mm i.d. was found to be satisfactory. Hanging mercury drop electrodes on gold-plated platinum were prepared according to standard procedures.9 When the dme was used, the measuring technique of Grahame was followed, except that time was calculated from the horizontal deflection of the oscilloscope after calibration. This procedure gave values of elapsed time with an uncertainty of *0.03 sec which led to values of differential capacitance for a KC1 solution precise to ca. 0.5% and in excellent agreement with Grahame's results.'O In measuring electrode capacitance as a function of time, ordinarily with the hanging drop electrode two operators were employed. One kept the bridge balanced and the other recorded the times of balance, measured from the time of formation of the drop. This mode of operation produced smooth capacitance-time curves for a constant electrode potential. Preliminary studies with this apparatus and procedure on the n-hexyl alcohol system yielded results in satisfactory agreement with published data.6 The temperature was 25.0' for all experiments reported.
3049
an equilibriuin value for a mercury surface fully covered by adsorbed cyanocobalamin. The first portion of the decay of capacitance can be considered the result of diff usion-limited coverage of the electrode surface by adsorbed cobalamin. The
0.0
Results and Discussion A typical capacitance-potential curve for cyanocobalamin at a dme is shown in Figure 1 for comparison purposes. These data are equilibrium values. As the concentration of cobalamin is decreased, the time necessary to reach equilibrium increased. This is shown in Figure 2. There is a plateau in the decay of the capacitance from which, at a time dependent upon concentration, the capacitance again declines until a final value is reached. The plateau on the capacitance-time curves persisted with variation of the potential of hde, the temperature, or a change in the identity of the cobalamin. Figure 2 also illustrates the fact that even a t the low concentration levels studied, it was impossible to observe values of differential capacitance approaching those for the pure electrolyte solutions. Experimental difficulties in dealing with more dilute solutions, arising from impurities and excessive time for equilibration, precluded their use in establishing the parameters of the adsorption isotherm. The final differential capacitance found in these experiments was assumed to be
-0.4
-0.8 -1.2 V o l t s u. S.C.E.
-1.6
Figure 1. Equilibrium differential capacitance of cobalamin solutions. Data were obtained with a fine-tipped dme (drop time ca. 32 sec). All solutions were 0.10 M in KCl. Concentrations of cyanocobalamin were: (1) 2.0 X M ; (2) 5.0 X 10-6 M ; (3) 1.0 X lO-'M; (4)2.0 X M hydroxocobalamin.
instantaneous surface excess of adsorbate r t may be approximated for the case of semiinfinite linear diffusion by eq 1, derived by Delahay and TrachtenbergaG
Equation 1, in which c is expressed in moles per cubic centimeter and D is the diffusion coefficient in square centimeters per second, is analogous to the Koryta (9) W. Kemula and Z. Kublik, Advan. Anal. Chem. Instr., 2 , 168 (1963). (10) D. C. Grahame, M. A. Poth, and J. I. Cummings, Technical Report No. 7, ONR, U. S. Department of Commerce, Office of Technical Services, PB No. 160620, Washington, D. C., Dec. 13, 1951.
Volume 71 Number 9 August 1967
NOTES
3050
equation" for the dme. Employing the values of obtained from eq 1 in the Frumkin relationship
rt/rmax = (Co=o - C)/(Ce=o - Ce=J
rt (2)
it is found that the capacitance C follows a t"' law in its decay from its original value CB=o.
Figure 2. Differential capacitance as a function of time. A hanging mercury drop electrode a t -0.71 v us. sce. Drop area varied from 0.325 to 0.333 cm2 among drops used in taking data. Concentrations of cyanocobalamin M , (3) 2 X 10-6 iM, were (1) 1.0 X M , (2) 4 X M , (5) 5.0 X lO-'M, ( 6 ) 3.0 X lO-'M. (4) 1.0 X All solutions were 0.10 M in NaNOa.
Figure 3. Test of eq 3; hde a t -0.71 v us sce. The data of Figure 2 were used: A, 3.0 X 10-7 M; B, 5.0 X lo-' M cyanocobalamin.
The capacitance data for various dilute cyanocobalamin solutions are shown plotted us. t l / * in Figure 3. The data are well represented by eq 3 until t becomes large, whereupon deviations are to be expected because of convection and the inappropriateness of the modified Koryta equation for situations where the The Journal of Phyaical Chemistry
thickness of the diffusion layer is large compared to the radius of the hanging drop electrode. The notable feature of Figure 2 is the abrupt drop in capacitance about halfway to its minimum value. The shape of the capacitance-time curves of Figure 2 suggests a metastable state in the adsorption before the stable equilibrium state of low differential capacitance is reached. This state may be a monolayer which is subject to rearrangement or to subsequent accretions of material leading to a multilayer of adsorbed material of substantially lower differential capacitance. Whatever this further process is, it is doubtless also affected by diffusion, since its rate is concentration dependent. The time at which the capacitance drops precipitately from its intermediate level, tl, may be associated with the maximum extent of the metastable adsorption rmax and should be related to concentration to a first approximation by the modified Koryta equation, eq 1. This relationship predicts constancy of the product ctll/' which, in fact, varies from 18.4 X 10-9 mole 0111-3 sec1lza t a concentration of 4 x 10-6 AI cyanocobalamin to 14.6 X mole ~ m set'" - ~ at a concentration of 1 x 10-6 M cyanocobalamin. As expected, for lower concentrations and correspondingly longer times, the relationship is no longer valid. Using a low concentration limiting value for ti"^ of 19 )( 10-9 mole cm-3 sec1I2and a diffusion coefficient of 2.9 X cm2 sec-1 in the Koryta equation yields a value of rmax for the metastable state of 0.37 X mole/cm2. A similar calculation for times when the equilibrium state is reached (indicated by the foot of the final capacitance decay) yields a rmax for this state of 0.46 X 10-lo mole/cm2. The present results are interpreted to suggest a process, besides diffusion, occurring at an observable rate in the equilibration of the solution with the mercury-solution interface. Rearrangement or orientation of adsorbed layers has been postulated although, to be sure, direct evidence on this subject is still lacking. The present data may be indicative of such a step, though the over-all process giving rise to the capacitance drop is doubtless also affected by further diffusion and possibly by other factors in the double layer.
Acknowledgments. This work was supported by Grant GM-11751 of the National Institutes of Health, Public Health Service, which we acknowledge with thanks. We are also grateful to Dr. E. Lester Smith of Glaxo Ltd. and Dr. David Perlman of Squibb Institute for Medical Research for gifts of samples. (11) J. Koryta, Collection Czech, Chem. Commun., 18, 206 (1953).
