NOTES
364
by Levich.’ Except for obvious errors ( k is used in the same equation to represent both Boltzmann’s constant and the rate constant, Avogadro’s number is missing), the two equations are essentially identical except that Levich’s equation contains the average distance of electron transfer while the equation derived here is expressed in terms of the component in the x direction of the transfer. For the faster system represented by Scheme 11, the electronic current is
then eq 14 reduces to
Let us compare the ionic and the electronic currents. The ionic diffusion current is (17) assuming that all diffusion coefficients are equal and also taking eq 15 into account. In order to evaluate the possible contribution of electronic current, we insert the following data into eq 16 and 17: kl = 10l2cm3 sec-l mole-’, kz = 4 X 10l2 cm3 sec-l mole-’ as experimentally observed for the system tris(4,7-dimethyl-l10-phenanthroline)iron(II) and hexachloroiridate(1V),6 From molecular dimensions, we estimate X = lo-’ cm; mole the concentrations we assume as Ca = c4 = ~ m - c1 ~= , mole ~ m - c3 ~ ,= 2.5 X mole cm-8; dc2/dz = mole C M - ~ ,dc4/dx = mole ~ m - ~ D = 10-6 om2sec-l. With these values we obtain ie = 0.13ii
It should be noted that there is an upper limit for the contribution of the electronic current to the total current. This upper limit is due to the fact that the electron-transfer rate constants IC1 and kz will approach diffusion controLg In fact, the rate constant values given in the latter example are less than one order of magnitude below the diffusion limit. Electronic Conductivity Due to Electric Field Gradient Referring again to Schemes I and 11,we will consider the case that all concentration gradients are zero. An electric field gradient V (v cm-l) is now applied with current flowing in the forward direction
and in the reverse direction
where A is the equivalent conductance in ohm-’ cm2 equiv-I, c is the concentration in moles ~ m - and ~ , n is the valency of ion, so that the ratio of electronic over ionic current is for a simple redox system (Scheme I)
i,- - F2X2kc1Cz ii R T Z hicin i
;
and for the faster redox system (Scheme 11)
- -- F2X2(kici~4 + kzczca)
ie
ii
R T ZA ic ini
(24)
We will now evaluate the order of magnitude of the electronic current with respect to the ionic current. Using the same data as above and assuming an equivalent conductance A = 50 cm2 ohm-’ equiv-l,1° we obtaini, = 7 X Only aqueous solutions have been considered here since electron-exchange reactions have been mostly studied in this medium. It is, however, obvious that these considerations apply to other solvents. Although difficulties in studying electronic conduction will arise from the fact that it constitutes only part of the total conduction, these studies are of interest since rate constants as well as ranges of electron transfer enter into the equations discussed above. (9) P. Debye, Trans. Electrochem. Soc., 8 2 , 265 (1942). (10) R. A. Robinson and R. H. Stokes in “Electrolyte Solutions,” Butterworth and Go. Ltd., London, 1959.
where a is the free energy fraction between initial and activated state, R is the gas constant, T is absolute temperature, and all other quantities are as defined previously. Taking into account that 2a 1 and developing the exponential term into a series, we obtain for the net current
-
Equation 20 can be compared with the one derived The Journal of Physical Chemistry
The correspondingionic currents are given by
Solute-Solvent Interactions:
Ethyl
Acetate in Water
by J. H. Stern and A. Hermann Department of Chemistry, California Sfate College, Long Beach, California Q0804 (Received August 1 , 1967)
Recently, some studies have been made to examine possible correlations of the change in heat capacity
NOTES
365
( ACpo2(g)), resulting from the solution of various
gases in water, with structural changes in the surrounding medium.' Frank and Evans2proposed that the solution of gases which are nonpolar or contain large nonpolar groups, in water, favors those iceberg forms of water which most easily can accommodate the solutes. An increase in temperature of the solution thus requires additional energy in order to melt the solute-induced iceberg forma of the water, and, thus, large positive values of ACpo2(g)should be observed. In this note, ACPo2(g)for the solution of gaseous ethyl acetate (EtO.Ac(g)) in water is reported, based on calorimetric enthalpies of solution of EtOAc(1) between 15 and 50" combined with its values of C,"(l) and Cp"2(g). Experimental Section Calorimeter and Measurements. The calorimeter,a materials, and experimental procedure4 have been described previously. All runs were carried out within f0.20" of the reported temperatures. Results and Discussion The means of the observed enthalpies of solution of liquid ethyl acetate in water, A H 2 " obsd, with their standard deviations, u, are recorded in Table I. No variation in enthalpies over the reported final molality range, m f , was observed within the limits of the over-all estimated uncertainty. The value at 298" has been reported previ~usly.~The calculated enthalpies, A H 2 " (calcd), are from eq 1, with values of the constants determined by the least-squares method, using weighting factors equal to l/a2 AH2" = -126.23
+ 0.7581T - 0.001148T2
(1)
The estimated uncertainty of enthalpies calculated from eq 1 is 10.1 kaal/mole.
m'x 10'
3 23 (4) 9 6
5-10 2-10 6-10 8-12
288 298 313 323
discussion. The financial assistance of the National Science Foundation is gratefully acknowledged. (1) (a) H. S. Frank and W. Wen, Discussions Faraday SOC.,24, 133 (1967); (b) L. A. D'Orazio and R. H. Wood, J . Phys. Chem., 67, 1435 (1963). (2) H. 8. Frank and M. W. Evans, J . Chem. Phys., 13, 607 (1946). (3) J. H. Stern and C. W. Anderson, J . Phys. Chem., 68, 2628 (1964). (4) J. H. Stern and A. Hermann, ibid., 71, 306 (1967).
p 626. (6) 8. W. Benson and J. H. BUSS,J . Chem. Phys., 29, 646 (1968).
Ethyl Acetate(1) in Water
Runs
Acknowledgment. The authors wish to thank Dr. L. Brooks and K. Baier for assistance with the leastsquares calculation, and Dr. R. H. Wood for fruitful
(6) Landolf-Bornstein, "Zahlenwerte und Funktionen," "Kalorische Zustandsgr6ssen," Part 4, Springer-Verlag, Berlin, Germany, 1961,
Table I : Enthalpies of Solution of
T, OK
quantity6 combined with ACPo2(l)a t 25" yields a calculated value for Cp02 of 116 cal/deg mole. This together with the calculated Cp02(g)6gives the calcu-, lated change in heat capacity ACpo2(g),92 f 5 cal/deg mole, upon solution of EtOAc(g) in water. The large positive value of ACpo2(g)supports the dynamic solution model for nonpolar gases discussed earlier. Group additivity methods have been very successful in the prediction of thermodynamic properties of gaseous organic compounds.6 It would be of interest to obtain similar additive group contributions to CPo2since these in turn could be used to estimate heat capacities of other aqueous nonelectrolytes. Meaningful values of group contributions could be calculated if sufficient and accurate supporting data were available. It appears that there are no Cpozdata for compounds containing methyl, ethyl, and carboxyl groups, and that there is a general lack of data for organic solutes in water. Lower order approximation methods of bond and atomic property additivity6 have also been useful in the gaseous state. Analysis of Cpo2values for methane and ethane1beBshows that these two approaches fail for even these two simple hydrocarbon solutes. Further studies with a variety of aqueous nonelectrolytes have been initiated.
-Alfao-
-kcai/mole obsd,
koai/moie
3.22 f 0.03 2.23 & 0.01 1.52 f0.02 1.08 i0.02
3.12 2.17 1.41 1.13
AHzO
~
4
,
Properties of Organicwater Mixtures. VIII. Dielectric Constants of N,N-Dialkylamides Containing Water'
The ACPo2in cal/deg mole for the above solution process is obtained directly from the temperature derivative of eq l.
Chemical Technology Division, Oak Rage National Laboratory, Oak Ridge, Tennessee (Received August 4 , 1967)
ACp02(1) = Cp"z - Cp" (1) = 758.1 - 2.296T (2) where CPo2 and Cpo(l) are the heat capacities of EtOAc(aq) and EtOAc(l), respectively. The latter
Dielectric constants of a series of amides at varying water contents were measured to test correlation with
by C. F. Coleman
Volume 76, Number 1 January 1968
