NOTES
May, 1959 Discussion The very slow exchange of Ols relative to that of deuterium suggests independent migration of protons (deuterons) and oxygen-bearing carriers (such as OH', 0- or HZO) through the boehmite crystal lattice. As might be expected, the diffusion coefficient of the proton is appreciably greater than that of any oxygen carrier. The crystal structure of boehmite was studied first by Reichertz and YostI3 and subsequently by Milligan and McAtee.14 One-half of the oxygen atoms (type I) can be assigned to A1-041 links while the other half (type 11) are associated with hydrogen bonds (Al-O-H-O-Al). It has been suggestedI3 that cleavage of boehmite crystals occurs along the sheets of hydrogen atoms in the H-bonds t o give the orthorhombic crystals. Recent work by Holm, et CLZ.,'~ has indicated that the 0-H-0 bond is asymmetric. It is postulated here that (1) hydrogen diffusion occurs along the sheets of bonded hydrogens, and (2) the observed oxygen exchange is limited to the type I1 oxygen atoms, accessible through the sheets of hydrogen bonds. It is of interest to compare the boehmite case with that of ice. The conductivity and proton mobility in polycrystalline ice has been measured by Spernol.lB Below -15" an activation energy of 3.9 & 0.2 kcal./moIe was obtained for the mobility. (13) (14) (15) (16)
P. Reichertz and W. Yost, J . Chem. Phua., 14, 495 (1946). W. Milligan and J. MoAtee, T ~ i JOURNAL, s 60, 273 (1956). C. H.Holm, C. R. Adam8 and J. A. Ibers, {bid.,6.2, 992 (1958). A. Spornol, Z . Elektrochem., (59, 31 (1955).
74 1
Using the Einstein relation between the diffusion coefficient and the mobility ( v ) : D = ( k T / e ) v , (where IC is the Boltzmann constant and e is the proton charge), the activation energy for the proton RT, which gives diffusion coefficient is ED = E , a value of 4.5 kcal./mole for the case of ice. It is not surprising that the value for E n in boehmite is significantly greater than this result. Recently Kuhn and Thuerkauf" reported measurements on the 0l8 and D diffusion coefficients They found these in polycrystalline ice a t -2'. to be the same (with a value of 1.0 X lo-'" see. -I), from which they deduced that the diffusing species in ice is the water molecule. This value for the diffusioii coefficient of water in ice is, of course, considerably larger than that of the proton in boehmite. The low value of D o for proton diffusion in boehmite implies an unusually large negative entropy of activation. It mould be of interest to extend this work to the study of proton diffusion in other crystalline hydrous oxides.18 Acknowledgments.-The authors appreciate the partial support of this research by the U. S. Atomic Energy Commission, Division of Research (Contract No. AT(l1-1)-321) and the Argonne National Laboratory (Chemistry and Metallurgy Divisions). Special thanks are due to J. E. Draley and H. H. Hyman of the A. N. L. for a number of valuable discussions.
+
(17) W. Kuhn and M. Thuerkauf, Helu. Chim. Acta, 41, 938 (1958). (18) I n this connection it should he noted' that the proton mobility
in bayerite (p-Al(OH)s) was found to he a t least an order of magnitude greater than t h a t in boehmite.
NOTES ELECTRODE POTENTIALS IN FUSED SYSTEM. V. CELLS WITH TRANSFERENCE BYKURTH. STERN Chemistry Department, University of Arkansas, Fauetteuille, Arkansas Received March 14, 19.58
Laity' recently has discussed fused salt concentration cells with transference. In particular he studied the cell AglAgNOdXd, NaN03; NaNOs, AgN03(XdIAg
Mobilities of silver and sodium ions are the same in AgNOa-NaNO, solutions over the entire composition range. It follows that the measured potential of the cell arises only from the difference in the activity of the AgN03 in the two electrode compartments. In the present work we treat a still simpler case: that in which the concentrations of the ions to which the electrodes are reversible are the same. Any measured potential ZO can then be expressed in (11 R. W. Laity, J . A m . Chem. Soc., 79, 1849 (1957).
terms of events occurring in the liquid junction alone, e.g., in terms of the difference in the mobilities of the ions to which the electrodes are not reversible. The cells studied are: (1) Clz I AgCl; NaCl I Clz, (2) Clz I NaCl; KC1 I Clz and (3) Clz AgCl; KC1 I Clz. Experimental Materials.-All salts were of C.P.grade. Matheson tank C ~was Z bubbled through concentrated H$04 and over anhydrous Cas04 before passing into the cells. Apparatus.-The cell consisted of a 15 mm. i.d. Vycor U-tube having a graphite membrane (spectrographic carbon) sealed into the bottom and separating the cell compartments. The permeability of this membrane could be varied by changing its thickness; 2-3 mm. were sufficient to prevent diffusion for an hour or so. Separate tanks of Clz were used for each compartment and the GIz was passed over the carbon electrodes. Other details of measurement were as described Cells recovered quickly after having current passed through them, indicating that reversible potentials were measured. All measurements were made isothermally at several temperatures between 800 and 900". (2)
K. H. Stern, THISJOURNAL, 60, 679 (1956).
Vol. 63
NOTES
742
Results All the above cells showed zero potential, within experimental error (hO.5 mv.). I n some runs AgCl was added to one side or the other of cells containing NaCl and KC1 in the two compartments. I n no case did the potential vary from zero. Discussion The measured potentials of the above cells can be attributed to events at the liquid junction. If we write the cell A2 I MIA; M"A I Az it is clear that composition in the "junction" must change continuously from M'A to M"A. The analysis which follows3applies to this region. Consider a system containing at any point x1 moles of MIA and x2 moles of M"A, with transference numbers tl for M', t 2 for M", and t~ for A, and corresponding mobilities ul, up and UA. At any point the conductance is proportional to ulzl ~ 2 x 2 U A . Then
+
+
11 =
2~1X1/(uITI
and
+
U2XZ
+
UA)
+
tl t 2 f tA = 1 The material flux per faraday a t any point is
tiM'
+ t2M" -
t.&!fA
= tlM'A
+ t2M"A - A
The last term is independent of the position in the cell and may be combined with the electrode process. I n these cells they cancel exactly, so
+
-(S/RT)dE = h d In al t 2 d In uz (1) = U M ' U A and a2 = (GM"aA. Hence, rising
where a1 the Gibbs-Dnhem equation1 -(S/RT)dE
= UIZI
d In '1ClXI
+
a1 UZXP d In a2 f U P 2 2 f UA (u, - U ~ ) Z dI In a1
U1X1
+
UZZP
+
UA
(2)
d E = 0 if uI - up = 0, as Laity' has found for the nitrat,es. The liquid junction pot,eiitial, L e . , the potential of our cells, is also zero if B (UI A UlXl
d In U I -
S + + where the integration is carried out over the whole u2)a U28
UA
(3)
range of composition. It might be assumed that (ul - ' u p ) is positive for some rnnges of composition and negative for others, the whole integral being zero, but this possibility appears very unlikely in view of some recent measurements by Miirgulesco and Marchidan4 on the concentration cell with liquid junction in which the mole fraction of AgCl in Ag
I AgCl 11 AgCI, KCI I Ag
the right-hand compartment was varied from 0.1 to 0.8. They report that, the diffusion potential is zero within experimental error (-1 mv.) in the system over this concentration range, as Laity had found for the nitrates. On the basis of this evidence it is reasonable to coiiclude that the integral (3) is zero because 211 - uz = 0. It seems likely that this explanation is valid for the AgCl-NaC1 and KCI-NaC1 systems also. Acknowledgment.-I wish to thank Dr. G. (31 G . Scatchard, personal communication. (4) I . G. Margnlesco and D. I. Marchidan, Reo. Chin., Acad. de la, Repub. Populaare Roumaine, 111, No. 1 (1958).
Scatchard for his derivation of equation 2 and Drs. F. R. Duke and R. W. Laity for some stimulating discussions.
VISCOSITY OF AQUEOUS SODIL~M PERCHLORATE SOLUTIONS BYE. R. NIGHTINGALE, JR. Department o j Chemistry, University o f Nebrnaka, Lincoln 8 , Nebraska Received J u l y 17, 1968
Accurate viscosity data for dilute aqueous sodium perchlorate solutions me not available in the literature.' In conjunction with diffusion studies being conducted in these laboratories, the viscosities of sodium perchlorate solutions at 25" have been measured in the concent,rntion range 0.001 to 2 M . These results are reported here.
.
Experimental To purify reagent grade sodium perchlorate sufficient sodium hydroxide was added to a 6 M sodium perchlorate solution to give p H 10. After standing 24 hours, the solution was filtered through a fine porous glass funnel to remove the insoluble heavy metal hydrosides. The solution was acidified to pH 6 with perchloric acid and then boiled to concentrate the solution. Upon incipient precipitation of the anhydrous sodium perchIorate, the solution was cooled to 55' rtnd filtered rapidly through a heated porous glass funnel. Care must be exercised not to cool the solution below about 55' and thus permit the crystallization of the monohydrate. The anhydrous sodium perchlorate was removed from the funnel and dried at 110' for 4 hours. The sodium perchlorate solutions were prepared by diluting weighed quantities of the purified salt t o volume; The densities of the solutions were measured at 25.0 f 0.1 using 25-ml. specific gravity bottles, and the densities are precise to 0.0001 g./ml. The viscosities of the solutions were measured a t 25.00 f 0.01' using an Ostwald viscometer with a flow time of 170 seconds for water. Flow times were measured to 0.02 sec. with a stopwatch. The average deviation for five to eight measurements of a single sample did not exceed h0.05 sec. The average flow times for replicate samples of a single solution agreed within 10.04 sec. The viscometer was calibrated with water, benzene and 20% and 30% sucrose solutions by means of equation 1 q/p =
Kt
- L/t
(1)
where q is the absolute viscosity, p is the density, and t is the flow time of the calibrating solution. The characteristic viscometer constants K and I; were 0.00005291 and 0.0011, respectively. The al,solute viscosities of water, benzene and the sucrose solutions were taken as 0.008903,2 0.006010,3 and 0.01701 rtnd 0.027414 poise, respectively; the densities of the solutions were taken as 0.09707,5 0.87370,3 and 1.07940 and 1.12517' g./ml., respectively.
Results and Discussion The viscosities of the sodium perchlorate sohtions were computed by means of equation 1. The relative and absolute viscosities for ten solutions in the concentration range 0.001 to 2 &I are presented in Table I. The values for the 1 and 2 M solutions compare well with those reported for concentrated solutions by Miller and Doran.6 The data have (1) R. Reyner, 2. pliyaik. Chem., 2 , 744 (1888). (2) J. R . Coe and T. E. Godfrey, J . Applied Phys., l S , 025 (1944). (3) American Petroleum Institute Research Project 44, "Solccted Values of Physical and Thermodynamic Properties of Hydrocarbons and Related CompoundR," Carnegie Press, Pittsburgh, 1957, tables 21a, 210. (4) E. C. Bingham and R. F. Jackson, Nnt. Bur. Standards (U.S.1, Tech. News Bull., 14, 59 (1918). (6) N. E. Dorsey, "Properties of Ordinary Water-Substance," Reinhold Publ. Carp., New York, N. Y . , 1940, p. 201. (0) bl. L. Miller and M . Doran, THISJOURNAL,60, 186 (1956).
.
