742
Vol. 63
NOTES
Results Scatchard for his derivation of equation 2 and Drs. All the above cells showed zero potential, within F. R. Duke and R. W. Laity for some stimulating experimental error (hO.5 mv.). I n some runs discussions. AgCl was added to one side or the other of cells containing NaCl and KC1 in the two compartments. VISCOSITY OF AQUEOUS SODIL~M I n no case did the potential vary from zero. PERCHLORATE SOLUTIONS Discussion BYE. R. NIGHTINGALE, JR. The measured potentials of the above cells can be Department o j Chemistry, University o f Nebrnaka, Lincoln 8 , Nebraska attributed to events at the liquid junction. If we Received J u l y 17, 1968 write the cell A2 I MIA; M"A I Az it is clear that composition in the "junction" must change conAccurate viscosity data for dilute aqueous sotinuously from M'A to M"A. The analysis which dium perchlorate solutions me not available in the follows3applies to this region. literature.' In conjunction with diffusion studies Consider a system containing at any point x1 being conducted in these laboratories, the viscosimoles of MIA and x2 moles of M"A, with transfer- ties of sodium perchlorate solutions at 25" have ence numbers tl for M', t 2 for M", and t~ for A, and been measured in the concent,rntion range 0.001 to corresponding mobilities ul, up and UA. At any 2 M . These results are reported here. point the conductance is proportional to ulzl Experimental ~ 2 x 2 U A . Then To purify reagent grade sodium perchlorate sufficient
+
+
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).
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).
.
NOTES
May, 1959
743
TABLE I to be -0.05, and this compares favorably with the RELATIVE A N D ABSOLUTE VISCOSITIESOF AQUEOUS SODIUM value of - 0.056 reported in this study. By virtue of its minimum solvation, the hydrated perchlorate AT 25' PERCHLORATE SOLUTIONS C, moles/l.
dno 1.0002 I . 0005 1,0009 1.0012 1,0021 1,0020 1.0038 1.0101 1,049 1.150
0.0008987 .004409 .01000
,01600 03600 ,06054 .loo0 .3048 1.0008 1.0975
poise
0,008905 .008907 .008911 .008914 .008922 ,008920 .008937 ,009003 ,009339 .01024
been analyzed using the Jones-Dole7 equation ?/VO =
1
+ A d / C + BC
*
(2)
ion is sufficiently small to loosen or disrupt locally the pseudo-tetrahedral structure of the water in the co-sphere about the ion and hence decrease the viscosity of the solvent about this ion. Such behavior is commonly observed only in water, and only for the few ionic species whose effective hydrated radii are minimal. Acknowledgment.-The assistance of Mr. H. D. Russell in measuring some of the densities of the sodium perchlorate solutions is acknowledged.
THE VIRIAL TREATMENT OF THE INTERhCTION O F GAS MOLECULES WITH SOLID SURFACES'
where r]/qo is the viscosity of the salt solution relaBY ROBERT S. HANSEN tive to that of the solvent, water, C is the molar Instilute for Alomic Research and Department of Chemistry, Tozaa State concentration, and A a.nd B are constants characC o l l e g e , Ames, Iowa teristic of the electrolyte. The A-coefficient repreReceiiwd Julu S I , 1068 sents the contribution from interionic electrostatic The virial treatment of gas-solid interactions forces and was first derived by Falkenhagen and Vernon.8 The B-coefficient appears to represent developed by Halsey and co-workers2-5 was exto interaction potentials based on the Lenthe contribution of the co-spheres of the i o i ~ s , ~ Jtended ~ although no satisfactory theoretical treatment has nardJones 6-12 potential for interniolecular atyet been given. This constant is a specific and traction, which is known to give a better representaapproximately additive property of the ions of a t>ionof gas second virial coefficients than does the strong electrolyte a t a given temperature.l' Re- rigid sphere model used by Halsey and co-work' this problem also has been arranging equation 2 and plotting (q/v0 - l)/dc e r ~ . ~ ,Independently, attacked by DeMarcus, Hopper and Allen8 and by us. the A-coefficient is the ordinate intercept, Freeman.9 This paper will therefore be limited to and the B-coefficient is given by the slope of the re- conclusions other than those reached by these sulting straight line. The experimental value for workers. the A-coefficient of G.8 X compares well with The second virial coefficient for gas-solid iiiterthe theoretical value of 6.4 X low3. The experi- action, including correction for quantum effect7** mental value for the B-coefficient is observed to be is given by +0.03 for sodium perchlorate at 25". Taking the value for the B-coefficient for the sodium ion to be +O.O86, 9,10 we calculate -0.056 as the magnitude of the B-coefficient for the perchlorate ion at this temperature. Recently, Gurney (ref. 9) has discussed the rela- where t(w) is the potential energy of a gas molecule tion between the viscosity B-coefficient for individ- at a distance n: from the solid, taken as a semi-infiual ions and the partial molar ionic entropy. This slab. The molecular 6-12 pot,entinl has been relation has been the basis for his selection of -5.5 taken in the form suggest,ed by Hirschfelder, Cure.u. as the absolute partial molar entropy of the hy- tiss and Bird' to fncilit,nte use of their tabular padrogen ion a t 250.12 In a separate study to be de- ramet,cr data scribed in another paper,13 it will be denionshrated P ( T ) = 4t" that a self-consistent set of radii for hydrated ions can correlate all the features of the viscosity Bcoefficient/ionic entropy relations. I n addition, if where p ( r ) is the interaction potential energy of two allowance is made for the configurational contribu(1) Work IVRS performed in the Ames Laboratory of the Atomic tions to the ionic entropy (e.g., rotational entropy), Energy Commission. ( 2 ) R'. A . Steelc and G . D. FIalsey, Jr., J . Chem. P h p . , 22, 979 the absolute partial molar ionic entropy can be (1954). shown to be a single linear function of the viscosity (3) W. A. Steele and G . D. Halsey, J r . , THISJOURNAL,59, 57 ionic B-coefficient. Using these relations, the B- (1955). ( 4 ) M . P. Freeman and G . D. Halsey, Jr., ibid., 69, 181 (1955). coefficient for the perchlorate ion has been estimated
z/c,
[(,)',
(7) G. Jones and M. Dole, J . A m . Chem. SOC.,6 1 , 2950 (1929). ( 8 ) H.Falkenhagen and E. L. Vernon, Physilc. Z . , 53, 140 (1932). (9) R. W. Gurney, "Ionic Process in Solution," McGraw-Hill Book Co., Inc., New York, N. Y.,1953, p. 160 ff. (10) M.Kaminsky, 2. Naturforsch., Ma, 424 (1957). (11) W. M. Cox and J. H. Wolfenden, Proc. Rov. SOC.( L o n d o n ) , A146, 475 (1934). (12) K. H. Laidler, Can. J . Chem., 54, 1107 (1956). (13) E.R. Nightingale, Jr., t o be published.
(97
(5) G. Constaharis and G. U. Halsey, Jr., J . Cliem. P h y s . , 2'7, 1433 (1957). ( 6 ) R. €1. Fowler and E. A. Guggenheim, "Statistical Thermodynatnics," T h e University Press, Cambridge, 19.19. (7) J. 0.Hirschfclder, C. F. Crtrtiss and R . B. Bird, "Molecular Theory of Gases and Liquids," John Wiley and Sons, Inc., New York, N . Y.. 1954. (8) W.C. DehIarcus, E. H. Hopper and A. M. Allen, A.E.C. Bulletin Ii1222 (1955). (9) B4. P. Freeman, THIs JOURNAL, 62, 723 (1958 I
