ALESSANDRO D’APRANO
3290
Acknowbdgment. The support of the rational Science Foundation (GP-6688X) and the Robert Welch Foundation is gratefully acknowledged. We also thank A h . John Somerville for constructing the esr cell
and Mr. Vincent Puglisi and Professor James R. Bolton for helpful advice and suggestions. The esr spectrometer was purchased under a grant from the National Science Foundation (GP-2090).
The Conductance and Association Behavior of Alkali Perchlorates in Water at 25’1 by Alessandro D’Aprano Institute o j Physical Chemistry, University o j Palerrno, Palermo, Italy
(Received June 89, 1970)
Publication costs borne completely by The Journal of Physical Chemistry
The conductance of the alkali perchlorates at 25” has been measured in water in a concentration range up to 0.06 M and the experimental values analyzed by a revised Hsia-Fuoss (1967) conductance equation. Association increases with atomic number; it is negligible for lithium and marginal for sodium. For the other ) 1.7. three alkali perchlorates, pair association constants are KA(K) = 1.0, KA(Rb) = 1.35, and K ~ ( c s =
Introduction Most previous work on the association of 1 : 1 electrolytes by conductometric methods was carried out in solvents or solvent mixtures in the range of dielectric constants below 30. In solvents of higher dielectric constant, and especially in water, association is slight and determination of the association constants is therefore difficult. The first estimate for 1:1 salts in water was made by Davies2 who used the Onsager limiting coefficient plus an empirical term to estimate the conductance hi of the free ions and then calculated the fraction y of free ions as A(obsd)/Ai. Based on his “rather tentative values,” he concluded that “salts containing a common anion fall, in strength, in the following order: Li > Na > K > R b > Cs > Tl.” More recently, a theoretical derivation3z4of the higher terms in the conductance function has been made, which permits a direct calculation of y from conductance data. This method has been applied to data on the alkali halides in water6I8 and to salts in mixtures of high dielectric Previous conductometric measurements for alkali metal salts in dioxane-water,l0,l1 in ethanol-water12 mixtures, and in various hydrogen bonded ~ o l v e n t s have shown that in contrast with direct coulombic interactions, the association of these salts increases as the crystallographic radii of the cations increase. The association sequence found, namely Li < Na < K < R b < Cs, has been explained by assuming that in hydrogenbonded solvents, the alkali metal cations are extensively The Journal of Physical Chemistry, Vol. 76,N o . g l , I971
solvated. The same behavior has been postulated by Kay15 for the association of alkali halides and perchlorates in aqueous solutions. In order to test this assumption experimentally, the conductance of the alkali perchlorates has been measured in water in a concentration range up to 0.06 M , corresponding to the upper limit of applicability of the present theory. Three of the perchlorates (lithium, sodium, and potassium) have already been rneasured,l6 the curve for potassium perchlorates lies on the limiting (1) Grateful acknowledgment is made to the “Consiglio Nazionale delle Richerche” for support of this research. (2) C. W. Davies, Trans. Faraday SOC.,23, 351 (1927). (3) R. M.Fuoss and L. Onsager, J . Phys. Chem., 61, 668 (1957). (4) R. &I. Fuoss and K. L. Hsia, Proc. Nat. Acad. Sei. U . S.,57, 1550 (1967); 58, 1818 (1967). (6) K. L. Hsia and R. M. Fuoss, J . Amer. Chem. Soc., 90, 3055 (1968). (6) Y. C. Chiu and R. M. Fuoss, J . Phys. Chem., 72, 4123 (1968). (7) A. D’Aprano and R. M. Fuoss, ibid., 72, 4710 (1968). (8) A. D’Aprano and R. M. Fuoss, J . Amer. Chem. SOC.,91, 211 (1969). (9) A. D’Aprano and R. M. Fuoss, ibid., 91, 279 (1969). (10) T . L. Fabry and R. M. Fuoss, J . Phys. Chem., 68, 971 (1964). (11) F, Accascina, A. D’Aprano, and R. Triolo, ibid., 71, 3469 ~(1967). ~~~~ (12) R. L. Hawes and R . L. Kay, ibid., 69, 2420 (1965). (13) R . L. Kay, J . Amer. Chem. SOC.,82, 2099 (1960). (14) G. B. Porfitt and A. L. Smith, Trans. Faraday SOC., 59, 257 (1963). (15) R. L. Kay in “Electrolytes,” B. Pesce, Ed., Pergamon Press, New York, N . Y., 1962, p 119. (16) J. H . Jones, J . Amer. Chem. SOC.,67, 855 (1945).
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CONDUCTANCE AND ASSOCIATION BEHAVIOR OF ALKALIPERCHLORATES tangent up to c = 0.015, while the curves for lithium and sodium perchlorates are visibly curving upward from the tangent a t c = 0.005. This result shows that the potassium salt is relatively more associated than the other two; using Davies’ method,zestimated a dissociation constant of 3.0 for potassium perchlorate, which corresponds to an association constant K A = 0.3. I n order to complete the series of the alkalis, we have measured the conductance of rubidium and cesium perchlorates in water at 25” and also redetermined the conductances of the perchlorates of the first three alkalis. For the latter, our values for limiting conductance agree with those of Jones within 0.1 A unit. Association for lithium perchlorate up to 0.06 N is too slight to detect; for sodium, it is marginal. For the other three, the sequence K A = 1.0, 1.35,1.7 was found, corresponding to increasing association with increasing atomic numbers, K < R b < Cs. Experimental Section The electrical apparatus and the technique used for the conductivity measurements have been described in a previous paper.18 The erlenmeyer-type cell (IC = 7.0897 cm-l) was calibratedlgusing aqueous potassium chloride solutions. The water ( K ~= 1-2 X ohm-l cm-I) was purified as previously described.20 All the perchlorates (Commercial reagent grade products) were recrystallized four to six times from water-methanol mixtures (1: 1by volume) and dried at 150” in a vacuum oven. The dried salts were kept in a desiccator containing PZOS. Conductance runs were made by the concentration method. All the solutions were prepared by weight and corrected to vacuum conditions. The densities of the solutions were assumed to follow the relationship d = do (1 y)where w is the electrolyte concentration in equivalents per 1000 g of solution. The constant y was 0.0625 for LiC104,0.0770 for NaC104,0.0866 for KC104, 0.0989 for RbClO4, and 0.0998 for CsC104. The experimental results for alkali perchlorates in water at 25” are summarized in Table IZ1where cis the volume concentration (equiv/l.) and A is the equivalent conductance. A dielectric constant of 78.35 and a viscosity of 0.8903 CPwere used for water at 25”.
+
Discussion The experimental data were analyzed by a computer using the conductance equation A = y[Ao(l
+ Ax/x) - A&]
(1)
where y is the ratio of free ion concentration to the stoichiometric one. The above equation is a revised version of the HsiaFuoss (1967) conductance equation4 with the following main changes. (1) The relaxation term Ax/x is the Hsia-Fuoss4 function in which the variable KQ is replaced by r = P K / ~P, = ez/DkT; this changezzcor-
responds to using the Bjerrum radius p/2 as the lower limit in the integration instead of the contact distance Q. (2) The association constant KA
= (1
- T)/c’)’?fz
is given by the relation
K A = (4aNfi3/6000)F(b)
b
=
P/Q
which contains the function
+ (l/b)] + 2.435
P(b) = EP(b) - (eb/b)[l
(2)
derived in 1961 by Fuoss and Onsagerz3and replaces the 1958 equationz4
K A = (47rNa3/3000)eb If the data lead to a very small (or slightly negative value!) for the association constant, it is assumed that association is negligible and that K A may be set equal to zero. The Q parameter can in this case not be evaluated, if the Justice modification of the Fuoss-Hsia equation is used. (3) Activity coefficients are computed by3& -1nf
= r/(1
+
7)
instead of Debye-Huckel limiting equation. (4) The electrophoresis term Ab,, formerly approximated4 by AA
=
+
[p~c”’/(l -k ~a)](l AX/%)
has been replaced by =
[Poc’”/(~
+ r)IF(r)
where F ( 7 ) explicitly gives the effect of interaction between relaxation and velocity fields instead of approximating it by multiplying the limit value & c ” ~ by (1 Az/x). Its principal effect is to introduce a previously missed term [-&c In c ] in the electrophoresis.26 ( 5 ) The volume term in volume fraction has been omitted. The revised conductance eq 1 has been programmed for the electronic computer to find the conductometric parameters (Ao, K A , and d). The program is a twoparameter search; given a set of data (cj, Ai), dielectric constant, viscosity, and temperature, it finds the values
+
(17) C. B. Monk, J . Amer. Chern. Hoc., 70,3281 (1948). (18) F. Acoascina, A. D’Aprano, and R. M. Fuoss, ibid., 81, 1058 (1959). (19) J. E. Lind, Jr., J. J. Zwolenick, and R. M. Fuoss, (bid., 81, 1557 (1959). (20) A. D’Aprano, Ric. Sci., 34(7), 433 (1964) (21) Table I will appear immediately following this article in the microfilm edition of this volume of the journal. Single copies may be obtained from the Reprint Department, ACS Publications, 1155 Sixteenth Street, N. W., Washington, D. C. 20036. Remit $3.00 for photocopy or $2.00 for microfiche. (22) J. C. Justice, J . Chim. Phys. Physicochem. Biol., 65, 353 (1968). (23) (a) R. M. Fuoss and L. Onsager, Proc. Nut. Acad. Sci., U . S., 47, 818 (1961), eq 30 and 37; (b) J. F. Skinner and R. M. Fuoss, J . Amer. Chem. Soc., 86, 3423 (1964), eq 21, 30-36. (24) R. M. Fuoss, ibid., 80, 5059 (1958). (25) P. C. Carman, J . Phgs. Chem., 74, 1653 (1970). The Journal of Physical Chemistry, Vol. 76, No. $1, 1971
ALESSANDRO D’APRANO
3292 Table 11: Derived Conductance Parameter for Alkali Perchlorates in Water a t 25“ Eleotrolytes
Runs
AQ
KA
1
105.9 f 0 . 2 105.9 h 0 . 2 105.9 f 0 . 3 117.3 * 0 . 2 117.3 2 ~ 0 . 3 117.3 + 0 . 4 140.71 2C 0 . 0 9 140.74 f 0.05 140.73 4E 0.13 144.202C0.09 144.214E0.05 144.21 4 0.10 144.5 f 0 . 2 144.55 3= 0.09 144.5 4 0 . 2
(-0.05 f 0.07) (-0.09 f 0.12) (-0.074E0.14) (0.19 f 0.07) (0.19 s’c 0.09) (0.20 4E 0 . 1 4 ) 0.98 i 0.03 0.99 4E 0 . 0 1 0.04 0.98 1 . 3 5 =t0 . 0 3 1 . 3 5 + 0.02 1.35 4 0.03 1.68 f 0.09 1.69 i 0.09 1.69 i 0.09
LiC104
2 1i-2 3 4 3+4 5 6 5+6 7 8
NaC104
KC104
RbClOa
7+8 CsClOa
9 10 9 + 10
of A 0 and K A which minimize the sum of the squares of the differences between observed values of A and those calculated by eq 1. Then b is obtained by solving the inverse of (2) and the contact distance is given by a = P/b. All calculations were made on an Univac 1108 computer. The results are summarized in Table I1 where A, is the limiting conductance, K A the association constant, d the center to center contact distance, and u the standard deviation.
result is in agreement with the value Ao(clor-)= 67.25, previously found by Goffredi.ZE Considering the experimental difficulties encountered with the hygroscopic perchlorates the results are better than expected. As shown in Table 11, all the perchlorates considered, except lithium perchlorate with a negative K A , are slightly associated in water; cesium perchlorate, in ~
~~
Table 111: Limiting Electrolyte and Ion Conductance in Water a t 25’ Electrolytes
AO
LiC104 NaClOa KC104 RbClOi csc104
105.9 117,3 140 7 144.2 144.5 I
A0
+
38. 7a 50. la 73.5” 77. Ob 77.3a
AO-
67.2 67.2 67.2 67.2 67.2
a Data are from It. A. Robinson and R. H. Stokes, ‘‘Electrolyte Solution,” Academic Press, New York, N. Y., 1959, p 463. (b) Voisinet’s corrected value, R. W. Kunze, R. M. FUOSS, and B. B. Owen, J. P h y ~ Chem., . 67, 1719 (1963). ~~
~
The Journal of Physical Chemistry, Vol, 75, N o . $1, 1971
I
*
0.03 0.05
0.04 0.03 3.32 3.31 3.31 2.69 2.69 2.69 2.28 2.27 2.28
0.03 0.04 0.008 0.005 0 * 009 0.009 0.005 0.007 0.03 0.01 0.02
spite of its largest cation size, is more associated than the other perchlorates. This result is fully consistent with the order postulated by Kay.16 Regarding the negative K A value found for LiC104: this result must be considered as merely curve-fitting without any physical significance. In fact, if we put the conductance equation in the form
EClog c
+ J~c’” - ( J + BAo - K&)c
and the computer will calculate ( B - K A )as K A and if B > KA, the resulting K A will be a negative quantity. The dilemma of a negative K A value is until now another shortcoming of the present theory and calls for a more detailed treatment including the modification of solvent structure by the ions, Since a negative number obviously can never be an association constant, at this stage it is only possible to conclude that the association of lithium perchlorate is nearly zero in water at 25’. Furthermore it must be assumed that the unknown positive terms are also present for salts which give positive K values and that the association constants for these salts are actually higher than the values obtained from the present analysis. It must be recognized, therefore, that the probability of eventually revising the (26)
M.Goffredi and R . Triolo, Ric. Sci., 37, 1137 (1967).
TRACER AND MUTUAL DIFFUBIVITIES IN CHLOROFORM-CARBON TETRACHLORIDE current values, once it will be known which kind of corrections to make. I n any case, independently of this revision, the association sequence found in the present work for the alkali perchlorates can be explained by taking into account the effect of solvation on ion pairing.11r27-29 If we consider, in fact, the extreme alkali perchlorates, the following considerations may be made. Sodium, as well as lithium ions, on account of their small radii and high charge densities, strongly orientate the water molecules. Due to the sheath of solvent molecules around the ions, ion pairing almost should not occur for them. The largest cesium cation, on the other hand, is almost un-
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able to orientate the water molecules and must be considered as a bare ion in aqueous solution. Cesium perchlorate should be, therefore, much more associated in water than the other alkali perchlorates.
Acknowledgment. The author wishes to acknowledge the valuable aid of Professor R. M. Fuoss in the present research. (27) A.D’Aprano and R. M. Fuoss, J . Phys. Chem., 67, 1704, 1877 (1963). (28) W.R. Gilkerson and E. Eaell, J . Amer. Chem. Soc., 87, 3812 (1965); 88,3484 (1966). (29) H. K. Bodenseh and J. B. Ramsey, J . Phys. Chem., 69, 543 (1965).
Tracer and Mutual Diffusivities in the System Chloroform-Carbon Tetrachloride at 25 by
O
C. M. Kelly,*l G. B. Wirth, and D. K. Anderson
Department of Chemical Engineering, Michigan State University, East Lansing, Michigan (Received November 12, 1970)
48883
Publication costs borne completely by The Journal of Physical Chemistry
Experimental measurements were made of tracer diffusivities, mutual diffusivities, viscosities, and densities at 25’ in the binary liquid system chloroform-carbon tetrachloride. The diffusivities are compared with those predicted by the Hartley-Crank equation for nonideal nonassociated liquid systems. The thermodynamic correction factor in the Hartley-Crank equation undercorrects the mutual diffusivity data. This undercorrection is an unusual result. Introduction and Theory A comprehensive model of diffusion must be able to predict both mutual and tracer diffusivities. It should be able to correlate diffusion coefficients to molecular size and shape, to intermolecular interactions, and to temperature and pressure. It must also describe the relationship between tracer and mutual diffusivities. One moderately successful model is the hydrodynamic model, which treats a diffusing molecule as a particle flowing through a continuous medium. I n its earliest form, as set forth by Sutherland2and E i n ~ t e i nit, ~considers the diffusing molecule as a sphere and predicts the diffusivity as a function of temperature, viscosity, and molecular radius. This has been a fairly good approximation for large molecules in dilute solutions. More recent developments of the hydrodynamic model have differentiated between mutual and tracer diffusion and have included the effectsof intermolecular associations, molecular size and shape (as distinct from molecular radius) , and solution nonideality.
It has been shown4 that according to the hydrodynamic model the tracer diffusivity of a component which is not associated in solution should be given by Di*= RT vat
(1)
where T is the temperature, v is the viscosity of the solution, R is the gas law constant, and ut is the “friction coefficient” of the component, assumed constant. The mutual diffusivity in such a system is related to the tracer diffusivities of the components by (2) (1) To whom correspondence should be addressed at Department of Chemical Engineering, Villanova University, Villanova, Pa. (2) W. Sutherland, Phil. Mag., 9, 784 (1905). (3) A. Einstein, Ann. Phgs. Chem., 17, 549 (1905). (4) L. S. Darken, Trans. Faraday SOC.,45, 801 (1949). The Journal of Physical Chemistry, Vol. 76, No. 81, 1971
