Oct., 1959
VISCOSITYOF AQUEOUSSODIUM FLUORIDE SOLUTION
0.1% total impurities. Moreover, the Pu:C1 ratio of the filtered PuC4 was in excellent agreement with the theoretical value. The melting point of NaCl agreed, within experimental error, with the values 800.4, 801 and 804’ reported in several recent reference^.^-^ A considerable amount of time was devoted to the determination of the melting point of LiCl because of the wide variation in the values reported in the literature. The melting points most commonly quoted, 61307J and 614°,6,8s10apparently are based on some of the work published between 1910 and 1925.l’ Numerous other values ranging from 600-609° were also reported11~12during (6) N. A. Lange. “Handbook of Chemistry,” 9th ed., Handbook Publishers, Inc., Sandrisky, Ohio, 1956. (7) “Handbook of Chemistry and Physics,” 40th ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1958. (8) 0. Kubaschewski and E. L. Evans, “lMetallurgica1 Thermochemistry,” John Wiley and Sons, Inc., New York, N. Y., 1956. (9) G. W. C. Kaye and T. H. Laby, “Tables of Physical and Chemir!al Constants,” 11th ed., Longmans, Green and Co., New York, N. Y., 1956. (IO) K. K. Kelley, Bull. U. S. Bur. Mines, No. 393, 1936. (11) R. J. Meyer, “Gmelins Handbuch der Anorganischen Chemie,” 8th ed., Vol. 20, Verlag Chemie, Berlin, Germany, 1027. (12) E. 11. Levin, H.F. McMurdieand B. P. Hal1,“Phase Diagrams for Ceramists,” The American Ceramio Society, Columbus, Ohio, 1956.
1777
this same period. More recent r n e a s ~ r e m e n t s ’ ~ - ~ ~ The value consistently range from 603-610’. obtained for all samples of LiCl prepared in the present work was 607’. It was not affected by changing the rate of stirring, the rate of cooling over the range O.P3’/min., or by changing the container from quartz to Pyrex or platinum. The melting point of LiCl under vacuum was the same as that of LiCl in equilibrium with an atmosphere of either dry argon or HC1. It is estimated that a freezing point depression of 6’ (from 613 to 607’) would require a t least 2 wt. yoof an impurity such as NaC1. In view of the analytical data in Table I, it is highly unlikely that such a concentration of impurities could have been present in the LiCl used in this work. Acknowledgments.-The authors are indebted to W. J. Maraman of this Laboratory for many productive discussions and to the members of the analytical group under the direction of C. F. Metz for the analytical data. (13) E. Elchardus and P. Laffitte, BulE. I O C . chirn., 61, 1572 (1932). (14) A. S. Botschwar, 2. anorg. allgem. Chem., SlO, 163 (1933). (15) Metalloy Corp. Minneapolis, Minn., 1944; cf. 12, p. 242. (16) G. A. Bukhalova and A. G. Bergman, Doklady Akad. Nauk, S.S.S.R., 66, 69 (1949). (17) G. Munzhskov, Doklady Akad. Naub, 87, 791 (1952).
VISCOSITY OF AQUEOUS SODIUM FLUORIDE AND SODIUM PERIODATE SOLUTIONS. IONIC ENERGIES AND ENTROPIES OF ACTIVATION FOR VISCOUS FLOW BYE. R. NIGHTINGALE, JR.,AND R. F. BENCK Department of Chemistry, University of Nebraska, Lincoln 8 , Nebraska Received April $8, I969
The viscosities of aqueous sodium fluoride and sodium periodate solutions have been measured in the concentration range 0.0005 to 1 molar. The viscosity data have been interpreted in terms of the Jones-Dole equation for strong electrolytes. Using this relation, the viscosity B-coefficients for the fluoride and periodate ions at 25” are calculated to be +0.0965 and -0.0647, respectively. The energies and entropies of activation for viscous flow at 25” have been calculated for a number of ionic species. Large ions such as Ba+2, ‘103and S01-2, which exhibit a minimal hydration for their reapective charge types, are observed to decrease the activation energy for viscous flow in the solution from that for the pure solvent even t’hough the ion itself increases the bulk viscosity of the solution. The influence of such ions upon the water structure is discussed. Experimental evidence for tshehydration of the 1 0 3 - ion is cited.
Accusate viscosity data for aqueous sodium fluoride solutions and sodium periodate solutions are not available in the literature. The viscosity B-coefficients from the Jones-Dole equation for the viscosity of strong electrolytes have not been reported for any of the fluoride or periodate salts. In conjunction with recent studies in these laboratories concerning the nature and relative sizes of hydrated ions,’ the viscosities of sodium fluoride and sodium periodate solutions have been measured at 25’ in the concentration range 0.0005 to 1 M . These data are interpreted in terms of the Jones-Dole equation, and the viscosity B-coefficients have been determined for the fluoride and periodate ions. The influence of strong electrolytes upon the viscosity of the solvent is interpreted as a rate process, and the energies and entropies of activation for viscous flow have been ( 1 ) E. R . Nightingale, Jr., THISJOURN~L, 63, 1381 (1959).
calculated for a number of salts. From these data the influence of the individual ions upon the energy and entropy of activation for viscous flow has been estimated. The nature of the ion-solvent interaction is considered, and it is demonstrated that for a given charge type, those ions which exhibit a minimal hydration a t 25” may decrease the activation energy for viscous flow in the solution even though the ion itself is sufficiently large to increase the viscosity of the solution over that of the pure solvent. Experimental Reagent grade sodium fluoride and sodium metaperiodate were each purified by twice recrystalling the salts from conductivity water. After recrystallization, the salts were dried at 110” for four hours. The salt solutjons were prepared on the molal basis by dissolving weighed quantities of salt into weighed volumes of conductitrity water. The densities of the eolutions were measured a t 25.00 f 0.05’ using
1778
E. R. NIGHTINGALE, JR.,AND R. F. BENCK
Vol. 63
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 0.02' using an Ostwald viscometer with a flow time of 170 seconds for water. Flow times were measured to 0.01 sec. with a calibrated stopwatch. The average deviation for six to ten measurements of a single sample of a solution did not exceed 0.03 sec. The average flow times for replicate samples of a single solution agreed within f 0.04 sec. The viscometer was calibrated with water a t 20, 25 and 3O0, and a t 25" with 20 and 30% sucrose solutions by means of equation l g l p = Kt - L/t (1) where 7 is the absolute viscosity, p is the density, and t is the flow time of the calibrating solution. The characteristic viscometer constants IC and L were 0.00005251 and 0.00011, resgectively. The absolute viscosities of water a t 20, 25 and 30 , and of the 20 and 30% sucrose solutions were taken as 0.01002, 0.008903, 0.007976a and 0.01701 and 0.027418 poise, respectively. The densities of the solutions were taken as0.99823,0.99707,0.995684and 1.07940and 1.125173 g./ml., respectively.
theoretical value of 0.00718 calculated according to the theory of Falkenhagen and V e r n ~ n . ~The B-coefficient is observed to be 0.0216. Taking the value for the B-coefficient for the sodium ion to be +0.0863,8 we calculate -0.0647 as the magnitude of the B-coefficient for the periodate ion a t 25". The periodate ion is similar in size t o the perchlorate ion, a,nd its behavior in disrupting the local structure of water in the cosphere about the ion and increasing the fluidity of the solution is identical with that of the perchlorate ion.9 The absolute viscosities for ten sodium fluoride solutions in the concentration range 0.0005 to 1 M are given in Table 11. The fluoride ion is the conjugate base of a moderately weak acid, and the p H of these solutions increases with concentration. The effect of hydrolysis upon the viscosity of the solution is negligibly small, however, and (V/VO - l ) / d c is linear in in the concentration Results range zero to 0.1 M. The experimental value for the The viscosities of the salt solutions were com- A-coefficient for this salt is 0.0073 a t 25' as computed by means of equation 1. The relative and pared with the theoretical value of 0.0071. At 20 absolute viscosities a t 25" for eight sodium perio- and 30°, the experimental values do not differ date solutions in the concentration range 0.0005 significantly from the calculated ones, 0.0078 to 0.1 M are presenbed in TabIe I. The data have and 0.0070, respectively. The B-coefKcients at been analyzed using the Jones-Dole equations TABLE I1 v/va = 1 A V T BC (2) ABSOLUTEVISCOSITIESOF AQUEOUSSODIUMFLUORIDE where V / V O is the viscosity of the salt solution SOLUTIONS AT 20, 25 AND 30" relative to that of the solvent, water, C is the molar -Absolute viscosity. poise-----m, 200 25' 30' moles/1000 g. concentration, and A and B are constants char0.008906 0.000568 acteristic of the electrolyte. The A-coefficient 1* 0020 .008907 0.007992 .001030 represents the contribution from interionic electro.008913 .003686 static forces.6 The B-coefficient measures the 1.0060 .008926 .008037 .01022 order or disorder introduced by the ions into the .008939 .01696 solvent structure; this constant is a specific and 1.0113 .008971 .008069 .03436 approximately additive property of the ions of a .009020 .06228 strong electrolyte at a given temperature,' al1.025 .009086 .008153 .lo14 though no satisfactory theoretical treatment has .009701 .4103 yet been given.
*
*
+
+
TABLE I RELATIVEAND ABSOLUTE VISCOSITIES OF AQUEOUS SODIUM PERIODATE SOLUTIONS AT 25' C. moles/l. dm q1 poise 0.000506 I . 00017 0.0089045 .000997 1.0002 .008905 ,003906 1.0004 ,008907 I.0010 .008912 .01007 .01712 1.0013 .008915 .03527 1.0021 .008922 .06181 1.0031 ,008931 1.0044 .008942 .09680
l)/v'c
Plotting (q/v0 vs..\/c, the A-coefficient is:the ordinate intercept, and the B-coefficient given by the slope of the resulting straight line. The experimental value for the A-coefficient for sodium periodate of 0.0072 compares well with the (2) J. R. Coe and T. 8.Godfrey, J. Applied Phys., 15, 625 (1944). (3) E.C. Bingliam and R . F. Jackson, Bull. U . S. Bur.Standarda, 14,
.9622
.010776
20, 25 and 30" are f0.224, 0.1828 and 0.141, respectively. Assuming that the B-coefficient for the sodium ion is +0.0863 and independent of temperature in this range: we calculate f0.138, 0.0965 and 0.055 as the magnitude of the B-coefficient for the fluoride ion at 20, 25 and 30°, respectively. The fluoride ion strongly orders the solvent in the cosphere about the ion. With increasing temperature, the solvent ordering is perturbed by the increase in the thermal energy, and the B-coefficient for the fluoride ion decreases in proportion to the increase in the entropy of hydration. Discussion The interpretation of viscous flow according to the theory of' absolute reaction rates has been presented by Eyring and co-workers.1° The energy of activation for viscous flow AE* is given by (3)
59 (1918).
(4) L. W. Tilton and J. K. Taylor, J. Research Natl. Bur. Standards, 18,205 (1937). ( 5 ) G . Jones and M. Dole, J . A m . Chem. Soc., 61, 2950 (1929). (6) H. Falkenhagen and E. L. Vernon, Physik. Z., 33, 140 (1933). (7) W. M. Coxand J. H. Wolfenden, Proc. Roy. S O C(London), . Al45, 475 (1934).
( 8 ) RI. Kaminsky, Disc. Faraday Soc., 24, 171 (1957). JOURNAL, 63, 742 (1959). (9) E. R. Nightingale, Jr., THIS (10) S. Classtone, K. J. Laidler and H. Eyring, "The Theory of
Rate Processes," MoGraw-Hill Book Co.,
New York, N. Y.. 1941.
VISCOSITY OF AQUEOUS SODIUMFLUORIDE SOLUTION
Oct., 1959
For associated liquids, the plot of In 9 vs 1/T is not linear, and the energy of activation varies with temperature. The influence of a strong electrolyte upon the viscosity of a solvent may likewise be interpreted as a rate process. Substituting equat ion 2 into 3
TABLE 111 FREEENERGY, ENERGY AND ENTROPY OF ACTIVATION FOR VISCOUS FLOWAT 25' ( C = 1 MOLE/L.) Salt
For solutions that are not too dilute (ca. 1 M ) , the contribution of the interionic electrostatic forces to the viscosity of the solution is negligibly small (except for the fortuitous case where B is identically equal to zero), and equation 4 may be rewritten as This expression is equivalent to adopting the Bingham relation" for moderately concentrated solutions in place of the Jones-Dole equation. I n a similar manner, the free energy of activation for viscous flow is given bylo AF* = RT in
where h is the Planck constant and N is the Avogadro number. V may be regarded as the volume of one mole of solution particles and is given by (7)
where v is the number of species into which a solute molecule dissociates and n2is the number of moles of solute per liter of solution. The number of moles of solvent, nl,per liter of solution is given by
a
Water LiCl NaCl NHdC1 KCl RbCl CSCl BeClz MgCh FeCh BaC12 CeCh NaF NaCl NaI NaNOs NaIO3 NaC103 NaOH Nasi304 Estimated.
A S * = (AE'
- AF*)/T
(9)
Table I11 evaluates the free energy, energy and entropy of actviation for viscous flow at 25" for one molar solutions of a number of salts whose E-coefficients are available in the literature.8J2 The activation free energy for these solutions is essentially constant and exhibits only a slight increase for solutions of multivalent ions over that of the pure solvent. The abnormally large energies and entropies of activation are characteristic of associated liquids and are attributed to the excess energy necessary to break the hydrogen bonds in the solutions.1° It is observed that the energy and entropy of activation for viscous flow are, with two exceptions, decreased as compared with the respective values for water. This usually is considered to be the general behavior for dilute aqueous salt solutions and interpreted energetically as evidence for a decrease in the hydrogen bonding in the solution. However, this behavior is directly a consequence of (11) E. C. Bingham, THIBJOURNAL, 46, 885 (1941). (12) R. W. Gurney, "Ionic Processes in Solution," MoGraw-Hill Book Co., New York, N. Y.,1953.
AF*, kcal.
AE*, kcal.
A S t , e.u.
2.19 2.26 2.20 2.19 2.18 2.17 2.17 2.40" 2.36 2.35" 2.30 2.45 2.28 2.20 2.20 2.21 2.22 2.23 2.29 2.37
4.01 4.00 3.81 3.69 3.56 3.30 3.36 4.27 3.99 3.06 3.10 3.74 5.27 3.81 3.67 3.79 3.75 3.70 3.79 3.77
6.1 5.8 5.4 5.0 4.6 3.8 4.0 6.3 5.5 5.4 2.7 4.3 10.0 5.4 4.9 5.3 5.2 4.9 5.0 4.7
the salts considered, primarily the alkali halides and should not be generalized. For this reason, it is of interest to consider the role of the individual ions rather than of the salt itself in influencing the viscosity of the solvent. For this purpose, we assume that the diflerence between the activation energy of the solution and the solvent is equal to the sum of the activation energies for the ionic components, and we write AE*
where M I and M2 are the molecular weights of the solvent and solute, respectively. Assuming that the activation enthalpy does not differ appreciably from the activation energy, the entropy of activation AS* may also be calculated as
1779
-
AEoS = v + A E + *
+
Y-
AE-*
(10)
where AE+* and AE-+ are the cation and anion activation energies, Y+ and v- are the number of cations and anions, respectively, per molecule of salt, and A&*, the activation energy for pure water, is identified as R d In vo/d(l/T) in equation 5. We further assume, in a manner similar to that for the evaluation of the ionic B-coefficients18 that the influence of the potassium ion upon the activation energy for viscous flow in the solution is approximately equal to that for the chloride ion. A previous discussion' has demonstrated that this is a satisfactory but not necessarily rigorous approximation. Using equation 10 and a similar expression for the ionic entropy of activation, Table IV presents the energies and entropies of activation calculated for a number of ions. These data indicate that the Li+, Na +, Be+2, Mg+2, Fe+2, Ce+S and F- ions increase the activation energy, while the remaining ions decrease the activation energy. These results may be correhted qualitatively with the order-producing properties of the ions at 25': order producing ions with positive Bcoefficients have positive activation energies, while order destroying ions .with negative E-coefficients have negative activation energies. For ions of small size and/or large charge, the surface charge density is sufficiently large to orient the water molecules immediately adjacent t o the ion more firmly than in the bulk solvent and increase the activation energy for viscous flow. Large ions
1780
E. R. NIGHTINGALE, JR., AND R. F. BENCK
Vol. 63
with weak electric fields collapse the normal water structure about the ion and increase the fluidity of the solvent molecules over that in bulk water.
increasing temperature must be less than that of the pure solvent, and the relative viscosity and hence the B-coefficient, increases with temperature. The recent discussion of negative hydration TABLE IV by Samoilov16 suggests, however, that this explaIONIC ENERGY AND ENTROPY OF ACTIVATION FOR VISCOUS nation is inadequate and that the ion-solvent interFLOWAT 25' ( C = 1 MOLE/L.) actions must also be considered for ions with Ion AE*, cal. AS*, e.u. negative B-coefficients. Li +210 +0.45 The behavior of the sulfate ion is similar to that Na+ 20 +0.05 of the barium ion except that, by virtue of its larger NHa - 100 -0.4 crystal radius and smaller surface charge density, K+ - 220 -0.75 the extent of its hydration a t 25" is considerably Rb -490 -1.55 less than for the barium ion. Nevertheless, the Cs - 430 -1.35 sulfate ion orders the solvent about the ion and Be f2 +700 +1.7 evidences a positive viscosity increment. Mg +2 +420 +0.9 The behavior of the iodate ion is more complex. Fe + 2 +390 +0.8 Traditionally the iodate ion has been considered to Bs + 2 -470 -1.9 be unhydrated, and in comparison with the Ce f a +390 $0.45 chlorate and bromate ions, the positive B-coefficient F+1240 $3.85 of the iodate ion appears to result solely from the inc1- 220 -0.75 creased size of the ion. However, since the posiNOS-240 -0.85 tive values of dB/dT for ions with positive B10s -290 -0.95 coefficients are interpreted to indicate a n increase clod -340 -1.25 in ion-solvent interaction, some degree of hyI-370 -1.25 dration must therefore be recognized at 25". OH - 240 -1.15 Further evidence for this hydration is obtained by sod-1 -280 -1.5 comparing the limiting equivalent conductances However, four ions in Table IV, Ba+2, IO3-, and the viscosity B-coefficients for the iodate and and OH-, exhibit the apparently anomalous periodate ions. At 25", Xo = 41.5 and 54.5, and relation of positive B-coefficients and negative B = +0.140 and -0.065 for the iodate and perioactivation energies. From equation 5, it is seen date ions, respectively. Both the conductance and that the sign of LIE*is opposite to that for dB/dT. viscosity parameters indicate the presence of some Hence the relation of the Ba+2, IO3- and S04-2 interaction between the iodate ion and water which ions may be explained by determining the condi- is present to a much lesser degree, or not a.t all, tions under which the positive B-coefficients may be with the periodate ion. This effect cannot be accompanied by positive values for dB/dT. explained solely on the basis of ion size, for the The extent of hydration of an ioni3 is a function crystal radius of the iodate ion is larger than that of the ionic charge, size and structure, and com- for the periodate ion. It appears that the lack parisons between ions are valid only for a given of appreciable interaction between the periodate classification of charge and structure. A previous and water stems from the double bond character discussion has presented a set of effective hydrated present in the periodates. Both the meta- and radii for solvated ions in waterel Referring to paraperiodate ions possess an appreciable amount Table I in that discussion, it may be noted that the of double bond character in the 1-0 bonds16J Ba+2, IO3- and S04-2 ions are those species, which which can prevent delocalization of the cbarge on in their respective classes, have the larger crystal the iodine atom and lessen to a considerable extent radius and smaller difference between the effective the amount of bonding that otherwise might be hydrated radius and the crystal radius, and which expected between the oxygen atoms and water. therefore are minimally hydrated a t 25". As the I n this respect, the periodate ion compares not untemperature is increased, the normal ordering of favorably with the tetramethylammonium ion in the water structure is destroyed, and the water which the charge is localized on the nitrogen atom. molecules are more susceptible to orientation in The B-coefficients for these latter two ions are not the relatively weak electric field about, for example, comparable, however, because of the difference in the barium ion. It should be noted that this be- their crystal radii. I n the iodate ion, on the other havior is not directly comparable with that pro- hand, the double bond character is much less posed by Kaminskys to explain the positive dB/dT pronounced (ca. 20%) than that in the periodate values accompanying negative B-coefhients. Ka- ion, and the charge is more effectively delocalized minsky's explanation for positive dB/dT values is by the oxygen atoms permitting more extensive that due to Cox and Wolfenden'*: since the fluidity interaction with the solvent. In addition, the of the solvent immediately surrounding order de- unshared electron pair on the iodine atom may itstroying ions is greater than that of the bulk sol(15) 0. Ya. Samoilov, Disc. Faraday SOC.,24, 141 (1957). vent, the decrease in the solution viscosity with (16) L. Pauling, "The Nature of the Chemical Bond," Cornell Uni-
+
+
+
+
+
(13) Hydration is used in this sense to denote ion-solvent interaotions whiah restrict the translational motion of water molecules in the vicinity of the ion as compared with those in the bulk solvent. A specific microscopic model is not implied. (14) W. M. Cox and J. H. Wolfenden, Proc. Rou. Soc. ( L o n d o n ) , Al46, 486 (1934).
versity Press, Ithaca, N. Y., 2nd Ed., 1948, pp. 175, 247. (17) In neutral solution a t 26O, the metaperiodate (104-) is the predominant species. See C . E. Crouthaniel, A. RI. Hayes and D. S. Martin, J . A n . Chem. Soc., '75, 82 (1951). Using the relations of Pauling. the double bond character in the metaperiodate is calculated as approximately 90%.
