PAOLO BRUNOAND MARIODELLAMONICA
3034
ensity, 'Viscosity, and Electrical Conductance of Sodium rmamide Solutions at 25"1
by Baolo Bruno and Mario Della Monica" bstituto di Chimica Analitica dell' Urbiversitd d i Bari, Italy
(Received February 8, 1979)
fublkatwn costs assisted by the Centro Analitica Strumentale, Bari
The densities, viscosities, and electrical conductivities of concentrated solutions of NaNBa, NaC104, NaSCN, NaBr, and NaI in formamide at 25' have been measured. In the range of concentration used the densities are linear functions of the concentration and the apparent molal volumes have a constant value, very close to the molecular volumes of the salts. A three-parameter equation, originally derived from a free-volume theory of liquid transport, has been applied to the viscosity and to the conductivity of the solutions of the studied salts. For each electrolyte the plots of log A and log 7 against l/(No - Y), where N O is the glasstransition concentration at 2 5 O , were linearized by the same No value, thus enhancing the idea that the proposed model can be extended to the interpretation of transport processes in concentrated noiiaqueous solutions.
In recent years many papers on the mass transport properties in dilute solutions have appeared, but relatively little work has been published for concentrated aqueous solutionq2 and no work at all for concentrated nonaqueous solutions. The reason for this is that in dilute solution the properties of electrolytes are accurately explained by the theory of Debye and Huckel,3 ~ h i l eat ir termediate and high concentration no equally successful theory exists. The numerous equations developed in the attempt to extend the validity of the Dehye-Huckel theory t o concentrated solutions, introducing empiriaal parameters, failed because these parameters often have no physical meaning. The basic model of this theory implies that around a given ion an ionic cloud of time-average charge density is formed Wihh increasing electrolyte concentration a point 1s reached where the ionic cloud becomes so small that t'ie time average of the charge density no longer represents the effective distribution of the ions.* As a consequence, the equations derived by the DebyeHuckel theory and describing electrical conductivity, diffusion, viscosity etc., have to fail at some point, although it is not clear at what concentration this happens. The aim of this work was to investigate the transport properkes as well as the densities of sodium salts in formarnide in a concentration range where the Dehye-Huckel tlieory is expected to fail in principle. The salts selected were 1: 1 electrolytes NaC104, SaNQ3,A aGCN, XaBr, and NaI. The concentration range (-0.5 to -4.5 M ) had an upper limit given by the saturation of the solutions. Conductivity data were analyzed by the semiempirical TiVishaw-Stokes equation5 and by the recently proposed Poatler equation,6 while viscosity data were The Journal of Physical Chemistry, Val. 76, N o . 81, 1979
treated by an equation proposed by Va,nd7 which extends, at higher concentration, the Einstein limiting theory.8 The viscosity and conductivity data were also treated following a new model originally derived by the Cohen and Turnbull theoryg and the results were compared.
Experimental Section Raker Analyzed Reagent formamide was dried with molecular sieves 3A (Union Carbide) in the form of 1/16-in.pellets and deionized by means of a mixed bed of Amberlite ion-exchange resins loaded respectively with H+ and HCONH- ions.'O The formarnide obtained in this way had a specific coriductance of 2-7 X ohm-1 cm--I, but its value was continuously changing; for this reason the conduetancc of various solutions was calculated taking into account the change of specific conductance of pure forrnamide during the experiments. Sodium nitrate (reagent grade) was recrystallized (1) Thesis for Doctor of Chemistry submitted by F. Antonacci a t the Chemistry Department of Bari University. (2) J. R. Hall, B. F. Wishaw, and R. H. Stokes, J . Amer. Chem. Soc., 75, 1556 (1953); C. A. Angell, J . Phys. Chem., 70, 3988 (1966); C. T . Moynihan, ibid., 70, 3399 (1966); C, A. Angell and E. J. Sare, J . Chem. Phys., 52, 1058 (1970); 15. R. Breslau and I. I?. Miller, J . Phys. Chem., 7 4 , 1056 (1970); 6.J. Janz, B. G.Oliver, G. R. Lakshminarayanan, and G. E . Mayer, %bid.,74, 1285 (1970). (3) P. Debye and E. Hdckel, 2. Phys., 2 4 , 185 (1923). (4) H . S. Frank and P. T . Thompson, "The Structure of Electrolytic Solutions," W. J. Hamer, Ed., Wiley, New York i Y Y., 1959, p 113. (5) B. F. Wishaw and R. H . Stokes, J , Amer. Chpm. Soc., 76, 2065 (1954). (G) M. Postler, ColZe& Czech. Chem. Commun., 35, 535 (1970). (7) V. Vand, J . Phys. Chem., 5 2 , 277 (1948). (8) A. Einstein, Ann. Phys. (Leipzig),19, 289 (1906). (9) M. H . Cohen and D. Turnbull, J . Chem. Phys., 3 1 , 1164 (1959); D. Turnbull and M. 13. Cohen, ibid., 3 4 , 120 (1961). (10) J. M.Notley and M .Spiro, J . Chem. SOC.R , 362 (1966).
I~ENSITY VISCOBITP, AND ELECTRICAL CONDUCTANCE OF SODIUM SALTS
3035
~
Table 1V: Appzmnt Molal Volumes and Density Equation of Some Sodium Salts in Formamide Solutions at 25"
Beat equation
Salt
NaNQ NaCiQI
NaXCN NaBr Na1
---
--__.e
d d d d d
+ ++
1.130'7 4.326 X 1.1289 6.455 X 1.1291 2.867 X = 1.1301 -t- 6.866 X = 1.1303 $- 1.021. X
= = =
10% 10% ~O-'C
10-% 10-'C
twice from double-distilled water; sodium bromide (reagent grade) and sodium iodide (reagent grade) were recrystallized three times from double-distilled water and dried .tn vacuo over phosphoric oxide a t 110". Sodium thiocyanate (reagent grade) was recrystallized tn-ice from methyl alcohol and twice from ethanol; sodium perchlarate (reagent grade) was recrystallized twice from n-butj7l alcohol and twice from doubletiistilled water The ccnduclmxe measurements were performed with :ibridge described i n a previous note.'l I n the frequency range 1000-8000 Hz no significant polarization effect at the platirurn electrodes was found. The densities, referred to the density of water at 4", were determined t o an accuracy of 0.03% using a 30-ml pycnometer Viscosity measurements were made with Ubbelohde viscosimeters (Schott Co.) of different constants which were calibr,sted with conductivity water and aqueous solutions of glycerol. The solutions were prepared by addition of forxnamide to a stock solution of the salts. Two thermostats controlled at 25.00 f. 0.005' were employed. The thermostat used for the density and for the viscosity measurements was filled with distilled water while the thermostat used for the conductivity measurements was filled with oil. The conductivity cell employed h a d a constant of 286.67 cm'-l and was calibrated i ~ sng j a L D KC1 solution.'2 All operations were performed in a drybox filled with dry nitrogen; the weights mere corrected to vacuum. a
The densities, viscosities, and electrical conductivities a t the corrmponding concentrations have been reported in Tables I, IT, and III.I3 Density. The densities of the studied solutions vs. concentration are straight lines. By the least-squares method thl. coefficients of the straight lines with the standard deviations were calculated and the results are reported in Table T V . The apparchnt molal volume of a salt in solution is related t o ~,hcexperjrnental densities by the equation14 =
1000
--(do cdo
- d)
+ Mz
where c is the comentration in equivalents per liter, do
range
Apparent moleX volurnl73
Molecular volumes
0.44.2 0.3-4.0 0.1-5.6 0.3-3.7 0.5-4.4
36.9 51.3 46.4 30.3 42.3
37.7 49.0 46.7 32, 1 40.9
Standard deviation
Conon
0.0008 0.0003 0.0006 0.0004 0 . 0007
---
and d are the density of the solvent and the the solution, respectively, and Ill, is the molecular weight of the solute species. If, as in our cases, the densities are h e a r function of the concentration, the substitution of the function density in eq 1 gives apparent molal volumes constant and equal to @"
=
1000b M , -I-do
do
In eq 2 b represents the slope of the straight lines relating density and concentration. The apparent molal volumes of sodium salts in formamide were calculated using eq 2 and the results are reported in Table IT. The order of these volumes is ClOe- > SCX- > I- > NO3- > Br-; the same trend is found in water. In the same table are also reported the molecular volumes of the pure salts; the compnrisort shows that they are quite close to the apparent molal volumes. It is vcorth pointing out the peculiar constancy of the apparent molal volume values of the studied salts in formamide, although at the present time ~e are unable to explain this behavior. In other solvents these volumes are related t o the square root of the salt concentration by the relationship @v
=
eo -I-S,dC
(3)
where is the apparent molal volume of the salt at infinite dilution and Sv is a constant value for all the electrolytes of the same valence type. This simple equation was found by :\lla~son'~for: dilute solutions but often extends t o concentrated mater solutions, as shown by measurements of densities of NaC104, Ka(11) P. Bruno and M.Della Monica, J . Phys. Chern., to be submitted for publication. (12) G. Jones and B. C. Bradshaw, J . Amel. Chem. Soc., 5 5 , 1780 (1933). (13) Tables I, 11, arid I11 will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 1155 Sixteenth Xt., W.W., Washington, D. 6. 20036, by referring t o code cumber JPC-723034. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche. (14) H. 9. Harried and B. B. Owen, "The Physical Chemistry of Electrolytic SoluLions," 3rd ed, Reinhold, New Uork, N. Y., 1958, p 358. (15) D. 0. Masson, Phil. Mag., 8 ( 7 ) , 218 (1929). The Journal of Physical Chemistry, Vol 7 6 , h;o 21, 1912
3036
PAOLO BRUNO AND M A R I O DELLA MONICA
SCN, and NaNCh solutions as concentrated as 9 M.16 1x1 recent years various equations have been suggesi;ecl t o explain the behavior of transport processes of salts in concentrated solutions. Wishaw and Stokes!’ proposed an equation that takes into account the change of the viscosity of the solution with concentration C’onductivity.
)(I
4-
$)
(4)
In eq 4 q / r o i s the relative viscosity of the solution; the relaxation effect A X / X is given by the Falkenhagen expressionI7
AX _-
x
.z+z-e2 _-
:S€kT (I
g
4 dj)(1
Standard Deviations Calculated by a Least-Squares Method from Conductivity and Viscosity Dataa Salt
A’OA
sh
NO,
NaNOa NaC104 NaSCN NaBr NaI
50 14 19 14 14
0.01 0.01 0.01 0.03 0.01
48 12 18 14 13
a1
0.005 0.01 0.01 0.006 0.007
Eq g b
Eq qb
2
4
3 20 20
9 13 12
Maximuni approach distances deduced from eq 4 and 5 . NaC104 are not reported since in the literature the ho value of this salt is not available.
* The maximum approach distances of
K
+ Ka)
which differs from the relaxation term in the Onsager equationla by the factor (1 f Ka) in the denominator. The moderate success of eq 4 in some concentrated systems is mainly due to two factors: (a) the introduction of the q / q o term which somehow compensates the conductance of the solution for the change in viscosity and (b) the presence of the adjustable parameter a,the maximLm approach distance of the ions. However at least LWO criticisms can be made about these factors : the correction of the conductivity through the viscosity term 7 / q 0 treats the ions as spheres moving in a continuuri at a41 concentrations; the introduction of the adjustable parameter a, although affording a better fit to the experimental data, can on the other hand mask the contribution of terms not considered in eq 4.19 -4n analysis of the curves of the specific conductivity against Concentration which takes into account longand short-range interactions between ions has been recently made by P o ~ t l e r . ~The derived equivalent conductivity equtk‘ ,. Ion was h = A, exp(-B‘c)
Table V : Hypothetical Glass Transition Concentration and
=
A further attempt to explain the mechanism of mass transfer in concentrated solutions has been made by Angell,21with a modified form of the Arrenhius equation
where A and k are constants and T ois the glass-transition temperature. Equation 6 originally derived from the free volume theory of viscous liquidsg was adapted to describe the temperature dependence of transport properties of electrolyte solutions.21 In an alternative way eq 6 can be derived by the entropy theory of Gibbs and This thermodynamic approach seems more promising when applied to concentrated electrolyte solutions as recently pointed out by However, eq 6, regardless of which model is used to derive it, certainly states that in the temperature range from 0 to To OK all processes involvin are hindered. A particular assumptionz4that in electrolyte solutions Toof eq 6 is linearly related to the equivalent coneentration N and that the parameters A and IC are composition independent leads to the follou-ing expression =
A exp(--
k’ No - .N
where the electrostatic contribution A, to the equivalent conductivity is given, this time, by the Pitts equationz0 and the slope of the plots log A/& against c gives the value of the B‘ parameters. For some salts in water, eq 5 fits the experimental conductance data as well as eq 4. This fact seems due once more to the adjustable parameter. a which consequently loses its original meaning. In fact when applied to our experimental data eq 4 and 5 give values either very high or absurdly low and, in any case, never coincident as Table V shows. In conclusion the above two equations seem to have little theoretical basis and do not solve the problem of understanding, on a molecular scale, the mechanism which controls the Inass transport processes. The Jownal of .Phg&cal Chr?mistry,Vol. 76, N o . 11,1971
which formulates the concentration dependence of the conductivity. In the above equation k‘ contains the proportionality constant between T oand N while N o is (16) G. J. Janz, B. G. Oliver, G. R. Lakshminarayanan, and G. E. Mayer, J . Phys. Chem., 74, 1285 (1970). (17) H. Falkenhagen, M. Leist, and G. Kelbg, Ann. Phys. (Leipzig), 11 (e), 51 (1952). (18) L. Onsager, Z . Phvs., 28, 277 (1927). (19) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Butterworths, London, 1959, p 235. (20) E. Pitts, Proc. Roy. Soc., Ser. A , 217,43 (1953). (21) C. A. Angell, J . Phys. Chem., 68, 218 (1964); 68, 1917 (1964); 70, 3988 (1966). (22) G. Adam and J . H. Gibbs, J. Chem. Rhus.. 43, 139 (1965). (23) C. A. Angell, J. Phys. Chem., 70, 2793 (1966). (24) C. A. Angell, ibid., 70, 3988 (1966).
DENBITY, V I S C ~ S I TAND ~ , ELECTRICAL CONDUCTANCE OF SODIUM SALTS the h y p o t h e t ~ cconcentration ~~ at which the system should become a, glass at this temperature. Equivalent conductance data reported in Table I11 have been analyzed by ee 7. A least-squares program has been used iii order t s check She N o value that linearizes the log .A(,) funetirxa against 1/(No - N ) . The final N o values of the salt8 studied are reported in Table V. V.iScosity. l a the past years many papers have appeared and diferenl, models have been proposed in order to inter:mt ths experimental viscosity data of on cent rate^^ solutions. In one of these attempts the Einstcin equation“ t i d i n g with viscosity of liquids containing rigid spheres has been extended to the viscosity of strongly liys.rated electrolyte solutions. lug
?re! =
2.5 r c
3037
I
2
I
_
4
5
c
Figure 1.
(8)
where P,by analogy with the Einstein equation, should represent the effective molar volume of ions expressed in liters per mole and Q is an arbitrary constant.’ Rearranging eci 8 we obtain (9)
which is the equation of a straight line. The plots of the quantity 2.542.3 log qrel against c for NaC104, I\’aKOB,NaSCX, NaBr, and NaI salts in formamide (Figure 1) show t’hat eq 9 is inadequate to describe the experimental data in the lowconcentration region. Disregarding $,he points at the lowest concentrations, the extrapolations at zero concentration give the following effective molar volumes-NaSCN, 156 ml; NaC104, 159 nil; NaT\‘03,171 ml; NaI, 177 ml; NaBr, 199 ml-whicl; oorrcspond at a volume of a single molecule of -3.9 As for XaSCN and NaC104, -4.1 A 3 for ;“\‘aPI’08 and NaI, -4.3 for NaBr. The free volume model theoryg and the configurational entropy theoryz2have also been applied to the viscosity or eonaentrated solutions and an equation similar to the eq 7 has been derived for solution visc o ~ i t y , l‘herefoipe ~~ the analysis of the viscosity data of KaClOq, NaNOr,NaSCN, NaBr, and WaI salts in formamide has been made with the same program used for conductivity data; the found concentrations N o are reported. in Table V. The concentralLon N o has been defined as the concentration ’vs here Ihe macroscopic configurational entropy of tbrx liquids is zero, so that under an applied force the system should require a very high energy t o ow. Since lmtk conductivity and viscosity processes imply mass transfer, the N o values found in the plots of log A and log t against l/(No - N ) should coincide. Table V shows in fact good agreement between the No values found via the two different plots. In Figure 2 the relative visco~,ityand the ratio &/A of the studied salts are reported against the concentration; as one can Dee, the rchmw viscosity and the conductivity ratio
x3
Figure 2.
at a given high concentration is higher for NaBr, NaI, KaSCN, and KaC104 characterized by small N o values than for NaNOa which presents the highest No value. There is no reasonable explanation for the high N O value of NaN03 salt which is greater than the charge concentration of pure NaNO3. In addition, the No value found in formamide contrasts with the results of some concentrated water solutions. Systems having high N o values at room temperature should be characterized, at the highest concentrations, by relatively low glass-transition temperature. I n water, by contrast, the glass-transition temperature of Ca(NQ3)z is higher than the glass-transition temperatures of Ca(SCN),, Ga(C104)z,CaBrz, and CaLIL6 A more detailed investigation about this point is under way and further communications regarding the influence of different ions as well as the temperature dependence of transport properties of somc appropriate salts in concentrated formamide solutions will be given subsequently. I n conclusion, the results of this preliminary work seem to indicate that the equations utilized to predict the composition dependence of transport properties in fused salts and in concentrated aqueous solutions can be extended to the interpretat,ion of transport in concentrated nonaqueous solutions. (25) C . A. Angell, J . Chem. Phys., 46, 4613 (196’7). (26) C . A. Angell and E. J. Sam, ibid., 52, 1058 (1970).
The Journal of Physical Chemistry, Vol. 7‘6,N o . $1, 1972
