Electrical Conductivity, Viscosity and Density of NaI in Formamide Solutions in the Temperature Range 35–80°C

ELECTRICAL CONDUCTIVITY, VISCOSITY AND DENSITY OF NaI IN FORMAMIDE SOLUTIONS IN THE TEMPERATURE RANGE 3%3O”C P. BRUNO,

C.

Istituto di Chimica

GA~[

and M.

Analitica.

DELLA MONICA*

Via Amcndola

173. Bari. Italy

Abstract-In this work the measurements of eleclrical conductivity, viscosity and density of NaI salt in formamide solutions in the composition range %21 mole “4 and in the temperature range 35-8O’C are reported. The experimental data have been analyzed with equations utilized for transport in glassforming liquids. The glass-transition temperatures deduced from conductiviiy and viscosity data. reported in graph against the salt concentration, lie on the same straight line. Alternatively, the experimental conductivity and viscosity data have been analyzed with a three-parameter equation which describes the isothermal composition dependence of transport proccsscs. At the four temperatures used the plots of Ig, and lg, against I/(x 0 - s). where Y,, is the glass-transition concentralion, were linearized by almost the same .Y~, value. The values of the apparent and partial molar volumes of salt_ deduced from density measurements. were found to be close to the value of the molecular volume of nure salt. This fact is intermeted in terms of equivalent cncrgics of the ion-dipole and of the dipole-dipole interactlons. glass-forming liquids it is the temperature interval above the glass-transition temperature which is of importance to transport. An attempt to extend the results of the Angel1 theory to salts dissolved in media other than water has been reported in previous articles[h]. The results of conductometric and viscosimetric investigations on some uni-univalent and uni-bivalent electrolytes in formamide showed that also non-aqueous concentrated salt solutions can be analyzed in terms of concepts for relaxation processes in glass-forming liquids. In the present work the investigation has been extended to the temperature of 35, 45, 60 and 80°C in order to study the influence of the temperature on energetic factors which control mass transfer processes. The selected electrolyte is Nal and the concentration range goes from zero to the saturated solution at 35°C. In the same solutions thz density has also been measured for a better understanding of the structural configuration of the formamide solutions.

INTRODUCTION

The properties of dilute electrolyte solutions have been widely investigated in the past years. A great number of publications have also been devoted to the electrochemistry of fused salts, which in some respects can be considered the upper concentration limit of electrolyte solutions. Nevertheless, up to this moment, the properties of electrolyte solutions in the interesting concentration region from the dilute solution to the pure salt have been neglected. This fact is essentially due to the lack of a theory interpreting the strong ion-ion and the ion-dipole interactions when the ratio between the number of solvent molecules and the number of ions is small. Various attempts have been made in order to extend the model of the Debye-Htickel theory to concentrated solutions[l]; Wishaw and Stokes[2], and more recently Postler[3], introduce empirical parameters in the conductivity limiting law. Although in some cases experimental results are well described by the proposed Wishaw-Stokes and/or Postler equations, the introduction of empirlcal parameters in the conductivity limiting law is a physically incorrect procedure when we are dealing with concentrated solutions where the ionic cloud is so small that the time average of the charge density no longer represents the effective distribution of the ions. Recently, Angell[4] interpreted the structure of some concentrated aqueous solutions in terms of the basic treatment of the fused salts theory[Q The interpretative model proposed by Angel], except for very diluted solutions where the DebyeHiickel theory is followed, assumes that the energq of a given mass transfer process is continuously changing with temperature; change occurs until a temperature is reached where the system undergoes glass transition. The implication of the above theory is that in terms of the mass-transfer processes of the * To whom inquiries

EXPERIMENTAL

Baker Analyzed Reagent formamide was dried with molecular sieves and then deionized by means of a mixed bed of ion-exchange resins[7]. The formamide obtained had a specific conductance of 5 2 7 x lo-’ R- ’ cm- ‘. Reagent grade sodium iodide was recrystallized 3 times from double-distilled water and then dried in LUCUOat 110°C over phosphoric oxide. The conductance bridge used and the cell employed have been previously described[8]. The viscosities of the solutions were determined with Ubbelohde viscosimeters of different constants; the densities, measured with a 30ml pycnometer, are referred to the density of water at 4°C. The two thermostats used were controlled as follows: 35 _t O-005; 45 + 0.002; 60 k @05; 80 f O-1. The solutions were prepared by addltlon

should be addressed. 533

P. BRUNU, c‘. Cial~i Table

I. Density

of sodium

<

iodide in formamide

1.1293 i.1609 I-lY46

80°C

0.2892 0.5914 0.9 I86 I ,2997 I .6783 2,3282 3~5028 4.3631 53237

l-1431 1. I 750 I.2091 l-2487 1.2883 I.3550 I .4763 15663 I.6657

0.2816 0.5757 0.8945

1.1 I34 1-1438 1.1773 1.2171 l-2557 I .322 1 I-4427 1~5335 I.631 I

to is the density

1.2344

I.2668

I.2733 I .34OO I .4h I I 1.5471 I ,6462

1.6357 2-2717 3-4230 4.2719 5.2133

of water

at 4’c‘.

where

of the solvent to a given quantity of a stock solution. All operations were performed in a dry-box saturated with dry nitrogen.

RESULTS

AND

DISCUSSION

and uiscosity

In Fig. 1 the logarithm of conductivity and the logarithm of viscosity are plotted against the reciprocal thermodynamic tern crature; as one can see, these plots are not a linear ‘&nction of the quantity l/T. In the attempt to explain the mechanism of mass transfer in concentrated water solutions, Angell[9] proposed treating the experimental conductivity and viscosity data in terms of a modtied Arrhenius rquation : (1) Table

2. Conductivity

2548 1 2 1.x49 18.227 IS.149 12.589 8.942 4.558 2.304 0.957

of NaI

W(x) is the mass transfer process involved and To are constants. The different interpretative models used to deduce equation (I) give different meanings to the temperadependent and is ture To, which is concentration known as the ideal glass-transition temperature. In the derivation of equation (1) by the Gibbs Adam entropic theory[l0], To represents the temperaturc where the configurational entropy of the system becomes zero; consequently in the temperature range from 0 to To “IL, to accomplish processes involving mass transfer, an infinite energy is required. Analysis of the experimental data through equation (I) has been made by quoting the quantities Ign and lgq with respect to the term l/(T - To). In order to linearize these plots values of T0 have been checked with an IBM 360/65 computer and a least-squares program. In this program the term T- ’ ” in the preexponential of equation (1) has been assumed constant since it has little influence on the linearity of the l/(T - r,) plots in the explored low-temperature region. The results of the above calculations are reported in Table 4 and in Fig. 2 where with Ton and To, values the values of the constants A and A. k and

Densities conductivities and viscosities of the investigated salts solutions at the temperatures of 35, 45, 60 and 8O”C, and the corresponding conccntrations in moIc/l. are given in Tables 1, 2 and 3, rcspcctively.

I I702 2-3933 3-7184 5~2627 6-79S6 94406 14.2269 17.7244 2 I .6490

at 35. 45. 60 and

d*

0.2857 G5844 0.9075 l-2848 1.6587 2.3025 3-4668 4.3097 5.2614

Comhcrioity

solutions

(6O'C)

(mole I- I)

rcfcrrcd

DELLA MONKA

1-ts13 ,I832 ,217l .2573 ,2964 I ,3633 .4857 ,572s +5719

0.29 I 2 0.5955 0.9247 1~3084 1%8X7 2.3425 3.525 I 4~3806 5-3437

* Density

.WD M.

m formamIde

3 I- I 62 26-69 I 23-005 19-347

1628X I I .876 6.456 3.503 I.639

solutions

at 35, 45. 60 and

4@869 35-329 30-193 26-26 I 22-45X 16.927 9.895 5.1784 3.147

80°C‘

55.636 48,542 42,777 36.984 32.093 24,989 IS.734 IO.212 6 225

Nal

Table

(moL

3. Viscosity

of NaI

in formamide in formamide

2.9806 3-3480 3.939 1 4.6730 56768 8~1809 18,113 37.421 loo.39

I.1702 2.3933 3.7184 5.2627 6.7956 9.4406 14.2269 I7.7244 21-6490

I 30

I2.505

I /T

Fig.

x

I

I

I

3 I

32

W(r)= Ig,

and I,gg against

i/T.

I.17 2-39 3-7 1 5-26 6.79 9.44 14.22 17-72 21.64

4. Values

148 147 151 156 162 166

17x 184 196

ol’ constants

2-97 2.96 2.92 2-M 2-82 2.8 I 2.75 2.79 2.82

&.

I ,307O I.4400 I-6062 l-8421 20999 2.7040 4.628 I 7-3801 12.930

AYT~“zexp[--K110/(7’

-

‘r,)]

(2)

7&Y) = 7‘“(.U = 0) + QX

(3)

where T,(u) is the glass-transition temperature at x mole’/, and T,(.\- = 0) is the glass-transition temperature when the salt concentration is zero. Substituting

A and k of equation

252 263 261 258 252 264 272 302 319

I,7940

where A and k do not depend on the concentration of the salt while T, is concentration dcpcndcnt. According to Angell[9] the glass-transition temperaturc is assumed to depend linearly on the salt concentration; in this case it can be written:

k of the modified Arrhenius equation are also reported. A survey of the plots of Fig. 2 shows that Ton and T,,, values reported against salt concentration lie on the same straight line; extrapolation to zero concentration gives a glass-transition temperature of 144°K. The fact that the same straight line interpolates the To values derived from viscosity and conductivity data is significant and can easily be understood Table

?nU W)

when it is realized that: (a) glass-transition\lemperature of a given solution depends on the salt concentration but is independent of the physical property used to determine It; and (b) the extrapolation to zero concentration of ‘I;,, and of T,, values gives the glass-transition temperature of pure formamide. Tt is also interesting to consider the depcndcncc on the salt concentration of parameters A and k of equation (I). Figure 2 shows that constants k,,, and k, increase with the salt concentration in the concentration range ?I:<~+ saturated solution. In the same range of concentration the ratio bctwccn k pammeters and TO temperature relative to the conductancc and viscosity measurements is approximately constant although the difference of the single ratios k,,/T,, from the average is greater than for corresponding k.,/T,., ratios, a fact probably due to the difficulties in attaining precise viscosity data. (Values of the ratio k,,/T,,, and k,,/Ton are shown in Table 4.) Also, the values of the pre-exponcntial term A derived from both conductivity and viscosity data can be considered constant, a fact shown in Table 4 and in Fig. 2. The circumstance that the composition dependence of the k parameter is exactly that of r, implicates that all processes involving mass transfer can be interpreted by an equation:

m3

I. Plots of the functions

VCI,II (cP) 2Go20 2.2646 2-6373 3.1060 4.0992 7-7304 13-472 21.227

23.700 56. I44

t-

I

at 35. 45, 60 and 8o’C

2.3944 2.6670 3%97 3.6270 4-3371 6.0632

, t

29

solutions

q41 (cW

Uns (cP)

“/;)

535

solutions

145 151

154 156 155 165 171 183 193

(I)

derived

from

l-18 I.15 I.14 I.10 I.15 I.10 I.14 1.09 1.17

conductivtty

270 ‘63 266 269 291 28X 330 333 365

and

viscosity

l-70 1.79 1.73 1.6s 1.55 I,59 1.52 1.64 163

data

I.86 I.74 1-73 1.72 1.88 I.75

1.93 I.82 I.89

P. BRUNO. C. GATTI AND M. DELLA MONICA

that the glass-transition temperature deduced from the two investigated mass transfer processes can bc interpolated by the same straight line strengthens the idea that modern theories and relative equations used MI the treatment of the temperature dependence and of the composition dependence of the transport properties in fused salts and in concentrated aqueous solutions can be successfully applied to interpret the mass transport processes in concentrated nonaqueous solutions.

o-

0-

a

35Q-

In a previous paper[6] where the properties of univalent electrolytes in formamide at 25°C have been Investigated, the measured density of the solutions was found to depend linearly on the salt concentration; the same result was obtained in solution of salts characterized by a high cation charge density. Although this bchaviour was not fully explained, it was supposed that the linear dependence of the density on the salt concentration and the structure of the solution were closely bound up with one another. In this case, in order to understand the structural configuration of formamide solutions we have extended this work to investigate the temperatures of 35, 45, 60 and 80°C. The experimental data are reported as density and corresponding concentration in mole/l. in Table 1. Using a least-squares program and an IBM computer the dependence of the experimental densities on the salt concentration at the four temperatures was calculated. The coefficients of the equations of best tit with their standard deviations are reported in Table 6. From the results of Table h it appears that the concentration dependence of density at the four temperatures investigated is described once more by a straight line; the slope of these straight lines is approximately constant. An approach to the interpretation of the properties of electrolyte solutions can be usefully made in terms of apparent and partial molar volumes of the solute species. The apparent mol$r volume of a salt in solution depends on the density of the solution through the relationship[ 121:

k

25*Cl-

A

3 -0

-

2

2 a-

0 A,

2

I

I

5

0

I

IO mol, % N,I

Fig. 2 Glass-transilion

15

temperatures

20

and constants

A of equation (1).

k and

equation (3) by equation (2) gives the dependence of all of the transport properties by the salt concentration through the relationship[ll]: W(x)

= rl;T-

’ 2 exp[ - V/(x, - x)]

(4)

where once more W(x-) is the mass transfer process considered; in equation (4) the constant x0 represents the concentration when the system becomes a glass at a given teinperature. The consequence of the above finding is that experimental conductivity and viscosity data can be treated through equations (2) and (4) by following two different routes: (a) at constant temperature in order to check the glass-transition concentration; and (bl at constant concentration and in this case the final result gives the glass-transition temperature. The glass-transition concentration x,, of NaI relative to the temperature of 35, 45, 60 and 80’C has been calculated by conductance and viscosity data and the results reported in Table 5. The .x0 value at 25°C given in a previous article in equivalent/ liter is given in this article in mole %. It is noteworthy that .\I~deduced from conductance and viscosity data are near values. This important result and the fact Table

5. Glass-transition ‘I

concentrations

%A

of NaI

9, = (d, - d)/cdo + MZ/do

(5)

where c is the concentration, d, and d are the density of the solvent and the density of the solution respectively and M, is the molar mass of the salt. The substitution of the equations of Table 6 in place of d in equation (5) gives for the apparent molar volumes the following expression:

in formamide

and viscosity

at various data

temperatures

deduced

from conductivity

YO,,

( ‘W

(mole “4)

g1

(mole 5;)

fiq

29X.16 308.16

49 54

4.0 x 10-3 1.4 X 10-Z

52 54

54 x 10-4 3.5 X 10 ’

318.16 333.16 353.16

58 56 R3

1.3 x 10-1 l-1 x lo-’ I.0 x 10 2

57 63 72

3.1 x 10 3 7.7 x IO 3 8.5 x 10-J

NaI in formamide Table

6. Density

equations

and

apparent

and

partial

molar

temperatures

d d d d d

35 45 60

80

= = = = =

I.1303 + 1.1220 + 1.1137 + 1~1006 + I.0836 +

volumes

of

Standard deviation

Best equation 25

537

solutions NaI

in

formamide

solutions

different

Apparent and partial molar volumes (cm’)

0.1021 c* 01029 c @1037<

O.ooo7 OGM4 OWKL3

42.3t 41.8 41.5

@lo38 c

0.0005

41.9

41.3

O~OOW

0.1051 c

at

c is given in mole/l. volume of the NaI salt at 25°C is 40.9cm3.

* The concentration

t The molecular

where the term h is the slope of the straight line relating density and concentration. Expressing the concentration in mole/l., the partial molar volume v, can be experimentally determined from the readily accessible apparent molar volume through the equation:

(7) Equation (7) establishes a v2 and @” as having the same value when the apparent molar volume is concentration independent. Consequently, data reported in Table 6 represent both the partial and the apparent molar volume of the salt in solution. On the ground of the results of Table 6 the interesting consideration can be made that the volume of a salt solution can be obtained simply by adding the volume of the salt to the volume of the solvent formamide used to dissolve it. In other words, the addition of a certain amount of salt to the same quantity of dilute or concentrate solution gives rise to an increase in volume equal to the volume of the pure salt added. This behaviour of the formamide salt solution appears singular when it is realized that in the more concentrate solutions there is no bulk solvent since the ratio of the solvent molecules to the ionic species is as small as 2. As a rule a salt dissolved in a medium gives rise to a tighter packing of solvent molecules around the ions. This phenomenon, known as electrostriction, is due to the electrostatic interaction between the ions and the dipoles of the medium and is more pronounced in the dilute than in the concentrate solution[13]. In water where most of the research on concentrate solutions has been made, the packing effect of the solvent molecules which is responsible for the large decrease of the partial molar volume of a salt in the region of dilute solutions disappears when concentrate salt solutions are involved. The partial molar volume of a salt in fact reaches the value of the molecular volume of the pure salt in highly concentrated solutions. In consideration of the fact that the electrostriction phenomena are mainly due to interaction between an ion and the dipoles of the solvent, one should expect the above effects to be more pronounced in formamide than in water since the dipole moment of :I lormamide molecule is almost twice as high as

the dipole moment of a water molecule. On the contrary, the results of density measurements in this solvent show no detectable packing effect of the solvent molecules around the ions in all the range of concentrations used. To understand the behaviour of the formamide solutions the structure of this solvent which is supported by hydrogen bonds and by strong dipole-dipole interactionsc 143 must be taken into consideration. Calculations of the corresponding energy and comparison with the mean energy of interaction of an ion with the dipole of the solvent can be made as follows: In an electrolyte solution the potential energy of interaction of a dipole with respect to an ion is equal to: Ui = - e,p cos e/r2

(8)

if the distance I of the dipole centre from the ion is sufficiently high. In equation (8) e,, is the charge of the ion, p is the dipole moment of the solvent molecules and the angle 8 gives the orientation of the dipole with respect to the ion. Under the field strength of the ionic charge equilibrium is reached when the angle 0 is equal to zero, but the thermal agitation continuously disturbs this equilibrium. If the temperature is sufficiently elevated, then the mean energy of a dipole with respect to the ion can be calculated by the relationship[ 153 :

ni = -e$?/3r4kT

(9)

where k is the Boltzmann constant and T is the absolute temperature. In an analogous way the mean energy of interaction between two molecules of equal dipole moment can be calculated as a function of the distance of the dipole centres; the result is: Ud = -2p4/3rbkT.

(10)

Considering that the dipole moment of a formamide molecule is 3.25 Du[16], one can calculate the mean ion-dipole and the mean dipole-dipole interaction energy as a function of the distance r. These functions, plotted in Fig. 3, have been calculated assuming also that at small r distances the mean interaction energy of an ion and a dipole and the mean interaction energy of two dipoles arc expressed by equations (9) and (10). An examination of Fig. 3 shows that if the distance r is great the ion-dipole interaction energy is high compared with the interaction energy of two dipoles of the solvent; on the contrary, at small r values, the ion-dipole and the dipole-dipole interaction energy values become comparable. In this case the replacement of a formamide molecule by an ion near a solvent molecule does

53x

P. BRUNO. C. GATTI

AND M. DELLA MONICA

be made by utilizing concepts and expressions for relaxation processes in glass-forming liquids. The results of the analysis of the experimental data made in terms of glass-transition concentration arc also in agreement with these conclusions. The densities of the solutions in the range of temperatures 3SSO”C show the same pattern of the densities at 25’C. The linear dependence of density on the concentration of the salt has been explained in terms of energetically equivalent substitution of a dipole with an ion near a solvent molecule. For a better understanding of this aspect of the problem concerning the concentrated non-aqueous salt solution a calorimetric investigation would seem promising. A~knowlrdyrnlprlt-This work has heen done financial support of C.N.R. Ct. 73/00941/03.

with

the

REFERENCES I. R. A. Robmson and R. H. Stokes Electroiyre Solutions. p. 7Y. Butterworths, London (1959). 2. B. F. Wishaw and R. H. Stokes. J. Am. them. Sot.

76, 2065 (1954).

Fig.

and dipole-dipole interaction a function of the distance r.

3. Ion-dipole

energy as

not involve large energy change; consequently occurs without any appreciable shrinkage in volume of the solution.

it the

CONCLUSIONS

The results of the measurements reported in this work show that the logarithm of the conductivity and viscosity of NaI in formamide depend linearly on the reciprocal of a corrected thermodynamic temperature, the correction being made in terms of the glass-transition temperature of the solution. The coincidence of the values of the glass-transition temperatures deduced from conductivity and viscosity data shows that the interpretation of the mass transfer processes in concentrated non-aqueous solutions can

3. M. Postler, Col[n. Czech. chew. Commun. 35, 535 (1970). 4. C. A. Angell, .I. phys. Chem. 70, 3988 (1966); C. A. Angel1 and C. J. Sare, ibid. 52, 105X (1970). 5. C. T. Moynihan, in Ionic‘ Intrractions (Edited by S. Petrucci), Vol. I, p. Xl. Academic Press (1971). 6. P. Bruno and M. Della Monica, J. phys. Chem. 76, 3034 (1972); P. Bruno and M. Della Monica. Elrctro-

chim. Acta 20, 179 (1975). 7. J. M. Noilcy and M. Spiro. J. them. Sot. B 362 (1966). 8. P. Bruno and M. Della Monica. J. phys. Chem. 76, 1049 (1972). 9. C. A. An&l, J. phys. Chrm. 70, 3988 (1966). I 0. G. Adam and J. H Gibbs, J. phys. Chwn 43, 139 ( 1965). Il. C. A. Angel1 and R. D. Bressel. J. phys. Chrm. 76, 3244 (1972). 12. H. S, Harned and B. B. Owen. The Physicof Chemistry of Electrolyric Solutions, 3rd edn, p. 358. ReInhold, New York, N.Y. (1958). 13. C. Kortum, Treatise on Elccrrochemisrry, p. 40. Elsevier, London (1965). and D. Fennel1 Evans, J phys. Chem. 74, 14. J. Thomas 3812 (1970). 15. lot. cit. in (I 3), p, 95. Chrm. Rev. 69, I (1969). 16. A. J. Parker,