J. C.S. Furaduy I , 1980,76, 1275-1 286

New Method of Separation of the Viscosity &Coefficient of the Jones-Dole Equation into Ionic Contributions

for Non-aqueous Electrolyte Solutionst

BY BORIS S. KRUMGALZ Israel Oceanographic and Limnological Research Institute,

Chemistry Department, Tel-Shikmona, P.O.B, 8030, Haifa, Israel

Received 30th July, 1979

A new method is pfoposed for the resolution of the viscosity B-coefficient of the Jones-Dole equation into ionic components for electrolyte solutions in organic solvents. The method was based on the assumption of the unsolvation of large tetra-alkyfammoninm cations in organic solvents. For the calculation of ionic B-coefficients, extrapolation of the -tion &NX = a + b & ~ + to zero cation radius was used. The ionic B-coeEcients at Merent temperatures in several orgaruc solvents have been calculated. The relationship between B-coeBcients of large tetraallcylammoniunl ions and the intrinsic solvent structure was examined. In methanol and N-methylfonnamide solutions, the B R ~ N + values for large tetra-alkylammonium cations are conditioned only by the Einstein effect. In N-methylacetamide and N-me$hylpropionami& solutions, the effects related to the destruction of solvent structure in the region of the ionic cosphere are significant togsther with the Einstein effect.

In the development of a theory dealing with electrolyte solutions much attention has been devoted to ion-solvent interactions. By separating molal functions of electrolyte solutions into ionic contributions it is possible to isolate the contributions due to cations and anions in the solute-solvent interaction. These depend on the intrinsic solvent structure and on the nature of the ions (dimension, charge and charge distribution in the case of large ions, H-bonding, etc.).

A number of the problems arising in working out methods of separating various molal functions into ionic components are general and independent of the kind of functions. The function additivity, relative to the constituent ions of the solute, is a necessary condition for the process of separation. The separation into ionic compon- ents of functions in which additivity is questionable, even with the help of the most perfect procedure, is absolutely unfounded. Again, in working out the methods of separation, it is necessary to take into consideration the mechanism of ionic sohation and also the phenomenon of ionic association, especially in separating the functions of solutions at moderate or high concentrations. One such function is the B-CO- efficient of the JonesDole viscosity equati0n.l The B-coefficient, in the case of the complete absence or insignificance of ionic association, is conditioned by the ion- solvent molecules’ interaction and also by ion-size and, at present, cannot be calcu- Iated a priori.

The purpose of the present communication is threefold : (1) to suggest a new method for the separation of the B values in non-aqueous (organic) electrolyte solutions into

t Part of the data presented at the 6th International Conference of Non-Aqueous Solutions, University of Waterloo, Waterloo, Canada, 7-11 August 1978.

1275

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1276 VISCOSITY B-COEFFICIENT OF THE JONES-DOLE EQUATION

ionic contributions; (2) to use this method for all known experimental data for the calculation of ionic B-coefficients in different solvents ; (3) to examine the relationship between the ionic B-coefficients and intrinsic solvent structure.

RESULTS AND DISCUSSION

The concentration dependence of the viscosity of electrolyte solutions is described by the Jones-Dole semi-empirical equation

where the A-coefficient determined by ion-ion electrostatic interaction can be calcu- lated from the ionic attraction theory by the Falkenhagen-Vernon equation and the 23-coefficient is an empirical constant determined by ion-solvent and solvent-solvent interactions. This means that the ionic B-coefficient is a measure of solvation effects, ionic influence on solvent structure and hydrodynamic effects which are conditioned by ionic size and shape. Desnoyers and Perron showed that Dc2 should be added to the Jones-Dole equation, where the D-coefficient depends on higher terms of ion- solvent and ion-ion interactions. However, since the D-coefficients have been calcu- lated for only very few systems, for all future calculations we will use only the B- coefficients calculated from eqn (1) without Dc2.

Many attempts have been made to resolve the B-coefficient into ionic components (B+ and B-) for non-aqueous electrolyte solutions. Most of them were based on the assumption of the equality of the B+ and B- values, if the limiting ionic equivalent conductances of the same ions are equal in the given solvent. Criss and Mastroianni resolved the B-coefficients for methanol electrolyte solutions at 25°C into ionic com- ponents assuming that BK+ and Bcl- are equal, since the mobilities of these ions are equal for the same solution^.^ The same authors4 adopted B&z4N+ = 0.25 as the initial value for acetonitrile solutions. Tuan and FUOSS,~ for acetonitrile solutions, proposed the equality BBuaN+ = BPh4*-, since they thought that these ions have similar mobilities. However, according to Springer et id.,' Ag,5Bu4N+ = 61.4 and A$&,,- = 58.3 in acetonitrile. Gopal and Rastogi resolved the B-coefficients in N-methyl- propionamide solutions, assuming (without proof) that BEt4N+ = BI- at all tempera- tures. The resolution of the B-coefficients in dimethylsulphoxide into ionic com- ponents was carried out by Yao and Bennion who assumed that Bi-Am3BuN+ = BPhdB- at all temperatures. This method has been widely used by other authors in recent years for sulpholan,1° hexamethylphosphotriamide and ethylene carbonate solutions.

Any method of resolution based on the assumption B+ = B- for certain ions, provided that the limiting equivalent conductances of these ions are equal, suffers from the major disadvantage that it is impossible to select any two ions for which Ao, + = Ao, - in all solvents at proper temperatures. For example, whereas the Ao, K + and Ao, cl- values are equal at 25°C in methanol, in ethanol and other organic solvents this equality does not hold l3 at the same temperature. In addition, if the mobilities of some ions are even equal at infinite dilution, from this it does not follow that they are equal at moderate concentrations for which the &coefficient values are calculated.

Previously, the present author 14* l5 has suggested that the phenomenon of unsolvation of large tetra-alkylammonium ions in organic solvents can be the physical basis of a method for the separation of the B values into ionic contributions in these solvents. The method developed was based on the assumption that the ionic B values for large tetra-alkylammonium ions R4N+ (where R > Bu) in organic solvents are proportional to their ionic dimensions.

qlyo = 1 +AC++BC (1)

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B. S . KRUMGALZ 1277 Recently we have shown l6 that

(2) Einst+B;;:nt+B.str+geinf Bion = B i o n ion ion

where BzFt is the positive increment arising from the shape and size of solvated ions (this increment is closely related to the Einstein effect 17) ; is the positive incre- ment due to the orientation of polar solvent molecules by the ions; Bf& is the incre- ment related to the destruction of solvent structure in the region of the ionic cosphere ; B!zf is the positive increment conditioned by the effect of “ reinforcement of the water structure ” by large tetra-alkylammonium ions due to hydrophobic hydration.

The values of BE? and Bfttf for organic solutions containing large tetra-alkyl- ammonium (beginning from Bu,N+) and other tetra-arilonium ions are negligible, the former due to the very small surface charge of these ions and the latter due to the fact that the phenomenon of hydrophobic hydration is only inherent in the intrinsic water structure. Then, for the above-mentioned solutions,

BR4N+ = BZgi + B i y N + .

According to the Einstein theory,17 (3)

2.5 v (4) BEinst =

where v i s the effective incompressible molal volume occupied in a liquid by hard spherical obstacles, at the surface of which the liquid remains stationary. It must be emphasized that eqn (4) is valid for incompressible spheres moving in a continuum. However, Robinson and Stokes l 8 have shown that the Einstein theory l7 could be successfully used to describe the viscosity of electrolyte solutions if the value is assumed to be equal to the molal volume of the solvated solute. For large unsolvated tetra-alkylammonium ions we have assumed that the Vvalues will be equal to the volumes of these ions. Therefore, one can write

BE!$/dm3 rno1-l = 2.5 $nri4N+N = 6.307 x 1 0 2 1 r i 4 N + ( 5 ) where N is Avogadro’s number and rR4N+ (in cm) is the radius of tetra-alkylammonium ions. The problem of the choice of the cation radius value will be discussed further.

We can also assume that the increment related to the destruction of solvent structure in the region of the ionic cosphere of large tetra-alkylammonium ions (B&+) will be proportional to the ionic dimensions in solutions. Then eqn (3) can be rewritten as follows :

BR4N+ = + B i y N + = 6.307 x 1O2’rZ4N+ +f’ (r i4N+) = f ( ~ g , N + ) . (6) The above speculations can be examined by using the existing literature data.

For some amides ** l9 and methanol 20* 21 solutions, B-coefficient values have been determined at different temperatures for series of salts containing tetra-alkylammonium cations and common anions (I- or Br-). Owing to the additivity of molal B- coefficients, relative to the constituent ions of the solute, and taking into consideration eqn (6), one can write for these organic solutions

BR4NX = BX-+BR4N+ = B X - + f ( r i 4 N + ) (7) where Bx- is the anion B-coefficient which is independent of the nature of the counter- cation in any proper solvent.

The B-viscosity coefficients for some solutions of tetra-alkylammonium iodide salts were plotted as a function of the dimension of the organic cation in fig. 1 and a strong straight-line relationship was obtained for each solution starting from either

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1278 VISCOSITY B-COEFFICIENT OF THE JONES-DOLE EQUATION

Pr4NI or Bu,NI. It seems reasonable to suppose that the plots in fig. I would not be linear for solutions with large tetra-alkylammonium cations if the cations were solvated in different ways and degrees. Therefore, we may suppose that it is correct to assume that in organic solvents of different structure and chemical nature the large tetra-alkylammonium cations are not solvated in the normal sense involving significant electrostatic interaction. All plots in fig. 1 are expressed by eqn (7), written in the form

BR4NX = a fb&+ CW where a = BI- and b is a constant dependent on temperature and solvent nature. Therefore, the extrapolation of the straight lines in the figure to the zero cation dimension should give directly the anion B-coefficient in proper solvents. The B-coefficients for other ions can then be calculated on the basis of the additivity of molal B-coefficients in every solvent.

Here we should pay special attention to the choice of the tetra-alkylammonium cation radius values. The lack of adequate theories or knowledge of such funda- mental ionic parameters, such as the radius, increases the difficulties of obtaining

+ /A3 FIG. 1 .-Values of the B-viscosity coefficient of R4NI salts in amides and methanol as a hctian of the iohic radius of the cations at 25°C (except the data for N-methylacetamide for which the results at 35°C were used). For the construction of the figure, the data from the following works were used : x methanol ; z O A, N-methylformamide ;19 0, dimethylformamide ;* 0, N-methylacetamide ;*

N-methylpropionamide.*

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B. S. KRUMGALZ 1279

absolute ionic properties. By considering the motion of a solvated ion in an electro- static field as a single entity, it is possible to calculate the radius, rf, of this moving entity from the Stokes equation

where z is the ionic charge, P and N are Faraday’s and Avogadro’s numbers, respectively, yjo is the solvent viscosity and A*,* is the limiting equivalent ionic con- ductance. However, the use of this equation requires a knowledge of the other ionic property, namely the ;to, + value. Fortunately the only ionic parameter which can be measured now is the limiting equivalent ionic conductance. For the calculation of the rR4N+ values by eqn (8) we have used all the precise values of A0,R4N+ determined with the help of the transference numbers, unfortunately known only for a few sol- vents. The examination of the values obtained in this way22 has shown that beginning from the Bu,N+ ion, the ionic radii calculated from eqn (8) are virtually independent of the nature of organic solvents. At the same time, these radii differ from the values in H 2 0 and D20, in which there is specific hydrophobic hydration associated with the formation of clathrate-like structures. The virtual organic solvent independence of the solvation radii of large tetra-alkylammonium cations allows us to suggest that these cations are unsolvated in organic solvents and therefore their radii, calculated by eqn (S), correspond to their true dimensions in solutions.22* 23

Taking into consideration all the latest conductance investigations, we have obtained the following values of the tetra-alkylammonium cations radii used in all our subse- quent calculations : rPr4N+ = 3.333 .$, rBU4N+ = 3.850 A, rArn4N+ = 4.2g3 A, rHex4N+ = 4.74,A and rHept4N+ = 5.062A. Additional evidence that our choice for the radii of large organic ions calculated from conductometric data by eqn (8) is reasonable is provided by the following consideration : the difference between the Calculated values of rph4As+ = 4.27 and rph4B’ = 4.08 A is equal to 0.19 A, while the difference between the ionic radii of As5+ and B3+ is 0.27 A (rASs+ = 0.47 and rB3 + = 0.20 .$ 24) and between their covalent radii is 0.30 A [r()As() = 1.18 and r()B<) = 0.88 A 2 5 ] .

Evidently, the agreement between these differences is within the accuracy of calcula- tions.

Using the most accurate literature values of the molal B-coefficient for tetra- alkylammonium bromide and iodide solutions in methan01,~Os N-methylfor- mamide,l dimethylformamide,8 N-methylacetamide and N-methylpropionamide at different temperatures, the coefkielzts of eqn (7a) were calculated by the least- squares method using the above-described values of the treta-alkylammonium cations radii. In amide solutions, for the calculations of the parameters of eqn (7a), the data for Bu,NI, AQNI, Hex4NI and Hept,NI were used; for methanol solutions, Pr4NX, Bu4NX and Am4NX (where X = Br- and I-). In table 1, the standard deviations of the a-coefficient [eqn (7a)] and the correlation coefficients for these data are presented. The a = Bx- values for all solutions examined are given in tables 2-6. In these tables the B-coefficients of other ions, calculated by using the most accurate literature data at different temperatures 6 9 8* 19-21* 26-28 and the obtained values of a = &-, are summarized.

It should be emphasized that an advantage of the present author’s method is its independence of the nature of the solvent, which makes it possible to examine the relation between ionic &coefficients and the intrinsic structure of the solvent. It should also be noted that in its present form this method can be used either in the absence of ionic association or for the solutions in which the ionic association is negligibie.

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1280 VISCOSITY B-COEFFICIENT OF THE JONES-DOLE EQUATION

TABLE l.-sTANDARD DEVIATIONS OF a = Bx- VALUES (IN NUMERATOR) AND CORRELATION COEFFICIENTS (IN DENOMINATOR)

solvent temperature / "C 20 25 30 35 40 45 50 55

N-methyl- formamide

N-rnethyl- acetamide

N-methyl- pro pi onamide

dimet hyl- formamide

methanol

0.009 0.9974

- -

0.011 0.007 0.9986 0.9994 --

0.003 0.9972

0.003 0.9996

- -

-

0.005 0.9992

0.010 0.9987

0.004 0.9944

- I - 0.007 0.9983

0.011 0.006 0.007 0.009 0.006 0.9974 0.99a2 0.9988 0.9982 -2

- - - 0.008 0.004 0.9993 0.9998 --

- - - 0.004 0.002 0.9944. 0.9982 --

TABLE PARAMETERS OF EQN (7a) AND IONIC B-COEFFICIENTS (dm3 mol-l) IN ?&METHYL- FORMAMIDE

ions temp. Et4N+ Pr4N+ Bu4N+ Am4N+ Hex4N+ Hept4Nf K+ CS+ i0c b x 103 u = q- Me4N+

25 6.303 0.46 -0.08 0.03 0.22 0.35 0.51 0.65 0.82 0.10 0.14 35 6.106 0.51 -0.09 0.01 0.20 0.34 0.49 0.64 0.79 0.03 0.07 45 6.062 0.54 -0.06 0.03 0.21 0.34 0.49 0.63 0.79 -0.03 0.03

TABLE 3.DARAMETERS OF EQN (7a) AND IONIC &COEFFICIENTS (dm3 m01-l) IN N-METHYL- ACETAMIDE

ions temp. Me4Nf Et4N+ PrrN+ Bu4N+ h 4 N + Hex4N+ Hept4N+ K+ pc bx103 U =

-~ ~ ~ ~~ __ 35 7.953 0.69 -0.08 0.11 0.30 0.47 0.62 0.83 1.05 0.32 40 7.663 0.75 -0.10 0.09 0.28 0.44 0.60 0.80 1.00 0.23 45 7.710 0.78 -0.10 0.11 0.27 0.45 0.60 0.81 1.01 0.18 50 7.831 0.79 -0.07 0.13 0.29 0.46 0.61 0.82 1.03 0.15 55 7.663 0.84 -0.07 0.12 0.28 0.44 0.60 0.80 1.00 0.07

TABLE 4.--pARAMETERS OF EQN (7a) AND IONIC B-COEFFICIENTS (dm3 m01-l) IN N-METHYL- PROPIONAMIDE

ions temp. Et4N+ Pr4N+ Bu4N+ Am4N+ Hex4N+ HeptdN+ Li+ K+ C1- 1°C b X 103 u = BI- M e 4 ~ +

20 10.662 0.75 -0.22 -0.01 0.30 0.60 0.86 1.11 1.39 0.48 0.58 0.81 25 10.465 0.80 -0.22 -0.02 0.30 0.59 0.84 1.10 1.36 0.38 0.50 0.87 30 10.540 0.83 -0.21 -0.02 0.30 0.59 0.85 1.10 1.37 0.32 0.45 0.90 35 10.467 0.86 -0.20 0.00 0.32 0.60 0.84 1.10 1.37 0.26 0.40 0.93 40 10.390 0.90 -0.19 0.02 0.32 0.59 0.83 1.10 1.35 0.19 0.35 0.96

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B. S. KRUMGALZ 1281

Sometimes the B values for a series of salts with increasing dimension of tetra- alkylammonium cations are absent and only the B values for two salts with large tetra-alkylammonium cations and a common anion exist. In this case the following equations can be obtained by solving eqn (7a) :

We have previously proposed 14* l5 this system of equations for the separation of B-coefficients into ionic components in some organic solvents. Gordon et aL2 compared this method with other methods in formamide solutions and found that our method is the preferred technique for the resolution of viscosity B-coefficients into ionic components. The ionic &coefficients for formamide solutions obtained by the application of eqn (9) and (10) to the data 2 9 * 30 are presented in table 6.

Now it is worth returning to the method of Yao and B e n n i ~ n , ~ in which the equality of Bi-Am3BUN+ = BPh4B- was proposed. Since earlier we showed 22* 23 that the dimensions of these ions are the same, we had thought that the above-mentioned

TABLE 5 . D A W E T E R S OF EQN (7#) AND IONIC B-COEFFICIENTS (dm3 m01-l) IN DIMETHYL- FORMAMIDE

ions

temp./"C b x lo3 a = Bt- Et4N+ Pr4N+ Bu4N+ &N+ Hex4N+ Hept,N+ K+

25 2.277 1.21 -0.14 0.04 0.13 0.19 0.24 0.30 -0.11 30 1.991 1.24 -0.18 0.02 0.11 0.16 0.20 0.26 -0.16 35 1.991 1.24 -0.18 0.01 0.11 0.16 0.20 0.26 -0.16 40 1.914 1.25 -0.18 0.00 0.11 0.16 0.21 0.25 -0.18

TABLE B.-IONIC B-COEFFICIENTS IN METHANOL AND FORMAMIDE AT 25°C

B* /dm3 mol-1 ions methanol formamide

Li+ Naf K+ Rbf Csf Me4N+ Et4N' Pr4N+ BLI~N+ n-Am4N+ (EtOH)4N+ Cl- Br- I- Pi-

- 0.23

- - 0.03

0.10 0.24 0.38 0.52 0.52 0.48 0.46 0.42 0.78

0.3 18 0.436 0.21 1

0.181 0.155

0.514 0.71 3

0.160 0.118 0.088

-

1 4 1

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1282 VISCOSITY B-COEFFICIENT OF THE JONES-DOLE EQUATION

method could be considered as a particular case of our more general method. How- ever, after the publication of new data relating to B-coefficients in sulpholan,l* hexamethylphosphotriarnide and ethylene carbonate,l doubts arose concerning the method of Yao and B e n n i ~ n , ~ due to the fact that from the equality of the dimensions of the i-Am,BuN+ and Ph4B- ions, the equality of the B-coefficients of these ions does not automatically follow. Since these ions, like large tetra-alkyl- ammonium ions, are unsolvated in organic solvents,14* 15* 2 2 s 23 equations similar to eqn (6) and (7a) can be written for them. However, the coefficients of these equations will probably be both solvent and ion structure dependent. In table 7 a comparison of the ionic B-coefficients calculated by different methods for hexamethylphosphotri- amide, ethylene carbonate, sulpholan and acetonitrile is shown. As can be seen from the table, the BimAmJBuN+ values calculated by different methods for the first three solvents are in poor agreement. A possible explanation of this fact could be the phenomenon that the pattern of streams of liquid near asymmetrical tetra-alkyl(ari1)- onium ions is different from the pattern neax symmetrical tetra-alkylammonium ions. Only in acetonitrile solutions, where the experimental B values from previous work6* 31 were used, are the BPh4B- values calculated by two different methods in good agreement. Therefore, only with the advent of new B-coefficients for series of salts containing tetra-alkylammonium ions will it be possible to apply the general method [eqn (7a)I for the separation of B-coefficients into ionic components, to verify the methods used in table 7 and to draw final conclusions.

As seen from tables 2-5, the &coefficients of tetra-alkylammonium ions are temperature independent in all four amide solvents. In this connection it is of interest to note that the temperature dependence of ionic B-coefficients of mineral ions in organic solvents is similar to the temperature dependence of ionic solvation

TABLE 7.-cOMPARISON OF S O W IONIC B-COEFFICIENTS CALCULATED BY DIFFERENT METHODS

hexamethyl- 25

ethylene 25

sulpholan 30

phosphotriamide

carbonate

40

50

ace t oni t rile 25

1.55a 3.1gb 0.59" 0.6gb 0.95' 1 .oob 0.84' 0.94b 0.75' 0.94b 0.735"

1.55"

0.59'

0.95'

0.84'

0.75'

- -

-

- -

0.735' 0.734'

- 2.6gb

0.5gb

0. 84b

0.7gb

0.7gb

-

- - -

- 0.616'

*The ionic B-coefficients were calculated by the Yao and Bennion rne th~d ,~ Bi-AmjBuN+ = B P ~ ~ B - ; b the ionic B-coefficients were calculated by the solution of the system of eqn (9) and (10) for Bu4NI and i-Am3BuNI solutions ; the ionic B-coefficients were calculated by the solution of the following system of equations :

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B. S. KRUMGALZ 1283 radii (rs). Earlier we have shown 32 that in N-methylacetamide dr,/dT < 0 for alkali cations and drs/dT > 0 for halide ions. The temperature dependence of ionic B-coefficients for mineral ions in N-methylacetamide is similar: dB+fdT < 0 and dB-/dT > 0. The same pattern is observed for all solvents studied.

Kaminsky 33 suggested that the values of B+ < 0 and dB+/dT > 0 are character- istic of ions breaking water structure. Gopal and Rastogi * extended this conclusion to amide solutions, considering that LiCl and KI in N-methylacetamide and N- methylpropionamide are structure-making salts, since dBLicl/dT < O and dBKI/dT < 0, and that salts containing tetra-alkylammonium ions are structure-breaking ones, since dBRdNI/dT > 0. As can be seen from the results given in tables 2-5, the temper- ature coefficients of ionic B-coefscients have different signs for cations and anions in all amide solutions examined. Consequently, the cations and anions affect these solvents' bulk structure in opposite ways.

1.50 -

1.00 - L 8 5 5 a 4 0.50-

P

C R 4 N + /A3 FIG. 2.-Relationship between B-coefficients of tetra-dkylammonium ions and their dimensions in

In fig, 2 the relationship between the average values of ionic B-coefficients of tetra-alkylammonium cations md their dimensions is presented €or all organic solvents studied. The calculation of the radii of tetra-alkylammonium cations (except Me4N+ and Et4N+) used for the construction of this figure is given above. The radius of the Me,N+ ion, which has a tetrahedral structure, was calculated as the sum of the C-N distance (& = 1.34A is the mean value from a number of literature values quoted by Emsley and Smith 34) and the height of the CH3 group (calculated previously by the present author : ZcH3 = 0.82 if 35). Then r M e 4 ~ + = I~-N+ZCH~ = 2.16k The radius of the Et4N+ ion, equal to 2.79& was found by the present

organic solvents. Symbols as in fig. 1.

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1284 VISCOSITY B-COEFFICIENT OF THE JONES-DOLE EQUATION

author by interpolating from the variation of the rR,N+ values with the number of carbon atoms in tetra-alkylammonium cations.22 For every organic solvent the experimental data are situated on two straight lines with the points of intersection situated between Pr4N+ and Bu4N+ ions. This fact provides the supporting evidence of the lack of solvation of large tetra-alkylammonium ions in organic solvents and the points of intersection allowed us to calculate the radius of a hypothetical ion of R4N+, starting from which the solvation of larger tetra-alkylammonium ions ceases in organic solvents. These radii of such a hypothetical ion in different organic sol- vents calculated by the least-squares method are as follows : for N-methylformamide, 3.50 ; for N-methylacetamide, 3.32 ; for N-methylpropionamide, 3.57 ; for dimethyl- formamide, 3.51 and for methanol, 3.38 A. The average value of the radius of such a hypothetical ion is equal to 3.46 + O . l O A. Taking into consideration the accuracy of determination of B values and their division into ionic contributions, it should be emphasized that this value is in good agreement with the assumption developed earlier that the lack of solvation in organic solvents is characteristic of tetra-alkyl- ammonium cations with dimensions larger than the Pr4N+ ion.l4* l5, 2 2 s 23

TABLE ~.-VALWS OF THE k - c o m m c ~ ~ ~ ~ FROM EQN (11) FOR DIFFERENT ORGANIC SOLVENTS

N-methyl- N-methyl- N-methyl- dimethyl- solvent formamide acetamide propionamide formamide methanol

k x 10-Z1/mol-l 6.1& 7.785 10.586 1.991 6.343

We would like to discuss here the relationship between the BR4N+ values for large unsolvated tetra-alkylammonium ions (starting from Bu4N+) and their dimensions in more detail (fig. 2). In this figure, the dashed line is calculated from eqn (5). For methanol and N-methylformamide, the experimental values of B for tetra-alkyl- ammonium ions are very close to the theoretical straight line, consequently the

As can also be seen from fig. 2, the BR4N+ values, starting from the Bu4N+ ion for all organic solvents studied, lie on straight lines described by the equation

B E h t R4N+ is a main contribution in the BR4N+ values in these solvents.

The coefficient k from eqn (1 I), calculated by the least-squares method for all systems studied, is given in table 8. First of all, k-coefficients for methanol and N-methyl- acetamide solutions are very close to the theoretical value of the coefficient in eqn (5). In addition, as seen from table 8, the k-coefficient is dependent on solvent nature and structure. It is interesting to compare the k values for N-methylformamide (NMFA), N-methylacetamide (NMAA) and N-methylpropionamide (NMPA), whose intrinsic structures are very similar owing to the H-bonds of the -NH(CH3) group. The differences in their structures are not qualitative ones ; they are only quantitative ones conditioned by the solvent molecules’ dimensions. Probably, therefore, for these solvents, the ratio of B-coefficients for any R4N+ ion (starting from Bu,N+)

is very close to the ratio of molal solvent refraction

or to the ratio of molal solvent volumes calculated in the studied temperature interval

(BR4N+)NMFA : (BR4N+)NMAA : (BR~N+)NMPA = ~ N M F A : ~ N M A A : ~ N M P A = 1 : 1.26 : 1.71

R-A : R m u : RNMpA = 1 : 1.30 : 1.60

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B. S. KRUMGALZ 1285

Recently, Feakins et ~ 1 1 . ~ ~ found that the B values depend on the molal volume of the solvent according to the equation

where 57:: and 7; are the partial molal volumes of the solvent and solute, respectively, as c -+ 0, Ap!* is the contribution per mole of solute to the free energy of activation for the viscous flow of the solution and A&* is the free energy of activation per mole of the pure solvent. From this equation it follows that B-coefficients are proportional to the molal solvent volume. It is precisely this equation that can explain the above- obtained results, that ionic B-coefficients of tetra-alkylammonium ions are propor- tional to the solvent molecule volume in a group of solvents with a similar nature and structure.

Eqn (3) and ( 5 ) allowed us to calculate the BEN+ values for large tetra-alkyl- ammonium cations. First of all the BE%+ values calculated for these ions from eqn ( 5 ) are as follows: BEE^+ = 0.36, B ~ : N + = 0.50, BHex4N+ = 0.67 and BHept4N+ = 0.82. The B E N + values calculated from eqn (3) using the above values of Bg&y: are presented in table 9.

Einst

Einst

TABLE g.-vauEs OF B:& + FOR LARGE TETRA-ALKYLAMMONIUM CATIONS IN ORGANIC SOLVENTS

N-methyl- N-methyl- N-methyl- dimethyl- ions methanol formamide acetamide propionamide formamide

Bu~N+ 0.02 - 0.02 0.09 0.23 - 0.24 Am4N+ 0.02 0.00 0.1 1 0.34 - 0.33 Hex4N+ - 0.03 0.14 0.43 - 0.46 Hept4N+ - - 0.02 0.20 0.55 - 0.55

The examination of this table shows that in methanol and N-methylformamide solutions, the B&+ values are neghgible and consequently the B&+ values for large tetra-alkylammonium cations are effected only by the Einstein effect. In N-methyl- acetamide and N-methylpropionamide solutions, the effects related to the destruction of solvent structure in the region of the ionic cosphere are also significant together with the Einstein effect. For the explanation of the negative values of BEN+ in dimethylformamide solutions, it is essential to obtain the B E N + values in other organic solvents without H-bonding, such as acetone, dimethylsulphoxide, etc.

It should also be emphasized that as more data concerning the B-coefficients at different temperatures become available for the solvents mentioned in this paper and for other solvents, the correlation equations can be improved. More precise ionic B-coefficients can then be obtained and more will be learned about ion-solvent interactions in various solvent systems.

The author thanks Dr. Colin A. Vincent for the use of his unpublished data for formamide solutions and Ms. K. Diskin for language corrections to the manuscript.

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1286 VISCOSITY B-COEFFICIENT OF THE JONES-DOLE EQUATION

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(PAPER 9/1202)

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