Indian Journal of ChemistryVol. 19A. December 1980. pp. 1153-1157

Viscosity of Concentrated Aqueous Solutions of I:I ElectrolytesB. SAHUt & B. BE HERA·

P. G. Department of Chemistry. Sambalpur University. Burla 768017

Received 13 March 1980; revised and accepted 12 May 1980

The variation of relative viscosity. 'Jr. of concentrated aqueous solutions of 1 : 1 electrolytes with electrolyteconcentration is represented by a general equation by extending the limiting equation of Einstein. An empirical equationrelating B and V of electrolytes in aqueous solutions is obtained by least squares analysis. This empirical equationresembles more closely B...., 2.5 V. Assuming the applicability of this equation to ions in solution. the hydrationnumbers of ions have been calculated and their dependence on ionic radii. ionic molar volumes and ionic B± have beendiscussed in the light of structure-making and structure-breaking properties of ions in solution.

THE viscosity behaviour of dilute aqueoussolutions of electrolytes has been studied indetail and numerous empirical relations havebeen reported+> to explain the variation of viscositywith concentration. The relative viscosity, ljr. i.e.the viscosity of solution with respect to solvent, isgenerally used in most of the empirical relations.

For dilute solutions (e ~ 0.1 M), the theoreticalrelation of Enstein+ gives

'Ir = I + 2.S,p .. (I)where ,p denotes the volume fraction and is equal toe'V, V being the molar volume of electrolyte insolution. On the other hand the Jones-Dole"semiempirical relation gives

'lr = I + A vie + Be .. (2)in which the constant A is identified as ion-ion inter-action and the constant B is identified as viscosityB-coefficient dealing with ion-solvent interactions insolution. These two relations have undergone con-siderable modifications for concentrated solutions(e :;;.O.IM). It has been seen in many cases that theJones-Dole equation is the most appropriate equa-tion for calculating the viscosity of dilute aqueoussolutions of electrolytes. This equation is used forconcentrated solutions in the following forme.

'lr = I + Be .. (3)Unlike the viscosity behaviour of dilute solutions,representation of viscosity at concentrations> O.IMby one general equation becomes difficult. Vand",Thomas" and Moulik" have extended the limitingequation of Einstein to higher concentrations andhave advanced some useful relations which havebeen tested for their general validity in higher con-centrations of limited range by Moulik-s. Based onthe Eyring's'! theory of absolute rate for viscous

tPresent address: Department of Chemistry. G. M.College. Sambalpur

flow of liquids, Goldsack and Franchetto-s andBehera-" successfully explained the variation ofviscosity with concentration for aqueous solutionsof electrolytes of alkali metal halides and non-elec-trolytes respectively.

Breslau and Miller-s utilised the Thomas' equa-tion;

ljr = I + 2.S,p + 1O.OS,p2 .. (4)and calculated the molar volumes of a number ofaqueous electrolyte solutions. The method thusemployed to calculate Y, is a risky one and it isclearly pointed out by Moulik-? that the main defectlies in selecting the constant, 10.0S in Eq. (4). Thecomparison of Einstein's equation (I) with Jones-Dole equation (3) brings out clearly the relation,

B = 2.S V, .. (S)

but the statistical analysis of Breslau and Miller-ssuggests the following relation between Band Vewhere Ve is the average effective rigid molar volume:

B = 2.90 v; - 0.Ql8. ..(6)Equations (S) and (6) do not agree well with eachother.

In view of the foregoing discussion we feel that ageneral equation may be developed to explain theconcentration dependence of viscosity of concen-trated aqueous solutions of electrolytes. In thispaper we have modified the Einstein's limiting equa-tion to a general equation of the form (7)

where k's are constants. A curve-fitting computa-tional method has been carried out to test the vali-dity of this equation for concentrated solutionsof some aqueous solutions of 1 : 1 electrolytes at2SoC.

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INDIAN J. CHEM., VOL. 19A, DECEMBER 1980

Materials and Methods

The relative viscosities of LiBr, LiI, NaI, NaN03,NH4Cl, NH4Br, NH41 and KNOa by the methoddescribed in our earlier paper". The pure salts wererecrystallised from water and were dried in an airoven for two days at 150°C before use. Most ofother experimental 'YJr data for our calculations weretaken from literatures,

Results

The relative viscosity data along with the cal-culated values of viscosities obtained from Eq. (7)are given in Table 1.

Since ,p = cY, Eq. (7) can be written as'ljr = I + 2.5 cY + k1c2V2 + k2c3V3 + k3C4Y4

.. (8)

Assuming V not to vary appreciably with concentra-tion we computerised Eq. (8) taking Tjr as a func-tion of c. Thus the computerised equation is :

'ljr = 1 + alc + a2c2 + aac3 + a4c& .. (9)The least error of estimate was considered in selectingat's. Comparing Eqs. (8) and (9) we see that, V =al/2.5; kl = a2/V2, k2 = aa/ya; and ka = a4/V4The correlation coefficients, kt's, the molar volumes(Y), the standard error of estimate and the standarddeviations in 'ljr for the concentrated aqueous solu-tions of 1 : 1 electrolytes at 25°C are presented inTable 2.

DiscussionThe values of Y obtained by Breslau and MiUer14

from the satistical analysis are quite different from

TABLE1 - EXPERIMENTALANDCALCULATEDRELATlVBVISCOSITIESOF AQUEOUSELECTROLYTESOLUTIONSAT25°C

'lr 'lr 'lr

M Expl Calc. M Expl Calc. M Expl Calc.

Lithium iodide Sodium iodide Ammonium iodide

0.0995 1.0038 1.0048 0.0975 1.0137 1.0123 0.3824 0.9716 0.97070.1990 1.0135 1.0118 0.1950 1.0150 1.0145 0.5736 0.9533 0.95820.2997 1.0181 1.0184 0.2925 1.0182 1.0170 0.9943 0.9361 0.93460.3996 1.0245 1.0247 0.3900 1.0202 1.0196 1.1473 0.9244 0.92770.4995 1.0311 1.0310 0.4875 1.0225 1.0225 1.7210 0.9075 0.90570.5990 1.3372 1.0374 0.5850 1.0243 1.0256 2.2985 0.8930 0.89270.6997 1.0447 1.0441 0.6825 1.0252 1.0290 2.8684 0.8880 0.88750.8006 1.0488 1.0511 0.7995 1.0285 1.0334 3.4420 0.8885 0.88891.0008 1.0682 1.0662 0.9946 1.0455 1.0417 4.2070 0.8990 0.90011.4982 1.1084 1.1088 1.9891 1.1115 1.1060 4.7807 0.9148 0.91412.0029 1.1453 1.1452 2.9837 1.2137 1.2179

3.9977 1.3971 1.3960

Ammonium chloride Ammonium bromide Lithium bromide0.4991 0.9964 0.9948 0.1379 0.9959 0.9952 0.1873 1.0182 1.020.6000 0.9954 0.9933 0.4136 0.9851 0.9857 0.3747 1.0430 1.03940.9998 0.9912 0.9883 0.7583 0.9752 0.9755 0.7494 1.0817 1.7781.4997 0.9860 0.9844 0.9927 0.9715 0.9697 1.1240 1.1147 1.01611.9996 0.9824 0.9829 1.3787 0.9613 0.9619 1.4987 1.1487 1.15482.4995 0.9823 0.9836 1.9991 0.9523 0.9536 2.2481 1.2376 1.23552.9994 0.9823 0.9863 2.4817 0.9507 0.9505 3.3722 1.3679 1.37233.4994 0.9866 0.9907 2.9918 0.9512 0.9499 4.4962 1.5536 1.54073.9993 0.9992 0.9968 3.4467 0.9509 0.9515 5.6202 1.7473 1.75444.4992 1.0192 1.01i9 6.7443 2.0258 2.02754.9991 1.0301 1.0330 8.2430 2.5093 2.5079

Sodium nitrate Potassium nitrate0.4936 1.0251 1.0286 0.0100 0.9999 0.99971.0284 1.0763 1.0826 0.0500 0.9985 0.99791.4809 1.1541 1.1430 0.1000 0.9963 0.99791.9745 1.2317 1.2216 0.6000 0.9961 0.99262.50 1.3105 1.3171 0.8400 0.9956 0.99262.9618 1.3949 1.4089 1.0800 0.9888 0.99433.4538 1.5107 1.5131 1.3201 0.9978 0.99774.1136 1.6691 1.6601 1.5601 1.0025 1.00284.9951 1.8764 1.8644 1.8001 1.0082 1.00975.4632 1.9652 1.9746 2.0401 1.0193 1.01826.1704 2.1390 2.1417 2.2801 1.0314 1.02857.3458 2.4205 2.4192 2.5201 1.0375 1.0405

2.7602 1.0571 1.0542 .3.0002 1.0681 1.0697

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SAHU & BEHERA : VISCOSITY BEHAVIOUR OF CONe. SOLUTIONS OF 1 : 1 ELECfROL YTES

TABLE 2 - VALUES OF v: THE CoRRELATION CoEFFICIENTS AND STANDARD ERRORS[B and V in dm" mol-t]

Electrolyte Cone. No. of B V- k, ka ka St. error (&'1].) Ref. to datarange(M) data points source

LiCI 0.10 -3.9 10 0.143 0.057 2.30 5.647 0.007 0.002 3LiBr 0.18 -8.2 11 0.106 0.042 -2.30 21.74 0.02 0.006 This workLil 0.10 -2.0 11 0.081 0.032 -45.86 1468.06 12535.0 0.004 0.001 -do-LiCIOa 0.02 -6.2 12 0.126 0.056 -1.17 19.09 O.oI 0.006 3LiNOs 0.1 -5.4 11 0.101 0.042 1.11 33.38 0.01 0.004 3NaCl 0.05 -5.0 12 0.0793 0.034 9.94 5.74 158.6 0.006 0.002 3NaBr 0.1 -7.0 16 0.0443 0.017 61.06 -309.6 4223.0 0.003 0.001 This workNaI 0.1 -4.0 12 0.0178 0.008 146.62 4893.3 0.01 0.001 -do-NaCNS 0.5 -5.0 6 0.064 0.022 15.40 310.14 0.002 0.001 18NaCI0. 0.001-2.0 7 0.030 0.007 473.25 0.003 0.002 3NaNOa 0.5 -7.3 12 0.040 0.016 184.21 1200.09 2905.9 0.023 0.009 This workKF 0.5 -6.5 12 0.113 0.046 7.47 -15.23 43.66 0.018 0.008 3KCI 0.4 -4.0 11 -0.014 -0.005 334.14 0.002 0 3KBr 0.05 -3.75 11 -0.049 -0.017 35.81 --5.80 0.001 0 3

KI 0.01 -6.0 16 -0.0755 -0.033 18.97 44.54 143.88 0.004 0.001 3KMnO. 0.001-0.45 9 -0.066 -0.024 1.34 6.59 0 0 3KNOs 0.01 -3.0 14 -0.0477 -0.008 206.93 139.53 0.009 0.003 This workRbNO. 0.1 -2.0 11 -0.076 -0.027 36.75 75.41 0.001 0 3CsCI 0.6 -4.0 5 -0.052 -0.019 36.01 29.16 0 0 3CsT 0.01 -2.0 11 -0.118 -0.047 9.47 32.59 -237.64 0.001 0 3AgNO. 0.005-5.2 15 0.0438 0.020 41.64 -69.48 476.0 0.002 0.001 3NH.Cl 0.5 -6.0 11 -0.0144 -0.008 80.94 419.07 0.011 0.004 This workNH,Br 0.1 -3.4 9 -0.0394 -0.016 35.64 118.00 0.003 0.001 -do-NH,I 0.4 -4.78 10 -0.080 -0.032 16.02 22.32 0.004 0.001 -do-NH,NO. 0.05 -9.46 12 -0.0537 -0.019 47.16 219.86 847.32 0.004 0.001 -do-

the values reported in this paper (Table 2). Theerrors in V values of Breslau and Miller are quitehigh (in some cases more than 100%) whereas inthis work the error of estimate and the standarddeviations in '1r are quite low.

In Fig. 1, we have plotted B, obtained from litera-ture8,14 against V for the 1 : 1 electrolytes taking thenew V values. A least square analysis of the BandV values suggests the empirical relation,

B = 2.50 V-O.OO23 .. (10)

which clearly resembles Eq. : (5) than Eq. (6) Theconstant involved in Eq. (10) has the same units asB or V The constant, 10.05 in Thomas' equation(4) is not valid for all the 1 : I electrolytes as evidentfrom Table 2. Instead of 10.05, one can use a gene-ralised constant, kl' which takes the value between-45 to 473 (Table 2). Examination of Table 2,shows that the V values of electrolytes are eitherpositive or negative. It is interesting to note thatboth B and V values are negative for those electrolyteswhich are considered as structure-breakers in solution.

The ionic molar volumes, V±, can be obtainedfrom the ionic B± coefficients by applying Eq (10)to ions in solution", Thus B± and V± for the ionsin solution are related by the relation (I I)

B± = 2.50 V± - 0.0023 .. (11)The hydration numbers, ns, of ions can be calcu-lated from Eq. (12),

.. (12)

0.15

0.1

0.05

80

-0.05

-0.1

-0.05 0 0.05

ii

Fig. 1 - Plot of B versus Y for different electrolyts [Both Band Vare in dm' mol" ']

where Vion is the bare ion valume and V~ is thevolume of water. Thus the hydration numbers ofions are given by the relation

V± - Vionno = V; _.(14)The results of such calculations, given in Table 3,

show that the structure-making ions like Li+, Na+,Ag+ and F- have positive ionic molar volumes andhydration numbers and the structure-breaking ionslike K+, ns-, cs-, Cl-, Be, 1-, NO; and CIO~

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INDIAN J. CHEM., VOL. 19A, DECEMBER 1980

8

6

4

tSt r ucf ure

making

nB 0StructurtbrQoking

-2 !-4

-G

-8

Fig. 2 - Plot of nB versus reA) for different electrolytes

8

6

4

+2 I

Structurernoking

na 0 ·0.1 -0.05 0~!:-uch;ra N~

-2 "rc·~;r.9 J 1-~ ~"/Ci

R,' I-4 (

Cs" :.:£e,-

] " NO;-r~ CI04

I

0.1 0.15B~

JFig. 3 - Plot of nB versus ionic B+ coefficients for different

electrolyts [The ionic B± values are in dm! mol-l]

have negative ionic molar volumes and hydrationnumbers in solution. The correlation of hydrationnumbers with ionic radii in solution is shown gra-.phically in Fig. 2. It is seen that the hydrationnumbers of alkali metal ions as well as of ammoniumion fall on a linear plot and those of halide ions andnitrate ion fall on a separate linear plot. Thedependence of hydration numbers of ions on theionic radii is in line with the work of Kestov-" whocorrelated the change in entropy of water in ionicsolutions with the ionic radii and clearly showedthat there exists linear relations between the twoparameters of the alkali metal ions and halide ionsseparately.

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TABLE3 - IONIC PARAMETERSAT 25 °C

Ion r B± VO!on V±(A) (dm! mol-l) (ern" mol-l) (ern" mol-t) nB

Li+ 0.94 0.1495 2.09 60.70 8.8Na+ 1.17 0.0863 4.04 35.40 4.7K+ 1.49 -0.0070 8.34 -1.88 -1.5Rb+ 1.63 -O.Q300 10.91 -11.08 3.3Cs+ 1.86 -0.0450 16.22 -17.08 -5.0NH~ 1.44 -0.0074 7.52 -2.04 -1.4Ag+ 1.13· 0.0910 3.64 37.3 5.1F- 1.16 0.096 3.93 39.32 5.3Cl- 1.64 -0.0070 11.12 -1.88 -2.0Br 1.80 -0.0420 14.70 -15.88 -4.61- 2.05 -0.0685 21.70 -26.48 -7.3NO; 2.03b -0.0460 21.10 -17.48 -5.8CIO~ 2.29b -0.056 30.30 -21.48 -7.8

(·)Goldschmidt radii; and (b)Pauling's ionic radii

The hydration numbers of ions are plotted againstthe ionic B± coefficients in Fig. 3. The hydrationnumbers of positive and negative ions bear differentlinear relationships with their ionic B± coefficients.This supports the idea that structure-making ionshave positive ionic molar volumes, positive hydra-tion numbers and positive entropy changes whilestructure-breaking ions have negative ionic molarvolumes, hydration numbers and negative entropychanges in aqueous solutions. The idea of positiveand negative hydration's and hence the positiveand negative hydration numbers get support fromthe work of Angel'? who correlated the ionic mobi-lity with ionic B± coefficients.

The use of Pauling's ionic radii to calculate the"ion of the bare ion shows that ions like Li+ (o.6A),Na+ (o.9SA), K+ (1.33 A), F- (1.36 A) and Ag+(1.13 A) fit well into the cavity formerly occupiedby a water molecule whose radius is 1.38 A (~ =6.62 cm3/mol). It is well-established that the K+ion is a structure-breaker in waterl-3 and hence theuse of Gourary and Adrian ionic radii19 clearlyshows that Li+, Na+ Ag+ and F- are electrostruc-tive structure-making and positively hydrating where-as K+, Rb+, cs-, NH!, Cl-, Be, 1-, NO; and CIO~are structure-breaking and negatively hydrating2o,21.

Inspection of Table 3 shows that the hydrationnumbers of ions vary from +9 (Li+) to -8 (ClO~).The magnitude of hydration numbers suggests thatthe structure-breaking effect is in the order Cs+>Rb+>K+ ::::::NHt for cations and CIO~>I->NO-;>Br" > CI- for the anions. The ions Cs+ and CIO~ dueto their bulky size disrupt the water structure in boththe primary and secondary hydration spheres insolution.

References1. HARRAP,B. S. & HEYMANN,E., Chem. Rev., 48 (1951), 46.2. PARTINGTON,J. R., Treatise on physical chemistry, Vol. 2

(Longmans Greens, New York), 1951, 70.3. The international encyclopedia 0/ physical chemistry and

chemical physics, VoL 3, edited by R. H. Stokes (PergamonPress), 1965.

SAHU & BEHERA : VISCOSITY BEHAVIOUR OF CONC. SOLUTIONS OF 1 : 1 ELECfROL YTES

4. EINSTEIN,A., Ann. Phys., 19 (1906), 289; 34 (1911), 591.5. JONES,D. & DOLE, M., J. Arn. chem. soe., 51 (1929), 2950.6. DAS, P. K., SATPATHY,B. M., MISHRA,R. K. & BEHERA,

B., Indian J. Chem., 16A (1978), 959; MOHAPATRA,P. K.,NAIK, K. B., MISHRA, R. K. & BEHERA,B., Indian J.Chem., 18A (1979), 402

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10. MOULIK, S. P., J. Indian chem. Soc., 49 (1972), 483.11. GLASSTONE,S•• LAIDLER,K. & EYRING,E., The theory of

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13. MISHRA,R. K. & BEHERA,B., Indian J. Chem., 18A (1979)445.

14. BRESLAU,B. R. & MILLER,F. R., J. phys. Chem., 74 (1970),1056.

15. KRESTOV,G. A., Zh. strukt. Khim., 8 (4) (1962), 402.16. SAMOILOV,O. YA., in Water and aqueous solutions edited by

R. A. Horne, (Wiley Interscience), 1972,597.17. ANGELL,C. A. & SARB,E. J., J. chem. Phys., 52 (1969),

1058.18. JANZ,G. J., OLIVERB. G., LAKMINARAYAN,G. R. & MAYER.

G. E., J. phys. Chem., 74 (1970), 1285.19. GOURARY,B. S. & ADRAIN, F. J., Solid State Phys., 10

(1960), 127.20. FRANK, H. & WEN, W. Y., Disc. Faraday ss«. 24 (1957).

133.21. SAMOILOV,O. Ya., Disc. Faraday Soc., 24 (1957), 141.

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