-
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.
l1S3
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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
1154
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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~
1155
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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.
1156
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.
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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
7. VAND, V., J. phys. colloid Chem., 52 (1948), 277.8. THOMAS,D.
J., J. colloid Sci., 20 (1965, 267.9. MOULIK, S. P., J. phys.
Chem., 72 (1968), 4682.
10. MOULIK, S. P., J. Indian chem. Soc., 49 (1972), 483.11.
GLASSTONE,S•• LAIDLER,K. & EYRING,E., The theory of
rate Processes (McGraw Hill, New York), 1941.12. GOLDSACK,D. E.
& FRACHETTO,R., Can. J. Chem., 55
(1977), 1062; 56 (1978), 1442.
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.
1157