Indian Journal of ChemistryVol. 24A, March 1985, pp. 180-186

Conductance of Some 1:1 Electrolytes in Water & the TransitionModel of Electrolytic Behaviour

PREM P SINGH

Department of Chemistry, Maharshi Dayanand University, Rohtak 124001

Receired 3 May 1984; revised and accepted 6 August 1984

An expression has been derived for the equivalent conductance, A, of an electrolyte in water by taking into considerationthe influence of the external electrical field on the behaviour of ions [P P Singh, J Am chem Soc, 99(1977) 1312]. The equationembraces all the characteristics of the Fuoss-Hsia and Debye-Huckel-Onsager conductance equations for solutions with C<0.02 M. It has been employed to evaluate /\ 0 at 2SoC for a number of I: I electrolytes from the corresponding /\ data at C=0.01 and 0.02 M only. The calculated /\0 values compare very well with the corresponding /\ 0 values reported for theseelectrolytes. Again, the calculated /\ values at 2ST for these I: I electrolytes in water at C =O.OOOS,0.001 and O.OOSM(utilizing/\

0 and S values obtained from /\ data at C =0.01 and 0.02 M only) also compare well with the corresponding experimentalvalues. The basic equation has also been reasonably successful in describing the available /\ data of NH.CI, KBr, HCt, HBrand HI in water at 2S"C (in the concentration range C = O.OS- 1.0 M).

Eversince the discovery of Kohlrausch andHeidweiller's empirical law of independent migrationof ions in infinitely dilute solutions, the interpretationof the phenomena of electrolytic conductance has beenengaging the attention of theoretical chemists 1 -7. Inthe existing approaches 1 -7 it has been assumed that anion is a rigid charged sphere that moves in ahydrodynamic and electrostatic continuum. Such anassumption, however, would be true for very dilutesolutions (C <0.005 M) so that the On sager andFuoss's expanded equation of conductance 1 would bestrictly valid for very dilute solutions of electrolytesonly; it would fail to explain the conductance ofconcentrated solutions (C >O. I M) of electrolytes. Theproblem is all the more acute" -14 when it comes to ananalysis of the conductance data of electrolytes thatform ion-pairs in water. This calls'5(a) for analternative approach to express the conductance dataof electrolytes (in the concentration range C >0.05 M)in water. Singh has recently presented a model of ionicbehaviour' (, in water that successfully explains anumber of thermochemical properties 17 -19 of simpleelectrolytes in water at 25 C. It would be instructive tosee as to how this model' (, could be employed todescribe ionic behaviour under an external electricalfield.

The model of ionic behaviour & the influence of external electricalforce on the ionic behaviour

A close examination?" of the statistical mechanicalfoundations of Debye-H i.ickel theory/ I has led to anappreciation of its limitations+' "20. Bahe!" hasrecently proposed that when an ion exists in acoordination sphere of water (solvent), the fieldgenerated by the ion changes the dielectric constant of

180

the medium surrounding it. The ion thus acts as acharged rigid sphere (with charge located at the centre)in a sea of dielectric gradient of certain depth so thation-ion interactions involve not only the charge on theions but also the interactions of the field of an ion withthe dielectric gradient sea surrounding the other ions.Bahe27 showed that, a + ve ion of charge ej and a - veion of charge e, in water at a center-to-center distanceR between them (i.e. R is the radius of the ionicatmosphere of the "lattice" cloud) would feel acoulombic force that varies as R -12 and a repulsivefield dielectric gradient force that drops off as R -4.

This led Bahe27 to assume that ions in solution tend toassume loose lattice arrangements, the particular typeof the lattice being dictated by the type of theelectrolyte. The actual situation may lie in between thetwo extremes 16 represented by the Debye-Huckeltheory and the Bahes model. At any concentration anion thus has a definite probability to exist (i) as a freeion and (ii) as a coordinated ion (by solvent molecules).The ions in the coordinated stage would tend toassume a loose lattice structure, while in the free statethey would cause structural alignment in the solventwhich together with the thermal energy would causethe ions, in the zeroth approximation, to behave likeDebye ions. Each ion would, therefore, have a definiteprobability to act as the Debye ion or the lattice ion.The difference between a concentrated and a diluteelectrolyte solution is merely of degree rather than ofkind.

Consider now a solution that contains only twoionic species of concentrations nand n (ions/ern 3) and

I }

charges e = z e and e. = ze, where z and z, are theirI' I } I)

respective valences and e is the proton charge. Whenno external field is applied. the ions are symmetrically

SINGH: TRANSITION MODEL OF ELECTROLYTIC BEHAVIOUR

distributed about the central ion. An external field willgenerate an asymmetry in the distribution of ionssurrounding the central ions which will then take adefinite time to re-establish the symmetry (relaxationeffect) and so retard the motion of the central ion. Atthe same time the external field also causes the ionssurrounding the central ion to move in a directionopposite to the central ion carrying with them thenearby solvent particles (electrophoretic effect). If DEand VRdenote respectively the electrophoretic andrelaxation velocities of an ion under the influence ofthe external field and D is its velocity in the direction ofthe external field in the absence of electrophoretic andrelaxation effects, then the drift velocity, Vd, in thedirection of the external field is given byi5(b) Eq. Lvd=VO-(IIE+VR) ... (1)

Since at any concentration an ion is assumed to have adefinite probabilityl6 to act as a Debye-Huckel (DH)ion or a lattice (L) ion, the drift velocity of the ith ionmay be expressed as

vii) = [viz)]DH [probability that an ion behaves as aDebye-Huckel ion] + [vil)]L [probability that anion behaves as a lattice ion] ... (2)

But the probability that an ion, in an electrolyticsolution of molality m, behaves as a Debye-Hiickel ionwas shown 16 to be given bye-15m, SO that,

viI) = [vil)DHe -15m+(ViIMl-e -15"') ... (3)

We now evaluate the [Vd(I)]L component of the driftvelocity.

When an ion exists in a coordination sphere of water(solvent) molecules, the net force along the line ofcentres between any pair of oppositely charged ions ofcharges e and e at a center-to-center distance R is

'7 Jgiven by2 Eq. (4)

ee 3 e2 I dE I I

F = - eRz + 4(;~2n) dR VscaR4 ... (4)

where Eis the dielectric constant of the bulk medium, Co

is the dielectric constant at the surface of the ion andV,ea is the volume of the dielectric gradient sea. Sincean external electrical field generates an asymmetry inthe distribution of ions surrounding the central ion,which then takes a definite time to readjust to the newposition of the central ion, the center of charge on themoving ion does not coincide with the center of itsoppositely charged "lattice" cloud. If d is the distancethrough which the center of charge of the central ionand the center of charge of the oppositely charged"lattice" cloud are displaced (i.e, d is a measure of thedistortion of the "lattice" cloud) and if the ions of the"lattice" cloud are assumed to relax by the random-walk process, then the relaxation force FR(i) acting on

the central ion i in the "lattice" configuration is givenby15(C),

[ee 3 e21de I 1 Jd

(F ilk = eRi + 8n e~ dR (VseJ R4 R ... (5)

where R is the radius of the ionic atmosphere of thelattice cloud. Since the migration of ions is due to theirdrift velocity acquired under the influence of theexternal electrical field and as it is superimposed 15(d)on their random walk, the time taken by the "lattice"cloud to relax can be estimated by the Einstein-Smoluchowski relationship if the ions constituting the"lattice" cloud are dispersed by a mechanism 15(0)"none other than the random walk process". Now ifthe charge density of the "lattice" cloud declines ratherrapidly at distances greater than R, the central ion, i,may be considered to have lost its "lattice" cloud whenthe "lattice" ions diffuse to a distance R. In that casethe distance dthrough which the center of the charge ofthe central ion and the center of the "lattice" cloud aredisplaced is given byI5(C),

d 0'R2/-O= Vj 2UabS kTwhere U~bsis the absolute mobility of the central ion.Eq. 5 then yields,

x [ DjoR J2U~bSkT

Further, as the velocity V~isdue mainly to the externalelectrical field, v/U~bSis given byl5(O the relation,

... (6)

v~u~bs=e.x/300 ... (7)

where X is the applied electrical field in volts cm -I

Hence, Eq.6 reduces to Eq. 8,

Since the slope of the dielectric within the "gradientsea" is assumed to be constant!", the quantity insidethe bracket in Eq. 8 is constant '", say K, so that,

., .(9)

It has so far been assumed that it is the motion of thecentral ion in the direction of the applied external fieldthat is responsible for destroying the sphericalsymmetry of the "lattice" cloud. Actually the externalfield produces a drift which issuperimposed on the

181

INDIAN J. CHEM., VOL. 24A, MARCH 1985

random walk of the central ion. This would then affectthe time-average shape of the "lattice" cloud andhence the relaxation field. Ifwe suppose that the erraticbehaviour of the central ion has a constant effect, 1., onthe time-average shape of the lattice cloud, then therelaxation field, corrected for this effect, would begiven by Eq. 10,

[F (~] [e:l:X KXe3]

R 1/ L=X 600elaR =»: L ... (10)

But the drift velocity, Vd('),is given byI5(g) the relation,

vil) = u~b.(FRU»Hence,

... (11)

where (U'L = conventional mobility in the latticeconfiguration defined by (u~bse/300 and Q = 300 K e;~

At the same time, under the influence of the externalfield, the ions of the "lattice" cloud surrounding thecentral ion, i, move in a direction opposite to that ofthe central ion. If the asymmetry of the ionssurrounding the central ion is ignored, then as the"lattice" cloud is accelerated by the external force,e;X/300, it is retarded by Stokes viscous flow. Since theelectrophoretic component of the drift velocity of thecentral ion is equal to the electrophoretic velocity of itslattice cloud (as the central ion i shares the motion of itscloud), it follows 15(g) that in the steady state,

... (12)

where R is the radius of the "lattice" cloud, '1 is theviscosity of the solution and [vrtl)]L is the steady stateelectrophoretic velocity of the central ion i.Consequently,

[vrti)]L=e;X/18001t'1R ... (13)so that Eq. 2 (in the lattice configuration) reduces toEq.(l4),

_ ° _ [ejx {eje;X(u~k QX(U~)L}, ](Vil))L-V 18001t'1R+ 2ekTR + R3 X

... (14)

Further, for ions of finite size, the drift velocity in theOH configuration is given byI5(h) Eg. (15),

[

(u?)oHee.(300)w) ] Xe I I K

(Vd(L))OH= vO - 6~f/ + 6ekT 300( I + Ka)

... (15)

182

where a\1 the symbols have their usual significance i "?'so that the net drift velocity of the central ion i, l"dU),given by Eq. 16,vii) = (vii»oHe- 15111 + (~'iI)k(l - e: 15111) ... (16)

yields

I 15[

eX {e e X(U<)Lem' + ~ I

-( - ) 18001tf/R 21;kTR

... (17)

Since the conventional mobility is given by ui = I)X,and as equivalent conductance, A, of an electrolyte isrelated to the mobilities u ; and u . of its constituentions by Eq. 18,A=F(u+ +uJ ... (18)where F=Faraday, Eg. 17 yields.

... (19)

where AO=F(u~+uo_=eguivalent conductance atinfinite dilution, ej=z+e, ej=z_e and z , =Z_ =z.

Further, as R represents the shortest distancebetween a cation and an. anion on a cubic lattice27

, fora solution of molar concentration C,

... (20)

Again K, in the DH configuration, is related 15(i) to themolar concentration C of the solution by Eq. 21,

... (21)

where r = c +z i + c _z ~ = ional strength of the sol ution= 21, so that Eq. (19) yields,

... (22)

... (23)

SINGH: TRANSITION MODEL OF ELECTROLYTIC BEHAVIOUR

... (24)

... (25)

... (26)

and <a has values!" between 1.3 and 1.5 Jl2, but forthe present case we have taken28(al it to be 1.4/1'2.

Results and DiscussionEq. 22 can be expressed in the form of Eq.(27),

A + M ° C I 3(1 - e . I)",) C(I - e - 15",)-- = A - S 1- - - -, -- - - Q 1 - - - -

I-G I-Ci I-G ... (27)

whereM=Ar12e 15"';(1 + 1.4/12) ... (28)

andG=Brl 2eI5"'/(1 + 1.4/' 2) ... (29)

Now for solutions with C <0.2 M, the contribution ofthe C(I-e-'Sm)/(I-G) term is negligibly small ascompared to that of the CI \1 -e-IS"')/(I-G) termand if Q I < S I and if the basic arguments used inderiving Eq. 22 are justified, then a plot of (A + M)(I-G) vs CI/3(1-e-IS"')/(I-G) should be linear withslope S1 and intercept A0. This was actually found tobe true for LiCl, NaCL KCI. KBr. KI, KN03•

KHC03, NaJ. AgN03. HCI, HBr, HI and NaOH inwater at 25 C. In fact. the linearity was found to extendto values upto even C = 0.1 M for most of the I: Ielectrolytes (except in the case of KN03• where it wasupto C =0.05 M)(see Fig. I). Further, the intercepts A°of the (A + M)/(1 - G) vs C 1/3(I - e -IS/,,/( I - G) plotsfor the various I:I electrolytes in water were found tobe in good agreement with the corresponding literaturevalues+"?'. In order to compare the slope SI of the (I\.+ M)/( 1- Ci) vs C I 3( 1- e 15"')/(1 - G) plots with thecorresponding SI values evaluated from Eq. 25. it wasassumed that (AO)l~ A° and that X was the same for allz.z valent electrolytes. This required the priorknowledge of the parameter 1. for the electrolyte and asthere is no independent method available to evaluate itfor the various ::: valent electrolytes, 1. for LiCi wasevaluated on the assumption that the slope SI ofthe(A+M)/(I-G) vs CI/3(1_e-IS"'/(1 -G) plot for LiCI(utilizing A data at 25°C in the range C <0.02 M) wasequal to the S, value evaluated for it from Eq. 25. Thisvalue of I. was next employed to calculate thetheoretical slope S, for the various I: I electrolytesfrom Eq. 25. Such SI values for the various I: I

~ electrolytes are indicated by an asterisk in Table I,andan examination of this table reveals that they compare

170

eo •70

0'1 0'2 0'3 0'41/3 -15mC (1-«)/( I-G)

Fig. I-Plots of (/\ + M)/( I - G) vs C 1 j (I - e -1',,)/( I - G) for LiCI(curve I). NaCI (curve 2). KCI and NH.C1 (curve 3). KBr (curve 4).Nal (curve 5). AgNOj (curve 6). KNOj (curve 7). KCIO. (curve 8.ordinate displaced by - 40.0). RbCIO •. (curve 9. ordinate displacedby -50.0). RbClOj and CsCIOj (curve 10. ordinate displaced b)

- 50.0). and HCI (curve II. ordinate displaced by - 26.0).

reasonably well with the S I values evaluated for LiCLNaCl, KCI, KBr, KHCOJ, NH4CI, HCI, NaOH, HBrand HI from the (A+ M)/(I-G) vs Ct/3(I_e -15/,,/(1- G) plots; the failure in the case of RbCI04, RbCIO 3.

CsCI04, CsCI03, KCI04, KCI03, KN03 and AgN03

may be due to the tendency of these electrolytes toform ion-pairs in water. In all these calculations thenecessary A data at 25"C were taken from theliterature28(bl.2

9(a.b' while the A and B parameters of

the I: I electrolytes were taken from elsewhere "?". Thedata necessary to convert molarities to molalities weretaken from Harned and Owen28

(dl.

Alternatively, if A data at 25°C for an electrolyte insolution at two concentrations (in the range C< 0.02 M) are available, then it should be possible to (i)

evaluate A° and SI for electrolyte and hence (ii)calculate A at any concentration (C <0.02 M) of theelectrolyte in solution. For this purpose, A data28(C).

29(a,b) at 25°C for the various I: I electrolytes in water atC =0.01 and 0.02 Mwereemployed to evaluate AOandSI for the electrolyte by means of Eq. (30),

A+M =AO_S1C1 3(1 -e-IS"')/(1 -G)(C<O.02M)I+G ... (30)

183

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SINGH: TRANSITION MODEL OF ELECTROLYTIC BEHAVIOUR

and these in turn were employed to evaluate A for theelectrolyte in water at C = 0.0005, 0.001 and 0.005 M.Such A values at 25°C for the various I: I electrolytes inwater are recorded in Table I and are also compared

. . I I 28c.29(a.blwith the corresponding expenrnenta va ues .Examination of Table I clearly shows that the A

values so calculated are in good agreement with thecorresponding experimental values. Further, the A0values at 25°C for these I:I electrolytes (as evaluatedfrom Eq. 30 utilizing A data at 25°C at C = 0.01 and0.02 M only) also agree well with the corresponding A0values obtained from A vs CI/2 plots.

However, when the equivalent conductance data?"at 25°C (in the concentration range C <0.02 M) ofRbCI04, RbCI03, CsCl04, CsCI03, KCI04 andKCI03 in water were analysed in terms ofEq. 30, it wasobserved that whereas the calculated A 0 values forthese electrolytes (employing A data at C=O.OI and0.02 M only) compared reasonably well with thevalues+" obtained from the Justice equation 9 (seeTable 1),the A values calculated from Eq. 30comparedwell with the corresponding experimental A0 values atC=0.005M only; at C=O.OOI M the two valuesdiffered by as much as 1.5 units. Further, the slopes of

the A+M vs CI/2(l-e-15m)/(i_G) plots do notI-G

compare well with the corresponding SI valuesevaluated from Eq.25 especially for RbCI04 andCsCI04 (see Table O. Since Eq. 30 is strictly valid forthose electrolytes that do not form ion-pairs insolution, the failure of this equation to describe wellthe A data a 25°C of these electrolytes as a function ofthe electrolyte concentration in water suggests thatthese electrolytes might be forming ion-pairs inaqueous solution. Bury et a/. 30also arrived at the sameconclusion from an analysis of the data at 25°C ofthese electrolytes in water in terms of the Justice

. 9equation".The present analysis of the A data for C < 0.05 Mat

25°C for simple I: I electrolytes (that do not form ion-pairs in water) in terms ofEq. 22 has thus revealed thatit yields Adata that agree well with the A data obtainedfrom the well known Fuoss-Onsager and Fuoss-Hsia(as modified by Chen) conductance equations'Y; thelatter conductance equations are however valid for Adata at C < 0.01 M. Again the form of Eq. 22 clearlyshows that for C > 0.05 M, especially for C > 0.3 M,since e -15m::::;0, values for any electrolyte in thisconcentration range would depend mainly on its SIand Q I' Thus, in the case of HBr and HI, although theSI obtained from Eq.25 are not equal to thecorresponding slopes of the (A + M)(I - G) vs CI13 (I-e-15',,/(I-G) plots (utilizing A data at 25°C in theconcentration range C <0.02 M), yet the use of A dataat 25°C at C =0.01,0.02 and 1.0 M would yield A0, SI

and QI values that would reproduce fairly well the Adata for these electrolytes in the concentration range0.0005 ~ C ~ 1.0M (vide infra).

On the other hand for C > 0.05 M, the contributionof the C(I-e-I~/(l-G) term is not small ascompared to that of the CI/3(I-e-lsnMI-G) termand if A 0 and SI for these electrolytes in water (with C>0.05 M) have the same values as in solutions with C< 0.02 M, Eq. 27 can be expressed as,

{(A + M)+SICI/3(l-e -ISnn(l-G) -I = Y=A 0

QIC(l-e-15m) . .. (31)(I-G)

so that a plot YvsC(l-e -15m)/(l-G)should be linearof slope Q I and intercept Ao. This was found to be trueof NH4CI, HCl and KBr and almost true of HBr andHI in water at 25°C when their AO and SI wereevaluated from Eq. 30 using A data at C = 0.01 and0.02 M only (see Fig. 2);the necessary A data at 25°C inconcentration range 0.05-1.0 M were taken from theliterature29(a.b.C).31.32while the data necessary tochange molarities to molalities were taken fromHarned and Owen28c. Further, AO values were foundto be in perfect agreement with the corresponding A0values obtained from an analysis of the A data in theconcentration range C<0.02M by means of Eq. 30.Alternatively, if A0and S I parameters of an electrolytein water are evaluated from Eq. 30 utilizing its A dataat C=O.OI and 0.02M only, it should be possible topredict A for the electrolyte in water at anyconcentration greater than 0.05 M if QI for theelectrolyte is known. For this purpose although anydatum for the electrolyte in the range C >0.05 M canbe utilized to evaluate its Q I' wehave evaluated Q I forthe electrolyte in water utilizing A datum at C = 1.0Min conjunction with its A0 and SI values. This value ofQ I alongwith the A0 and the S 1 values of the electrolytewas utilized to evaluate A for the electrolyte in water at

180

0'2 0·4 0'6 0'8 1'0

15mC(1-& )/(I-G)

Fig. 2-Plots of Y vs C (I -e-15m)f(l - G) for NH.CI (curve I), KBr(curve 2), Hel (curve 3, ordinate displaced by - 260.0), HBr(curve 4.ordinate displaced by - 254.0). and HI (curve 5. ordinate displaced

by -250.0).

185

INDIAN J. CHEM .• VOL. 24A. MARCH 1985

any concentration C > 0.05 M. Such A values at 25°Cfor NH4CI, KBr. HCI. HBr and HI in water arerecorded in Table I and are also compared with thecorresponding experimental values.

Examination of Table I reveals that whereas the Adata evaluated in the present study at 25' C for HCI.HBr, NH4CI and KBr compare well with thecorresponding experimental values, the calculatedvalues for HI in water compare only moderately wellwith the experimental values; in some cases, however,the two values compare well with each other. Further,Table I shows that QI <SI'

On the other hand when SI values for NH4C1, KBr,HBr, HCI and HI were evaluated from Eq. 30 (on theassumption that(A O)L:::::A0), it was observed that Y wasa linear function of C(1-e-'5mXI - G) -I for NH4Cl,KBr and HBr (and almost a linear function for HC\)when their A data in the range 0.5 ~ C ~ 1.0 M wereanalysed in terms of Eq. 31. Further, the intercepts A°of the YvsC(1 -e -15"XI - G) -I plots for HBr and HCI(i.e. A~Cl =428.9 and AflBr =428.80 Int. mhos) weredifferent from the AO values (A~CI=428.\3 and A~Br= 427.7 lnt. mhos) obtained from an analysis of their Adata (in the range C<0.02 M) by means of Eq. 30.This, however, was not the case for NH4C1 and KBr.In view of this it is suggested that S I for an electrolytebe regarded as an adjustable parameter to be evaluatedfrom its A data in the range C < 0.02 M by means ofEq.30.

Considering the overalI simplicity of the approach,Eq.22, which embraces all the characteristics of thewell known conductance equations 1.4, provides aconvenient means to (i) evaluate A° of the electrolyte ifits A data at two concentrations only (in the range C< 0.02 M) are available and (ii) to predict A data for theelectrolyte at any concentration if an additional Adatum at 1.0 M is also available. Again, the slopes SIof the lines so obtained compare reasonably well withthe corresponding SI values predicted by Eq.25.Further, the basic equation reduces to the well known

186

conductance equations 1.4; the present approach alsoprovides a reasonably rigorous analysis of con-ductance data.

ReferencesI Onsager L & Fuoss R M. J phys Chern. 36 (1932) 2689.2 Fuoss R M & Accascina F. Electrolytic conductance(lnterscience

Publishers. New York) 1959 and other refs cited therein.3 Fuoss R M & Onsager L. J phys Chern, 68 (1964) I.4 FuossR M & Hsia K L. ProcNatl AcadSci(US).57(1967) 1550.5 Chen M S & Onsager L. J phys Chern. 81 (1977) 2017.6 Chen M S, J phys Chern. 81 (1977) 2022.7 Fuoss R M, J phys Chern. 82 (1978) 2427.8 Fuoss R M. Faraday Disc chem Soc. 64 (1977) 324.9 Justice J Co Electrochim Acta. 16 (1971) 701.

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274.12 Pitts E, Tabor B E & Daly J, Trans Faraday SOl'. 65 (1969) 849.13 Fuoss R M. J phys Chern. 79 (1975) 525.14 Glueckauf E, Faraday Disc chem SOl', 64 (1977) 330.IS Bockris J'O M & Reddy A K N. Modern electrochemistry. Vol. I

(Plenum, New York), (a) 439. (b) 426. (c) 430. (d) 374. (e) 42l\.!O 431. (g) 427. (h) 433. (i) 210.

16 Singh PP,JAmcherr. Soc, 99(1977) 1312.17 Singh P p, J Am chem Soc. 100 (1978) 681.18 Singh P P. J Am chem Soc. 100(1978) 2041.19 Singh P p, Indian J Chern. 22A (1983) 650.20 Frank H S & Thompson PT. J chem Phys. 31 (1959) 1086.21 Debye P& Hucke! E. Z Phys. 24(1923) 185.22 Friedman H L, Krishnan C V & Jolicoeur C, Ann Y Acad sc: 204

(1973) 79.23 Rasaiah J Co J chem Phys. 52 (1970) 704.24 Anderson H C & Chandler 0, J chem Phys. 54 (1971) 149.25 Outhwaite C W. Molec Phys, 20 (1971) 705.26 Spitzer J J & Bennetto H P. J chem SOl' Faradav Trans, 174( 1977)

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solutions, 3rd edn (Reinhold. New York) 1967. (a) 524. 525:(b) 697; (e) 179; (d) 725; (e) 544; !O 165: (g) 231.

29 Handbook of chemistry & physics. edited by R C Weast (CRCPress Inc. Florida) 61 st edn, 1978. (a) 0-171. (b) 0-172: (c) 0-170.

30 Bury R, Justice M C & Justice J Co J chim Phys, 67 (1970) 2045.31 Wishaw B R & Stokes R H, J Am chem SOl', 76 (1954) 2064.32 Jones G & Brickford C F, J Am chem Soc. 56 (1934) 602.