Indian Journal of Chemistry Vol. 25A, March 1986,pp. 266-268nopr.niscair.res.in/bitstream/123456789/48122/1/IJCA 25A(3) 266-268.pdfgiven by the equation, Ta = IliXi where J, is the

Indian Journal of ChemistryVol. 25A, March 1986, pp. 266-268

Interpretation of Ion-Ion & Ion-SolventInteraction Patterns in Aquo

Hydrochloric Acid System on theBasis of Diffusion Studies

M ADHIKARI·, P CHATTOPADHYAY & (Mrs) SCHAUDHURI

PC Roy Research Laboratory, Department of Agriculture, CalcuttaUniversity, Calcutta 700017

Received 18 March 1985; recised and accepted 27 August 1985

Integral diffusion coefficient, 75, for the system HCI-HzO has beendetermined experimentally using modified diaphragm celltechnique. Failure of the equations based on classical ion-ion andion-solvent interactions is explained by the use of irreversiblethermodynamics. A kinetic model for the system is also proposed toexplain anomalous behaviour of H + and CI- in the system.

As specific ion effects become important inconcentrated solutions, it is clear that the flow of anion must be influenced by the other ions present andthe gradient of their properties as well. Themacroscopic frame-work necessary to cover thiscomplex situation is provided by thermodynamics ofirreversible processes 1.

Assuming local equilibrium and using balances ofmass, energy and momentum, the entropy producedirreversibly, a, for an isothermal electrolytic system isgiven by the equation,

Ta = IliXi

where J, is the flow of ions and solvent inmolcm -2sec - 1 and Xi is the force, in terms ofelectrochemical potential gradient. of these ions.

It is necessary to have independent J, and Xi for theOnsagers reciprocity relation (ORR) to be valid.Consequently, contribution due to solvent Y, iseliminated using Gibbs-Duhem equation and liS arereferred to a solvent-fixed reference frame. For thischoice, the linear relations are,

And according to ORR,

lij = Iii

M iller I has shown that values ofli/or a I : I electrolytein a neutral solvent like water may be calculated from aknowledge of equivalent conductance, transferencenumber and thermodynamic diffusion coefficient (D)"

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which in turn is related to (D)v, the volume fixeddiffusion coefficient; the value of (D) v can be obtainedfrom experimental integral diffusion coefficient (15). Ifthe distinction between If and If (the cell transferencenumber and Hittorf transference number respectively)is omitted, which actually means the validity of ORR,the three lijs can be calculated from the equation,

I IN _ liljA (D)oijl - 1000 Fl + 1000 x 2RT(l +cdlny/dc)

An inverse description of transport process usingfriction coefficients (Rij) can also be used where.

Xi= I RiJij = 1,2

Rij can also be determined from the equation given byMillerl.

Integral diffusion coefficient D for the system HCI-H20 was measured over the concentration range0.01 M-3.0 M using a modified diaphragm cell at 25°Cas described earlier".

An azeotropic mixture of HCI-H20 was initiallyprepared from A R grade HCI by distillation. Later,the stock solution was used to prepare all dilutesolutions. The concentrations (initial and afterdiffusion run of both compartments) were determinedboth by conductometric titrations (using a DIGISUNdigital conductivitymetre bridge, model 909) and bypotentiometric titrations (using a Systronic ExpandedpH metre, 331) against standard NaOH solution. In allthe cases conductivity water (specific conductance lessthan 1 micromho percm) was used. The densities of thesolutions were measured by Ostwald modification ofthe Sprengel pyknometer (having IS ml capacitity),and viscosities were measured by an Ostwaldviscometer (having 12ern long capillary with 0.06 eminternal diameter). The temperature was maintained at25UC ± O.lcC with the help of a thermostat.

A comparison of the (D)'h values given in Table I(columns 10 and II, obtained either by the Onsagerand Fuoss relation:' or by Stokes' self-consistentequation:'), with the (D)v values (Table I, column 5)obtained from D values (Table I, column 4) shows thatvalues obtained using Stokes' self-consistent equationagree well with the experimental values upto 0.1 M(error, ± 1;',) after which disagreement becomesprominent with increase in concentration.

If we consider that a major reason for the deviationin concentrated solutions is the modification ofvarious viscous forces by the presence of a largenumber of ions, then by Agar equation Tthe plot of

NOTES

Table I-Experimental Values and Verification of Classical Theories

C p rJ Dx 10' (D), X 10' Dhh X 10' DhH X 10' rJ/rJ° f(D)rJ/rJ°(g mol/l) (centipoise) (em+see -I) (em+see -I)

0 0.99707 0.895 3.336 3.336 3.336 3.336 IU.UI 0.99737 0.916 3.229 3.188 3.211 3.202 1.023 1.0160.02 0.99724 0.951 3.196 3.158 3.179 3.167 1.063 1.0570.04 0.99772 0.984 3.172 3.118 3.149 3.131 1.099 1.0900.05 0.99803 0.991 3.164 3.104 3.147 3.121 1.107 1.0960.08 0.99844 1.002 3.135 3.084 3.131 3.106 1.119 1.1060.10 0.99886 1.007 3.122 3.080 3.132 3.104 1.125 1.1110.15 0.99952 1.011 3.108 3.070 3.144 3.112 1.130 1.1100.20 1.00058 1.014 3.109 3.070 3.166 3.133 3.133 1.1070.30 1.00237 1.020 3.113 3.115 3.230 3.193 1.140 1.1110.40 1.00415 1.025 3.120 3.164 3.302 3.262 1.145 1.1130.50 1.00590 1.031 3.141 3.222 3.382 3.340 1.152 1.1170.60 1.00764 1.037 3.161 3.278 3.468 3.424 1.159 1.1190.80 1.01113 1.049 3.203 3.401 3.652 3.604 1.172 1.1221.00 1.01459 1.061 3.254 3.495 3.848 3.798 1.185 1.1141.20 1.01801 1.073 3.300 3.594 4.053 4.001 1.199 1.1141.60 1.02481 1.097. 3.406 3.790 4.494 4.437 1.226 1.8952.00 1.03153 1.122 3.512 4.000 4.971 4.907 1.254 1.0783.00 1.04801 1.185 3.806 4.500 6.305 6.228 1.324 1.015

f(D)rJ/rJ° = I +0.036m (D'H,o/ DO -h).

+Using the relation DTh =(Do + ~I + ~,) X (I + cdlny/de)tUsing the relation DTh =(Do + ~I) x (I +cdlny/dc).

1J/ri°f(D) vs m should be linear with a slope of 0.036«D)*H,oIDo -h) where,

f(D) = Dobs

[(DO + L\! + L\z)(l +m(dlnrldm»]

and h is hydration number. A plot of values in column9 (Table I) against m gives a negative hydrationnumber for hydrochloric acid which makes theapplicability of the equation doubtful.

Failure of the classical approach may be attributedto ion association, alteration in the solvent structure,short range ion-ion interactions and the specific ioneffects. These effects can be considered in the lij terms;diffusion coefficient turns out to be combined effect ofthe lij' Consequently, a systematic study of lij as afunction of concentration of electrolyte solutionshould lead to a better understanding of transportmechanism in the system.

An examination of I;JN values (Table 2, columns 9& II) shows that the relative deviation of lijN from itslimiting value at C =0 is not large upto 0.08 Mconcentration. In solutions of moderate con-centrations, at least the magnitude of I;JN should bedetermined largely by interaction of ion i with thesolvent. lijN will also be affected by long rangecoulombic interaction, ion association and alterationin solvent structure due to ions. The slow decline of thevalues with concentration suggests an increasingnegative i-i coulombic contribution.

Most interesting is the rapid rise of 1!2/N withconcentration (Table 2, column 10). This rise isresponsible for both the rapid decline of theconductance and the catastrophic failure of theNernst-Hartley equation with increasing con-centration. l!zlN is a measure of the degree of couplingbetween the motion of ions 1 and 2 and is a function oflong range coulombic ion-ion interactions, ion-solventinteractions and specific short range ion-ioninteractions which may be interpreted in terms of ionpair formation. So the increase in the values of IlzlN(Table 2, column 10) indicates an increase in the ionpair formation.

A theoretical calculation of lij/N shows that 112INvalue should contain a factor 1Jnwhere n is morenegative than - 2. According to Frank (cited in ref. I),this means that the effect is essentially relaxational.However, it has also been observed earlier that atheoretical calculation of li)N from a Debye-Huckelion atmosphere model shows that specificities in IzzlNmay also result from the relaxation effect and ion pairformation effects which are results of nonzero anion-cation interaction", The failure of the classicialOnsager-Fuoss theory is possibly due to non-inclusionof the ion pair term.

In translational diffusion, the ions will form ion-water cluster shell either by building up a water clustershell around an ion or by forming water cluster shell firstand then capturing an ion. The latter appears to be more

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INDIAN J. CHEM .• VOL. 25A. MARCH 1986

Table 2-Calcl!lation of Linear Transport Coefficients

C m -Inr I

(gmolfl) +m(d1nr/dm) 1+ cf..dlny/dc) (D)o x 105 A t. I"IN X 10.2 I,,/N x 1012/22/N x 10.2

(em+see -.)

0 I I 3.336 426.50 0.8210 37.60 0 8.200.01 0.01003 0.07302 0.96794 0.96839 3.189 412.02 0.8251 36.77 0.256 8.000.02 0.02007 0.09803 0.95960 0.96047 3.161 405.01 0.8261 36.32 0.389 7.950.04 0.04015 0.12885 0.95161 0.95323 3.123 400.00 0.8280 36.06 0.490 7.880.05 0.05019 0.13986 0.94949 0.95151 3.111 399.12 0.8292 36.07 0.524 7.840.08 0.08036 0.16422 0.94698 0.95009 3.094 394.25 0.8309 35.81 0.619 7.780.10 0.10048 0.17599 0.94720 0.95106 3.093 391.34 0.8314 35.61 0.668 7.750.15 0.15087 0.19671 0.95097 0.95664 3.088 385.25 0.8328 35.21 0.749 7.760.20 0.20135 0.20986 0.95767 0.96515 3.094 381.50 0.8338 34.95 0.788 7.600.30 0.30259 0.22375 0.97653 0.98714 3.149 373.50 0.8353 34.42 0.916 7.520.40 0.40422 0.22802 0.99657 1.01099 3.210 367.00 0.8365 33.98 1.013 7.460.50 0.50624 0.22642 1.01888 1.03728 3.280 360.86 0.8376 33.57 1.106 7.40

0.60 0.60866 0.22082 1.04269 1.06504 3.348 354.75 0.8385 33.13 1.181 7.330.80 0.81469 0.20136 1.09317 1.12407 3.497 343.00 0.8397 32.25 1.316 7.221.00 1.02236 0.17426 1.14643 1.18670 3.618 323.30 0.8407 31.37 1.370 7.051.20 1.23169 0.14174 1.19470 1.25207 3.376 321.50 0.8414 30.51 1.460 6.941.60 1.65548 0.06482 1.31400 1.39191 4.015 300.75 0.8425 28.74 1.532 6.622.00 2.08633 -0.02406 1.44521 1.54228 4.269 281.66 0.8429 27.07 1.577 6.333.00 3.19603 -0.28494 1.82694 1.96367 4.837 237.74 0.8430 23.11 1.589 5.60

probable in view of the relaxational effect that arisesdue to continuous formation and destruction of shell.The difference in diffusion pattern ofH + ion from thatof CI - ion suggests different mechanisms of diffusionof the two ions. It seems that at first H l> + ion isformed and then solvation sheath is built up around itso that the diffusion mechanism of H + ions is governedby the jumps of the H30+ ion from one shell toanother and by the movement of H30+ ion withsolvation shell. The low charge density has relativelyweak electrostatic field and thereby causes a netdecrease in hydrogen-bonded water cluster structure.So, a series of proton jumps will be involved (of course,water molecules close to a proton are not arrival pointsfor another proton after 'one of its jumps).

In the CI - ion transport mechanism, the high chargedensity will lead to a net structural increase around the

268

ion. So, movement of the ion with formation anddestruction of ion-duster shell and the ion with thesolvation shell around it become controlling factors indiffusion, and at higher concentrations ion pairformation plays an important role in the diffusionmechanism.

The authors wish to thank Dr S K Sanyal, Lecturer,V C K V Kalyani (W 8) for several helpful suggestionsregarding the interpretation of experimental results.

ReferencesI Miller D G. J phys Chem, 70 (1966) 2639.2 Adbikari M.Ghosh Oft Chattopadbyay P. Proceedings of Sir J C

Ghosh memorial conference on strong electrolytes, March1982, SAEST, KARAIKUDI (India).

3 Robinson R A & Stokes R H, Electrolyte solutions, (Butterworths,London) 1959, Chapter II.

4 Miller D G & Pikal M J, J sol Chem, 1 (1972) III.