Indian Journal of Chemical Technology Vol. 10, January 2003, pp. 7- 1 3

Articles

Conductometric and ultrasonic studies on ion-solvent interaction of K+ of KeNS in water + methanol/ethanol mixtures

J lshwara Bhat a* & H R Shiva Kumarb

a Department of Chemistry, Mangalore University, Mangalagangothri 574 199, India b Chemistry Department, K V G College of Engineering, Sullia 574 327, India

Received 23 May 2002: revised received 20 September 2002; accepted 28 November 2002

The results of the ion-solvent interaction of K+. potassium thiocyanate in water + methanoVethanol and their various mixtures (v/v) at 288, 298, 308 and 313K, using conductivity principle are reported. The solvation number of cation was determined by ultrasonic and mobility methods. Conductivity data were analysed by three major conductivity models. Limiting molar conductance decreases sharply with increase in co-solvent concentration. Association constant, Walden product, corrected Stoke's radius (r.) and activation energy (E.) of rate process were calculated for all solvent compositions and temperatures. Measured viscosity and ultrasonic velocity were used to determine solvation number of potassium ion (K+) and is found to be maximum in methanol. The Born relations were used to compute thermodynamics of solvation. All these data were used to investigate the nature of ion-solvent interaction existing in the sY�lem under prevailing conditions.

An extensive study on the electrolytic conductivity in various pure and mixed solvents has been the active subject of interest to physical chemists 1 .2 . Potassium thiocyanate is water soluble, stable and it finds its use in industrial and analytical fields . In the present study its conducting behaviour in water + methanol/ethanol mixtures as a function of temperaturehas been investigated. The solvation, viscosity and ultrasonic velocity measurements were carried out to obtain solvation number and to understand the nature of ion­solvent interaction.

Experimental Procedure Potassium thiocyanate [Ranbaxy make AR Grade]

was dried at 100- 1 20°C for 3 h and stored in a vacuum desiccator. Triply distilled water and purified methanol and ethanol (conductivity of the order of lxlO·6 n' l cm' l ) were used. Potassium thiocyanate solution (0. 1 M) in water and various compositions of water + MeOH and water + EtOH (v/v) mixtures were prepared and diluted further for the required concentration using solvent/solvent mixtures (0. 1 -0.00 I M). Conductance measurements were made Wilil a digital direct reading conductivity meter (model CM- 1 80, Elico-Private Limited, Hyderabad).

*For correspondence (E-mail : bhatij @yahoo.com; Fax: 0824 287 376)

A dip type conductiyity cell with platinized electrode, was calibrated3,4 (cell constant 0.999 cm' l ) and used in the entire work. All the measurements were made in a thermostat maintained at the desired temperature to an accuracy of ±D.O 1 °C.

The viscosity and sound velocity were measured using an Ostwald' s viscometer and an ultrasonic interferometer, respectively. The accuracy of the ultrasonic interferometer was examined with sound velocity of doubly distilled water. The observed value of sound velocity is 1 501 ms' l at 298K as against the reported 1496 ms' l .

Results and Discussion Limiting molar cOllductallce

The molar conductance, Am of potassium thiocyanaie was determined from the experimental specific conductance in water, methanol, ethanol and various compositions (v/v) of water + MeOH, water + EtOH at four different temperatures (288, 298, 308 and 3 1 3K). Conductance data were analyzed by Debye .. Huckel-Onsager, Kraus-Bray and Shedlovsky model of conductivitl'lO to evaluate molar conductance at infinite dilution Am°.

The limiting molar conductance was determined from the intercept of the Onsager' s linear plot (Am versus -YC) and by the Kraus-Bray plot ( l /Am versus AmC) at four different temperatures and in various

Articles I ndian J. Chern. Technol., January 2003

Table I-Molar conductance at infinite d i lution (Amo : S cm2

mor l ) for KCNS by different models in d ifferent % compositions (v/v) of water + methanol and water + ethanol at di fferent temperatures

% Comp

288 298 308 3 1 3K 288

AmO (S cm2 morl )

2

298 308

water+methanol

3 1 3 K 288

3

298 308 3 1 3 K

o --1 0�8-. 1---1-4-1 .�0 ---1�6-1 .-2----1 7�3-.2�---1-0-7.�0-----1 3�8-.5-----� 5-7-.4-----1 6�7-.-1 ---1-0-9-. 3---1-3-8-.0---1-6-0-.0----1-7-I C-Y -

( 1 39) 20 80.0 1 03 .4 40 58. 1 78. 1 60 55.3 70.0 80 60.0 73.3 1 00 8 1 .2 1 1 2. 1

1 32 .3 90.2 88. 1 92. 1 1 1 6.3

1 43 . 1 1 1 7.4 95.4 1 04.6 1 20.7

78.9 57.0 52.8 58. 1 78.0

1 04.7 76. 1 68.4 70.4 1 1 3 .0

1 26.0 90.4 86.0 90. 1 1 1 6.4

1 36.0 1 1 4.2 92.0 1 00.0 1 2 1 . 1

78.0 57. 1 55 .3 6 1 .3 84.6

1 07.0 78.5 70.4 74. 1 1 1 2 .0

( 1 14)

1 3 1 .0 90.4 87.9 94.2 1 1 6.3

1 40.0 1 1 3.0 96.4 1 06.2 1 22.3

water+ ethanol

o 1 08. 1

1 0 72.0

20 7 1 .0

40 46.4 60 4 1 .2 80 32.7

1 00 42.4

1 40.7 98.0 86.0 64.3 5 1 .0 48.4 49.0

I . From D.H.O. Equation

1 60.8 1 23. 1 1 03 . 1 73 .3 63.0 56.4 53 .3

2 . From Kraus-B ray Equation 3. From Shedlovskey Equation.

1 73 .0 1 30.3 1 23.6 84.0 7 1 . 1 62. 1 6 1 .2

1 07.3 72.2 7 l .0 45.3 4 1 . 1 3 1 .0 40.0

Values in the paranthesis are from References 5 and 6

1 38. 1 98.4 85.0 62.3 50.2 46. 1 5 1 .4

1 57. 1 ! 2 1 .9 1 03.0 72.8 6 1 .0 53 .2 52.2

1 67.2 1 27.4 1 23 .0 8 1 .9 74.0 59.0 58.3

1 09.0 1 38.0 7.9 1 0 1 .3

70.2 87.4 46.2 64.2 60.0 52. 1 34.2 49.2

39.2 52.0

(5 1 .0)

1 60.2 1 22.3 1 03. 1 74.4 63. 1 57.3 60.0

1 72.0 1 30.0 1 2 1 .3 84.3 70.4 64.0 66.0

Table 2--Ca1culated values of Kc and K" for KCNS in water+ methanol and water + ethanol (v/v) at different temperatures

water + methanol

0% 1 0% 20% 40% 60% 80% 1 00%

Kc

288 0.37

298 0.20

308 0.25

3 1 3 0. 1 3

Ka

2 . 1 3 .6 5 .3 6.6

Kc Ka Kc

0.03 0.04 0.06 0.04

Ka

1 3 .8 27.8 23.0 23.7

Kc

0. 1 5 0.08 0.08 0.07

Ka

9.0 1 0.0 1 5 . 1 25.0

Kc

0. 1 2 0. 1 5 0. 1 7 0. 1 6

Ka

7.7 9 . 1 1 3 . 1 1 1 . 1

Kc

0. 1 0 0. 1 0 0. 1 0 0.09

Ka

1 7 .3 25.3 1 2.6 34.4

Kc

0. 1 1 0.07 0.06 0.05

Ka

2 1 . 1 6 1 .0 72. 1 1 0:!.2

water + ethanol

288 0.37

298 0.20

308 025

3 1 3 0. 1 3

2 . 1 3 .6 5 .3 6.6

0.08 4.6 0.39 1 .9 0. 1 3 5 .8 0.07 4.7

0. 1 9 0.20 0. 1 8 0. 1 1

3 .5 :!.5 2.8 6. 1 1

0. 1 0 0. 1 4 0. 1 0 0. 1 6

solvents/solvent mixtures and these are shown in Table l . The Kraus-Bray model of conductivity also gave the dissociation constant Kc value from its slope. Kc values are shown in Table 2. But these "'mo values are not absolute, as they do not give any account for the interionic effect on mobil ity and also the relaxation effect. Shedlovsky model of conductivity takes care of all these and gives the value of

8

9.2 5.6 3 .5

0. 1 1 0. 1 8 0.05 0. 1

8.7 6.3 1 1 . 1 20.0

0.09 0. 1 0 0.08 0.08

1 5 .6 0.06 24.0 0.05 32.0 0.04 37.0 0.04

99 1 77 195 239

association constant. The equation may be represented as:

1 1 CAm Sf} Ka -- = -0 + --m-sAm Am Am . . . ( I )

where C is the concentration, f± is the mean aCl i v i ty coefficient, Ka i s the association constant and S is-

Bhat & Shiva Kumar: Conductometric and ultrasonic studies on ion solvent interaction of K+ A rticles

Table 3--Estimated Walden product (AO ml10 : S cm2 mori poise) of KCNS in various solvents and their mixtures as a function of

temperature

TOK 0% 1 0% 20% 40%

1 & 2 2 2

288 1 .23 1 .2 1 1 .36 1 .55 1 .2 1

298 1 .2 1 1 .08 1 .33 1 .29 1 .2 1

308 1 . 1 5 1 .04 1 .2 1 l . l 1 0.92

3 1 3 1 . 1 1 1 .07 1 . 1 3 l . l 8 1 . 10

1 == water + methanol: 2 == water + ethanol

The 1..0 m and Ka values thus obtained from the intercept and slope of the linear plot 1/o5')...m versus CAmsf2 ± are shown in Tables 1 and 2. Limiting molar conductance values obtained by various models for pure solvents at 25°C are well comparable with each other and they are also in excellent agreement with literature values7.8 for methanol and water. (Literature values are shown in the parenthesis in Table 1 ) .

Temperature increases the thermal energy of the system, due to which number of conducting species increases and also the frequency of movement. So limiting conductance increases (Table 1 ) . Effect of solvents on limiting conductance

Limiting conductance sharply decreases on the addition of co-solvent (either methanol or ethanol) to water till 60% MeOH (around 80% EtOH) with a later decrees in AOm. Addition of alcohol (MeOH or EtOH) to water brings about strong and well-organized alcohol-water bonds 7. At this stage, oxygen atom of methyl gets partial negative charge and hydrogen gets partial positive charge due to the inductive effect of methyl group, this results in the methanol to be more basic than water. So interaction between solvent molecules will be very high and a new structure of solvent mixture will be formed with a large molecular size. Hence, viscosity and limiting molar conductance decrease. Viscosity of the solvent mixture is the measure of rigidity of the system and 1..° m is the measure of the solute-solvent interaction. The viscosity of water + EtOH is greater8 and hence its conductivity is smaller than that in water + MeOH.

The initial decrease in AOm is due to the solvation of cation either by water or bulky solvent mixture molecules. When the amount of co-solvent in water

60% 80% 1 00%

2 2 2 2

1 .52 1 .09 1 .30 0.98 0.82 0.5 1 0.54

1 .36 l . l 7 l . l 5 0.93 0.89 0.58 0.56

l . l 6 0.96 0.99 0.84 0.80 0.54 0.55

1 .2 1 0.97 0.97 0.89 0.78 0.54 0.52

increases, a competItIOn for hydrogen bonding in water by anion and co-solvent arises9• As a result, some water molecules are removed from the solvadon shell of anions which decreases the size of the solvation shell thereby increasing conductivity. At 1 00% co-solvent, the solvent-solvent interaction is absent and hence ionic size will be larger and conductivity is found to be high.

Dissociation/association constant: Dissociation constant (Ke) and association constant

(Ka) are determined respectively from slopes of the l inear plots of Kraus-Bray and Shealovsky. The values are shown in Table 2. From the data of Table 2, it is c lear that, Ke is decreasing in case of water and MeOH and there is a marginal decrease in case of EtOH with respect to temperature. This is an indication of endothermic behaviour of the system under existing conditions. Values of Ke vary in the order of water>MeOH>EtOH, whereas Ka follows the reverse order.

Walden product, (,1°111 Yfo): Walden product (the product of viscosity, Yf" of the

solvent and limiting mJlar conductance, 1..0 m) was calculated9 for KCNS in different solvents and their mixtures at different temperatures. These values are shown in Table 3 . From the data in Table 3 it is evident that increase in temperature brings about slight change in the product in both the cases of solvent and solvent mixtures indicating non-variation of Stoke' s molecular radius. This negative temperature coefficient of Walden product indicates the solvent structure-breaking behaviour of KCNS. Further nearing constancy of product at different temperatures at certain compositions is presumably due to the compensating behaviour of the temperature co-efficient of the conductivity by the negative temperature coefficient of the viscosity of the solvent.

9

Articles Indian J. Chern. Techno! . , January 2003

Table 4----Calculated energy of activation for KCNS in water, methanol, and their mixture (vlv)

water + methanol

0% 1 0% 20% 40% 60% 80% 100%

Ea (kJmor l ) 1 3 .8 1 7.4 19. 1 16. 1 1 6.7 10.2

Log A 4.54 5.07 5.22 4.75 4.8 1 3.80

water + ethanol

Ea (kJmorl ) 1 3 .8 1 7.6 1 5.6 1 7 . 1 1 6.2 1 8 .2 14.2

Log A 4.54 5.07 4.49 4.78 4.57 4.96 4. 1 8

Table 5---Corrected Stoke's molecular radius r i n A 0 for KCNS in water, methanol, ethanol and their mixtures (vlv) at di fferent temperatures

TO K 0% 1 0% 20%

1 &2 2 2

288 2.64 2.59 2.47 2.38 2.52

298 2.62 2.63 2.26 2.45 2.43

308 2.61 2.6 1 2.49 2 .51 2.6 1

3 1 3 2.61 2.58 2.52 2.46 2.44

I = water + methanol; 2 = water + ethanol

Activation energy of the rate process (Ea) The activation energy (Ea) of rate process was

calculated using Arrhenius equation (Eq.2) and the values are shown in Table 4.

. . . (2)

where A is the frequency of the movement of molecules, Ea is the activation energy of the rate process which determines the rate of movement of ions in solution. The slope of the plot, (",Om versus 1/7) gives the value of Ea. They are shown in Table 4. Ea varies in the order of EtOH>water>MeOH. indicating the requirement of high energy for the movement of species in EtOH. Therefore ",om is minimum in this case, Ea increases with composition.

Thermodynamics of solvation The change in the free energy of solute-solvent

interaction, �Gs.s was calculated using the Born equation of solvation9,

N(Z;eo ) 2 ( 1-11 Es) 2 r;

. . . (3)

where N is the A vagadro number, Z is the charge on the ion, eo is the electronic charge, £ is the dielectric constant of the solvent. Stoke ' s corrected radius rr was calculated7.8 using the semi-empirical relationship based on the Stoke' s law,

1 0

40% 60% 80%

2 2

2.28 2.43 2.62 2.43

2.30 2.35 2.5 1 2.54

2.37 2.48 2.59 2.52

2.39 2.45 2.60 2.45

ZF 2 r; 0 +O.0 103E+ rl'

6rrNA A m1J o .

1 00%

2 2

2.5 1 3 . 1 1 2.90

2.39 2.86 2.80

2.49 2.96 2.80 2.49 3.04 2.90

. . . (4)

where Z is the charge on the ion, F is the Faraday constant, N is the A vagadro number, £ is the dielectric constant of the solvent and ry =1 . 13 A. applies to protic and other associated solvents. The calculated values of rl are given in Table 5 .

The free energy change arising from solute-solvent interaction is a measure of stability of the species in a solution. Larger the negative L1Gs-s, higher will be the stability of the species in the solution. The computed L1G,,-5 in all the cases are shown in Table 6. Virtually no change in values is observed with temperature either in pure solvents or solvent mixtures. A plot of L1G.,-s versus lIri is obtained and found to be linear indicating system to follow the Born model. The change in entropy, �s.\-S of the system was also calculated using the Born equation (Eq. 5). The values are shown in Table 6.

�S,_,\ NA (Z;eo ) 2 1 &,\

2r; c ; DT . . . (5)

all the terms in the above equation have usual meaning. L1G,_s values are small but increased with increase in percentage composition of either MeOH or EtOH. Entropy is connected with the solvent structure perturbation brought by disordered ions . The small

Bhat & Shiva Kumar: Conductometric and ultrasonic studies on ion solvent interaction of K+ Articles

Table 6--Computed thermodynamic parameters for KCNS in water, methanol, ethanol and their mixture (v/v) at different temperatures

water + methanol water + ethanol

Thermodynamic 0% 20% 40% 60% 80% 1 00% 0% 1 0% 20% 40% 60% 80% 100%

parameters

288K

-LlGs-s(kJ mor ' ) 268 275 270 279 278 2 1 6 268 264 286 306 258 268 229

LlSs-s(kJ/Klmol ) 0.014 0.0 1 9 0.023 0.035 0.050 0.083 0.0 14 0.Q 1 8 0.023 0.033 0.033 0.060 0. 1 05

-LlHs-s(kJ mor' ) 263 279 263 268 263 192 263 258 279 296 248 250 198

298K -LlGs-s(kJ mor ' ) 270 275 279 288 265 234 270 260 278 294 269 28 1 234

LlSs-s(kJ/Klmol) 0.0 1 6 0.0 1 9 0.027 0.038 0.056 0.080 0.0 1 6 0.020 0.025 0.039 O.04C 0.07 0. 122

-LlHs-s(kJ mor ' ) 265 279 270 272 248 2 10 265 254 270 282 256 258 197

308K -Ll Gs-s(kJ mor ' ) 265 272 258 273 268 226 265 26 1 27 1 287 260 269 233

LlSs-s(kJ?Klmol) 0.01 7 0.0 1 9 0.028 0.042 0.06 1 0.042 0.0 17 0.023 0.027 0.041 0.043 0.076 0. 140

-LlHs-s(kJ mor' ) 259 275 249 259 248 1 98 259 252 262 274 247 243 1 89

3 1 3K

-LlGs-s(kJ mor' ) 274 264 278 276 274 220 274 264 276 290 260 269 227

LlSs-s(kJ/Klmol) 0.Q1 8 0.024 0.032 0.045 0.066 0.092 0.0 1 8 0.023 0.029 0.040 0.045 0.083 0. 1 47

-LlHs-s(kJ mor ' ) 268 286 267 261 253 190 268 256 266 277 245 242 1 80

Table &-Values of viscosity (poise) of various compositions (v/v) of water + methanol and water + ethanol at different temperatures

water + methanol

T(K) 0% 1 0% 20% 40% 60% 80% 1 00%

288 0.Q 1 14 0.01 74 0.01 95 0.0198 0.01 62 0.0062

299 0.0089 0.01 25 0.0 1 56 0.0 1 68 0.0 1 27 0.0053

308 0.0072 0.0093 0.01 02 0.0 1 09 0.0089 0.0047

3 1 3 0.0065 0.0080 0.0097 0.0 1 03 0.0085 0.0044

water +ethanol

288 0.0 1 1 4 0.0 1 68 0.0222

299 0.0089 0.0 1 07 0.0 148

308 0.0072 0.0085 0.0 108

3 1 3 0.0065 0.0082 0.0097

positive value has been considered to decrease in orientation of solvent molecule and the ion pair bonds. LlS'.I-S increased sharply with increase in percentage composItIOn and with temperature indicating increased electrostiction, which in turn suggests the decrease in conductance.

Heats of solute-solvent interaction Mis-s was calculated from the system making use of the following equation 6,

. . . (6)

The values are shown in Table 6. The tllfs-s is found to be negative in all the cases indicating that the system is exothermic.

0.0330 0.03 1 7 0.0247 0.01 30

0.02 1 3 0.0226 0.0 1 85 0.0 1 07

0.0 1 59 0.0 1 57 0.0 140 0.0092

0.0 143 0.0 1 37 0.0 1 25 0.0083

Solvation numbers (Sn)

Solvation number of an ion or the solute is the number of solvent molecular present in the primary solvation shell of the ion or molecule. These solvent molecules always move with central ion by surrendering their own translation degree of freedom. Solvation number reflects the magnitude of ion­solvent interaction of the system. In the present study the solvation number was determined9 by compressibility method (Eq. 7) (based on ultrasonic measurements, ultrasonic velocities obtained in the case of water + methanol/ethanol mixtures are shown in Table 7) and by using Eq. 8 (viscosity based, experimental viscosity values of the system are shown

1 1

rr. 8 N C co :::l <= co ....,

"0 <= ..c:

� E 0) ..c: U

.-; <= co :.a .5

III aJ -<:oJ .... ..... 100 <

Table 7-Experimentally determined ultrasonic velocity (U:m1sec) at different concentrations of KSCN in water+ methanol and water+ethanol mixtures at different temperatures

% comp 0 10 20 40 · 60 80 1 00

C(M) 298K 308K 313K 298K 308K 3 1 3 K 298K 308K 3 1 3K 298K 308K 3 1 3K 298K 308K J I3K 298K 308K 3 1 3K 298K 308K J I 3 K

0.01

0.5

1.0

om 0.5

1 .0

1 5 1 2

1524

1 545

1 5 1 2

1 524

1545

1521

1 533

1 55 1

1 5 2 1

1 533

1551

1530

1545

1560

1 530

1 545

1560

1533

1545

1 560

1557

1 563

1575

1542

1547

1 566

1 563

1569

1581

1542

1 563

1 569

1566

1572

1587

1 554

1560

1572

1599

1 599

1602

1557

1563

1575

1 596

1599

1605

1 557

1 563

1 512

1 596

1 596

1602

water + methanol

1554

1557

1 560

1 548

1551

1554

water + ethanol

1 587

1 590

1 593

1572

1578

1 590

1 539

1542

1545

1563

1 566

1 569

1 476

1485

1491

1476

1482

1496

1449

1464

1473

1458

1 467

1470

1440 1452

1463

1446

1464

1467

1320

1 350

1 356

i 296

1 320

1323

1 284

1 302

1 3 1 5

1095

1 1 34

1 1 73

1 197

1 22 1

1233

1059

1 1 1 0

1 149

! l76

1200

1 2 1 6

Table 9----Experimentally determined solvation number of r by ultrasonic interferometer at different temperatures. % compositions of methanol & ethanol with water (V IV) for different concentration of KCNS

0% Cone 298K 308K O.IM 4 4 0.5M 5(5) 4 I .OM 5 4 O. I M 4 4 0.5M 5(5) 4

1 M 5 4

3 I 3K 6 4 4 6 4 4

10% 298K 308K

4 3 4 4 4 6 2 3 3 3

20% 3 1 3K 298K 308K

4 4 4 4 3 4 3 3 4 4 4 2 2 2 3 3

water + ethanol

3 1 3K 298K 6 4 3 3 3 35 2 5 2 3 2 2

40% 308K

4 3 2 5 4 2

3 I3K

3 2 4 3 2

298K

5 3 5 5 3

60% 308K

5 3

4 2

3 1 3K 8 4 5 4 2 3

80% 298K 308K

7 8 6 6 4 3

3 13K 3 7 3

298K 8 6 6 7 4 3

100% 308K

I3 8 7 8 4 3

1050

1080

1 1 34

1 1 64

! l85

1206

3 1 3K I I

6(5) 7 7

4(4) 3

N

Bhat & Shiva Kumar: Conductometric and ultrasonic studies on ion solvent interaction of K+ Articles

Table 1 0- Solvation number of r ion in water, methanol and ethanol (by viscosity method) at different temperatures

T(K) water

288 4.4

298 4.23(5)

308 4.06

3 1 3 4. 1 6

( ) = literature value

in Table 8) in pure solvents. The results are shown in Tables 9 and 10.

. . . (7)

where 11 1 and 112 are number of molecules of the solvent and solute, Bad and Boad are the adiabatic compressibilities of solution and solvent respectively. The results are shown in Table 9. The values obtained for pure solvents are well comparable.

3 3 rl -r cry." S " 3 r H20 . . . (8)

where rJ is the corrected Stoke's radius and rcrysl is the crystallographic radius. The values obtained are shown in Table 10. Values obtained by both the models for pure solvents are well comparable with literature value9.

Conclusions Water is a better solvent as the species is more

conductive in this solvent. Ethanol is the least

methanol ethanol

5.25 3.97

5. 1 5(5) 3.9(4)

5. 1 3.89

5.07 3.86

preferred solvent. The association process I S endothermic, whereas the solvation process i s exothermic. Solvation size of the species does not change much. Viscosity and ultrasonic models give almost the same value for solvation number. Hence to evaluate it one can make use of any models.

References 1 Ishwara Bhat J, Mohan T P & Susha C B, Indian J Chem,

35A ( 1996)825

2 Gregorowicz J, Bald A, Szegis & Chmielewska, J Molecular Liquids, 84(2) (2000) 1 49.

3 Ishwara Bhat J & Shivakumar H R, Indian J Pure Appl Phys, 38 (2000) 306; J Electrochern Soc, India, 48-4( 1 999) 37 1 .

4 Susha C B & Ishwara Bhat J, Indian J Chern, 35A ( 1 996) 1 052.

5 Paul G Sears, Richard R Holmes & Lyler Dawson. J

Electrochern Soc, 1 02 ( 1 955) 145.

6 Bark M & Harold H, Z Physik Chern, A 1 65 ( 1933) 272.

7 Sagar E E, Robinson R A & Bates R G, J Research N B S. 68A ( 1 964) 305.

8 Ishwara Bhat J & Bindu P, J Indian Chern Soc, 72 ( 1 995) 783.

9 Bockris J 0 M & Reddy A K N, Modem Electrochemistry, VoLl (Pleunm Press, New York), 1 977.

1 3