Indian Journal of Chemistry Vol. 38A, November 1999, pp. l l 06- 1 1 1 5

Thermodynamic and transport properties of sorbitol and mannitol in

water and in mixed aqueous solutions

T S Banipal"', S Shanna', B S Larkb & P K Banipalb "Department of Phannaceutical Sciences and bDepartment of Chemistry,

Guru Nanak Dev University, Amritsar 1 43 005, India

Received 24 May 1999; revised 24 August 1999

Apparent molal volumes, apparent molal adiabatic compressibilities and viscosities of sorbitol and mannitol have been determined in water at 288. 1 5, 298 . 1 5, 308. 1 5 and 3 18 . 1 5 K and in aqueous solutions of urea and sodium chloride (0.5 m) at 298. 1 5 K from density, sound velocity and efflux time measurements respectively. Partial molal volumes (V'2) and adiabatic compressibilities (K"s) at infinite dilution have been fitted to a suitable polynomial to estimate their first and second derivatives with respect to temperature. Bcoefficients have been obtained using lones-Dole equation. The activation energy for viscous flow has been estimated from the temperature dependence of viscosity. These quantities have been discussed in terms of structure-making and structure-breaking processes. Estimated transfer parameters have been rationalized in terms of the interactions between polyols (solutes) and urea or sodium chloride

(cosohites).

The properties of solutions of polyols and of sugars in aqueous and mixed aqueous solutions are important in many areas of applied chemistry and are essential for understanding the chemistry of biological systemsl.2 . However until recently, there have been comparatively few thermodynamic and other physico-chemical investigations in this field 1,3. Poly hydroxy compounds are well-known stabilizing agents4.5 for the native state of proteins/enzymes but the mechanism of this process is still not clear. Therefore, the data revealing the hydration behaviour of these solutes are desirable for better understanding of such processes.

In continuation of our investigations6 on poly hydroxy compounds, in the present paper, we report the apparent molal volumes (

BANIPAL et al. : THERMODYNAMIC PROPERTIES OF MANNITOL & SORBITOL 1 1 07

flowing around the measuring cell was again controlled with an accuracy of± O.OI K. The values of velocity are reproducible within ± 0.5 ms·1 and measured value for water at 298. 1 5 K ( 1 496.74 ms·l ) agrees very well with the literature value ( 1 496.69 ms· I) .

Ubbelohde type capillary viscometer calibrated using deionised doubly distilled and degassed water was used for precise measurements of viscosities. The values are reproducible within ± O.OOl cP.

Results and Discussion Values of 4>v and Ks.2.� for sorbitol and mannitol in

water at 288 . 1 5, 298 . 1 5, 308. 1 5 and 3 1 8 . 1 5 K and in aqueous solutions of (0.5 m) urea and sodium chloride at 298 . 1 5 K were calculated from density and sound velocity measurements using Eqs ( 1 and 2).

= M/d-[(d-d) lOOOlmdd.,l . . . ( 1 ) K,.2.+ = MzKJd - [(K,"d - K,d.,)lmdd.,l . . . (2)

where M2 is the molecular weight of the solute, d" and d, and K " and K are dens ities and adiabatic s s compressibilities of the solvent and solution respectively and m is the molality of the solution. Ks values were calculated from the corresponding sound velocities (u) of the solutions using Eq. (3).

K s . . . (3) =

4>v and Ks.2.� values as a function of molality in water at different temperatures and in aqueous solutions of urea and sodium chloride at 298 . 1 5 K are summarised in Table 1 alongwith sound velocities and densities. Plots (not shown) of 4>v or KS•2., vs m show linear dependence over the concentration range studied. Consequently the values of apparent molal volumes and apparent molal compressibilities at infinite dilution (4)''v = V"2 , K"S.2.$ = K"s) have been obtained by least squares regression analysis using Eqs (4 and 5).

K,.z.+

""'z + S,m

K" + S m s.2 k

. . . (4)

. . . (5)

where Sv and Sk are experimental slopes. Values of V"2' K"S.2' Sv and Sk are summarised in Tables 2 and 3.

Parti al molal volumes ( V"2.) and adiabatic compressibilities (K"s.2.t) of transfer from water to aque-

ous urea or sodium chloride solutions at infinite dilution (Table 3) were estimated as follows:

V'z.Lr or K",.z.Lr = � or K",.z ( in aqueous sodium chloride or urea) - V'z or K",.z (in water) . . . (6) Relative viscosities (11) calculated as the ratio of vis

cosity of the solution (11) and the corresponding solvent (11) i .e. 11, = 11/11" , are given in Figs 1 and 2 (density data summarized in Table 1 were used to estimate 11). These values showed linear concentration dependence and were fitted by the method of least squares to J ones-Dole equation of the following form to evaluate B-coefficients.

11 = l+ Bc r

. . . (7)

where c is molarity. Transfer B-coefficient (M3) for sorbitol and mannitol from water to aqueous urea or sodium chloride solutions [estimated from equation similar to Eq.(6)]are given in Table 4.

Both sorbitol and mannitol have positive V"2 values (Table 2) in water and these increase with temperature. Present '0'2 values of sorbitol ( 1 1 8 .97 cm3 mol·l) and mannitol ( 1 1 9 .48 cm3mol· l) at 298 . 1 5 K are in excellent agreement with the values reported by Dipaola and Belleau8 ( 1 1 9 . 1 6 and 1 19.7 1 cm3 mol·1 respectively), by Jasra and AhluwaliaY ( 1 1 9 .26 and 1 19.53 cm3 mol·1 respectively) and by Hoiland and HolviklO ( 1 1 9.5 and 1 1 9.4 cm3mol·1 respectively). Vishnu et aU have reported V"2 at 308 . 1 5 K for sorbitol ( 1 23 .63 cm3mol·l ) which is quite higher than the present value ( 1 1 9 .68 cm3 mol' I) and it seems to be in error as our values at 298 . 1 5 K are in excellent agreement with the values reported by other workers.

(dV"/d1)p and ( d2V"/d'P)p (Table 5) have been calculated by fitting the "V'2 data, obtained at all the four temperatures using the method of least squares to Eq. (8).

V" = a + bT+ c'P 2 . . . (8)

where a, b and c are constants. (dV"/d1)p values decrease with increase in temperature in both the cases and the value for sorbitol falls to about half (from 0. 1 73 to 0.093 cm3 J'nol'IKI) and for mannitol to very small magnitude (from 0.233 to 0.069 cm3 mol·1 KI) in the temperature range 288 . 1 5 to 3 1 8 . 1 5K. The trend of positive (dV"/d1)p values and their fall with temperature for the two polyols is similar to the trend reported by Bernal and van Hook for sugars I I .

1 108 INDIAN J CHEM, SEC. A, NOVEMBER 1 999

Table 1 - Densities, apparent molal volumes, sound velocities and apparent molal adiabatic compressibilities of sorbitol and mannitol in water at different temperatures

and in aqueous sodium chloride and urea solutions at 298. 1 5 K

m (mol kg'l) d (g cm,J)

BANIPAL et al. : THERMODYNAMIC PROPERTIES OF MANNITOL & SORBITOL 1 109

Table 1 - Densities, apparent molal volumes, sound velocities and apparent molal adiabatic compressibilities of sorbitol and mannitol in water at different temperatures

and in aqueous sodium chloride and urea solutions at 298. 1 5 K(coqtd)

--. m (mol kg·l ) d (g cm·1) v (cml mol· l ) u ( m S·I) K x 1 015 (ml mol·1 Pa·l) ,.2 .• Mannitol

Water 288. 1 5 K 0.05 1 39 1 .002439 1 1 6.8 1 1 470.37 - 1 6.50 0.0803 1 1 .004277 1 1 7. 1 2 1 472.25 - 1 6.41 0.09958 1 .005522 1 1 6.95 1473.46 - 1 6.36 0.40957 1 .024432 1 1 7.36 1493.57 - 1 5.75 0.49803 1 .029520 1 1 7.55 1499.30 - 15.37 0.75 1 64 1 .043496 1 1 7.9 1 1 5 1 5.9 1 - 14.74 0.8 1 87 1 1 .047069 1 1 7.97 1 520.38 - 1 4.66 298. 1 5 K

)(T 0.04932 1 .000 1 29 1 1 9.49 1499.95 - 1 4.39 0.07 1 58 1 .00 1 502 1 19.56 1 50 1 .43 - 1 4.32 0.09428 1 .00289 1 1 1 9.66 1 502.95 - 14.29 0.20756 1 .009730 1 1 9.72 1 5 1 0.50 - 14.09 0.34666 1 .0203 1 9 1 1 9.88 1 5 1 6. 14 - 1 3.83 0.63565 1 .033739 1 20.22 1 539.52 - 1 3.39 0.756 1 6 1 .0401 93 1 20.36 1 547.59 - 1 3.05 0.827 1 8 1 .043630 1 20.43 1 552.86 - 1 3.02 308. 1 5 K 0.03579 0.996243 1 20.46 1 522.78 - 1 3 . 1 0 0.04407 0.996757 1 20.39 1 523.34 - 1 3 . 2 1 0.09259 0.9997 1 8 1 20.43 1 526.57 - 1 3 .08

� 0.20098 1 .006 1 94 1 20.55 1 533.86 - 1 2.99 0.41 628 1 .0 1 8526 1 20.74 1 548.65 - 1 2.97 0.6 1 354 1 .0292 1 1 1 20.96 1 562.52 - 12.90 0.9 1 1 82 1 .044356 1 2 1 .27 1 584.2 1 - 12.93 3 1 8. 1 5 K 0.0389 1 0.99259 1 1 2 1 .47 1 538.8 1 - 1 2.52 0.05855 0.993774 1 2 1 .50 1 540. 1 2 - 1 2.34 0.0802 1 0.99507 1 1 2 1 .60 1 54 1 .60 - 1 2.41 0. 1 8032 1 .009970 1 2 1 .65 1 548.38 - 1 2.29 0.21 238 1 .002864 1 2 1 .66 1 550.59 - 1 2.34 0.4 1 7 1 8 1 .0 14395 1 2 1 .88 1 564.69 - 1 2. 1 2 0.77 1 35 1 .032972 1 22. 1 6 1 589.35 - 1 1 .70 Sodium chloride (0.5 m) 0.05 1 93 1 .020280 1 20.56 1 533.6 1 - 1 2.53 0.07050 1 .02 1 390 1 20.58 1 534.94 - 1 2.47 0.09204 1 .022669 1 20.59 1 536.49 - 1 2.48 0.20241 1 .029080 1 20.73 1 544.49 - 1 2.41 0.4 1 3 1 8 1 .0408 1 8 1 20.95 1 560.01 - 1 2.32 0.501 74 1 .045530 1 2 1 .06 1 566.56 - 1 2.20

). 0.655 1 5 1 .053342 1 2 1 .40 1 578.28 - 1 2. 1 3 0.8 1067 1 .06 1 1 46 1 2 1 .4 1 1 585.39 - 1 1 .99 Urea (0.5 m) 0.04928 1 .007864 1 19.89 1 5 1 3.69 - 12.42 0.06969 1 .009091 1 20. 1 8 1 5 1 5.05 - 1 2.25 0.09247 1 .0 10469 1 20. 1 9 1 5 1 6.60 - 1 2.39 0.09937 1 .0 1 0878 1 20.26 1 5 1 7.05 - 1 2.27 0.20659 1 .0 17246 1 20.27 1 524.29 - 12.34 0.4 1 1 1 5 1 .028894 1 20.43 1 538.27 - 1 2.23 0.89255 1 .054004 1 20.8 1 1 572.62 - 1 2.26

1 1 1 0 INDIAN J CHEM, SEC. A, NOVEMBER 1 999

Table 2- Partial molal volumes and adiabatic compressibilities at infinite dilution for sorbitol and mannitol at various temperatures

288. 1 5K 298. 1 5K Vo2 (cm) mol·l) Sorbitol

1 1 6.88 (0.908) 1 1 8.97 (0.70 1 ) 1 1 9.26' 1 19. 1 6� 1 1 9.5c

Mannitol 1 16.86 ( 1 .380) 1 19.48 ( 1 . 1 52)

1 19.53' 1 1 9.7 1 � 1 1 9.4'

K",.2 x 1 015 (mlmol-IPa-l)

- 1 6.84 ( 1 .634) - 1 4.29 ( 1 . 1 66) 14.0'

- 1 6.62 (2.430) - 14.46 ( 1 .773) - 14.9'

Parenthesis contains Sy and Sk values. 'Ref.9, � ref.8, cref. 1 0, dref.2

Sorbitol

Mannitol

308. 15K 3 1 8. 1 5K

1 1 9.68 (0.737) 1 2 1 .06 ( 1 .007) 1 23.63d

1 20.36 (0.976) 1 2 1 .47 (0.340)

- 1 3. 5 1 ( 1 . 1 27) - 1 2.78 (0.244) - 1 03.Qd

- 1 3. 1 1 (0.268) - 1 2.50 (0.999)

Table 3 - Partial molal volumes and adiabatic compressibilities of sorbitol and mannitol in water and in aqueous (0.5 m each) urea and sodium chloride solutions and their transfer values at infinite dilution at 298. 1 5 K

Water Urea Sodium . Urea Sodium chloride chloride

V" /cm3 mol-l) V" (cm3mol·l) 2.tr Sorbitol

1 1 8.97 1 20.07 1 20. 1 3 1 . 1 0 1 . 16

Manntiol

1 1 9.48 1 20.47 1 20.49 0.99 1 .0 1

K" x l OIS (m3 mol-I Pa-I) K" X l OIS (ml mol-I Pa-I) s,2 li.2.1r

Sorbitol

- 1 4.29 - 1 2.34 - 1 3 .26 1 .95 1 .03 Mannitol

- 1 4.46 - 1 1 .88 - 1 2.55 2.58 1 .9 1

1-

'1

-r

- -�

BANIPAL et aI.: THERMODYNAMIC PROPERTIES OF MANNITOL & SORBITOL 1 1 1 1

1.6 ( b )

1 .4 1 .4

1 .2

1.2 /29S.1 5 K

1 .2 1 .0

'1 1 .0 1 .4 r . 'lr 1 .2

1 .2

· 1 . °0�. 0�--"70.-=-2---:-0-.4--0-.6--0....J. 8 - m - 0. 8

-- m -Fig. l - Plots of 11, vs m for (a) sorbitol and (b) mannitol in water

KS.2,� values , summarized in Table I reveal that these become less negative with increase in temperature and their concentration dependence flatten off (plots of KS,2.� vs m of various temperatures are linear with positive but falling slopes).

K",.2 values reported by Hoiland and Holviklo at 298 . 1 5 K, - 1 4.0 ± 0.5 c 1 0- 15 and - 1 4.9 ± 0.5 x 1 0- 15 m3 mol-IPa-1 are in excellent agreement with the present values of - 1 4.29 x 1 0- 15 and - 14.46 x 1 O-15 m3 mol- IPa-1 for sorbitol and mannitol respectively. There are no data available at other temperatures, except for sorbitol at 308 . 1 5 K for which a value of - 1 03.0 x 1 0- 15 m3 mol-IPa-1 , as reported by Vishnu et al.

2 is much different

from the presently determined value of - 1 3 .5 1 x 1 0- 15 m3 mol-IPa-1 . Being of much different magnitUde, it certainly seems to be erroneous.

Surdo et aL. 12 from large negative K"s 2 values for sug- . ars in aqueous solutions have concluded that these molecules are highly hydrated and the degree of hydration increases with the number of functional groups which can form hydrogen bonds with water molecules. Presently determined large negative values of K"S.2 (of same order as of sugars) for both the polyols suggest that these are also highly hydrated molecules. The increase in K"S,2 values with increase in temperature is suggestive of decrease in hydration with temperature

(dK" 2/dn and (d2K" 21dP) values calculat�d from s. p s. r fitting the data to the equation Similar to Eq. (8) are sum-marised in Table 5. The values of (oKo../onp decrease with temperature for both the polyols. The signs of both the derivatives are again similar to those of sugars as reported by Bernal and van Hookl l .

1 1 1 2 INDIAN J CHEM, SEC. A, NOVEMBER 1 999

' r

1 . 2

1 . 4

1 . 4

1 . 2

1 .4

1 . 2

1 . 0 0 O.

I n sod i um chlo r i d e ( 1 )

o

I n u r ea o ( 2 )

o

so d i u m ch lor ide ( 3 )

0. 4 0.6 0.8 -- m ---

Fig.2 - Plots of 1], vs m for sorbitol ( I & 2) and mannitol (3 & 4) in aqueous sodium chloride and urea solutions (0.5 m) each at 298. 1 5 K

B-coefficients for both the polyols are positive and decrease with temperature. For example B-coefficient value decreases from 0.698 to 0.537 dm3 mol-I for sorbitol and 0.854 to 0.523 dm3 mol- I for mannitol when the temperature was increased from 288. 1 5 to 3 1 8 . '1 5K. Their negative dB/dT values (-0.0054 and -0.0 1 1 0 dm3 mol-I KI for sorbitol and mannitol) are indicative of their structure making propensity as suggested by Tyrell

and Kennerley 13, thus both · sorbitol and mannitol promote the structure of water.

Energy of activation for viscous flow (Esol) for a dilute solution may be calculated by Arrhenius 14 equation:

In 1] = In A + (E,.,/RT) . . . (9) and the differential activation energy for viscous flow (M?) by the relation,

!:1E* = E - E sui water . . . ( 1 0) where E is the energy of activation for viscous flow water for pure water which as obtained from the viscosity data at 288 . 1 5 , 298. 1 5, 308. 1 5 and 3 1 8 . 1 5K reported by Korson et aL. 15 is 3893.45 cal mol- I .

M? values for both sorbitol and mannitol are positive at all the concentrations as illustrated in Fig.3 and also the values increase with concentration confirming that both the solutes are structure makers . M? for mannitol is almost double the value for sorbitol at lower polyol concentration, the difference tapers off asymptotically as m increases. This suggests mannitol to be stronger structure maker when solute-solvent interactions are predominant (which is also evident from the large negative magnitude of dB/dT for mannitol than sorbitol) and the two polyols in concentrated solutions try to match the behaviour, because of stronger solute-solute interactions

The present conclusions are similar to the earlier ones reported by Jasra and Ahluwalia9 and Banipal et aL.6 for various polyhydroxy compounds from large positive CO 2 values. Further it has also been reported9 that mannitol due to its planar zigzag conforn1ation in aqueous solution fits better into the tetrahedral water structure than sorbitol with its sickle-bent structure. Thus co

P•2'

KO dB/dT and 1lE* values are all equivocal to sug-

- 1'

BANIPAL et al. : THERMODYNAMIC PROPERTIES OF MANNITOL & SORBITOL

Table 4 - B-coefficients of sorbitol and mannitol in water and in aqueous (0.5 m each) urea and sodium chloride solutions and their transfer values at 298. 1 5K

Compound B-coefficients (dm3 mol·l) �B (dm3mol·l)

Water Urea Sodium chloride Urea Sodium chloride

Sorbitol 0.624 0.7 1 7 0.662 0.093 0.038 Mannitol 0.626 0.692 0.648 0.066 0.022

Table 5 - Values of (dV'!d1)p' (d'iV'!d'P)p' (dK",./d1)p and (d2K"jd'P)p for sorbitol and mannitol at different temperatures

Compound Temp. (dV'!d1)p (d2V'!d'P)p

(K) (cm3 mol·1 KI) (cm6mol·2 K2)

Sorbitol 288. 1 5 0. 1 73 298. 1 5 0. 1 46 -0.0027 308. 1 5 0. 1 1 9 3 1 8. 1 5 0.093

Mannitol 288. 1 5 0.233 298. 1 5 0. 1 78 -0.0055 308. 1 5 0. 1 24 3 1 8. 1 5 0.069

properties of polyols and the l imitation 1 7 ofthe qualitative classification of solutes by Eq.(9) seems to be untenable at least for these polyols.

Partial molal volumes of sorbitol and mannitol in O.S m aqueous solutions of each of urea and sodium chloride at 298 . 1 SK (Table 3) are more positive than the corresponding values in water resulting in positive V'2 values. These positive i7i'2 values compare J J very well with the corresponding positive values as reported by Jasra and Ahluwalia9 at different cosolute concentrations. Vishnu et at. 2 have also reported positive V02•1I values for sorbitol in aqueous sodium chloride solution at 308 . 1 S K but the magnitude is quite high.

(dK"jd1)p

(cm3 mol·1 Pa·1 KI)

0.230 0. 1 63 0.096 0.029 0.233 0. 1 66 0. 1 08 0.05 1

•

(d2K" Id'P) s,2 J'I

(cm6 mol·2 p-2 K2)

-0.0067

-0.0057

1 000r-----------------�

...-" 'T_

o

800

� 600 u

'-"

* 4 00 w

1 1 14 INDIAN J CHEM, SEC. A, NOVEMBER 1 999

Some investigators 19.20 have approximated intrinsic volume as:

. . . ( 1 3)

VYOid is the associated void or empty volume and VyW is the van der Waal' s volume.

Shahidi et ai. 19 modified Eq. ( 1 3) to find the contribution of one molecule towards the partial molal volume of a non-electrolyte solute as given in Eq. ( 1 4).

V', = V + V . - no 2 v.w VOId !ii . . . ( 1 4)

where cr is the shrinkage in volume caused by interac-s tion of hydrogen bonding group with water molecules and n is the potential number of hydrogen bonding sites in a molecule. Partial molal volume of a polyol molecule can be presented as :

\1"2 = Vv.w + V void - V'hrink,g, . . . ( 1 5)

If one assumes that VY.w and Vyoid have the same magnitude in water and mixed aqueous solutions, the positive volume change accompanying the transfer of sorbitol and mannitol from water to aqueous urea solutions might arise from the decrease in V h ' k s nn age in mixed aqueous solutions. Therefore the positive vo in the case of urea solution can be rationalized by 2.lr considering the interactions between urea molecule and hydroxyl groups of polyols resulting in shadowed effect of hydroxyl groups on water structure causing decreased V . . Similarly these interactions cause reduction in shrinkage structure breaking effect of urea on water structure. Due to solute-cosolute interactions, more water from hydration shells is released as bulk water which has higher volume contribution than structure broken water21 , therefore this factor will also contribute to the positive volume change. The most probable interaction between urea and polyols is through the hydrogen-bonding. The higher magnitude of V, observed in sorbitol ( 1 . 1 0 cm3 mol·l) 2,Ir than in mannitol (0.99 cm3mol·l) might be a reflection of the stronger interactions of sorbitol with urea than mannitol9•

Similarly positive lih values for the polyols from 2,lr water to aqueous sodium chloride solutions may arise from stronger mutual interactions with concomitant fall in their effect on structure of water consequently releasing more water from their hydration shells to the bulk.

Positive values of KO (Table 3) for sorbitol and s,2.lr mannitol from water to aqueous urea and sodium chlo-

ride solutions indicate that compressibility of solutions increases in the presence of urea and sodium chloride. Vishnu et ai. 2 have also reported positive KOs.2.lr values for sorbitol in aqueous sodium chloride solution at 308. 1 5K but the magnitude is quite large. The positive values of K"S.2.lr can be explained by giving similar argument as for ifi'2,lf Due to strong interactions between polyols and cosolutes (urea or sodium chloride) than their interactions with water, more water is released as bulk water. This released bulk water is more compressible than the water in the hydration shells of solutes and cosolutes which results in positive K"s.2.lr values. Higher K"s.2,lr values in the case of mannitol than sorbitol from water to aqueous urea or sodium chloride solutions in the light of i\.lr data indicate that the solute-cosolute complex formed in the case of sorbitol is less compressible which may be attributed to the stronger interactions between sorbitol and cosolutes than in the case of mannitol. This compliments the idea that planar structure of mannitol is compatible with water structure and the availability of its molecules for interactions with cosolutes is less than sorbitol9•

B-coefficients of sorbitol and mannitol in the presence of aqueous urea and sodium chloride solutions (0.5 m each) have higher values than the corresponding values in water which result in positive transfer B-coefficients (ill) indicating that these polyols are in more structured environment (Table 4).

Further the increase in B-coefficients of polyols in the presence of cosolutes may be due to solute-cosolute interactions arising from hydrogen-bonding in the presence of urea and ion-hydrophilic interactions in the case of sodium chloride. The higher magnitude of �B for sorbitol than for mannitol both in the presence of urea and sodium chloride is in line with the conclusions drawn from other results that the interactions between sorbitol and coso lutes are stronger than the interactions between mannitol and cosolutes.

Referentes

Bastos M, Volkoava N N & Wadso I, J chern Soc Faraday Trans, 89 ( 1 993) 1 35 1 and references therein.

2 Vishnu, Wadhwani R & Akhrat Y, Indian J Chern, 34 A ( 1 995) 954.

3 Franks F, Pure appl Chern., 59 ( 1987) 1 1 89.

4 Gupta M N, Biotechnol Appl Biochern, 1 4 ( 1 99 1 ), 1 .

5 Gekko K & Koga S, J Biochern (Tokyo), 94 ( 1 983) 1 99.

6 Banipal P K, Banipal T S, Lark B S & Ahluwalia J C, J chern Soc Faraday Trans, 93 ( 1997) 8 1 .

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7 Banipal T S, & Sehgal G, Thermochim Acta, 262 ( 1 995) 1 75. 1 5 Korson L, Hanson W D & Millero F J, J phys Chem, 73 ( 1 969) 8 DiPaola G & Belleau B , Can J Chem, 53 ( 1 975) 3452; Can J 34.

Chem, 55 ( 1977) 3825. 1 6 Hepler L G , Can J Chem, 47 ( 1 969) 46 1 3. 9 Jasra R V & Ahluwalia J C, J chem Soc Faraday Trans I, 78 1 7 Reading J F, Watson I D & Hedwig G R, J chem Thermodynam-

( 1 982) 1 677. ics, 22 ( 1 990) 1 59. 1 0 Hoiland H & Holvik H , J soln Chem, 7 ( 1 978) 587. 1 8 Frank F, Quickenden M A, Reid D S & Watson B, Trans Fara-I I Bernal P J & Van Hook W A, J chem Thermodynamics, 1 8 ( 1 986) day Soc, 66 ( 1 970) 582.

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1 97 . 20 Terasawa S, Itsuki H & Arakawa S, J chem Phys, 79 ( 1 975) 1 3 Tyrell H V & Kennerley M , J chem Soc, A ( 1 968) 2724. 2345. 1 4 Mason L S , Kampmeyer P M & Robinson A L, JAm chem Soc, 2 1 Fortier J C , Philip P R & Desnoyers J E, J soln Chem, 3 ( 1 974)

74 ( 1952) 1 287. 523.