Indian Journal of ChemistryVol. 34A, December 1995, pp. 954-960

Ultrasonic and thermodynamic studies of interactions in ternary solutionscontaining glycerol or sorbitol and aqueous electrolytes

Vishnu' & R WadhwaniDepartment of Chemistry, K.S. Saket Postgraduate College, Faizabad 224 001, India

andYasmin Akhtar"

Department of Chemistry, University of Allahabad, Allahabad 211 002, India

Received 26 December 1994; revised 2 May 1995; accepted 31 July 1995

Ultrasonic velocities and densities of glycerol and sorbitol in aqueous alkali halide solutions ofdifferent concentrations at 308 K have been measured. The values of adiabatic compressibility (K.),apparent molar volume (t.), apparent molar compressibility (+Ks) and hydration number (Hn) havebeen deduced from densit)' and ultrasonic velocity data. Results show that: (i) there are short rangeand weak interactions in the present ternary systems, (ii) ions such as Na +, K +, Cl-, Br " are struc-tun! makers (SM) in both glycerol and sorbitol in the order Na" >.le > CI- > Br " > 1-, while 1- isstructure breaker (SB).

The structural interactions of non-ionic soluteswith ionic ones in different solvents are importantin many fields of chemistry. The studies on suchinteractions of polyhydroxy compounds with elec-trolyte substance in aqueous and non-aqueoussolvents are very significant and useful for investi-gating their physico-chemical behaviour! -10. Ro-binson et aLII.12 and Vishnu et aL\3-18have extensively studied aqueous and non-aque-ous ternary systems containing polyhydroxy com-pounds, such as mannitol, glucose, sucrose, fruc-tose, maltose etc. and electrolytes like alkali ha-lides. Ultrasonic propagation parameters havebeen used recently to study interactions inbinary 19 - 2 I and ternary'? - 24 systems, as well asthe ion-solvents and ionic interactions in aque-OUS25 - 26 and mixed aqueous'? and non-aque-OUS28•29 systems.

In the present work ultrasonic study of aque-ous ternary systems comprising poly hydroxy alco-hols (nonelectrolytes) and alkali halide (electro-lyte) has been carried out at constant temperature308 K for predicting the solution properties ofsome polyhydroxy alcohols in terms of differentapparent molar properties as well as to investigatethe effect of factors like ionic concentrationsand size. We have undertaken the study of glycer-ol-water-alkali halides and sorbitol-water-alkalihalides. The measurements of ultrasonic velocity

'Ex-Professor of Chemistry, University of Gorakhpur,Gorakhpur.

and density were carried out and these data wereused to deduce various apparent molar parame-ters, such as adiabatic compressiblity, apparentmolar isentropic compressibility, apparent molarvolume and hydration number. These parameterswere used to study the structural interactions tak-ing place in ternary solutions.

Materials and MethodsUltrasonic interferometer and pyknometer were

used for measurements of ultrasonic velocity anddensity of solutions at a constant temperature of308 K in the present study. The chemicals usedwere A.R. grade and were used without furtherpurifications. To estimate the uncertainty of theexperimental data the ultrasonic interferometerand pyknometer were carefully calibrated with thepresent samples of liquids such as distilled water,benzene ~AR, BDH, of purity 99.8%) and car-bon tetrachloride (AR, BDH, of punty 99.8%) at20°e. Aqueous alkali halide solutions (0.5~ 1 and1.5 mol dm-3) prepared by weight dilution meth-od using doubly distilled deionised water (specificconductance K = 2.48 mhos, pH = 7.8) were usedas electrolytic solvents for preparing glycerol andsorbitol solutions of different molar concentr-ations.

The densities of these solutions were measuredat the same temperature by calibrated single ca-pillary pyknometer. The viscosity and density datawere found to be accurate within + 0.20% and+ 0.02% respectively.

VISHNU et aL: ULTRASONIC & THERMODYNAMIC STUDIES OF GLYCEROL& SORBITOL 955

The apparent molar compressibility (ck hasbeen calculated from the relation

'K,=(1000/cpo)(Kspo-K~p)+(M'K/pO) ... (1)

where K, and K ~are the isentropic compressibilit-ies of solutions and solvent respectively and M isthe molecular weight of the solute. Isentropiccompressibility, Ks' is obtained from the relation,

K.=(pu2tl ... (2)The apparent molar volume (,) of the solute atvarious concentrations can be computed fromdensity data using the equation'v=(lOOOlepO). (pO_ p)+(MlpO) ... (3)

The hydration number (Hn) is a solution parame-ter related to the adiabatic compressibility of thesolution. Hydration number is assumed to be theaverage number of water molecules bound to thesystem being hydrated. For aqueous solutions, theprimary solvation number (SJ is usually called hy-dration number (Hn). The hydration number isgiven by

H; = (n/l~Jx (1 - K/ K~) ... (4)

Results and DiscussionThe variation of ultrasonic velocity of glycerol

in water and in 1.0 mol dm - 3 aqueous sodiumchloride at different concentrations, and the var-iations of ultrasonic velocity of sorbitol in water

~-----------------------------~1~~

to 2.0 3.0 4.0 5.0 6.0 8.0C/rnol r'

Fig. I-'-Variation of ultrasonic velocity (u) and adiabaticcompressibility (K.) of glycerol with its molar concentrations(c) in water and aqueous sodium chloride solutions of differ-ent ~oncentrations at 308 K. (u for water- -0-0- 0.25 MNaC} -A-A-, 0.5 M NaC!, -x-x-, 0.75 M NaC}, -13-11-1.0 M NaCI -e-e-, P. for water -0-0-, 0.25 M NaCI,- A-A-, 0.50 M NaCI, -0-0-, 0.75 M NaCI -_-_-, 1.00 M

NaQ-O-o-

and in 1.0 mol dm - 3 aqueous potassium halide atdifferent concentrations are shown respectively inFig. 1 .and Fig. 2. Similar trends have been foundin the presence of other alkali halide also (Figs 3and 4). The variations have been found to benon-linearly convergent towards higher concentr-ations in the case of glycerol and linear in thecase of sorbitol. This shows that the ultrasonic ve-locity in the case of glycerol is a non-linear func-tion of molar concentration and that there is sign-ificant and considerable interaction: in the ternarysystems containing glycerol while weak interac-tion occurs in the case of ternary system contain-ing sorbitol.

The variation of ultrasonic velocities of glyceroland sorbitol with their molar concentrations inwater and different aqueous alkali halide solutionscan also be expressed in terms of density (p) andadiabatic compressibility (Ks). by Eq. (5)(dulde) = - (U/2) x [(lip ).(dpl de) + (1/KJ( dK/ de)]

... (5)Equation (5) shows that concentration depend-

ence of ultrasonic velocity is influenced by thedensity (p) and adiabatic compressibility (K.). Thequantity (dpl de) is positive while (dK/ de) is ne-gative in the present case. Since these factorshave opposite signs, H-bonded structure Of wateris either promoted or disrupted by the addition ofsolutes. Consequently, ultrasonic velocity of wateris increased or decreased depending on the struc-tural properties of solutes. The solutes which in-

1680 70

o-ue- ~s

1500~.n~~~~~~~~~~ __ ~n~~~ 12 1~

C/m~.i'Fig. 2-Variation of ultrasonic velocities (u) and adiabaticcompressibility (K.) of sorbitol in water and in aqueouspota-ssium chloride solutions of different concentrations with itsmolar concentration (c)1 at 308 K (I, Water; 2, 0.5 MKCI; 3,

1.0 M KCI and 4, 1.5 M KCI.

956 INDIAN J CHEM. SEC. A, DECEMBER 1995

.-------------------------~~

4

,.Or---------------------------~4·70

1700

350 ":'. 80":'cf'.• E ~-€ ~ '>-••-; ::> :ocet:.. 1600><

k-----:\;,...._~-;';:_____:':__,,':;,...._~--;t_;:;__"'IIl:_'1500to 2.0 ao 4.0 5.0 6.0C/mor1

Fig. 3-Variation of ultrasonic velocity (u) and adiabaticcompressibility (K,) of glycerol with its molar concentrations(cj in] water and 1.0 M-aqueous sodium halide solutions at308 K. (ul for water -0-0-, 1.0 M NaCI -ll.-ll.-, 1.0 MNaBr - x- x -, 1.0 M NaI, -e-e-, ~,for water -0-0-,

1.0M NaCI -ll.-ll.-, 1.0 M NaBr -0-0- 1.0 M NaI -0-0-

crease the ultrasonic velocity are, therefore, struc-ture makers (SM) and those decreasing the veloc-ity are structure breakers (SB).

Nambinarayanan and Ra030 have also discussedthe ultrasonic velocity in terms of 8M and SBproperties of ions and correlated the decrease invelocity with SB properties of ions. Sirkumaret al:31 studied the effect of electrolytes onsound velocity maxima in water and discussed theresults in the light of SM and SB characters ofions. Kaurova and Roschina+' correlated the ion-ic size with velocity change and found that thesmaller the cation the greater is the velocitychange from ultrasonic measurements of solutionof MgCI2, CaCl2 and ZnCl2 in methanol. In thepresent case ultrasonic velocity has been found toincrease with increase in glycerol or. sorbitol con-centrations. This shows that the factor (dK.I de) isdominant.

In the present investigation, NaCI, NaBr, KCIor KBr generally increase the ultrasonic velocityof glycerol, and sorbitol with increase in theirconcentrations while NaI and Kl decrease' thevelocity (Figs 3 and 4). These results reveal thatultrasonic velocity decreases with increase in sizeof the ions and anions are more effective thancations in bringing about the change in velocity.

Ultrasonic velocities of glycerol and sorbitol in-crease in the presence of alkali halidesMX(M=Na+ or K+ and X=Cl- or Br-) and de-

Fig. 4- Variation of ultrasonic velocities (u) and adiabatic com-Rressibility (K.) of sorbitol in water and in aqueous potassiumchloride solutions of different concentrations with its molar con-centration (e) at 308 K (1, water; 2,0.5 MKCl; 3, 1.0 MKBr and 4,

1.5MKI)

crease in the presence of NaI or KI with increasein their respective concentrations. Cl- and Br "ions are therefore structure making and 1- ion isstructure breaking. The structure making propert-ies of ion may be expressed in the order of crys-tallographic size: Na " >K+ >Cl- >Br- >1-.Since I - ions has the largest size among theseions, it is least structure breaking. Similar resultshave also been found by Vishnu et al:13 - 18. Thestructure making and breaking properties of ionsand molecules may be interpreted in terms ofbreaking of hydrogen bonded structure of waterand structural rearrangement.

In aqueous solutions of alkali halides MX(M=Na+ or K+ and X=CI- or Br : or 1-) ionsoccupy the interstitial spaces of water. These ionsexcept I - ion do not disrupt the original orderedstate of water due to their smaller size. The struc-tural rearrangement does not occur .in the presenceof I - ions. It is therefore structure breaking andother ions such as Na ", K+, Cl-; Br : are struc-ture making.

Ultrasonic velocities of glycerol and sorbitol inaqueous solutions of alkali halides of given con-centration increase with increase in glycerol orsorbitol concentrations. Glycerol and sorbitol areexpected to be structure.· breakers because assoon as the glycerol or sorbitol molecules occupythe 'interstitial space of water, it tends to breakthe original ordered state of water due to its larg-er molecular size, but there occurs a structuralrearrangement as a result of the hydration (glycer-

VISHNU et aL: ULTRASONIC & llIERMODYNAMIC snrorss OF GLYCEROL & SORBITOL 957

01 and sorbitol) leading to a comparatively more interpreted in terms of SM and SB characters ofordered state. Glycerol and sorbitol, therefore, ionic solutes.behave like structure makers and increase ultra- The validity of Bachem's relation,sonic velocity with increase in concentration. The va- .((s-K~}fc=A+B [c ... (6)riation in ultrasonic velocity in the case of sorbitolin an aqueous alkali halide solution is much more can be tested by plotting (Ks - Kr;J/c versus [C,distinct and pronounced than glycerol revealing where c is the molar concentration of glycerolthat sorbitol is a better structure maker or a poor and sorbitol, and A and B are constants. Suchstructure breaker than glycerol. plots in the present case are found to be linear. The compressibility of solution in water is max- which indicate that adiabatic compressibility of

imum and decreases with increase in NaO and glycerol or sorbitol in aqueous alkali halide solu-xo concentrations (Figs 1 and 3). It also de- tions obey Bachem's relation.creases in the presence of sodium and potassium The hydration number, Ho' obtained from Eq.halides and increases with increase in ionic size. (4) at 308 K for all the systems are presented inThe effect of NaI and KI on compressibility is not Tables 1 and 2. The hydration number (Ho) inreversed. The compressibility change may also be water and aqueous alkali halide solution at a giv-

Table I-Hydrogen number (H,,) of glycerol in aqueous alkali halide solutions at 308 K

Aqueous aIkali halide solution Aqueous aIkali halide solution

Glycerol Hn (mol dm-J) Glycerol H.{moldm-J)mol dm=? rnol dm ?

0.00 0.25 0.50 0.75 10.0 0.00 0.25 0.50 0.75 10.0

Sodium chloride Potassium bromide

0.0 0.01.0 3.39 3.03 2.53 2.83 2.66 1.0 3.39 3.19 3.07 2.67 2.352.0 2.88 2.74 2.54 2.54 2.47 2.0 2.88 2.75 2.61 2.35 2.253.0 2.51 2.44 2.28 2.28 2.12 3.0 2.57 2.38 2.22 2.19 2.074.0 2.27 2.11 1.97 1.97 1.83 4.0 2.27 2.07 1.96 1.90 1.765.0 1.95 1.82 1.71 1.71 1.63 5.0 1.95 1.79 1.71 1.60 1.516.0 1.64 1.55 1.42 1.42 1.37 6.0 1.64 1.53 1.45 1.35 1.277.0 1.37 1.30 1.19 1.19 1.13 7.0 1.37 1.27 1.20 1.08 1.018.0 1.10 1.06 0.94 0.94 0.89 8.0 1.10 1.01 0.94 0.86 0.78

Potassium chloride Sodium iodide0.0 0.01.0 3.39 3.20 3.04 2.55 2.58 1.0 3.39 3.19 3.07 2.67 2.352.0 2.88 2.93 2.66 2.48 2.33 2.0 2.88 2.75 2.61 2.35 2.253.0 2.57 2.46 2.34 2.18 2.16 3.0 2.57 2.38 2.22 2.19 2.074.0 2.27 2.21 2.05 1.93 1.84 4.0 2.27 2.07 1.96 1.90 1.765.0 1.95 1.87 1.77 1.68 1.57 5.0 1.95 1.79 1.71 1.66 1.576.0 1.64 1.59 1,:48 1.32 1.29 6.0 1.64 1.53 1.45 1.35 1.277.0 1.37 1.36 1.23 1.18 1.14 7.0 1.37 1.27 1.20 1.08 1.018.0 1.10 1.04 0.95 0.91 0.88 8.0 1.10 1.01 0.94 0.86 0.78

Sodium bromide . Potassium iodide0.0

0.01.0 3.39 3.20 3.18 2.86 2.76 1.0 3.39 3.19 3.07 2.67 2.352.0 2.88 2.80 2.69 2.57 2.31 2.0 2.88 2.75 2.61 2.35 2.253.0 2.57 2.47 2.34 2.20 2.01 3.0 .2.57 2.38 2.22 2.19 2.074.0 1.27 2.14 2.06 1.96 1.79 4.0 2.27 2.07 1.96 1.90 1.765.0 1.95 1.85 1.74 1.64 1.53 5.0 1.95 1.79 1.71 1.60 1.516.0 1.64 1.57 1.45 1.37 1.29 6.0 1.64 1.53 1.45 1.35 1.277.0 1.37 1.28 1.20 1.13 1.05 7.0 1.37 1.27 1.20 1.08 1.018.0 1.10 1.04 0.97 0.90 0.84 8.0 1.10 1.01 0.94 0.86 0.78

958 INDIAN J CHEM. SEC. A, DECEMBER 1995

•Table 2-Hydration number (Hn) of sorbitol in aqueous sodium and potassium halide solutions at 308 K

Aqeous alkali halide solution Aqeous alkali halide solution

Sorbitol H; (mol dm-3) Sorbitol Hn (mol dm=')c(moldm-3 c(moldm-3

0.0 0.05 1.0 1.5 0.0 0.05 1.0 1.5

Sodium chloride Potassium bromide

0.0 0.00.2 7.37 7.04 6.30 6.14 0.2 7.37 7.19 6.29 5.660.4 7.21 6.73 6.08 5.88 0.4 7.21 7.02 6.01 5.38

0.6 6.96 0.56 5.86 5.68 0,6 6.96 6.46 5.75 5.350.8 6.68 6.32 5.69 5.48 0.8 6.68 6.19 5.56 5.191.0 6.34 6.13 5.40 5.17 1.0 6.34 6.02 5.24 4.971.2 6.20 6.00 5.20 4.96 1.2 6.20 5.77 5.07 4.841.4 5.92 5.57 5.00 4.78 1.4 5.92 5.67 4.88 4.661.6 5.67 5.38 4.80 4.64 1.6 5.67 5.34 4.77 4.48

Potassium chloride Potassium iodide

0.0 0.00.2 7.37 6.88 6.28 6.08 0.2 7.37 6.36 5.69 5.600.4 7.21 6.54 6.19 5.84 0.4 7.21 6.24 5.61 5-,400.6 6.96 6.42 5.88 5.60 0.6 6.96 6.23 5.52 5.240.8 6.68 6.13 5.67 5.52 0.8 6.68 5.93 5.27 5.161.0 6.34 5.94 5.45 5.28 1.0 6.34 5.70 5.16 4.981.2 6.20 5.62 5.41 4.95 1.2 6.20 5.63 5.02 4.821.4 5.92 5.58 5.17 4.77 1.4 5.92 5.40 4.84 4.621.6 5.67 5.35 4.91 4.54 1.6 5.67 5.24 4.68 4.43

Sodium bromide Sodium iodide

0.0 0.0

0.2 7.37 6.91 6.77 6.08 0.2 7.37 6.26 5.70 5.300.4 7.21 6.70 6.47 5.97 0.4 7.21 6.10 5.60 5.20

0.6 6.96 6.49 6.20 5.75 0.6 6.96 5.95 5.44 5.04

0.8 6.68 6.36 6.00 5.43 0.8 6.68 5.82 5.35 5.001.0 6.34 6.01 5.71 5.31 1.0 6.34 5.65 5.20 4.921.2 6.20 5.74 5.07 5.05 1.2 6.20 5.58 5.11 4.711.4 5.92 5.47 5.21 4.78 1.4 5.92 5.35 4.9\ 4.501.6 5.67 5.20 4.93 4.58 1.6 5.67 5.12 4.79 4.38

en concentration gradually decreases with in-crease in size of anion and cation. Since the num-ber of water molecules decreases with increase inglycerol or sorbitol concentration the pumber offree water molecules for desired hydration of gly-cerol and sorbitol obtained from breaking of hy-drogen bonded structure therefore - decreases.Hence, hydration number of glycerol and sorbitoldecreases with their increasing concentrations,There is significant and considerable interactionin the system containing glycerol and weak inter-action in the system containing sorbitol.

The experimental data of +v for the sorbitol arepresented in Tables 3 and 4. The limiting appar-ent molar volumes (+~) were obtained by extrapo-

lating the plots of +v versus J c up to zero con-centrations. The concentration variation of appar-ent molar volume is very useful for understandingthe interactions in the present system and is dis-cussed in terms of Masson's relation:

... (7)

where cjIv is the apparent molar volume at infinitedilution and S, the experimental slope. The so-lute-cosolute and solute-solvent interactions canbe studied from these empirical parameters.

Tables 3 and 5 show that the value of +~and S;for glycerol are positive and large, which revealthe existence of significant and strong interactionsin glycerol-water-alkalik halide systems, while ne-

VISHNU et al.: ULTRASONIC & lHERMODYNAMIC STIJDIES OF GLYCEROL & SORBITOL 959

Table 3-Limiting apparent molar volume +ox 103/m3 mol-I and limiting apparent molar compressibilities +;,x 10,s/ms N-Imol- I of glycerol in aqueous sodium and potassium halide solutions at 308 K

Halides Aqueous alkali halide solutions Aqueous alkali halide solutions+~moldm-3 ' +~moldm?

0.00 0.25 0.5 0.75 1.00 0.00 0.25 0.50 0.75 1.00

SOdium chloride 71.18 70.68 70.18 69.74 69.66 -18.0 - 6,0 +11.0 + 4.0 +11.0Potassium chloride 71.18 70.80 67.00 71.58 72.25 -18.0 ~24,0 + 5.0 +47.5 + 0,0

Sodium bromide 71.18 68.40 71.00 68.75 71.95 -18.0 -15.0 -15.0 -15.0 + 9.0Potassium bromide 71.18 69.60 71.22 70.92 71.85 -18.0 -29,0 - 0,0 - 2.5 + 12.5Sodium iodide 71.18 70.28 71.58 72.32 71.00 -18.0 + 6.0 + 11,0 + 16.0 +20.0Potassium iodide 71.18 70.48 70.22 71.26 72.23 -18.0 -15.0 -23,5 - 5.0 +20.0

Table 4-Limiting apparent molar volume +0x lOj1m3 mol-I and limiting apparent molar compressibilities +;, x 10's/m" N-Imol- I of sorbitol in aqueous sodium and potassium halide solutions at 308 K

Aqueous alkali halide solution Aqueous alkali halide solution+~,mol dm-3' +0 mol dm "?K,

0,0 0,05 1.0 1.5 0.0 0.5 1.0 1.5

Sodium chloride 123,63 125.20 126.78 125.85 -103.0 -46.0 + 9.0 +23.0Potassium chloride 123.63 124.60 125.25 1'22.63 -103,0 -18.0 + 2,0 + 8.0Sodium bromide 123,63 118.50 125.88 126.48 -103.0 -105.0 +30.0 - 6,0Potassium bromide 123,63 123.28 125.65 124.50 -'103.0 -88.0 + 8.0 + 6.0Sodium iodide 123,63 125.90 126.34 123.04 - 103.0 - 15.0 +74.0 +97.0Potassium iodide 123.63 124.18 126.10 122.85 - 103.0 + 19.0 +65.0 +64.0

Table 5-Experimental slopes SyX lOY12(mYl2, mol-312) and S", x 1033 (ml3/2 N-I moP/2) of glycerol in aqueous sodium and po-tassiumhalide Solutions at 308 K

Halides Aqueous alkali halide solutions Aqueous alkali halide solutionsSymoldm-3 S",moldm-3

0.00 0.25 0.50 0.75 1.00 0.00 0,25 0.50 0.75 1.00

Sodium chloride +0.34 +0.48 +0.82 +0.90 + 1.24 +45.0 +35.0 +34.0 +41.0 +38.0Potassium chloride +0.34 +0.44 +0.68 +0.28 +0.00 +45.0 +51.0 +32.0 + 17.0 +38.0Sodium bromide +0,34 + 1.40 +0.55 + 1.40 +0.45 +45.0 +43.0 +45.0 +45.0 +34.0Potassium bromide +0,34 + 1.00 +0.32 +0.56 +0.06 +45.0 +48.0 +33,0 +40.0 +29.0Sodium iodide +0.34 +0.50 +0.12 +0.14 +0.48 +45.0 +38,0 +40.0 +41.0 + 19.0Potassium iodide +0.34 +0.56 +0,74 +0.40 +0,00 +45.0 +46,0 +53,0 +35.0 +25.0

Table 6-Experimental slopes SyX 1091.! (mYl2,mol-312 and SIC.x 1023/2 (ml3/2 N-I moPI2) of sorbitol in aqueous sodium and po-tassium halide 'solutions at 308 K

Halides Aqueous alkali halide solutions Aqueous alkali halide solutionSymoldm-3 SK,mol dm-3

0,05 0.5 1.0 1.5 0.0 0.5 1.0 1.5

Sodium chloride -1.375 -2.000 -2.275 -0.725 +60.0 +37.0 +36.0 +37.0Potassium chloride -1.375 - 1.325 +0.250 + 1.200 +60.0 + 18.0 +38.0 +44.0Sodium bromide -1.375 -0.540 - 1.330 -1.980 +60,0 +98.0 +47.0 +48,0Potassium bromide -1.375 +0.620 +0.280 +0.150 +60,0 +59.0 +40.0 + 0,0Sodium iodide -1.375 -2.780 -2.600 +0.680 +60.0 +28.0 -21.0 -21.0Potassium iodide -1.375 -1.130 -1.650 +0.300 +60.00 -14.0 -18.0 -19.0

960 INDIAN J CHEM. SEC. A, DECEMBER 1995

gative and low positive value of S" for sorbitolsystems shown in Tables 4 and 6, reveals the weakinteraction in the system containing sorbitol-water-alkali halide system.

The experimental values of cP", obtained fromEq. (1), for glycerol-water-alkali halides andsorbitol-water-alkali halides systems are reportedin Tables 3 and 5. The limiting isentropic molarcompressibility (cp2) was obtained from the plotsof CPK, versus Tc, the concentration dependence ofthis parameter has been expressed in terms ofEq.8

CPK, = cp2,+ SK)~ ... (8)These parameters were also used to investigatethe solute-solvent and solute cosolute interactions.The values of cp~ are positive for all glycerol-wa-ter-alkali halides showing strong interactions. It isnegative for aqueous solution of sorbitol in water,0.5 mol dm - 3 alkali halide and positive for aque-ous solution of 1.0 mol dm-3 and 1.5 mol dm-3alkali halide.

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