partial molar heat capacities and volumes of aqueous...

Partial molar heat capacities and volumes oftransfer of some saccharides from water toaqueous urea solutions at T = 298.15 K

P. K. Banipal," T. S. Banipal,6 J. C. AhluwaliaDepartment of Chemistry, Indian Institute of Technology, Hauz Khas,New Delhi, 110016, India

and B. S. LarkDepartment of Chemistry, GuruNanakDev University, Amritsar, (Ph.),143005, India

Apparent molar heat capacities <t>Cp and volumes <j>V of seven monosaccharides {D(—)-ribose, D(—)-arabinose, D(+)-xylose, D(+)-glucose, D(+)-mannose, D(+)-galactose,D(—)-fructose}, seven disaccharides {sucrose, D(+)-cellobiose, lactulose, D(+)-melibiosehemihydrate, D(+)-maltose monohydrate, D(+)-lactose monohydrate, D(+)-trehalosedihydrate} and one trisaccharide {D(+)-rafEnose pentahydrate} have been determinedin (0.5, 1.0, 1.5, and 3.0) mol • kg"1 aqueous urea solutions at T = 298.15 K fromspecific heat and density measurements employing a Picker flow microcalorimeter and avibrating-tube densimeter, respectively. By combining these data with the earlier reportedpartial molar heat capacities C° 2 and volumes V£ in water, the corresponding partial

molar properties of transfer (C° 2 tr and V^^) from water to aqueous urea solutions atinfinite dilution have been estimated. Both the C° 2 tr and F2°tr values have been found tobe positive for all the sugars and to increase with increase in concentration of the cosolute(urea), suggesting that the overall structural order is enhanced in aqueous urea solutions.This increase in structural order has been attributed to complex formation between sugarsand urea molecules through hydrogen bonding and to a decreased effect of urea on waterstructure. The transfer parameters have been rationalized in terms of solute-cosoluteinteractions using a cosphere overlap hydration model. Pair, triplet and higher-orderinteraction coefficients have also been calculated from transfer functions and their signand magnitude have been discussed.

KEYWORDS: saccharides; heat capacity; volume; interaction coefficients; stereochemicaleffects

1410 P. K. Banipal et al.

1. Introduction

The hydration characteristics of saccharides(1~6) and their interactions with electrolytes andnonelectrolytes(7~15) in aqueous media are of significant biological and thermodynamicimportance. It has been widely reported(1622) that sugars and polyols act as efficientstabilizing agents for proteins/enzymes because of their ability to enhance the structureof water. Lee and Timasheff^17) attributed the stabilizing effect of sucrose to the positiveGibbs free energy required to form a cavity in the solvent due to an increase in the solventcohesive force when sucrose was added to water. Bull and Breese(23) suggested that sugarsenhanced the structure of water in the immediate neighbourhood of the protein.

On the other hand, urea forms nearly ideal mixtures because of possible compensatinginteractions with water and can exhibit a chaotropic action on ordered systems suchas micelles, folded globular proteins and water soluble synthetic polymers/24'25) It hasalso been reported that urea enhances the solubility of the nonpolar compounds due tothe weakening of hydrophobic interactions, which contribute to the stability of micellesand folded globular proteins and thus devoid water of its unique property of promotinghydrophobic interactions/26) Furthermore, it is well known(27~30) that the extent ofdenaturation of certain proteins by urea-type denaturants is reduced in the presence ofsugars or polyhydroxy alcohols. However, the mechanism by which this renaturating effecton protein structure is induced, either by the direct binding of urea with the polyhydroxycompound/protein molecule or through the alteration of water structure, is not clearlyunderstood. Thus the investigation of interactions between urea and saccharides havingdifferent stereochemistry will help to clarify the nature and specificity of these interactions.

In continuation of our investigations of the solution behaviour of saccharides, we reporthere, apparent molar heat capacities <fiCp and volumes <fiV of various mono-, di- and tri-saccharides in (0.5, 1.0, 1.5 and 3.0) mol • kg"1 aqueous urea solutions at T = 298.15 K.By combining these data with the earlier reported1^ partial molar heat capacities C° 2 andvolumes F2° in water, the corresponding partial molar properties of transfer (C° 2 tr andV^ respectively) at infinite dilution have been determined. These transfer parameters areinterpreted in terms of (solute + cosolute) interactions. The effect of cosolute concentrationhas also been discussed. Coefficients of pair, triplet and higher-order interactions in termsof (solute + cosolute) have also been calculated from transfer functions.

2. Experimental

A picker differential flow microcalorimeter (Sodev Inc., Sherbrooke, Canada) wasemployed for measuring the heat capacities per unit volume of the solutions. Its oper-ating principle and procedure have been described elsewhere/31) The precision ofthe microcalorimeter used was ±0.5 per cent with a limit of detectability of7 • 10~5 J K " 1 g"1. A programmable circulating thermostat supplied with the in-strument was used to maintain the temperature within ±1 • 10~3 K. The current andvoltage were measured with accuracies of ±1 • 10~4 A and ±1 • 10~3 V, respectivelyusing a Systronics digital multimeter. The signals were recorded by using a Bryans-2800potentiometric strip chart recorder. The specific heat capacity for the reference water at

Heat capacities and volumes of transfer of saccharides 1411

T = 298.15 K was taken(31) as 4.1796 J • K"1 • g"1. The performance of the calorimeterwas checked by measuring the apparent molar heat capacities of aqueous sodium chloridesolutions at T = 298.15 K. A good agreement with the literature was found.(31)

A digital vibrating-tube densimeter (model DMA 60/602, Anton Paar, Austria) was usedto measure the densities of the solutions. The details of its principle and operation havebeen described elsewhere.(32) A Tronac PTC-40 proportional temperature controller and anMK-70 ultracryostat were used to control the temperature of the bath used. The temperaturewas checked by using an NBS thermometer with an accuracy of ± 0.01 K and the thermalstability of the bath was found to be better than ±1•10~3 K. The instrument was calibratedwith dry air and water to yield density values accurate to within ±3 • 10~6 g • cm"3. All themeasurements of the densities of the various solutions were made with reference to purewater having a density of 0.997047 g • cm"3 at T = 298.15 K.(33) The densities of aqueoussodium chloride solutions were in excellent agreement with the literature values/32' 34)

The various saccharides whose mass fraction purities are given in parentheses werepurchased from Sigma Chemical Company: D(-)-ribose (0.98), D(-)-arabinose (0.98),D(+)-glucose (0.997), D(-)-fructose (0.98), sucrose (0.995), lactulose (0.98), D ( + ) -melibiose hemihydrate (0.98) and D(+)-raffinose pentahydrate (0.99). D(+)-xylose,D(+)-mannose, D(+)-galactose, D(+)-cellobiose, D(+)-maltose monohydrate, D ( + ) -lactose monohydrate and D(+)-trehalose dihydrate were obtained from the AmericanNational Institute of Standards and Technology (NIST). Their characterization has beenreported elsewhere.(35~38) These sugar samples were used without further purification,however, before use they were dried over P2O5 in a desiccator. Analar grade urea obtainedfrom BDH was used after drying for 48 h at T = 333 K. All the solutions were preparedusing distilled and deionized water obtained by passing double distilled water through aCole-Parmer ion-exchange resin mixed bed column. The water was then degassed beforeuse. The solutions were made by weight using a Mettler balance with a resolution of0.01 mg.

3. Results

The apparent molar heat capacity <$>CP and volume <$> V of the sugars studied were obtainedfrom the experimentally measured specific heat capacity and density data in (0.5, 1.0, 1.5and 3.0) mol • dm"3 aqueous urea solutions using the following relations:

<f>Cp = Mcp - {1000(C; - cp)/m] (1)

<PV = (M/p) - {1000(p - pl)/mppl} (2)

where M is the molar mass of the solute, m is the molality of the solution, c° cp and po,and p are the corresponding specific heat capacities and densities of the solvent and thesolution, respectively.

The values of p, cp, <fiCp and <j> V for the various sugars in the aqueous urea solutions atT = 298.15 Kas a function of molality are summarized in table 1. At infinite dilution, thepartial molar heat capacities (<t>C° = C° 2) and partial molar volumes {<t>°V = F2°) werecalculated from the corresponding 4>CP and <p V data by taking the average of all the data


TABLE 1. Densities p, specific heat capacities cp, apparent molar heat capaci-ties 4>Cp and apparent molar volumes 4>V of some saccharides in aqueous solu-

tions of urea at T = 298.15 K

m

(mol -kg^1)

0.058020.096170.110590.140720.185050.243520.259410.27101

0.069950.103190.139660.183170.22142

0.062330.116600.151330.21193

0.073690.103200.163970.212620.23912

0.061570.106120.189340.199930.26444

0.075460.128300.132470.151210.25999

0.053000.121870.154690.25944

P(g-cm~3)

1.0079831.0100191.0107841.0123801.0147111.0177441.0185621.019150

1.0159321.0176931.0196021.0218751.023844

1.0225551.0254021.0272141.030320

1.0422111.0437331.0468431.0492671.050592

1.0083011.0107691.0153231.0159101.019384

1.0163861.0192881.0195071.0205251.026410

1.0221701.0259321.0277111.033270

Cp

( J - K - i - g - 1 ) ( J -K-

D(-)-Ribose

0.5 mol • kg urea solution4.08344.07174.06754.0582

4.02784.02294.0199

1.0 mol • kg urea solution4.01094.00193.99273.98013.9714



D(—)-Arabinose

0.5 mol • kg urea solution

4.08254.06884.04414.04104.0226



pcP1 -mol-1)

298299301300

301300302

320323328322329

344348350345

377375376377379

300301303303305

322320323326327

351350345350

<pV(cm3 -mol^1)

95.6795.7095.7095.6995.6895.7295.7495.77

95.6895.6995.7795.7595.80

95.7895.8395.8095.90

95.8295.8495.8396.0096.01

93.6193.6293.6493.5893.60

93.5993.6193.6893.7093.58

93.8093.8093.7893.92


TABLE 1—continued

m

(mol-kg"1)

0.057520.104580.150430.199980.24205

0.060890.109930.134130.165190.206960.219260.35378

0.052190.100500.149960.212060.25318

0.102970.110790.111520.158140.22970

0.064150.108140.146570.187900.25411

0.070320.102710.137990.152060.190720.25917

0.067010.156020.178280.20566

P(g-cm~3)

1.0413611.0437971.0461541.0486831.050794

1.0081231.0107271.0120021.0136361.0158051.0164611.023309

1.0149701.0175111.0201111.0233391.025398

1.0246351.0250541.0250801.0274731.031110

1.0416661.0439101.0458401.0479001.051135

1.0095741.0117191.0140401.0149641.0174801.021870

1.0166571.0224971.0239181.025670

Cp

( J - K - L g -

3.0 mol • kg"1

3.78763.77903.77013.76133.7540

c

l) ( J -K-

urea solution

D(+)-Xylose

0.5 mol • kg"1

4.08244.06744.06034.05044.03854.03433.9946

1.0 mol-kg"1

4.01594.00243.98923.97313.9623

1.5 mol-kg"1

3.93993.93813.93773.92633.9097

3.0 mol • kg"1

3.78573.77753.77063.76313.7511

urea solution

urea solution

urea solution

urea solution

D(+)-Glucose

0.5 mol • kg"1

4.07574.06424.05154.04594.03264.0092

1.0 mol-kg"1

4.00743.97783.97083.9618

urea solution

urea solution

pcP1 -mol"1)

380382378379380

296298301297301298297

322320323325325

339340338339342

370374376377377

365367366362364366

376378380379

<pv(cm3 -mol"1)

96.0095.9095.8295.7695.79

95.8995.9095.9195.8995.9295.8495.95

95.9896.0895.9795.9196.11

96.3396.2196.3196.3896.40

96.5596.5096.5796.6196.76

112.33112.36112.37112.35112.36112.40

112.42112.39112.50112.54


TABLE 1—continued

m

(mol-kg"1)

0.072440.100440.160910.188840.228620.23128

0.073070.112730.163190.188960.23751

0.054800.096440.120700.161290.22839

0.059330.102370.153230.20742

0.078230.108550.179760.18305

0.053520.117570.125130.157850.24343

0.059580.074340.119640.130440.161510.175020.24060

(§

111111

11111

11111

1111

1111

11111

1111111

P; • cm"3)

.024144

.025864

.029778

.031556

.034090

.034256

.042986

.045440

.048549

.050133

.053078

.008562

.011348

.012961

.015635

.020006

.016173

.019033

.022387

.025909

.024440

.026439

.031113

.031306

.041827

.045907

.046414

.048481

.053733

.008945

.009963

.013036

.013755

.015832

.016726

.021083

1.

(.

,5

Cp

I ' K - ' - g "

mol • kg"1

3.94373.93543.91753.90933.89723.8971

3.0 mol • kg"1

0.

1.

1.

,5

3.77973.77033.75843.75153.7402

c

l) ( J -K"

urea solution

urea solution

D(+)-Mannose

mol • kg"4.08144.06644.05784.04314.0192

.0 mol • kg"1

,5

4.01013.99563.97903.9616

mol • kg"3.94083.93133.90963.9084

3.0 mol • kg"1

0.,5

3.78493.76853.76683.75983.7384

urea solution

urea solution

urea solution

urea solution

D(+)-Galactose

mol • kg"1

4.07934.07394.05734.05344.04274.03754.0147

urea solution

pcP1 -mol"1)

404406405405402405

425430432428429

365367367365363

377378380381

389390391390

430425426433427

359360360360363361362

<pv(cm3 -mol"1)

112.59112.60112.66112.64112.65

114.41114.57114.55114.49114.47

111.87111.88111.87111.89111.90

111.97111.96111.89111.90

112.21112.14111.88111.99

113.17113.20112.98112.98113.28

110.70110.70110.77110.80110.84110.74


TABLE 1—continued

m

(mol-kg"1)

0.042020.106760.153710.220180.23792

0.055580.123780.137170.154180.198770.23100

0.057890.109420.156560.206750.23974

0.061270.104010.162520.203060.23864

0.062470.114930.161480.205720.26706

0.079200.131810.154100.187340.214170.24153

0.053350.104700.122970.150920.204820.25038

P(g-cm~3)

1.0150691.0194611.0225841.0269701.028124

1.0230631.0276011.0284901.0296151.0325301.034619

1.0421451.0454731.0484711.0516231.053690

1.0090321.0119091.0157931.0184661.020802

1.0164141.0199181.0229841.0258951.029866

1.0246061.0280501.0294861.0316511.0334271.035187

1.0418801.0452191.0463891.0481971.0515901.054435

Cp

( J -K-Lg-

1.0 mol-kg"1

4.01623.99433.97913.95753.9523

1.5 mol-kg"1

3.94833.92803.92393.91913.90593.8972

3.0 mol • kg"1

3.78363.77093.75983.74773.7401

c

l) ( J -K-

urea solution

urea solution

urea solution

D(—)-Fructose

0.5 mol • kg"1

4.07964.06464.04474.03104.0193

1.0 mol-kg"1

4.00953.99273.97803.96493.9454

1.5 mol-kg"1

3.94153.92553.91863.90913.90193.8943

3.0 mol • kg"1

3.78493.77223.76783.76043.74883.7377

urea solution

urea solution

urea solution

urea solution

pcP1 -mol-1

381380382381383

395402401403402405

426428431430431

374376378378379

385390391395392

402401399401404405

428429430426433431

) (cm3 -mol^1)

110.78110.73110.87110.88110.90

110.87110.89110.90110.99111.04

112.60112.54112.59112.64112.60

111.30111.33111.42111.39111.34

111.47111.48111.54111.44111.43

111.46111.64111.63111.45111.46

112.05112.07112.13112.03112.20112.25


TABLE 1—continued

m

(mol-kg"1)

0.069840.096230.107640.147620.24110

0.055980.095290.188140.25733

0.056350.094100.183720.22611

0.050160.087100.107460.148870.179750.26012

0.047440.093850.104460.11262

0.075210.078280.116090.131210.151110.21738

0.046690.089050.143310.24637

0.057840.092540.148070.196970.21028

P(g-cm~3)

1.0137851.0170911.0185051.0234251.034606

1.0193191.0242201.0354971.043619

1.0263441.0309961.0417661.046722

1.0445351.0491251.0514181.0562841.0598481.068933

1.0109551.0168141.0181251.019142

1.0217201.0221001.0269141.0286311.0310341.038942

1.0251401.0304001.0369981.049110

1.0453071.0496711.0562271.0618711.063417

Cp

( J -K-Lg-

c

l) ( J -K-

Sucrose

0.5 mol • kg"1

4.05164.03314.02533.99813.9375

1.0 mol-kg"1

3.99233.96583.90663.8644

1.5 mol-kg"1

3.92903.90513.85093.8266

3.0 mol • kg"1

3.77003.75003.73913.71783.70123.6617

urea solution

urea solution

urea solution

urea solution

D(+)-Cellobiose

0.5 mol • kg- 1

4.06784.03594.02874.0234

1.0 mol-kg- 1

3.9797

3.95293.94313.93013.8898

1.5 mol-kg- 1

3.93533.90853.87533.8154

3.0 mol • kg- 1

3.76613.74693.71793.69283.6862

urea solution

urea solution

urea solution

urea solution

pcP1 -mol-1

669668668667667

682678678677

690691692694

724728728731726728

678680680682

686

684683680684

692693694695

730726729728728

<pv) (cm3 -mol-1)

212.11212.12212.16212.13212.15

212.33212.39212.36212.36

213.04213.13213.11213.10

214.32

214.32214.33214.38214.36

212.00211.91212.03211.99

212.46212.49

212.40212.49212.43

212.99212.88212.86212.90

214.03214.10214.13214.00


TABLE 1—continued

m

(mol-kg"1)

0.049550.089020.126740.144640.20935

0.036330.058760.15240

0.051530.099420.103640.15472

P(g-cm~3)

1.0113471.0164261.0212041.0234551.031396

1.0169381.0198361.031631

1.0258911.0319381.0324691.038784

Cp

( J - K - L g -

<pcP-1) (J-K-1 -mol-1

Lactulose

0.5 mol • kg~'4.06644.03924.01364.00193.9610

1.0 mol • kg~'4.00603.99133.9321

1.5 mol-kg"1

3.93363.90443.90183.8719

urea solution680680679680684



<pv) (cm3 -mol^1)

209.50209.50209.48209.41209.55

209.56209.54209.62

210.25210.28210.25210.22

D(+)-Melibiose hemihydrate

0.058820.085120.132490.13722

0.063850.101220.127700.12914

0.052090.086990.095050.16012

0.056260.108480.110390.175130.209390.26548

0.064000.115730.136120.22902

1.0124111.0157241.0215801.022147

1.0203311.0249711.0282331.028412

1.0258111.0301291.0311101.038966

1.0121301.0186751.0189511.0268781.0310401.037546

1.0203641.0268071.0292961.040362

4.06054.04254.01134.0082

1.0 mol-kg"1

3.98843.96463.94823.9471

1.5 mol-kg"1

3.93353.91253.90783.8705

urea solution

urea solution

D(+)-Maltose monohydrate

0.5 mol • kg"1

4.06104.02484.02363.98113.95823.9239

1.0 mol-kg"1

3.98733.95413.94063.8833

urea solution

urea solution

726724727727

740741742740

760760762764

740741742746741744

760764759756

220.70220.74220.90220.99

220.80221.00220.92220.90

221.82221.81221.88221.79

228.82229.23228.88228.99228.74229.15

229.40229.35229.40229.49


TABLE 1—continued

m

(mol-kg"1)

0.061560.096540.150770.22690

0.076160.108280.155600.207180.25793

P(g-cm~3)

1.0270201.0313321.0379051.046870

1.0477361.0515951.0571621.0630231.068757

Cp

( J - K - ' . g - 1 ) ( J -K-

1.5 mol • kg^1 urea solution3.92623.90433.87173.8279


pcP1 -mol-1)

769769770771

808806808809810

<pv(cm3 -mol^1)

230.10230.20230.13230.05

230.81230.75230.78231.12230.95

D(+)-Lactose monohydrate

0.5 mol • kg"1 urea solution0.074580.077550.103140.128640.172510.203630.23002

0.077340.125410.147420.153300.177290.20970

0.060640.099530.166880.22619

0.068670.113110.156720.218090.24352

0.057510.108430.157500.213620.24565

1.0145211.0148961.0181231.0213211.0267331.0304991.033644

1.0221271.0281261.0308321.0315421.0344401.038308

1.0269931.0318441.0400511.047067

1.0469531.0523611.0575601.0646901.067600

1.0123621.0188411.0249381.0317441.035530

4.04704.02934.01253.98353.96373.9475

1.0 mol-kg"1

3.97853.94813.93433.93063.91573.8970

1.5 mol-kg"1

3.92693.90353.86283.8298

3.0 mol • kg"1

3.76203.73913.71703.68813.6763

urea solution

urea solution

urea solution

D(+)-Trehalose dihydrate

0.5 mol • kg"1

4.06014.02493.99293.95673.9359

urea solution

753750752750751752

760765764764763767

772779774778

825823820823823

812814820818814

227.99228.04228.14228.04227.99228.02228.07

228.28228.31228.31228.36228.42228.48

228.70228.78228.79228.83

229.12229.15229.17229.23229.20

245.35245.31245.29245.24245.31


TABLE 1—continued

m

(mol • kg-1)

0.052080.104900.163990.22728

0.058440.101820.154690.24359

0.055380.108000.134250.22519

0.051850.105150.150500.23703

0.067000.103780.155660.23359

0.055130.092040.101110.16722

0.055140.095250.14754

(§

1111

1111

1111

1111

1111

1111

111

P; • cm-3)

.018931

.025598

.032849

.040383

.026737

.032174

.038648

.049114

.045305

.051717

.054847

.065388

.014759

.024533

.032536

.047061

.024783

.031417

.040458

.053364

.029532

.036180

.037782

.049120

.048298

.055244

.063976

Cp

( J - K - L g -

1.0 mol-kg-1

3.99503.96023.92323.8852

1.5 mol-kg"1

3.92813.90123.86973.8206

3.0 mol • kg- 1

3.76873.74193.72883.6864

<pcPl) ( J -K- 1 -mol-1)




D(+)-Raffinose pentahydrate

0.5 mol • kg- 1

4.04703.99423.95163.8766

1.0 mol-kg- 1

3.96383.92953.88323.8189

1.5 mol-kg- 1

3.91333.88003.87203.8166

3.0 mol • kg- 1

3.75353.72273.6847





<pv(cm3 -mol-1)

245.72245.71245.75245.81

245.87245.78245.72245.90

246.49246.50246.55246.62

398.50398.47398.49398.54

398.89398.90398.93399.05

399.56399.49399.50399.57

401.65401.65401.67

points where a negligible concentration dependence within the experimental uncertaintywas observed. However, in cases where a concentration dependence was observed, theseproperties were determined by least-squares fits of the corresponding data to the followingequations:

<$>cp = 4>ci -<pv = <p°v- • sytn.

(3)

(4)


The values of sc and sy, the respective slopes and the C° 2 and F2° values for the varioussugars in different concentrations of urea are presented in tables 2 and 3 along withtheir standard deviations. The uncertainties in (pCp and <pV vary in the range ±(1 to3) J • K"1 • mol"1 and ±(0.02 to 0.10) cm3 • mol"1, respectively.

The partial molar heat capacities of transfer C° 2 tr and partial molar volumes of transfer^"tr from w a t e r to aqueous urea solutions have been determined as follows:

C° 2 tr(water -> aqueous urea) = C° 2(aqueous urea) - C° 2(water), (5)

F2°tr(water -> aqueous urea) = V2°(aqueous urea) - F2°(water). (6)

The transfer parameters are given in tables 2 and 3.

4. DiscussionPARTIAL MOLAR HEAT CAPACITIES OF TRANSFER C° 2 tr

The C° 2 values for the sugars in aqueous urea solutions are higher than the correspondingvalues in water resulting in positive heat capacities of transfer (table 2). These valuesincrease systematically with the concentration of urea in all the cases. Very few studieson partial molar heat capacities of sugars in urea solutions are available in the literature.Jasra and Ahluwalia(11) have reported C° 2 t r values at T = 303.15 K for some saccharidessuch as D(+)-glucose, sucrose, D(+)-cellobiose and D(+)-maltose monohydrate fromenthalpy of solution data at T = 298.15 K and T = 308.15 K and these are: (17,10, and 42) J • K"1 • mol"1 for D(+)-glucose; (54, 88, and 100) J • K"1 • mol"1 forsucrose; (9, 94, and 85) J • K"1 • mol"1 for D(+)-maltose monohydrate and (13, 30,and 61) J • K"1 • mol"1 for D(+)-cellobiose in (2, 4, and 6) mol • kg"1 urea solutions,respectively. The present C° 2 tr value at T = 298.15 K in 3 m urea, 80 J • K"1 • mol"1, for

sucrose is quite comparable while the values of (87, 112, and 63) J • K"1 • mol"1 for D ( + ) -glucose, D(+)-maltose monohydrate and D(+)-cellobiose, respectively are comparativelyhigher than those reported in the literature/1 X) The present values emanating from directmeasurements are believed to be more accurate.

A simple examination of the data in table 2 reveals that the C° 2 values of the varioussugars increase from mono- to di- to trisaccharides, however this trend is not found in thecorresponding transfer values. Furthermore, among the monosaccharides it can be seenthat the C° 2 tr values decrease somewhat from the aldopentoses to aldohexoses and thatfor a single ketohexose the decrease is quite appreciable. The dependence of the C° 2 tr

values for various sugars on the concentration of urea is depicted in figure 1. It can be seenthat the C° 2 tr values for the studied monosaccharides tend to level off except for D ( + ) -mannose and D(-)-fructose where the increase is almost linear. However, in the case ofdi- and tri-saccharides the C° 2 tr values increase almost linearly except for D(+)-maltosemonohydrate and D(+)-melibiose hemihydrate, for which the values tend to level off.These trends indicate that the level of saturation of the interactions of these solutes withurea vary in the different cases.

Significant positive transfer values of heat capacities suggest that the overall structuralorder is enhanced in aqueous urea solutions. The cosphere overlap model developed

Heat capacities and volumes of transfer of saeeharides 1421

TABLE 2. Partial molar heat capacities C° 2 of some saeeharides in water and aqueous ureasolutions at infinite dilution along with their corresponding transfer values Cp;2,tr a* T = 298.15 K,

m represents the molality of urea solutions

Compound

MonosaccharidesD(-)-RiboseD(—)-ArabinoseD(+)-Xylose

D(+)-GlucoseD(+)-MannoseD(+)-Galactose

D(—)-Fructose

DisaccharidesSucrose

D(+)-Cellobiose

LactuloseD(+)-Melibiose-hemihydrate

D(+)-Maltosemonohydrate

D(+)-LactosemonohydrateD(+)-Trehalosedihydrate

TrisaccharideD(+)-Raffinosepentahydrate

Water"

279(2)284(3)279(2)

342(2)346(3)345(3)

365(2)

648(3)

665(3)

663(3)660(3)

694(3)

729(3)

799(3)

1337(4)

Ch

0.5

300(2)302(2)298(2)

365(2)365(2)361(2)

373(3)26.76*

±8.41

668(3)

675(3)51.19*

±31.63681(4)726(2)

740(2)

16.72*±23.60

751(3)

813(3)

18.53*±43.96

1349(3)

25.54*±8.62

/ ( J - K - 1 -

1.0

324(3)324(2)323(2)

378(2)379(3)381(3)

385(2)36.89*

±31.22

679(2)

683(2)

697(3)741(4)

760(3)

764(4)

826(4)

18.95*±8.20

1359(3)

21.30*±10.54

mor1)

m/(mol1.5

347(3)349(3)340(3)

405(3)390(3)401(4)

402(2)

689(3)20.92*

±8.45692(4)

14.63*±4.36718(3)758(3)

39.24*±22.54

770(4)

776(3)

839(3)

17.95*±7.86

1371(4)

27.26*±18.32

•kg"1)3.0

377(2)380(2)369(2)35.25*

±22.19429(3)428(3)425(3)26.31*

±15.50427(2)

19.59*±27.50

728(4)

728(3)

806(3)

16.04*±13.92823(2)

887(4)

41.18*±11.76

1415(2)

32.76*±7.36

Cp,2,tr/

0.5

211819

231916

8

20

10

1866

46

22

14

12

(J-K-1

1.0

454044

363336

20

31

18

3481

66

35

27

22

1 -mor1

1.5

686561

634456

37

41

27

5598

76

47

40

34

3.0

989690

878280

62

80

63

112

94

88

78

Parentheses contain standard deviations.Uncertainties in C° 2 tr values range from 3 J • K^1 • mol^1 to 5 J • K^1 • mol^1, estimated by taking the squareroot of the sum of the squares of the standard deviations in aqueous and mixed aqueous solutions.* Values of Sc /unit.a Reference 6.


TABLE 3. Partial molar volumes V£ of some saccharides in water and aqueous ureasolutions at infinite dilution along with their corresponding transfer values V2 tr at T =

298.15 K, m represent the molality of the urea solutions

Compound

MonosaccharidesD(-)-Ribose

D(—)-Arabinose

D(+)-Xylose

D(+)-Glucose

D(+)-Mannose

D(+)-Galactose

D(—)-Fructose

DisaccharidesSucrose

D(+)-Cellobiose

Lactulose

D(+)-Melibiose-hemihydrate

D(+)-Maltosemonohydrate

D(+)-Lactosemonohydrate

Water"

95.26(0.02)

93.43(0.05)

95.68(0.09)

111.91(0.08)

111.70(0.07)

110.29(0.04)

111.06(0.06)

211.92(0.08)

211.31(0.04)

208.65(0.07)

214.17

(0.01)

228.14

(0.07)

227.03

(0.04)

V2

0.5

95.72(0.03)

93.61(0.02)

95.90(0.03)

112.36(0.02)

111.88(0.01)

110.76(0.05)

111.36(0.05)

212.11(0.02)

0.17*±0.29

211.98(0.04)

209.49(0.04)

220.46

(0.05)3.45*

±1.34

228.97

(0.17)

228.04

(0.05)

/(cm • mol

1.0

95.74(0.05)

93.63(0.05)

96.05(0.13)

112.46(0.06)

111.93(0.04)

110.83(0.06)

111.47(0.04)

212.36(0.02)

212.45(0.03)

209.57(0.03)

220.90

(0.07)

229.41

(0.05)

228.13

(0.03)1.57*

±0.64

- 1 )

m/(mol1.5

95.83(0.04)

93.82(0.05)

96.33(0.07)

112.63(0.03)

112.05(0.13)

110.94(0.06)

111.53(0.09)

213.10(0.02)

212.91(0.05)

210.25(0.02)

221.80

(0.03)

230.12

(0.06)

228.68

(0.03)0.68*

±0.42

•kg"1)3.0

95.90(0.13)

95.85(0.09)

96.60(0.09)

114.50(0.06)

113.12(0.12)

112.59(0.05)

112.12(0.08)

214.34(0.03)

214.06(0.05)

230.88

(0.14)

229.09

(0.02)0.55*

±0.25

v°2,tr

0.5

0.46

0.18

0.22

0.45

0.18

0.47

0.30

0.19

0.67

0.84

6.31

0.83

1.01

/(cm3

1.0

0.48

0.20

0.37

0.55

0.23

0.54

0.41

0.44

1.14

0.92

6.73

1.27

1.10

•mol

1.5

0.57

0.39

0.65

0.72

0.35

0.65

0.47

1.18

1.60

1.60

7.63

1.98

1.65

- 1 )

3.0

0.64

2.42

0.92

2.59

1.42

2.30

1.06

2.42

2.75

2.74

2.06


TABLE 3—continued

K°/(cm3 • mor1) K°tr/(cm3 • mol"1)

m/(mol -kg" ' )Compound Water" 0.5 1.0 1.5 3.0 0.5 1.0 1.5 3.0

D(+)-Trehalose 243.75 245.30 245.67 245.82 246.43 1.55 1.92 2.07 2.68dihydrate

(0.06) (0.04) (0.02) (0.08) (0.02)0.54* 0.81*

±0.49 ±0.29

TrisaccharideD(+)-Raffinose 397.10 398.50 398.80 399.53 401.66 1.40 1.70 2.43 4.56pentahydrate

(0.08) (0.02) (0.03) (0.03) (0.01)0.97*

±0.42

Parentheses contain standard deviations.Uncertainties in V£tr values range from (0.04 to 0.10) cm • mol , estimated by taking the squareroot of the sum of the squares of the standard deviations in aqueous and mixed aqueous solutions.* Values of Sy /unit.a Reference 6.

by Gurney(39) is invoked to explain the transfer heat capacity and volume data. Theproperties of the water molecules in the hydration cosphere depend on the nature of thesolute species.(40'41) The region occupied by the solvent that is markedly affected by thepresence of the solute molecules is termed the cosphere. According to this model, whentwo molecules approach each other, their hydration cospheres overlap and some of thecosphere material is displaced resulting in changes in the thermodynamic properties/42 44)

This overlap comes into play because of the following interactions between the saccharide(solute) and urea (cosolute) molecules: the interaction between the hydrophilic ureamolecules and the polar/hydrophilic, hydroxy sites of the sugars; and the interactionbetween the hydrophilic urea molecules and the hydrophobic parts/groups of the sugars.

The first type of interaction contributes positively, whereas the second type contributesnegatively to C° 2 ^ values. The significant positive C° 2 tr values observed for all thesugars suggest that the hydrophilic-hydrophilic interactions dominate over thehydrophobic-hydrophilic interactions. The increase in C° 2 tr values with increasein concentration of urea, indicates a further strengthening of the hydrophilic-hydrophilicinteractions. Since urea can form hydrogen bonds easily both with proton donors andacceptors, and as saccharides contain embedded in them large numbers of potentialhydrogen bonding sites, the mutual overlap of the hydration cospheres of urea and sugarmolecules will lead to an increase in the magnitude of hydrogen-bonding interactions.

For hydrophobic solutes, negative heat capacities of transfer(45"52) and, positive en-thalpies and entropies of transfer(47"50'53"55) from water to aqueous urea solutions havebeen reported, indicating a net bond breakage and thus an increase in disorder of the solvent


1

'o

li

°

i

1it

-o

10090onoU

70

6050

40

3020

100

140

120

100

on

60

40

20

01 1.5 2

m/(mol • kg"1)

1 1.5 2 2.5

m/(mol • kg"1)

FIGURE 1. Partial molar heat capacity transfer values C° 2 tr against the molality m of urea solutionsfor some saccharides at T = 298.15 K. a, 0, D(—)-ribose; •, D(+)-arabinose; A, D(+)-xylose;O, D(+)-glucose; X, D(+)-galactose. b, •, D(+)-mannose; •, D(—)-fructose. c, •, D(+)-maltosemonohydrate; •, D(+)-melibiose hemihydrate. d, •, sucrose; •, D(+)-cellobiose; A, lactulose;x, D(+)-lactose monohydrate; *, D(+)-trehalose dihydrate; •, D(+)-raffinose pentahydrate.

system. On the other hand, the ionic solutes (e.g. alkali metal halides)(56) are accompaniedby positive heat capacities of transfer and, negative enthalpies^5'51'57) and entropies oftransfer from water to aqueous urea solutions which result in a decrease in the disorder ofthe solvent system and an increase in hydrogen bonding. Similarly, positive C° 2 tr valueshave also been reported(50) for hydrophilic groups such as the peptide group (-CONH-),and the peptide backbone unit (-CH2CONH-) with potential hydrogen-bonding sites, fromwater to aqueous urea solutions. Therefore, the significant positive C° 2 tr values observedin this work for sugars from water to aqueous urea solutions indicate a behaviour similarto ionic or hydrophilic solutes. This strengthens the view that positive values of C

!,tr in-


3.00

0.00

0 0.5 1 1.5 2

m/(mol-kg )

2.5 0 0.5 1 1.5 2

m/(mol-kg )

2.5

^ 2.00

1 1.5

m/(mo\- kg )

FIGURE 2. Partial molar volume transfer values V^ir, against the molality m of urea solu-tions for some saccharides at T = 298.15. a, •, D(+)-arabinose; •, D(+)-glucose; A, D(+)-mannose; x, D(+)-galactose. b, •, D(—)-ribose; •, D(+)-xylose; A, D(—)-fructose, c, •, sucrose;D, D(+)-maltose monohydrate; A, D(+)-lactose monohydrate; x, D(+)-trehalose dihydrate; c, (in-set) • , D(+)-melibiose hemihydrate. d, • •••••• , D(+)-cellobiose; —•—, lactulose; — A — , D(+)-raffinose pentahydrate.

dicate an increase in the structural order of the solvent system. This increase in structuralorder can be attributed to a complex formation between sugars and urea molecules throughhydrogen bonding. Jasra and Ahluwalia have also reported(58) negative enthalpies of trans-fer for D(+)-glucose, sucrose, D(+)-cellobiose and D(+)-maltose monohydrate from waterto aqueous urea solutions and suggested the existence of hydrogen bonding interactions be-tween urea and sugar molecules which increase with increase in urea concentration.

PARTIAL MOLAR VOLUMES OF TRANSFER V°

All the mono-, di- and trisaccharides in aqueous urea solutions (0.5, 1.0, 1.5, and3.0) mol • kg"1 at T = 298.15 K have F2° values higher than the corresponding values


in water and thus exhibit positive F2°tr values which increase with the concentration ofthe cosolute. Very few studies on partial molar volumes of sugars in urea solutions areavailable in literature. Sangster et a/.(14) have reported some data for sucrose alone and theV° values at T = 298.15 K in (0.3214, 0.7037 and 1.4834) mol • kg"1 urea solutions are(213.28,216.87 and 222.25) cm3 • mol"1, respectively and thus the F2°tr values range from(1.5 to 10) cm3 • mol"1, which are appreciably higher than our values (table 3). There areno other data available for comparison. Positive V£^ values from water to aqueous ureasolutions have also been reported(39> 59~61) for hydrophobic and ionic solutes.

Plots of F2°tr against the molality of urea (figure 2) for the studied saccharides shownonlinear behaviour in the majority of the cases. However, in some cases, such asD(+)-xylose, D(-)-ribose, D(+)-maltose monohydrate, D(+)-lactose monohydrate, D ( + ) -trehalose dihydrate, and D(+)-melibiose hemihydrate, the F2°tr values tend to level offwith urea concentration. This trend, as in the C° 2 tr values, certainly arises from multiplecontributions.

Franks et alS6T) have reported that the partial molar volume at infinite dilution of anonelectrolyte is made up of an intrinsic molar volume F;nt of the non-hydrated solute anda contribution due to the interaction of the solute with water, Vs:

V°=Vmi+Vs. (7)

Some investigators^3'64) have suggested that Vmt is made up of two types of contribu-tions.

V'mt = Vv,v/ + K'oidi (8)

where FViW is the van der Waals volume and Fvoid is the associated void or emptyvolume.(6^67)

Shahidi et alS6^ have modified this equation to find the contribution of one moleculetowards the partial molar volume of a hydrophilic solute as follows:

V% = Fv,w + ^void - nas, (9)

where as is the shrinkage in volume caused by interaction of hydrogen bonding groups withwater molecules, and n is the potential number of hydrogen bonding sites in a molecule.Therefore, the partial molar volume of a sugar molecule can be represented as,

'1 = ^v,w ~\~ ''void ~~ ^shrinkage- (10)

If one assumes that FViW and Fvoid have the same magnitudes in water and aqueous ureasolutions, the positive volume change accompanying the transfer of sugars from water toan aqueous urea solution may result from a decrease in the shrinkage in volume shrinkagebecause of interactions between urea and -OH groups of sugars. The interaction of ureawith sugars diminishes further the structure breaking effect of urea on water. In otherwords, more water is released as bulk water in the presence of sugars. Since bulk waterhas a higher volume contribution(68) than broken structure water, this factor may thereforecontribute positively to the F2°tr values. Another way to express the solute-cosoluteinteractions is through the cosphere overlap model, where hydrophilic-hydrophilic-type interactions contribute positively and hydrophobic-hydrophilic negatively to F2°tr


values/39'42) The positive F2°tr values obtained in this work (table 3) for all the sugarssuggest that the former type of interactions dominates over the latter and the C° 2 tr valuessupport this observation.

Sangster et a/.(14) have attributed the positive F2°tr values for sucrose from water to anaqueous urea solution to dehydration of sucrose in the mixed solvent and to decreasedsucrose-sucrose interactions, reflected in the depressed <fi V against m slope. These twoobservations lead to a corresponding increase in the interactions between the solute andcosolute that provide the dominant contributions to the transfer parameters.

INTERACTION COEFFICIENTS

Kozak et alS69) have proposed a theory based on the McMillan-Mayer(70) theory ofsolutions which permits the formal separation of the effects due to interactions betweenpairs of solute molecules and those due to interactions involving three or more molecules.Friedmann and Krishna^40) and Franks et a//41) have further included solute-cosoluteinteractions in the solvation spheres. Various workers(71~73) have used the theory tostudy solute-cosolute interactions in aqueous media. According to this treatment, athermodynamic transfer function at infinite dilution (Y^) can be expressed as:

F2°tr(water -> aqueous urea) = 2>-AB'«B + S^ABB^I + ^ A B B B ^ B H > (u)

where A stands for saccharide and B stands for urea, and m-Q is the molality ofurea (cosolute), and >>AB, >"ABB and >"ABBB are pair, triplet and quartet intermolecularinteraction coefficients. The corresponding parameters, namely CAB, CABB, CABBB for theheat capacities and DAB, I>ABB, f ABBB for the volumes determined from the C° 2 and F2°tr

values are summarized in table 4.The pair interaction coefficient CAB is positive for all the saccharides. For monosacchar-

ides the values range from (13 to 22) J • K"1 • mol"1 (mol • kg"1)"1 with an exceptionallylow value for D(+)-fructose {3 J • K"1 • mol"1 (mol • kg"1)"1}. For di- and trisaccharidesthe CAB values are almost of the same order (11 to 26) J • K"1 • mol"1 (mol • kg"1)"1

as those of monosaccharides except for D(+)-melibiose hemihydrate and D ( + ) -maltose monohydrate for which the values are exceptionally high: {(109 and60) J- K"1 • mol"1 (mol • kg"1)"1 , respectively}. The CABB values are positive formonosaccharides except for D(+)-mannose and negative for disaccharides which indicatesthat in the case of monosaccharides triplet interactions enhance the structural orderwhereas the reverse is true in the case of disaccharides. From the signs of the CABBB

values, it can be seen that quartet interactions in mono- and disaccharides are opposite tothe corresponding triplet interactions. Large positive CAB values suggest that due to theoverlap of hydration spheres of the saccharides and urea molecules strong interactions areoccurring between them, most probably through hydrogen bonding. This is in line withthe conclusion drawn from the cosphere overlap model in the previous section.

The DAB values are also positive for all the saccharides except for sucrose. The UABB

values are negative and those of UABBB are positive in all the cases with few exceptions;this is not in line with the trends observed in the corresponding interaction coefficientsof the heat capacity data. Large positive DAB values indicate an increase in volume as

Jto00

TABLE 4. Interaction coefficients CAB, CABB> CABBB> VAB, VABB a n d ^ABBB of some sugars in aqueous urea solutions calculated by usingequation (11) at T = 298.15 K

Compound

MonosaccharidesD(-)-RiboseD(—)-ArabinoseD(+)-XyloseD(+)-GlucoseD(+)-MannoseD(+)-GalactoseD(—)-Fructose

DisaccharidesSucroseD(+)-CellobioseLactuloseD(+)-Melibiose hemihydrateD(+)-Maltose monohydrateD(+)-Lactose monohydrateD(+)-Trehalose dihydrate

TrisaccharideD(+)-Raffinose pentahydrate

CAB

{J-K^1 - m o r 1

(mol-kg-1)-1}

1813191722133

2411

21109602615

12

CABB

{J-K^1 - m o r 1

(mol-kg-1)-2}

4.26.92.03.3

-4.95.06.5

-6.9-1.5-6.0

-69.3-21.6

-7.0-1.3

-1.0

CABB

{J-K-1 - m o r 1

(mol-kg-1)-3}

-1.17-1.56-0.76-0.97

0.74-1.22-1.22

1.140.362.33

17.673.121.180.31

0.30

"AB

{cm3 -mol^1

(mol-kg-1)-1}

0.570.230.160.600.230.650.41

-0.100.731.67

11.380.781.062.06

1.58

"ABB{cm3 • mol-1

(mol-kg-1)-2}

-0.24-0.13

0.05-0.29-0.10-0.33-0.17

0.31-0.12-1.41-8.17-0.05-0.32-0.87

-0.53

"ABB{cm3 • mol-1

(mol-kg-1)-3}

0.0350.043

-0.0120.0630.0260.0680.030

-0.0500.0150.4532.120

-0.0060.0410.129

0.087

td


the hydrogen-bonding interactions take place between saccharides and urea and this againsupports the view that hydrophilic-hydrophilic interactions dominate over the others. Therelative weightings of the various coefficients may also be judged from their contributionsto transfer parameters at different molalities of urea by plotting these contributions againstthe concentration of urea. It has been observed that up to 1.0 mol • kg"1 urea transferparameters arise mainly from pair solute-cosolute interactions in almost all the casesand triplet and quartet type interactions contribute effectively only at urea molalitieshigher than 1.0 mol • kg"1. The interaction coefficients derived from the heat capacityand volumes data have almost similar trends for disaccharides but this is not the case forthe monosaccharides. However, more data are required at more concentrations of urea toconfirm this trend.

STEREOCHEMICAL EFFECTS

Various experimental as well as theoretical13' 74~82) attempts are underway to explore thecorrelation between the hydration characteristics of saccharides and their stereochemistry.The hydration of carbohydrates has been explained by invoking the concept of compati-bility (between the water structure and carbohydrate molecules) through a specific hydra-tion model. Galema et alS1'2^ have reported that the relative position of the next-nearest-neighbour hydroxy group within the carbohydrate molecule is the most important one indetermining the hydration characteristics, and the extent of hydration is largely determinedby the position of OH(4) in conjunction with the relative position of OH(2).

On the basis of compressibility studies Galema and Hoiland(1) have suggested thatD-arabinose among the pentoses (D-ribose, D-xylose, and D-lyxose) and D-galactoseamong the hexoses (D-mannose, and D-glucose) are the least compatible with thewater structure. D-fructose (ketohexose) is less compatible with the water structure thanD-glucose. Disaccharides consisting of a glucose and a fructose unit (sucrose, palatinoseand turanose), two glucose units (maltose and cellobiose) and glucose and galactoseunits (melibiose, lactose and lactulose) are the most intermediate and least compatible,respectively with water. Although it is difficult to rationalize completely the C° 2 tr valuesin terms of stereochemistry of the saccharide molecules, nevertheless, some importantobservations can be made: (i) the C° 2 tr values among the mono-saccharides decreaseslightly from the aldopentoses to the aldohexoses to the ketohexoses inspite of an increasein their C° 2 values, which may certainly be ascribed to some stereochemical effects,in the case of D(-)-fructose, the change in the C° 2 tr value is particularly appreciable;(ii) D(+)-melibiose hemihydrate and D(+)-maltose monohydrate have the largest C° 2 tr

values among the various disaccharides studied.Among the currently studied disaccharides, the C° 2 tr values for D(+)-melibiose

hemihydrate, D(+)-maltose monohydrate and D(+)-cellobiose decrease in the followingorder: D(+)-melibiose hemihydrate > D(+)-maltose monohydrate > D(+)-cellobiose.

If it is assumed that the sugars most compatible with the water structure have the leastability to interact with the cosolute molecules and vice versa, then in the light of thecompressibility data,(1) the strength of the interactions of the above three saccharides


with the cosolute molecules should decrease in the following order: D(+)-melibiosehemihydrate > D(+)-cellobiose « D(+)-maltose monohydrate.

The higher C° 2 ^ values observed here for D(+)-melibiose hemihydrate fit well in theabove order which indicates that this sugar interacts extensively with urea than D ( + ) -cellobiose and D(+)-maltose monohydrate. However, the appreciable difference betweenthe C° 2 tr values for D(+)-maltose monohydrate and D(+)-cellobiose is certainly due to adifference in the strength of the interactions with urea, which contradicts the observationmade by Galema and Hoiland(1) on the basis of the compressibility data which indicatethat maltose and cellobiose have the same hydration characteristics. In addition, Neal andGoring(79) have reported that folding of maltose is more important than in cellobiose dueto hydrophobic interactions. If the observation made by Neal and Goring(79) is correct,then the higher C° 2 tr value for maltose is justified. Because for maltose folding is moreimportant than in cellobiose, its interactions with urea will be stronger than those withcellobiose resulting in a higher C° 2 tr value. Higher pair interaction coefficients (table 4)for maltose than for cellobiose also support this view. Furthermore, this may also be due tothe more flexible a 1 -> 4 linkage present in maltose than the /S1 —> 4 linkage present incellobiose.(83) Similarly, in other disaccharides, folding may occur to different extents as nosystematic trend has been observed. As a carbohydrate exists as an equilibrium mixture ofseveral forms in aqueous solutions this complicates the study of stereochemical aspects ofhydration in aqueous solutions. Moreover, the presence of urea may influence the positionof one or several of these equilibria resulting in even more complexity. Further studies arerequired to rationalize the stereochemical effects.

The authors are grateful to Drs R. N. Goldberg and Y. B. Tewari of the American NationalInstitute of Science and Technology, Gaithersburg, MD, U.S.A. for providing some sugarsamples. P. K. Banipal is also grateful to the Council of Scientific and Industrial Research,New Delhi, India, for the award of a Senior Research Fellowship.

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(Received 21 September 1999; in final form 15 March 2000)

WA99/051

partial molar heat capacities and volumes of aqueous...

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