J . Chem. Soc., Faraday Trans. I , 1983, 79, 845-852 Apparent Molar Volumes of Aqueous Cellobiose Solutions BY THELMA M. HERRINGTON,* ALAN D. PETHYBRIDGE, BRIAN A. PARKIN AND MICHAEL G. ROFFEY Department of Chemistry, University of Reading, Reading RG6 2AD Received 21st June, 1982 Apparent molar volume data for solutions of cellobiose and water are reported for 25, 35, 45, 55 and 65 O C . Osmotic coefficients were determined at 0 and 25 O C . Theories of dilute solutions are applied to solute-solvent and solute-solute interactions, assuming a rigid particle model for the repulsive potential. Sucrose and cellobiose are disaccharides of the same molecular formula but differing ring structures. Cellobiose is 4-0-( P-D-glucopyranosy1)-D-glucopyranose and sucrose is a-D-glucopyranosyl-P-D-fructofuranoside. They apparently have the same number of hydroxyl groups available for bonding in aqueous solution but differ considerably with respect to their solubilities in aqueous solution.Sucrose is ca. 5 times as soluble as cellobiose at 25 OC and dissolves much more quickly. Values for the solute-solvent and solute-solute interactions can be calculated from thermodynamic properties on the basis of rigorous statistical mechanical theories1* Information on the solute-solvent interaction is obtained from the partial molar volume of the solute at infinite dilution; data for the osmotic coefficient of the solvent then give values for the solute-solute interaction. It was decided to obtain these data for cellobiose and compare them with existing data for sucrose to try and throw some light on the problem.EXPERIMENTAL M A T E R I A L S The cellobiose purity was > 99.5% (polarimetry, rng = 34.6"). Deionized water was used in the preparation of all solutions; any non-ionic impurities present were less than one part in lo6. Water was always deaerated immediately before use. The hydrolysis of cellobiose was checked on a polarimeter as each run took 24 h. A 3 x lop2 rnol dm-3 solution in 2 rnol dm-3 HCl was not hydrolysed after 24 h at 40 OC, and a 0.22 mol dm-3 aqueous solution was not hydrolysed after 12 h at 75 "C. D E N S I T Y MEASUREMENTS The densities of cellobiose solutions over the concentration range 0.05-0.3 mol kg-' were determined using weight dilatometers of the type described by Gibson and L~effler.~ The densities were determined at 10 "C intervals in the range 25-65 "C.The dilatometers, six in all, were sealed with silicon rubber gaskets and immersed in a water thermostat controlled to & 0.002 "C. The temperature was determined using an NPL calibrated resistance thermometer and an ASL transformer ratio bridge. After equilibrium had been reached at each temperature, the mercury pots were removed and weighed on a Sartorius MP 3004 electronic balance. Buoyancy corrections were applied to all weighings. Each concentration was duplicated so that each 25 -+ 65 -+ 25 "C (check) run gave data for three concentrations. 845846 DENSITIES OF AQUEOUS CELLOBIOSE SOLUTIONS SOLUBILITY MEASUREMENTS A saturated solution of cellobiose prepared at 70 "C was allowed to cool and equilibrated at 10 O C intervals from 65 "C to 25 "C.Samples were taken at each temperature using a warmed syringe and added immediately to preweighed deionized water. The concentrations of the resulting solutions were determined by polarimetry. FREE Z I N G-POI N T M E AS U REM E N TS The freezing-point depressions were measured with a model 3WII osmometer (Advanced Instruments Inc.). The solution was supercooled and the formation of ice crystals initiated by internal vibrations. The temperature at which ice crystals started to form was recorded. 'l'he instrument was calibrated with sodium chloride solutions to give the freezing point depression to 10-4 K. V A POU R-P RES S U RE ME A S U R EM EN TS If a drop of solution and a drop of solvent are suspended, side-by-side, in a constant temperature enclosure saturated with solvent vapour, differential mass transfer occurs between the two drops and the vapour phase.This transfer causes a temperature difference between the two drops, which is proportional to the vapour pressure l ~ w e r i n g . ~ ? ~ This phenomenon is applied in the Mechrolab 301 vapour pressure osmometer which was used in the present work to determine the osmotic coefficients of cellobiose solution at 25 O C . It was calibrated using sodium chloride solutions. RESULTS APPARENT MOLAR VOLUME FROM 25 TO 65 O C Density values are given in table 1. These are the results of three runs: two to 65 O C and one to 55 O C . The densities at 25 "C were checked after the high-temperature values.Values for the density of water were taken from Ke11.6 The apparent molar volumes obtained from these densities were fitted to the equation QV= Vp+Arn TABLE DENSITIES (IN g ~ m - ~ ) OF AQUEOUS CELLOBIOSE SOLUTIONS BETWEEN 25 AND 65 "C 298.15 308.15 318.15 328.15 338.15 water 0.0500 0.0916 0.1012 0.1096 0.1235 0.1506 0.1761 0.1931 0.1987 0.2191 0.2245 0.2364 0.249 1 0.2758 0.3007 0.997 05 1.003 50 1.008 76 1.009 96 1.011 01 1.012 73 1.016 06 1.019 16 1.021 20 1.021 87 1.024 30 1.024 94 1.026 34 1.027 83 1.030 92 1.033 78 0.994 04 1 .OOO 42 1.005 63 1.006 82 1.007 86 1.009 56 1.012 86 1.015 93 1.017 95 1.018 62 1.021 02 1.021 65 1.023 04 1.024 52 1.027 58 1.030 41 0.990 22 0.996 55 1.001 73 1.002 91 1.003 94 1.005 63 1.008 90 1.011 95 1.013 96 1.014 62 1.017 00 1.017 63 1.019 01 1.020 47 1.023 52 1.026 33 0.985 70 0.991 98 0.997 12 0.998 29 0.999 31 1.001 00 1.004 25 1.007 28 1,009 28 1.009 94 1.012 31 1.012 94 1.014 31 1.015 76 1.018 80 1.021 60 0.980 55 0.991 92 0.994 11 0.995 78 1.002 03 1.004 02 1.007 04 1.007 66 1.009 03 1.013 50 1.016 28 - - - -HERRINGTON, PETHYBRIDGE, PARKIN A N D ROFFEY 847 TABLE 2.-cOEFFICIENTS OF THE EQUATION 4 v = vp -k Am FOR AQUEOUS SOLUTIONS OF CELLOBIOSE BETWEEN 25 AND 65 "C T/K Vp/cm3 mol-l A/cm3 kg molP2 298.15 21 1.98 1.92 308.15 213.58 1.51 318.15 214.90 1.31 328.15 216.35 0.28 338.15 21 7.40 0.48 where V p is the partial molar volume of cellobiose at infinite dilution.The values for V p and A at each temperature are given in table 2; the apparent molar volumes are represented to within f 0.03 cm3 mol-l up to 55 O C and & 0.06 cm3 mo1-1 at 65 "C.SOLUBILITY DETERMINATIONS The solubility of cellobiose in water, expressed as a concentration (molarity), at temperatures from 25 to 65 OC, is given in table 3. TABLE 3.-sOLUBILITY OF CELLOBIOSE IN WATER BETWEEN 25 AND 65 O C moles per 1000 cm3 T/K solution 298.15 0.612 308.15 0.674 318.15 0.736 328.15 0.797 338.15 0.859 OSMOTIC COEFFICIENTS AT 0 "c The freezing point apparatus was calibrated using aqueous sodium chloride solutions of accurately known molality ; the osmotic coefficients for these were taken from ref. (7). Values for the osmotic coefficient of aqueous cellobiose were calculated using the equation (higher terms were ignored as they contribute < 0.001 to 4 at the highest molalities used).The experimental values for the osmotic coefficient are given in table 4. They are well represented by the equation 4 = 8/(1.8606 kg mo1-1 K)m (2) 4 - 1 = (0.1495/kg mol-l)m -(0.0447/kg2 mol-2) m2 In y = (0.2990/kg mol-1)m-(0.0671/kg2 molP2) m2. (3) (4) (the standard deviation in 4 is I x The activity coefficient is given by OSMOTIC COEFFICIENTS AT 25 O C Solutions of cellobiose varying in concentration from 0.1 to 0.3 mol kg-l were studied ; vapour pressures were determined against aqueous solutions of sodium848 DENSITIES OF AQUEOUS CELLOBIOSE SOLUTIONS TABLE 4.-oSMOTIC COEFFICIENTS OF CELLOBIOSE AT 0 AND 25 O C 273.15 K 298.15 K m/mol kg-l 4 m/mol kg-l 4 0.161 4 1.02 1 0.099 97 1.006 0.228 0 1.035 0.139 9 1.007 0.353 9 1.046 0.180 0 1.010 0.451 3 1.059 0.199 7 1.011 0.550 5 1.069 0.239 3 1.014 0.643 2 1.077 0.279 5 1.015 0.760 8 1.088 0.299 4 1.017 chloride using the solution-matching technique.Accurate values for the osmotic coefficients of aqueous sodium chloride were required at molalities < 0.2 mol kg-l. The e.m.f. data of Brown and McInnes* and of Longsworthg at 25 O C were smoothed using the equation In y =-am& (l+brn$)-l+om. ( 5 ) Values for the osmotic coefficient of aqueous sodium chloride at 25 O C were then calculated from the equation (4) where, at 25 OC, a = 1.173 kgi mol-g and b = I .O kgi mol-i. The experimental values for the osmotic coefficients of aqueous cellobiose are given in table 4. They are well represented by the equation 4 - 1 = - abW3rn-l[ 1 + brna - (1 + brn;)-l- 2 In (1 + bm:)] + corn/2 4- 1 = (O.O557/kg mol-l)rn In y = (0.11 14/kg mol-l)rn.(7) (8) (standard deviation in 4 is 3 x and hence the activity coefficient is given by DISCUSSION S 0 L U TE-SO L V E N T AT T R A C TI ON The solute-solvent cluster integral byl is related to the partial molecular volume of solute at infinite dilution by10-12 by, = vp -I- kTu. (9) Thus values for the solute-solvent interaction, NB,*P (where B,*,O = -byl), can be calculated from eqn (9) and values are given in table 5. Compressibility data for water were taken from the compilation of Bradley and Pitzer.13 Now byl is given by byl = -47~ Jam [l -exp (-coll/kT)] r2 dr (10) where is the potential of mean force between one molecule of solute and one of solvent in the pure solvent (including averaging of the force over all rotationalHERRINGTON, PETHYBRIDGE, PARKIN A N D ROFFEY 849 ?'ABLE 5 .-ATTRACTIVE CONTRIBUTION TO THE SOLUTE-SOLVENT INTERACTION COEFFICIENT.CELLOBIOSE DATA, THIS WORK; OTHER DATA, REF. (12). v,e RTK NB,*,O -NfDA T/K /cm3 mol-l /cm3 mo1-l /cm3 mol-' /cm3 mol-l sucrose + water 278.15 288.15 298.15 303.15 308.15 323.15 343.15 glucose + water 298.15 cellobiose + water 298.15 308.15 318.15 328.15 338.15 hexamethylene te tramine -+ 278.15 water 288.15 298.15 t-butyl alcohol + water 298.15 urea +water 298.15 207.62 209.97 21 1.49 2 12.43 212.87 214.92 216.95 112.2 21 1.98 213.58 2 14.90 216.35 217.40 108.87 109.76 110.58 87.8 44.2 1.14 1.13 1.11 1.11 1.14 1.17 1.27 1.11 1.11 1.14 1.15 1.19 1.24 1.14 1.13 1.11 1.11 1.11 206.48 208.84 210.38 21 1.32 21 1.73 213.75 21 5.68 11 1.1 210.87 212.44 213.75 215.16 216.16 107.73 108.63 109.47 86.7 43.1 270 267 266 265 264 262 260 246 194 191 191 190 189 193 192 191 146 143 coordinates) and r is the distance apart of the centres of the molecules.The cluster integral byl consists of two parts, the attractive and repulsive contributions. Let R be the distance of closest approach of the two molecules, then repulsion exists for values of r < R and attraction for values of r > R, and the integral can be split into repulsive and attractive parts as follows PR roc Blr,o = 471 J ~- [ 1 -exp (- oll/kT)] v2 dv+ J [l -exp ( - o l l / k ~ ) r2 dr (1 1) R = S + @ A (12) where Sis the repulsive and OA the attractive contribution and cull has the appropriate value for the range of integration.If the form of the potential function d1 is known, then the integration can be performed to yield B::. From Corey-Pauling models and crystallographic data14 the cellobiose molecule approximates to a prolate ellipsoid with semi-axes 5.6 and 3.2 A. The water molecule is assumed to be spherical with diameter 3.04 A. For a hard sphere of radius a, and a hard prolate ellipsoid with long axis 2b, and short axis 2a,15 Po 11 = &a: -+gnu: b, + 2na1 b, I +T 1 - & 2 l n l e ) ] --E (13) where c2 = (&--ai)/bi. This gives for the repulsive contribution to BT: NS = 405 cm3 mol-1 so that, by difference from eqn (9), at 25 O C the attractive contribution is N@" = - 194 cm3 mo1-l.850 DENSITIES OF AQUEOUS CELLOBIOSE SOLUTIONS Values at the other temperatures are given in table 5.It can be seen that the attractive contribution increases with decreasing temperature. Data for sucrose +water, hexamethylenetetramine + water, glucose + water, t-butyl alcohol +water and urea + water are also given in table 5.12 The values of V p are very similar for cellobiose and sucrose. The temperature dependence of the attractive contribution for cellobiose + water is the same as for sucrose + water and hexamethylenetetramine + water. The magnitude at a given temperature is comparable with the interaction between hexamethylenetetramine and water but less than that of sucrose with water. The cellobiose is much more compact than sucrose and this is reflected in the lower magnitude of NQA. SOL U T E-S 0 LUTE I N T E R A C T I ON From ref.(12) the solute-solute virial coefficient is given by and A,, is related to the activity coefficient of the solute by In y =A,,%+ B?h2+ . . . (1 5 ) BY = B,,, -;A;, etc. so that a value for B,*,O can be calculated from the partial molar volume at infinite dilution and the activity coefficient data. From eqn (8) and (15), A,, = (0.1 114/kg mol-l)/M, and hence NB,*,O is 267 cm3 mol-l at 25 O C . B;: can be considered, like B::, to be composed of an attractive and a repulsive contribution from the intermolecular forces B;: = S+OA. (17) Using the method of Isihara,16 the repulsive contribution for hard ellipsoids is S =fT4v2) with v, = 4d1 1,/3 for 1, > 1,. The cellobiose molecule approximates to a prolate ellipsoid with semi-axes 3.2 and 5.6 A and f factor 1.075, so that NS = 622 cm3 mol-l.The attractive contribution NQA is -355 cm3 mol-l; this is a measure of the pairwise interactions between two cellobiose molecules in water. A value for NOA at 0 O C of - 264 cmP3 mo1-l is calculated using the A,, value from eqn (4) and an extrapolated value of 2O7.8 cm" mol-1 for V p at 0 "C. In table 6 these values for NQA are compared with values for other non-electrolytes calculated by the same method.,, As can be seen from table 6, the attraction between two solute molecules is considerably greater for sucrose than for cellobiose at both 0 and 25 O C . TABLE 6.-ATTRACTIVE CONTRIBUTION TO THE SOLUTE-SOLUTE INTERACTION COEFFICIENT. CELLOBIOSE DATA, THIS WORK ; GLUCOSE DATA REF. ( 1 7); UREA DATA, REF.( 1 8). NB,*,O NS -NOA T/K /cm3 mo1-I /cm3 mol-l /cm3 rno1-l sucrose glucose cellobiose urea hexame th y 1 ene te tramine 298. I 5 2 7 3 . 1 5 298.15 273.15 2 9 8 . 1 5 273.15 298.15 2 7 3 . 1 5 2 9 8 . 1 5 285 330 1 1 7 132 267 357 1 - 14 338 783 498 4 5 3 520 403 3 8 8 622 3 5 5 264 179 178 193 396 58HERRINGTON, PETHYBRIDGE, PARKIN A N D ROFFEY 85 1 CONCLUSIONS For sucrose, glucose, cellobiose and urea both the solute-solvent and solute-solute attraction decreases in the order sucrose > glucose > cellobiose > urea. Hexamethy- lenetetramine has the lowest value of the solute-solute attraction and this is consistent with the molecule having no suitable electron donors for intermolecular hydrogen bonding. The attraction between hexamethylenetetramine and water is the same as that for cellobiose + water.Hexamethylenetetramine has four possible hydrogen-bond accepting sites and this implies that cellobiose behaves similarly. Sucrose behaves similarly to glucose with water and both probably have five hydrogen-bond sites. However, cellobiose is considerably less soluble than sucrose in water and the differ- ence is greater than might be expected from these differences in the intermolecular attractive forces. Our experimental data for cellobiose, given in table 3, show that its solubility at 25 O C is only 0.6 mol dm-3, whereas sucrose is soluble to the extent of 2.6 mol dmW3.l9 The packing of cellobiose and sucrose molecules in their crystals is determined by hydrogen bonding. Molecules of cellobiose are arranged in the crystal with screw axis symmetry, and are held together by a three-dimensional network of eight hydrogen bonds per molecule.20 One is an intramolecular link joining O’(3) with the ring oxygen O(5); two form a helical system of bonds, O’( 1)-0(2) and O(2)-0’(5), and the other five form a continuous system of hydrogen-bond chains.In this way all the available hydroxyl-group hydrogen atoms are used in hydrogen-bond formation. In com- parison, the sucrose molecule in the crystal only forms seven hydrogen bonds from its eight hydroxyl groups.21 Of these two are intramolecular Of( 1)-0(2) and O’(6)-O(5) and five are intermolecular O(2)-0’(6), O’(3)-0’(4), O’(4)-O’( l), O(3)-O’(3) and O(6)-O(3). One hydroxyl grouping, that on 0(4), is not involved at all with intermolecular or intramolecular bonding.The availability of this hydroxyl grouping, the smaller number of intermolecular hydrogen bonds per molecule in the crystal and the greater magnitude of N#* for the molecules in solution dramatically increases the solubility of sucrose over cellobiose. We thank CERL for the award of a Research Studentship to M. G. R. GLOSSARY OF SYMBOLS cluster integral for two molecules of solute in pure solvent cluster integral for one molecule of solute and one of solvent in pure solvent integral defining the interaction between two solutes integral defining the interaction between solute and solvent Gibbs energy Boltzmann constant mole ratio of solute to solvent (N2/N1) molality of solute molar mass of solvent in kg mol-1 Avogadro constant gas constant repulsive contribution to the cluster integral absolute temperature partial molecular volume of solvent molecular volume of pure solventDENSITIES OF AQUEOUS CELLOBIOSE SOLUTIONS partial molecular volume of solute partial molecular volume of solute at infinite dilution total volume of solution partial molar volume of solute at infinite dilution apparent molar volume of solute activity coefficient of solute on the molality scale osmotic coefficient attractive contribution to the configuration integral density of solution isothermal compressibility coefficient of solvent freezing point depression W.G. 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