Aqueous Solutions containing Amino-acids and PeptidesPart 2.-Gibbs Function and Enthalpy Behaviour of the Systems Urea + Glycine,Urea + a-Alanine, Urea + a-Aminobutyric Acid and Urea + Glycylglycine at 298.15 KBY TERENCE H. LILLEY* AND R. P. SCOTT-/-Chemistry Department, The University, Sheffield S3 7HFReceived 14th April, 1975The osmotic coefficients and enthalpies of mixing of aqueous solutions of urea+ glycine, urea+a-alanine, urea + cr-aminobutyric acid and urea +glycylgIycine and the enthalpy of dilution of gly-cylglycine have been determined at 298.15 K. The experimental results are discussed in terms ofthe McMillan-Mayer theory of solutions.This is the second in a series of papers in which the thermodynamic propertiesof aqueous solutions containing aminoacids and some small peptides are investigated.Our long term objective is to obtain information on the mechanism of protein de-naturation which would seem to be a problem in non-covalent bonding interactions.The current objective is to gain some understanding of solute-solute interactions onsmaller and structurally less complex species in the hope that a greater knowledgeof these systems might lead eventually to an understanding of the protein problem.There is a considerable amount of information on aqueous solutions containingnon-electrolytes and electrolytes but thermodynamic data on aqueous solutionscontaining single and mixed non-electrolytes are relatively rare and the molecularbasis for the properties is little understood.Several authors have proposed modelsto explain the observed thermodynamic properties for a few systems in terms ofsolute-solute association 2* and solute with some success, but generallythe behaviour of such systems is not understood.A major advance in the under-standing of solutions containing a single non-electrolytic solute was made by Knight,Kozak and Kauzmann.’ They applied the exact theory of solutions proposed byMcMillan and Mayer to all of the systems at that time studied.In this paper an investigation of the osmotic and enthalpy behaviour of binarysolutions containing urea and the amino-acids, glycine, a-alanine and a-aminobutyricacid and the dipeptide glycylglycine is described. The results obtained are discussedin terms of the McMillan-Mayer approach.EXPERIMENTALISOPIESTIC APPARATUSThe apparatus used was basically that previously de~cribed.~ The aluminium block wasmodified so that better contact between it and the isopiestic vessels was obtained.CALORIMETEREnthalpy change measurements were performed using an L.K.B.10700-2 batch calori-meter. In the enthalpy of mixing experiments equimolal solutions of the two solutes undert present address : Chemical Defence Establishment, Porton Down, Salisbury.$ References are given in ref. (1) and in the following paper.18T. H . LILLEY AND R. P . SCOTT 185investigation were mixed in various mass ratios. The enthalpy of dilution measurementson glycylglycine were performed by mixing known masses of a 1 molal solution with knownmasses of water.All of the experiments were made at 298.15 K.MATERIALSThe method of purification of water has been given KCI was purified from theAnalaR reagent using the method of Pinching and Bates.'' The other materials used wereof the highest purity commercially available (all were stated by the manufacturers to be atleast 99.9 % pure) and were dried for several days over P205 before use.RESULTSThe molalities of the solutions in isopiestic equilibrium with aqueous MCl solutionsare given in table 1.The enthalpies of mixing of aqueous urea solutions with aqueousamino-acid solutions are given in table 2 and the enthalpies of dilution of aqueous 1mold glycylglycine are presented in table 3.TABLE 1 .-MOLALITIES OF SOLUTIONS IN ISOPIESTIC EQUILIBRIUMrn(KCl)*/mol kg-1 m/mol kg-1 Yt Y t m(KCI)* /mol kg-1 4% lmol kg- 1urea 4- glycine1.378 1 2.802 92.744 42.707 12.700 92.693 92.690 02.709 90.773 9 1.523 61.500 21.483 81.476 11.473 31.463 71.462 6urea + a-alanine0.913 0 1.618 21.652 81.668 71.682 11.689 71.716 11.737 60.639 6 1.147 41.158 21.166 81.173 81.181 01.190 81.199 300.200 50.394 00.492 90.627 S0.727 5100.200 50.394 00.492 90.627 80.727 5100.212 20.418 00.521 70.620 80.813 2100.208 90.412 00.515 80.611 90.809 21urea + a-aminobutyric acid0.865 3 1.478 41.513 21.543 51,569 21.593 81.614 31.628 91.647 20.550 4 0.959 70.982 00.994 31.001 71.008 S1.020 31.027 7urea + glycylglyci ne0.778 4 1.621 81.592 11.552 21.534 71.515 41.486 81.470 70.547 0 1.129 31.105 81.074 91.059 81.047 91.031 31.023 400.143 40.283 60.414 80.544 20.665 90.781 0100.212 80.422 10.516 G0.623 20.815 3100.188 50.388 30.489 80.590 60.795 0100.184 80.380 00.483 10.577 90.791 21* m(KC1) is the molality of a KC1 solution in equilibrium with the solutions investigated.-f y isthe molality fraction of urea in the solution = murca/m186 AQUEOUS SOLUTIONS OF AMINO-ACIDSTHERMODYNAMIC FORMALISMThe Gibbs function for a system containing solutes and 1 kg of solvent is given by(1) G = Gid+ Gexandi 1TABLE 2.-ENTHALPIES OF MTXING OF UREA AND AMINO-ACID SOLUTIONS AT 298.15 KY - A P l x / J kg-1 Y -AHmir/J kg-11 molal urea+ 1 molal glycine0.130 5 17.2 0.106 5 51.60.250 5 30.5 0.260 9 97.00.497 8 38.6 0.505 0 117.70.743 4 29.6 0.753 6 92.80.904 3 14.5 0.901 0 40.41 molal urea+ 1 molal a-aminobutyric acid2 molal urea+ 2 moIal glycine 1 molal urea+ 1 molal glycylglycine0.1 14 3 65.1 0.103 40.246 1 110.7 0.254 40.498 0 162.1 0.500 70.886 4 68.2 0.755 10.911 21 molal urea+ 1 molal a-alanine41.499.6114.489.138.00.102 10.270 30.507 60.757 40.894 642.181.8111.576.844.5TABLE 3.-ENTHALPIES OF DILUTION OF 1 MOLAL GLYCYLGLYCINE AT 298.15 Kmolality after dilution/ AHd""]J kg-1mol kg-10.102 3 86.40.237 6 177.20.481 7 227.00.768 2 152.40.902 9 71.2Ideality is defined on the molal scale for each solute species such that for any speciesThe corresponding definition of ideality for the solvent isThe excess specific Gibbs function of the solvent may be expressed l1pid = pP+RT In milme; rn + 0.(3)G:d = GP-RTm. (4)GrlRT = ~ ( 1 - 4 ) (5T. H . LILLEY AND R . P . SCOTT 187andIt is assumed that Gex may be expressed as a polynomial in the molalities of thesolute speciesConsequently using eqn (9, (6) and (7)If eqn (8) is applied to a binary solute mixture and it is assumed that the higherorder terms may be neglected, thenWhen yi = 1, y j = 0 and when yi = 0, y j = 1, so the expressions for the osmoticcoefficients of the single solutes areGexIRT = ZC,Xjgijm,mj + ZiZj&gijkmimjmk + higher order terms.(7)(8) 4 = 1 + mXiZjgijyiyj + 2m2&~j&gijkyiYjYk +higher order terms.4(g) = 1 + (gity: +&,jyiyj +gj,Y~)~~z+2(giiiy,3 + 3giij~i?yj + 3gijj~iUj” +gjjj$)*Z2* (9)#(i) = 1 + g i i ~ ~ + 2 g i i @ ~ ’ (10)4(j) = 1 +gjj~z+2gjj~z~*The coefficients in eqn (10) may be obtained from appropriate analysis of the singlesolute experimental osmotic coefficients. The cross terms gij, giij and gijj may beobtained by combination of osmotic coefficient data on binary solute mixtures withdata on single solute mixtures. Appropriate manipulation of eqn (9) and (10) giveswhere 4(i) now denotes the osmotic coefficient of a solution containing only solute iat molality mi.The excess enthalpy may be obtained from eqn (7)m+(ij)-mi$(i) - mj#(j) = 2gijmimj + @ i i jmi +gijjmj)mim j (11)a( GeX/RT)= ( a(l/T) >,,= hijmirnj+C hijkinirnjrnk+ higher order terms.(12)i j i j kIf a solution of a single solute i at molality m containing y kg of solvent is mixedwith a solution of a single solute j at the same molality but containing (1 - y ) kg ofsolvent, then using equation (12) the enthalpy of mixing can be shown to be given byThe enthalpy change on diluting a solution containing (1 -y) kg of solvent and asingle solute i of molality m, with y kg of pure solvent is-AHdiln*/R = m2y(l -y)(hit+m(y-2)hiit) +higher order terms. (14)Expressions for the entropy changes accompanying the above processes are easilyobtainable.AHmix/R = m2y( 1 -y)(2hi - hit - hjj) +higher order terms. (1 3)SOLUTIONS CONTAINING A SINGLE SOLUTEThe principal object of the present work was to obtain the terms in eqn (7) and (12)which contain information on the interaction of unlike solute species.Before thiscould be achieved it was necessary to have information on the terms which arise formlike-like solute interactions188 AQUEOUS SOLUTIONS OF AMINO-ACIDSEllerton et uf. l 2 have investigated the aqueous single solute systems glycine,a-aminobutyric acid and glycylglycine at 298.15 K using the isopiestic method. Theparameters presented by these workers were used in the present analysis of the binarysolute systems.The aqueous a-alanine system has been investigated by Smith and Smith l 3 butthe osmotic coefficients given by them are in error because of the incorrect valuesadopted for the osmotic coefficients of the sucrose reference solutions.We havereanalysed the osmotic coefficients for the sucrose +water system using the resultsobtained by Scatchard et a1.14 and by Robinson and Stokes.15 A slight differenceis apparent between the results obtained from these two sources but all of the resultswere combined and the osmotic coefficients fitted to an equation of the form ofeqn (10). It was necessary to include four ternis in the osmotic coefficient expansionbecause of the niolality range covered by the experiments. These parameters werethen used to re-analyse the osmotic coefficient data l 3 onthe a-alanine water systemJ . 0 C0.98' 0.960.940.92 ~rnufea /mol kg-'FIG. 1.-The osmotic coefficient of aqueous urea solutions at 298.15 K.0 Scatchard ef al.; (D Dunlop et a!.; this work; A Robinson and Bower.The aqueous urea system has been investigated at 298.15 K using the isopiestictechnique by several workers.14* 169 l7 The data of Scatchard et aZ.14 were re-analysed, since they had used incorrect values for the osmotic coefficients of the KClisopiestic reference solutions. The values given by Robinson and Stokes l 8 for thissalt were used in the re-analysis.Comparison of the various sets of results showedthem to be in fairly good agreement, although some discrepancies are evident. Weare uncertain which set or sets of results are the most reliable and so the osmoticcoefficients for the aqueous urea system, which were used in the analysis of the binarysolute systems, were obtained by interpolation from a large scale graph. The linedrawn through all of the experimental points was our assessment of the " best " lineT.H. LILLEY AND R. P. SCOTT 189The experimental results obtained by others (where necessary after re-analysis) andthe results obtained by us are shown in fig. 1, as is the '' best " line.The enthalpy of dilution data of Gucker et aZ.19* 2o for the aqueous glycine andaqueous urea systems at 298.15 K were used, together with their data analysis, toobtain the enthalpy coefficients for these systems. The results of Robinson et al.for the aqueous a-alanine 21 and a-aminobutyric acid 22 systems at 298.15 K werere-analysed, the enthalpy of dilution being regressed to an equation of the form ofeqn (14).The coefficients resulting from this analysis are given in table 5. Theenthalpy of dilution data given in table 3 for the aqueous glycylglycine system wereanalysed in a similar way to that described above and the coefficients for this systemare included in table 5.TABLE 4.-cOEFFICIENTS DEFINING THE EXCESS GIBBS FUNCTION FOR AQUEOUS SOLUTlONS AT298.15 K [SEE EQN (1111I lo3 gij/mol-i kg 1 0 3 gttj/mol-z kgz lo3 gt,,/mol--2 kgzgly cine urea -41.0k2.3 4.2+ 0.3 3.2k0.3a-alanine urea - 31.9k5.5 2.8f 1.3 5.2f 1.2gl ycylgl ycine urea -48.2k5.3 6.0+ 1.2 4.8+ 1.4a-aminobutyric acid urea - 14.0k4.5 -2.2k1.1 - 1.7k1.0SOLUTIONS CONTAINING TWO SOLUTESThe experimental osmotic coefficient results on the binary solute systems investi-gated together with the osmotic coefficients of the appropriate single solute solutionswere fitted, by a least squares procedure, to eqn (9).The results obtained are givenin table 4. There does not appear to be any simple relationship between the grjcoefficients and the corresponding gti and gij coefficients. The systems urea+a-aminobutyric acid and urea + glycylglycine have been investigated previously 9 24 usingthe isopiestic method. The methods used to analyse the experimental results weresimilar to that used here but because of the larger molality ranges in~estigated,~~. 24higher order terms in the equations analogous to eqn (1 l), were included. The agree-ment obtained for the pairwise unlike-unlike species interaction terms (g!!J> with thosegiven in table 4 is within experimental error.The problem of using solubility measure-ments 24* 25 to obtain gij coefficients has been discussed elsewhere.24TABLE 5 .-ENTHALPY COEFFICIENTS FOR AQUEOUS SOLUTIONS CONTAINING A SINGLE NON-ELECTROLYTE AT 298.15 Ksolute h"/K kg mol-1 hitt/K kgz mol-2glycine - 54.0 -a-aminobutyric acid 65.4k0.7 - 1.OkO.8gl ycylgl ycine - 144.0f9 23.04 6urea -43.0 2o --a-alanine 26.0k 0.3 - 0.41 0.4Eqn (13), without inclusion of higher order terms was found to be an adequaterepresentation of the enthalpy of mixing data presented in table 2. The average ofthe quantity AHmiX/nz2y(l -y) was found for each system and the unlike-unlike speciesenthalpy coefficient hij was obtained using eqn (13) and the like-like terms given intable 5.The values of hij are listed in table 7 and included in this table are the valuesobtained for the corresponding entropy coefficients s i j using the results in tables 4and 7190 AQUEOUS SOLUTIONS OF AMINO-ACIDSTABLE 6.-MCMILLAN-MAYER PARAMETERS FOR THE INTERACTION OF AMINOIACLDS WITHUREA AT 298.15 KsoluteLBd I [L&$--LB$(HS)I/i j cm3 mol-1 cm3 mol-1glycine urea 4a-alanine urea 45a-aminobutyric acid urea 91gl ycylgl ycine urea 24- 345- 371- 375-446TABLE 7.-cOEFFICIENTS DEFINING THE EXCESS ENTHALPY AND EXCESS ENTROPY FOR AQUEOUSSOLUTIONS AT 298.15 Ksolutei i --htj/K kg mol-1 --stj/kg mol-1gl ycine useaa-alanine ureaa-aminobutyric acid ureaglycylgl ycine urea5835191210.1540.0850.0500.358DISCUSSIONThe aim of the present work is to investigate intermolecular interactions of solutemolecules in aqueous solutions and it is important to know how these interactionsare manifested in the observed experimental properties.have developed an exact theory of solutions and havedescribed the thermodynamic properties of solutions in terms of certain integrals ofthe radial distribution functions. The osmotic pressure of a solution can be expressedin terms of the number density of solute species asMcMillan and Mayern/kT = pi +c BEp? +(&) 1 Bcpipj +higher order terms.(15)i C i jThe first term on the r.h.s. of eqn (15) represents Van’t Hoff’s law and the otherterms give rise to deviations from “ ideality ”. If we consider solutions containinga single solute i, eqn (15) becomesThe coefficient B i is given by 2 7n/kT = pi + B:p: +higher order terms.(16)[exp( -- Wii/kT) -- l} dr, drb. JvJy B; -- -(1/2V)Higher terms in eqii (16) are related to interactions between three or more solutemolecules in an infinitely dilute solution. In the present work we consider onlypairwise interactions. The coefficients gi obtained from the present data analysisare related to eqn (16) and (17) by 2 9 9 30gii = (2Bz - v?+ b,i)M,/2~? iwwhere bSi is related to solute-solvent interactions and is defined 27 asbSi = (I/v) J (expi- W,,/kT)- 1) dr, dr,. (19)v vIt has been shown 30 thaT. H. LILLEY AND R . P. SCOTT 191and consequently combination of eqn (1 8) and (20) givesgii = (2Bz-2~7+ kT~)M,/2v?.Thus to obtain information on the solute-solute interactions as expressed by eqn (17),from the experimental osmotic coefficients, requires information on the volumetricproperties of the solute and the solvent and the isothermal compressibility of thesolvent. The expression corresponding to unlike-unlike solute coefficients is 30Eqn (21) is similar to an equation given by Knight 31 except for the presence of thecompressibility term and Knight, Kozak and Kauzmann have tabulated thermo-dynamic data compiled from many sources for a variety of aqueous solutions contain-ing a single non-electrolyte.The results presented by these authors for which bothosmotic coefficients and partial molar volumes of the solute at infinite dilution 32existed were treated to obtain the gif terms.Using these Sir terms and the partialmolar volumes at infinite dilution 32 in conjunction with a value 33 of RTrc of 1.1 cm3mol-l for water at 298.15 K allowed the quantity LB; to be calculated. Fig. 2 showsa plot of LB; against the partial molar volume of the solute. There is a very real26I I1 f zoo 400@/crn, mol-FIG. 2.-PIot of LB,*, against Vd* for solutions of a single solute in water, Results at 298.15 K : 1,glycine ; 2, cc-alanine ; 3, ct-aminobutyric acid ; 4, x-aminobutyric acid ; 5, rx-aminoisobutyric acid ;6 , a-aminoisovaleric acid ; 7, 8-alanine ; 8, ,3-aminobutyric acid : 9, P-aminovaleric acid ; 10,y-aminobutyric acid : 11, c-aminocaproic acid ; 12, y-aminovaleric acid ; 13, glycylgIycine ; 14,glycylalanine ; 15, alanyiglycine ; 16, alanylalanine ; 17, triglycine ; 18, serine ; 19, proline ; 20,hydroxyproline ; 21, betaine ; 22, glucose ; 23, fructose ; 24, mannitol ; 25, sucrose ; 26, raffinose ;27, urea; 28, glycolamide; 29, lactamide; 30, glycerol.Results at approximately 273 K : 31,methanol ; 32, ethanol ; 33, propan-1-01 : 34, propan-2-01 ; 35, 2-methylpropan-1-01 ; 36,2-methyI-propan-2-01 ; 37, butan-1-01 ; 38, butan-2-01 ; 39, dioxan ; 40, methylamine ; 41, ethylamine ; 42,dimethylamine ; 43, diethylamine ; 44, urea ; 45, formamide ; 36, acetamide ; 47, urethane ; 48,acetone ; 49, formic acid ; 50, acetic acid ; 51, propionic acid ; 52, butyric acid.difficulty in trying to continue further since the information which is required is howthe intermolecular potential function varies with distance and angle for non-sphericalspecies.The experimentally determined properties only give this information underan integral and without further information an infinite number of models could befitted to each experimental result. There have recently been several discussions 34using a specific model but this model, not withstanding its plausibility, is not unique1 92 AQUEOUS SOLUTIONS OF AMINO-ACIDSnor has it been claimed to be so. The approach adopted here is simpler, ratherdifferent and essentially that used earlier.'If the solutes are represented by " hard-spheres " thenand if the approximation is made thatthen the line drawn in fig. 2 represents the values LB: take for this " hard-sphere "interaction [LR:(HS)].It is apparent from fig. 2 that subject to the assumptionsmade, all of the solute-solute interactions represented are attractive compared toLB:(HS). It has been shown 35* 36 that LB; may be calculated for " hard-core "interactions between molecules having ellipsoidal and " dumb-bell " symmetry andthat the differences between these and LB:(HS) are relatively small if the asymmetryof the species is not too great. The " hard-sphere " line drawn for the moleculesrepresented in fig. 2 is therefore a reasonable approximation. Knight et aL7 havetabulated the quantity [LB: -LBE(HS)] which characterises that part of the virialcoefficient not accounted for by " hard-sphere " interactions. In fig.3 this quantityvi = v yy;8/cm3 mol-1 ~ P l c m 3 mo1-1(4 (b)FIG. 3.--Plot of [LB;,--LB,*,(HS)] against V p for aqueous solutions at 298.15 K, of (a) alkan-1-01s(b) alkanoic acids.is plotted against the partial molar volume of the solute for the homologous seriesof the alkan-1-01s and the alkanoic acids and it is apparent that for both series anapproxiinately linear variation with zero intercept results. It was suggested ' thatthe increasing solute-solute interaction between species containing aliphatic sidechains, as the side chain is lengthened, is a manifestation of hydrophobic bonding 37. 38and head group-head group interactions were presumed to give a constant contribu-tion, within a given series, to [LB; -LBz(HS)]. This explanation seems reasonableif we coiisider a situation where the solute molecules are spherical and we assumethat the solute species interact through a " square-well " intermolecular potential offixed depth which extends over a given fixed distance froin the surface of the solute.Substitution of these assumptions into eqn (17) leads to the result that as the sizeof the solute increases so too does the attractive contribution to LB;.This argumentassumes a great deal about the intermolecular potentials but its conclusions are sup-ported by the fact that the two homologous series represented in fig. 3 have approxi-mately the same slope, suggesting that the contribution from the head groups havelittle erect on the observed interaction.Fig. 4 is an analogous plot to fig.3 for some ct-, p- and y-amino acids.' It iT. H. LILLEY AND R. P. SCOTT 193apparent that the values of LBE-LB:(HS) are similar within a given homologousseries and here it appears that the interactions are predominantly of a dipole-dipolenature and consequently head group effects overwhelm side chain interactions.Similar behaviour is observed for the dipeptides ’ and a similar explanation may beused.400r200-I 3L oO O L0 I00 uI 0 100i I- f I - 0 100@/cm3 mot-1(4 (6) (c)FIG. 4.-Plot of [LB:i-LB?i(HS)] against V? for aqueous solutions, at 298.15 K, of (a) a-, (6) /3- and(c) y-amino-acids.Using eqn (24) and the appropriate volumetric data 32 the values of LB; forurea-amino acid interactions were calculated and are given in table 8.The “ hard-sphere ” contribution for i-j interactions is 30B$(HS) = (n/6)(di + dj)3and if we continue to use our earlier assumption regarding the equalities of theintrinsic and partial molar volumes of solute species then B;(HS) is calculable. Infig. 5 we display the experimentally derived values of LB? against the partial molar5 0 0 ri E“I . I2 0 40 6 0 8 00V? /cm3 mol-1The solid line represents “ hard sphere ” interaction.FIG. 5.-Plot of LB; against V*e. The subscripts i and j refer to amino-acid and urea respectively.volume at infinite dilution of the amino-acid. The line represents the “hard -sphere ”term. Included in table 6 are values of [LB; -LB$(HS)J and as with systems contain-ing single solutes this quantity is always negative and corresponds to solute-soluteattractive forces.For the three a-amino acid +urea systems studied this attractiver-194 AQUEOUS SOLUTIONS OF AMINO-ACIDScontribution is the same, within experimental error, no side chain effects beingobserved. The constancy suggests a predominating interaction of the urea with thehead group of the amino-acids. The attraction is greater for the urea-glycylglycineinteraction and may be due to the greater dipole moment 39 of the dipeptide comparedto the amino-acids although a contribution from the peptide group might wellcontribute to the observed effect.TABLE &-THE VARIOUS TERMS IN EQN (25) FOR AQUEOUS SOLUTIONS CONTAINING UREA,GLYCINE AND UREA+ GLYCINEi i mol-1 kg K-1urea urea - 10.7 540 34 34 1.8glycine glycine - 24.7 637 28 28 1.8urea glycine - 10.5 702 34 28 1.8(dlnVse/dT) and K were taken from ref.(33), the temperature coefficients of the partial molarvolumes of the solutes were estimated from ref. (3), (42) and (43).T12t o9 0.?- 2 1 FIG. 6.-Enthalpy and entropy coefficients for the interaction of i and j species in water. Resultsat 298.15 K : 1, glycine + glycine ; 2, a-alanine + x-alanine ; 3, a-aminobutyric acid + a-amino-butyric acid ; 4, glycylglycine + glycylglycine ; 5, urea + urea ; 6, or-alanine + urea ; 7, glycine + urea ;8, a-aminobutyric acid + urea ; 9, glycylglycine + urea ; 10, or-aminovaleric acid + a-aminovalericacid ; 11, or-aminoisobutyric acid + a-aminoisobutyric acid ; 12, a-aminosiovaleric acid + a-amino-isovaleric acid ; 13, /3-alanine + /3-alanine ; 14, y-aminoisovaleric acid + y-aminoisovaleric acid ;1 5, z-aminocaproic acid + E-aminocaproic acid ; 16, glycolamide + glycolamide ; 17, glycerol + gly-cerol ; 18, sucrose+ sucrose.Results at approximately 273 K : 19, methanol + methanol ; 20,ethanol + ethanol ; 21, propan-1-01 + propan-1-01 ; 22, propan-2-01 + propan-2-01 ; 23, 2-methyl-propan-2-01 + 2-methylpropan-2-01 ; 24, butan-1-01 + butan-1-01 ; 25, butan-2-01 + butan-2-01.Combination of the definition for the enthalpy interaction coefficienT. H . LILLEY AND R. P. SCOTT 195with eqn (22) gives, assuming the temperature coefficient of the isothermal com-pressibility may be neglectedConsequently if one wishes to discuss the temperature variation of the solute-soluteintermolecular interaction the free energy parameter gi is required as are the expansi-bilities of the interacting solutes.There is not a great deal of experimental informa-tion on these quantities and as examples only the single solute aqueous systemscontaining urea and glycine and the binary solute system of urea+glycine in waterwill be discussed to get some estimate of the several terms in eqn (25). (Furtherdiscussion will be given el~ewhere.~~) In table 8 we present the various contributionsto the right-hand side of eqn (25) for these systems. It is apparent for these systemsthat the first term on the right-hand side is small compared to the second term andthat this latter term is dominated by the contribution from (dB$/dT).The relativelysmall contribution from the term containing grj means that entropy-enthalpy com-pensation 41 will occur. This is illustrated in fig. 6 where hi, is plotted against sijfor many systems including those just discussed, and it would seem that generally forsolutes interacting in water gi is small whereas its temperature coefficients are large.The reason for such compensation behaviour is not known although there have beenseveral discussions regarding its origin.41 We prefer not to speculate further on thissince it is apparent that before an acceptable explanation is possible a considerableamount of information is required on the intermolecular potential and its temperaturederivative, of solutes interacting in water.NOTATIONbB*d9GhHkLm423MPrRSintegral defining the interaction ofsolute with solventintegral defining the interactionbetween two solutesdiameter of a solute speciesGibbs function interaction coefficientGibbs function of a solution contain-ing 1 kg of solventen t ha1 p y interact ion coefficiententhalpy of a solution containing 1 kgof solventBoltzmann constantAvogadro constantmolalitytotal molality (sometimes called theTVWY2,471:PPAKtemperaturemolecular volumevolume or partial molar volumepotential of average forcesolute mole fractionosmotic coefficient, $ ( i j ) refers to theosmotic coefficient of a solution con-taining the solutes i andjosmotic pressuresolute number densityisothermal compressibility of solventchemical potentialchange in a propertySUPERSCRIPTS AND SUBSCRIPTSid idealex excess8 standard statei, j,k, solute speciess solventosmolality) = Ximimolecular weightpressuredistance separating two speciesgas constantentropy interaction coefficient =(h/ TI - 9We thank L.K.B.Instruments Ltd. for the loan of the calorimeter and one of us(R. P. S.) thanks the S.R.C. for the award of a Research Studentship196 AQUEOUS SOLUTIONS OF AMINO-ACIDSADDENDUMAfter this paper hzd been prepared Cassel and Wood 4 4 3 45 reported experimental dataon the enthalpies of mixing of urea+glycine aqueous systems at constant molality. Theresults agree, within experimental error, with those obtained here (see table 2).C.C. Briggs, T. H. Lilley, J. Rutherford and S . Woodhead, J. Solution Chem., 1974, 3, 649.J. A. Schellman, Compt. Rend. Trav. Lab. Carlsberg, 1955, 29, 223.R. H. Stokes, Austral. J. Chem., 1967, 20, 2087.R. H. Stokes and R. A. Robinson, J. Phys. Chem., 1966,70,2126.F. Franks, J. R. Ravenhill and D. S . Reid, J. Solution Chem., 1972, 1, 3.M. J. Tait, A. Suggett, F. Franks, S. Ablett and P. A. Quickenden, J. Solution Chem., 1972,1, 131.W. S. Knight, J. J. Kozak and W. Kauzmann, J. Chem. Phys., 1968,48, 675.W. G. McMillan and J. E. Mayer, J. Chem. Phys., 1945, 13,276.C. C. Briggs, R. Charlton and T. H. Lilley, J. Chem. 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Kauzmann, Advances in Protein Chemistry, ed. C. B. Afinson, M. L. Anson, K. Bailey and38 T. S. Sarma and J. C. Ahluwalia, Chem. SOC. Rev., 1973, 2,203.39 J. T. Edsall and J. Wyman, Biophysical Chemistry (Academic Press, New York, 1958), vol. I,40 T. H. Lilley, to be submitted for publication.41 See e.g. R. Lumry and S . Rajender, Biopolymers, 1970, 9, 1125.42 H. J. V. Tyrell and M. Kennerley, J. Chem. Soc. A , 1968, 2724.43 F. T. Gucker, W. L. Ford and C. E. Moser, J . Phys. Chem., 1939,43,153.44 R. B. Cassell and R. H. Wood, J. Phys. Chem., 1974, 78, 2465.45 R. H. Wood, personal communication.J. T. Edsall (Academic Press, New York, 1959), vol. 14.chap. 6.(PAPER 5/708