Aqueous Solutions Containing Amino Acids and Peptides Part 5.-Gibbs Free Energy of Interaction of Glycine with some Alkali Metal Chlorides at 298.15 K BY BARRY P. KELLEY? AND TERENCE H. LILLEY* Chemistry Department, The University, Sheffield S3 7HF Received 17th March, 1978 Cells with transference have been used to investigate the free energy of interaction of glycine with LiCI, NaCl and CsCl in aqueous soIutions at 298.15 K. The experimental data were analysed to give the Lewis-Randall free energy coefficients which represent pairwise interactions between the salt ions and the amino acid. The Lewis-Randall coefficients were transformed to the McMillan-Mayer scale and these were then deconvoluted in an approximate manner to give the contributions arising from excluded volume (hard-sphere), electrostatic (Kirkwood) and solvent reorganisation effects. The excluded volume and solvent reorganisation contributions are found to be approximately equal in magnitude but opposite in sign, so that the frequently used Kirkwood electrostatic model represents the nett interactions well.This is part of a continuing series of investigations on the thermodynamic behaviour of amino acids and peptides in aqueous solutions. Our principal aim is to obtain information on pairwise intermolecular interactions between solute mole- cules in such systems and in this paper we present results for the Gibbs free energy of interaction of lithium, sodium and caesium chlorides with glycine in water at 298.15 K, from cells with transference. EXPERIMENTAL The cells used were similar in design to those used by Covington and Prue.2 E.m.f.measurements were made using a Fenlow digital voltmeter with a resolution of 1 pV. The digital voltmeter was frequently checked and calibrated against a certified Weston standard cell. Silver-silver chloride electrodes were of the thermal electrolytic type and were pre- pared using previously described procedure^.^ Pairs of electrodes were selected which had bias potentials <3OpV. The procedure used to remove uncertainties arising from bias potentials was similar to that described ear lie^.^ All measurements were made on cells immersed in a water bath thermostatted at (298.15k0.01) K. The water used in the preparation of solutions was obtained by passage of laboratory distilled water through a mixed bed ion exchange column.UltraR grade sodium chloride was used without further purification after drying at 470 K for 48 h. The purification methods for lithium chloride and caesium chloride have been described elsewhere.’ AnalaR grade glycine was recrystallised twice from methanol+ water mixtures and dried at 320 K under vacuum. The apparatus used in the present investigation has been checked using aqueous sodium chloride solutions and used to obtain activity coefficients of LiCI6 and CsC17 in water. METHOD AND RESULTS Cells with transference have been used fairly extensively in the past to obtain information on either ionic transport numbers or activity coefficients.2* 4 9 * Their i Present address : Chloride Technical Ltd, Swinton, Manchester M27 2HB.27712772 AQUEOUS SOLUTIONS OF AMINO ACIDS use may be extended solutions containing added non-electrolyte. to the determination of activity coefficients of electrolytes in The cells used in the present investigation may be represented by : Ag I AgCl I MCl(m) 11 MCl(m), glycine(m,) I AgCl I Ag I I1 in which the aqueous phase I, containing alkali metal chloride (MCl) at molality m, is separated from aqueous phase 11, containing MCI at the same molality and glycine at molality mi, by a liquid junction. The e.m.f. (E) of such a cell is given by '9 lo f 11 l-11 E = -2k' J t d In (my)-RT J ti d In (miyi) I I where k' = RT/F, t is the cationic transference number, ti is a term allowing for the transference of the non-electrolyte across the liquid junction and y and yi are respec- tively the electrolyte mean ionic activity coefficient and the activity coefficient of the non-electrolyte.At present there is no experimental information available on the magnitude of ti but theoretical predictions based on an incompressible ion- dielectric continuum model indicate that the contribution to the e.m.f. from the second integral on the right hand side of eqn (1) is negligible compared with our experi- mental precision. It is worth pointing out however that it is possible to use Feakins' procedure l2 to measure the Washburn number (which is closely related to ti) and we have recently initiated a collaborative series of experiments with Prof. Feakins to investigate the theoretical predictions. For the present we shall use the information available and ignore the second term on the right hand side of eqn (1).Using this approximation eqn (1) may be rearranged to give In ( y / y o ) = -(E/2k'to)+(l/2k't:) At dE J o in which y and yo are respectively the mean ionic activity coefficients of the salt in the presence and absence of glycine and a term At is defined as where t and to are the cationic transference numbers in the presence and absence of the non-electrolyte. No experimental information is available on the rnolality dependence of At but unpublished observations indicate that the effect of added amino acid 011 the cationic transference number can be represented by where a is a constant characteristic of a given electrolyte-non-electrolyte system. If we now make the usual assumption that the logarithm of the activity coefficient of the salt may be expressed as a power series in mt and mi, i.e.( 5 ) then since the first term on the right hand side of eqn (2) is dominant, from eqn (2), (4) and (5) we have, At = t-to (3) At = ami (4) In ( y / y o ) = Ami + Bmtmi + Cmf + Dm mi + . . . At dE = ami dE rr -2k'toami d In ( y / y o ) = -2k'to~mi(A+Bmt+2Cmi+ Dm) dmi. (6) (7) Combination of this with eqn (2) and ( 5 ) yields, after slight rearrangement, in which F = Aa/2, G = &/2, H = Da/2 and .I = 2Ca/3. - E = 2k'mi { to ( A + Bm* -k Dm) + mi (Ct, -+ F -I- Gm3 % Hm + Jmi) 1B . P . KELLEY AND T . H . LILLEY 2773 Before this expression can be used in the analysis of experimental results, it is necessary to have values of the transference numbers of the cations at each molality of salt used in the experiments.The transference numbers of lithium l3 and sodium l4 ions in chloride solutions were obtained from published experimental data. The transference number of caesium ion in caesium chloride solutions has not been determined experimentally and it was necessary to estimate this. According to one formulation of the interionic attraction theory the cationic transference number in a solution of a 1 : 1 electrolyte is given by and the limiting (infinite dilution) transference number is where the symbols have their previously l 5 defined meanings. If t $ is 0.5 exactly then it is predicted that to does not vary with salt concentration. For potassium chloride in water at 25 "C, t $ = 0.4905 and the agreement between experimental values and those calculated from eqn (8) is excellent.The limiting transference number of the caesium ion in caesium chloride solutions is 0.5030 l6 and to predict its concentration dependence we have assumed an ion size parameter of 0.35 nm, although the concentration dependence is so small that any physically realistic value would be suitable. The transference numbers were then calculated from eqn (8) using appropriate density data to perform the conversion from the molar to the molal scale. The experimental results obtained are given in table 1 and the results for each system were fitted to eqn (7) by a least squares program. This program was such that if the 95 % confidence limit of a coefficient was greater than its numerical value, then the program reanalysed the data with this coefficient excluded.This procedure continued until all remaining coefficients had 95 % confidence limits less than their numerical values. It was found in the present investigation that the only coefficients required to fit the data were A , B, C and sometimes D. Table 2 represents the coefficients and their 95 % confidence limits. TABLE 1 .-EXPERIMENTAL E.M.F. VALUES FOR THE SYSTEM ALKALI METAL CHLORIDE+ GLYCINE AT 298.15 K LiCl + glyciiie mlmd kg-1 rn,/mol kg- 1 t 0 EImV AElmV 0.010 024 0.009 7445 0.022 478 0.022 837 0.039 998 0.039 965 0.062 408 0.089 848 0.099 788 0.301 55 0.490 63 0.302 98 0.502 39 0.100 12 0.302 69 0.492 47 0.100 26 0.504 23 0.100 46 0.296 47 0.452 80 0.099 994 0.488 51 0.300 44 0.506 11 0.3290 0.3291 0.3255 0.3255 0.3225 0.3225 0.3198 0.3175 0.331 0.928 1.427 0.945 1.514 0.302 0.850 1.327 0.289 1.354 0.273 0.754 1.128 0.246 1.098 0.657 1.022 - 0.01 1 O.OO0 0.022 - 0.01 1 - 0.03 1 - 0.005 0.007 0.007 0.008 0.005 om1 0.01 6 0.003 0.003 O.OO0 - 0.01 3 - 0.0032774 AQUEOUS SOLUTIONS OF AMINO ACIDS m/mol kg-I 0.010 127 0.023 942 0.040 117 0,062 187 0.090 594 TABLE 1 .-cont.mijmol kg-' fo 0.100 00 0.207 15 0.293 46 0.395 26 0.501 92 0.101 42 0.201 23 0.302 84 0.398 24 0.510 57 0.105 12 0.205 41 0.294 47 0.401 82 0.504 42 0,099 54 0.198 79 0.297 38 0.406 60 0.505 04 0.100 39 0.198 95 0.304 67 0.402 27 0.511 98 0.010 080 0.101 27 0.305 44 0.506 64 0.022 824 0.302 62 0.512 82 0.022 908 0.102 03 0.206 04 0.414 77 0.040 668 0.100 40 0.303 22 0.506 02 0.062 475 0.112 46 0.307 03 0.527 98 0.090 923 0.104 40 0.511 25 NaCl + glycine 0.391 8 0.3898 0.3883 0.3869 0.3857 CsCl + glycine 0.503 1 0,503 1 0.503 1 0.5032 0.5032 0.5033 E/mV 0.401 0.802 1.086 1.470 1.803 0.363 0.699 1.043 1.309 1.621 0.346 0.674 0.928 1.21 1 1.441 0.299 0.583 0.855 1.135 1.350 0.280 0.548 0.812 1.050 1.287 0.552 1.400 2.183 1.251 1.958 0.439 0.882 1.656 0.410 1.113 1.763 0.401 1.03 I 1.681 0.310 1.462 AE/mV - 0.003 0.001 0.027 - 0.01 1 -0.003 0.000 0.001 - 0.020 0.000 0.000 0.001 -0.017 -0.012 - 0.003 0.025 0.007 0.008 0.001 - 0.009 0.001 0.01 1 0.009 0.010 - 0.003 -0.010 - 0.064 - 0.004 - 0.004 0.007 0.023 0.006 - 0.009 - 0.005 - 0.01 1 0.017 - 0.003 0.008 0.012 - 0.029 0.041 0.001 TABLE 2.-cOEFFICIENTS OF EQN (7) FOR ALKALI METAL CHLORIDE+ GLYCINE SYSTEMS system A/kg mol-1 B/kg* mol-3 C/kgz mol-2 Dlkgz mol-2 LiCl+ glycine - 0.2191 0.006 0.254+ 0.01 6 0.0391 0.01 2 - KCl+ glycine* - 0.202+0.003 0.216f 0.009 0.034+ 0.004 - NaCl+glycine -0.2481 0.007 0.520+0.070 0.049* 0.007 -0.652kO.173 CsCl+ glycine - 0.232f0.017 0.45410.160 0.047+0.015 -0.43240.397 * Obtained from the data of Roberts and Kirkw~od.~B .P. KELLEY AND T. H . LILLEY 2775 Included in this table are the results we obtained from a reanalysis of the KClf glycine ~ystem,~ using only those experimental points for which the molality of the glycine was <0.5 mol kg-l and the molality of the salt was <0.1 mol kg-l. The final column of table 1 gives the difference (AE) between the experimental e.m.f. values and those calculated using the appropriate least squares parameters.COMPARISON WITH OTHER WORK It can be seen from table 2 that the A coeficients, which represent painvise inter- actions between the ions and the glycine, are all negative, indicating an attractive interaction between the electrolytes and glycine. This is what one would intuitively expect and is confirmed by other studies mentioned below. The sodium chloride + glycine system has been previously studied by a number of workers. Joseph l7 obtained activity coefficients for sodium chloride in glycine solutions, from cells without transference, utilising sodium amalgam and silver-silver chloride electrodes. Most of the work described was performed at 274.6 K and reanalysis of his data using our procedure gave a value for A of - 0.30 +O.10 kg mol-l. The rather large error arises because the e.m.f. values were only measured to a pre- cision of 1 mV. The few measurements at 298.15 I< reported by Joseph were obtained on solutions of such high molalities to preclude comparison with the present work. Scatchard and Prentiss * investigated the sodium chloride + glycine system using the freezing temperature depression technique and the value they quote of -0.327 kg mol-1 for the pairwise interaction term agrees favourably with the value obtained by Joseph. More recently Phang and Steele obtained activity coefficients of sodium chloride in mixtures with glycine by the use of sodium responsive glass and silver-silver chloride electrodes in cells without transference. The experimental results, as analysed by them, for the more dilute solutions investigated gave a value for A of -0.221 kg mol-1 at 298.15 K.No error limits were given for the various coefficients and it would have been interesting to reanalyse their data using our procedure but this was not possible, since the experimental e.m.f. data were not presented. There must be some uncertainties in the presented coefficients since, when an extended form of eqn ( 5 ) was used in order to allow the activity coefficients in the more concentrated solutions investigated to be included in the data analysis, the value obtained for the leading term was -0.203 kg mol-l. The result obtained at 0 "C of -0.252 kg mol-1 is at variance with that obtained from precise freezing temperature measurements. The sodium chloride + glycine system has also been investigated over a wide molality range by Schrier and Robinson,20 using the isopiestic vapour pressure technique.A polynomial expansion in solute molalities, [analogous to eqn (5)] containing ten coefficients, was necessary to represent the osmotic coefficient data. The value obtained for the A coefficient was -0.146 kg mol-l, which is in marked contrast to the value of -0.248 kg mol-l obtained from the present work. The large discrepancy almost certainly arises because of the relatively high molalities used in the isopiestic studies. It seems certain that the present result is the more nearly correct, since it was obtained from experiments in a molality range in which the A term was dominant, whereas in the molality range covered by the isopiestic experi- ments, very large contributions to the osmotic coefficient from triplet and higher order solute-solute interactions would be present.The discrepancy between results obtained from isopiestic measurements and those obtained from cells with transference is also apparent on comparing results obtained using the two methods for the KCl+glycine system. The value obtained for the leading term from cells is -0.202 kg mol-' and this contrasts with the value of 1-882776 AQUEOUS SOLUTIONS OF AMINO ACIDS - 0.130 kg mol-1 obtained from an isopiestic investigation.21 The KCl + glycine system has also been studied using a precise freezing temperature method and the value obtained for the A coefficient at the freezing temperature was - 0.21 8 & 0.008 kg mol-? The freezing temperature method was also used for the LiCl + glycine and CsCl + glycine systems and the respective values obtainedforthe A term were -0.158 kO.010 and -0.127+_0.006 kg mol-l.Mixtures of glycine with LiCl, NaCl and KCl were investigated many years ago 22 using solubility measurements but since these were performed in necessarily rather concentrated solutions, it is not possible to get a meaningful comparison between these and the present work. DISCUSSION The leading term in eqn (9, as stated above, arises from pairwise interactions between the ions and the non-electrolyte. In terms of our earlier nomenclature 5 * 23 we may identify A with ( g M i + g X i ) . It is apparent from the information given in table 2 that : (a) the ( g M i + g x i ) values are all negative indicating an attractive interaction between the electrolyte and the non-electrolyte and (b) these values change little with increasing cation size.TABLE 3.-cONTRIBUTIONS TO EQN (1 2) L(B&+ B&)/cm3 mol-1 experimental hard sphere Kirkwood solvent-reorganisation LiCI - 336+ 12 382 - 348 - 340 NaCl - 394f 14 386 - 360 - 420 KCI -292+ 16 432 - 350 - 373 CsCl - 340k 34 483 - 340 - 482 When trying to relate the experimental information to solute-solute inter- molecular potentials it is necessary to transpose the painvise interaction coefficients from the Lewis-Randall to the McMillan-Mayer (MM) These are related by : 5 9 2 3 The transposition from one scale to the other was performed using appropriate volumetric data " 9 2 8 and the values obtained for the MM coefficients are given in L(BGi+B&) = 2(~,i+g,i)F/,OM~~ + V L , + ~ V : - ~ R T K .(10) table 3. These second virial coefficients in eqn (10) are of the form BLi = 4n (1 -exp (- WMi/kT))r2 dr s," for spherically symmetric species. The intermolecular potential interaction of an ion and a non-electrolyte like glycine may be function for the considered to be composed of three contributions. These are : (a) short-range repulsive interactions, (b) long-range interactions arising from electrostatic ion-dipole effects, and (c) a solvent-reorganisation contribution. In order to proceed further, approximations must be made about these contribu- tions to WMi and Wxi. The electrostatic part of the intermolecular potential function is assumed to be given by the treatment of Kirkwood 29 and the short-range repulsive effects may be approximated by " hard-body " ' 9 23* 27 interactions between theB.P . KELLEY AND T. H. LILLEY 2717 ions and the non-electrolyte. The difference between the real intermolecular potential function and the contributions from these two calculable components is ascribed to solvent reorganisation effects or alternatively co-sphere-co-sphere or Gurney effects. 30 It should be recognised that the solvent reorganisation contributions must also include contributions arising from deficiencies in the approximations used to obtain the electrostatic and repulsive components. We may thus write where the subscripts refer to hard-sphere (HS), Kirkwood or electrostatic (K) and solvent reorganisation (SR) respectively.The first two terms on the r.h.s. of eqn (12) were estimated as b e f ~ r e , ~ by treating the ions as spheres of known radius and assuming that glycine could be represented as a sphere with a point dipole at its centre. The dipole moment of the glycine was taken to be 13.5 Debye.20 The values obtained for the three contributions to the virial coefficients derived from the experimental results are included in table 3. The most striking feature is that the hard sphere (excluded volume) term and the solvent reorganisation term are, for each system investigated, approximately equal but of opposite sign. This leads to a close correspondence between the experimental quality and the electrostatic contribution. This can only be fortuitous but it does explain the apparent success of earlier treatments 9* 18-21* 31 for the free energy of interaction of amino acids with salts.It should be pointed out that the same happy coincidence does not apply for the enthalpic and entropic contributions to ion-amino acid interactions.l* 3 2 9 3 3 (Bzi + BzJ = (B&i + B&)HS + (B&i + Bgi), + (BLi + B,*i)sR (12) We thank the S.R.C. for the award of a studentship to one of us (B. P. K.) and R. H. Wood for discussions. Addendum. Preliminary measurements from Prof. Feakins laboratory 34 indicate that the neglect of the second term on the r.h.s. of eqn. (1) is justified for the systems investigated. B. P. Kelley and T. H. Lilley, J. Chem. Thermodynamics, 1978,10,703. A. K. Covington and J. E.Prue, J. Chem. SOC., 1955, 3701. C. C. Briggs, Thesis (University of Sheffield, 1973) ; C. C. Briggs and T. H. Lilley, J. Chem. Thermodynamics, 1974, 6, 599. A. S. Brown and D. A. MacInnes, J. Amer. Chem. SOC., 1935,57, 1356. T. H. Lilley and R. P. Scott, J.C.S. Faraday I, 1976,72, 197. B. P. Kelley and T. H. Lilley, J. Chem. Thermodynamics, 1977, 9, 99. (a) T. Shedlovsky and D. A. MacInnes, J. Amer. Chem. Soc., 1936,58,1970 ; (b) T. Shedlovsky and D. A. MacInnes, J. Amer. Chem. SOC., 1937,59,503 ; (c) W. J. Hornibrook, G. J. Janz and A. R. Gordon, J. Amer. Chem. SOC., 1942,64,513; (d)R. E. Verrall, J. Solution Chem., 1975, 4, 319 ; (e) J. C. Ku, Thesis (University of Pittsburgh, 1971). R. M. Roberts and J. G. Kirkwood, J. Amer. Chem. SOC., 1941,63,1373.lo G. Scatchard, J. Amer. Chem. Soc., 1953,75,2883. A. M. Squires, Thesis (Cornell University, 1947). l 2 (a) D. Feakins, J. Chem. SOC., 1961, 5308 ; (6) D. Feakins and J. P. Lorrimer, Chem. Comm., 1971,646 ; (c) D. Feakins and J. P. Lorimer, J.C.S. Faraday I, 1974,70,1888 ; (d) D. Feakins, K. H. Khoo, J. P. Lorrimer and P. J. Voice, J.C.S. Chem. Comm., 1972, 1336; (e) D. Feakins, K. H. Khoo, J. P. Lorrimer, D. A. O'Shaugnessy and P. J. Voice, J.C.S. Faraday I, 1976,72, 2661. ' B. P. Kelley, Thesis (University of Sheffield, 1977). l 3 L. G. Longsworth, J. Amer. Chem. SOC., 1932,54,2741. l4 (a) L. G. Longsworth, J. Amer. Chem. SOC., 1935, 57, 1185 ; (6) R. W. Allgood, D. J. LeRoy l 5 R. H. Stokes, J. Amer. Chem. SOC., 1954, 76, 1988. and A. R. Gordon, J. Chem.Phys., 1940,8,418 ; 1942, 10,124.2778 AQUEOUS SOLUTIONS OF AMINO ACIDS l6 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 2nd edn, 1970), p. 463. N. R. Joseph, J. Biol. Chem., 1935,111,489. l8 G. Scatchard and S. S . Prentiss, J. Amer. Chem. SOC., 1934,56,2314. l9 S. Phang and B. J. Steele, J. Chem. Thermodynamics, 1974, 6, 537. 2o E. E. Schrier and R. A. Robinson, J. Biol. Chem., 1971,246,2870. 21 V. E. Bower and R. A. Robinson, J. Res. Nat. Bur. Standards, 1965,69A, 131. 22 References to this work are given by E. J. Cohn, in Proteins, Amino-acids andPeptides, ed. E. J. Cohn and J. T. Edsall (Reinhold, New York, 1943), chap. 10. 23 T. H. Lilley and R. P. Scott, J.C.S. Faraday I, 1976, 72, 184. 24 W. G. McMillan and J. E. Mayer, J. Chem. Phys., 1945,13,276. 25 H. L. Friedman, J. Solution Chem., 1972, 1, 387, 413, 419. 26 R. H. Wood, T. H. LiHey and P. T. Thompson, J.C.S. Faraday I, 1978,74,1301. 27 J. J. Kozak, W. S. Knight and W. Kauzmann, J. Chem. Phys., 1968,48,675. 28 F. J. Millero, in Water and Aqueous Solutions: Structure, Thermodynamics and Transport Processes, ed. R. A. Horne (Wiley-Interscience, New York, 1972), chap. 13. 29 J. G. Kirkwood, Chem. Rev., 1939,24,233 ; Proteins, Amino-acids and Peptides, ed. E. J. Cohn and J. T. Edsall (Reinhold, New York, 1943), chap. 12. 30 P. S. Ramanathan and H. L. Friedman, J. Chem. Phys., 1971,54,1086. 31 C. C. Briggs, T. H. Lilley, J. Rutherford and S. Woodhead, J. Solution Chem., 1974,3, 649. 32 J. W. Larson and D. G. Morrison, J. Phys. Chem. 1976,80, 1449. 33 B. P. Kelley, T. H. Lilley, E. M. Moses and I. R. Tasker, to be published. 34 D. Feakins, personal communication. (PAPER 8/502)