Aqueous Solutions Containing Amino Acids and Peptides Part 8.-Gibbs Free Energy of Interaction of some a,u-Amino Acids with Sodium Chloride at 298.15 K BY BARRY P. KELLEY 7 AND TERENCE H. LILLEY * Chemistry Department, The University, Sheffield S3 7HF Received 5th April, 1978 Cells with transference have been used to obtain information on the free energy of interaction between sodium chloride and the amino acids jl-alanine, y-aminobutyric acid and c-aminocaproic acid. The results obtained are compared with those obtained for some a-amino acids. It is shown that, whereas with the a-acids there is little change in the pairwise interaction parameter as the hydrocarbon side chain is extended, for the a,w-acids the interaction with the ions of the salt becomes increasingly attractive as the homologous series is ascended.In the last few years we have been involved with some thermodynamic investigations on aqueous solutions containing amino acids and salts and have recently presented a study of the free energy of interaction of sodium chloride with some a-amino acids.' The present work is complementary to this in that we now present results to illustrate the effect of the separation of the charged amino and carboxylate groups on the extent of interaction of sodium chloride with some apamino acids. EXPERIMENTAL The general experimental arrangement used was the same as that previously described.2 The purification of water and sodium chloride was as before.2 The racemic amino acids were of the best quality commercially available and were recrystallised from methanol+ water (fl-alanine) or ethanol+ water (7-amino-n-butyric and s-amino-n-caproic acids) before drying at 323 K.RESULTS The cells used may be represented schematically as Ag I AgCl I NaCl(m) 11 NaCl(m), amino acid (mi) 1 AgCl I Ag in which an aqueous phase I, containing sodium chloride at molality my is separated from another aqueous phase 11, containing sodium chloride at the same molality and amino acid at molality mi, by a liquid junction. As discussed if transport of the non-electrolyte is negligible, the e.m.f. (E) of such a cell is given by I I1 E = -2k' tdln(my) 1:' where k' = RT/F, t is the transference number of the cation and y is the mean ionic activity coefficient of the electrolyte. Eqn (1) may be re-expressed as - E = 2k'm,(t,(A+Bm*+ Dm)+mi(Cto+F+~m~+Hm+Jm,)) (2) t Present address : Chloride Technical Ltd, Swinton, Manchester M27 2HB.27792780 AQUEOUS SOLUTIONS OF AMINO ACIDS in which A , By C and D are coefficients in an activity coefficient series expansion in molalities, and F, G, H and J are composite terms which include contributions from A , B, C and D and a term representing the dependence of the cationic transference number on the molality of the non-electrolyte. In eqn (2) and (3), yo and to are the activity coefficient and the transference number in aqueous solution I and y is the activity coefficient in solution 11. The experimental results obtained are given in table 1. The results for each system were fitted by a least squares procedure to eqn (2) and the resulting co- efficients, with their 95 % confidence limits, are given in table 2.Not all of the In (yIyo) = ( A + Bma + Cmi + Dm)m,, (3) TABLE 1 .-EXPERIMENTAL E.M.P. VALUES FOR THE SYSTEMS SODIUM CHLORIDE+ AMINO ACID AT 298.15 K rn/mol kg-* 0.010 034 0.022 650 0.041 951 0.062 730 0.062 535 0.089 212 0.010 125 0.022 443 0.039 841 0.062 292 0.090 295 0.089 695 rnJmo1 kg-1 t0 E/mV p-alanine + NaCl 0.101 41 0.304 84 0.490 39 0.103 11 0.298 10 0.497 72 0.104 04 0.310 22 0.529 53 0.102 67 0.198 47 0.422 62 0.302 45 0.505 17 0.105 60 0.305 99 0.511 98 0.391 8 0.478 1.306 2.009 0.3899 0.449 1.156 1.821 0.3881 0.385 1.076 1.712 0.3869 0.374 0.630 1.300 0.3869 0.968 1.490 0.3858 0.317 0.864 1.370 y-aminobutyric acid+ NaCl 0.097 364 0.316 24 0.514 61 0.099 007 0.307 60 0.499 05 0,099 925 0.301 20 0.515 52 0.100 10 0.304 44 0.497 70 0.099 319 0.500 12 0.212 99 0.302 02 0.408 27 0.3918 0.590 1.661 2.490 0.3899 0.585 1.460 2.167 0,3883 0.459 1.255 1.981 0.3869 0.400 1.144 1.660 0.3857 0.328 1.508 0.3858 0.699 0.996 1.255 AEIrnV -0.019 0.005 - 0.001 - 0.025 0.005 0.007 0.000 0.002 0.000 - 0.025 0.023 - 0.01 3 - 0.006 0.004 0.01 1 0.018 - 0.010 - 0.01 2 0.03 1 - 0.009 - 0.067 0.006 - 0.003 -0.001 0.014 -0.014 0.001 - 0.019 0.032 0.01 8 -0.018 0.01 5 - 0.01 8 0.012B .P . KELLEY AND T. H . LILLEY 278 1 TABLE 1 .-contd. 8-amino-n-caproic acid+ NaCl m/mol kg- mi/mol kg - to EImV AEImV 0.010 087 0.100 32 0.3918 0.297 08 0.498 82 0.022 385 0.099 514 0.3899 0.293 07 0.508 30 0.040 253 0.099 873 0.3883 0.301 66 0.512 82 0.062 891 0.099 582 0.3869 0.302 38 0.509 86 0.089 563 0.104 73 0.3858 0.301 80 0.509 29 0.819 2.01 5 2.952 0.700 1.685 2.541 0.579 1 SO2 2.223 0.514 1.276 1.872 0.455 1.114 1.622 - 0.041 0.01 6 - 0.012 - 0.037 0.041 0.014 - 0.01 1 0.005 - 0.030 - 0.029 0.01 8 0.003 - 0.01 5 0.005 0.001 TABLE 2.-cOEFFICIENTS OF EQN (2) FOR NaCl+CC,O-AMINO ACID SYSTEMS A/kg mol-1 B/kgq rnol-9 C/kg2 mol-2 D/kgz mol-2 F/kg2 mol-2 NaCl+ p-alanine - 0.274 f0.011 0.470 fO.1 14 0.055 fO.0 1 1 - 0.3 18 k0.285 - NaCl+ y-amino-n- - 0.390 fO.040 0.883 f0.303 4.509 f 3.544 - 0.636f0.560 - 1.71 5 & 1.376 NaCI+ 6-amino-n- - 0.545 rt0.041 1.499 f0.3 12 6.952 5 3.90 1 - 1.447 f 0.594 - 2.633 f 1.5 1 6 butyric acid caproic acid coefficients in eqn (2) were required to represent the experimental results. Included in table 1 are the differences (AE) between the experimental e.m.f.values and those calculated using the least squares parameters. The leading term in the activity coefficient expansion [ A in eqn (2)] represents pairwise interactions between the sodium and chloride ions and the amino acid and is equivalent to the term (gNa+, +gel-, i) in our earlier termin~logy.~ We will revert to our earlier notation when discussing this pairwise interaction term since to do so stresses its molecular origin. TABLE 3 .-COMPARISON OF THE PRESENT RESULTS FOR THE PAIRWISE INTERACTION PARAMETER WITH THOSE OBTAINED FROM ISOPIESTIC STUDIES --(SNa+.f+gC1-.i)lkgmol-l amino acid (i) present work isopiestic glycine 0.248+ 0.007 0.146 p-alanine 0.274+ 0.01 1 0.196 y-aminobutyric acid 0.390~0.040 0.246 &-aminocaproic acid 0.545-+_0.041 0.245 In table 3 we compare the present values of interaction terms with those obtained from an earlier isopiestic vapour pressure investigation.The agreement between the two sets of information is poor. There is some uncertainty in the values obtained from the present investigation because of possible non-electrolyte transport contri- butions to the measured e.m.f. values although theoretical predictions indicate that these should be rather small and within our experimental errors. Our experience with the isopiestic technique leads us to believe that it is not a very satisfactory method to use to obtain painvise interaction coefficients in those situations when the2782 AQUEOUS SOLUTIONS OF AMINO ACIDS solute-solute higher order interactions are relatively strong since, because of the fairly high molalities necessarily used in isopiestic investigations, the pairwise effects may be masked by many-body interactions. This comment should not be taken to imply that the data obtained earlier are inaccurate or that isopiestic investigations are not useful for the determination of osmotic and thence activity coefficients.We simply wish to point out that in systems such as those investigated here, isopiestic measurements have limited application in the determination of pairwise interaction coefficients. DISCUSSION The interaction between sodium chloride and the a,o-amino acids and the cc-amino acids l s 2 is qualitatively the same, in that for the molality range investigated, attractive interactions occur between each of the acids and the salt.The general features \ I I I I I I I I I 0 0.0 2 0.04 0.06 0.0 8 rnlmol kg-' FIG. 1.-Trace activity coefficients of amino acids in sodium chloride solutions at 298.15 K. The numbers on the curves correspond to glycine (l), a-alanine (2), a-aminobutyric acid (3), norvaline (4), norleucine (5), /3-alanine (6), y-aminobutyric acid (7) and E-aminocaproic acid (8). Curve 1 was constructed from data presented in ref. (2) and curves 2-5 were constructed using data from ref. (1). associated with ascending the two homologous series are, however, different. This is illustrated in fig. 1 where we have used the parameters of eqn (2), for each system, to calculate the trace activity coefficient of the amino acid as a function of the saltB.P. KELLEY AND T. H. LILLEY 2783 molality. This trace activity coefficient (which corresponds to the situation when amino acid-amino acid interactions make no contributions) is given by It is apparent from fig. 1 that, not only are the values of the trace activity coefficients of the a-amino acids smaller than those for the corresponding a,w-acids, but also the trends within the two series are different in that the a-acid-salt interaction increases in a repulsive sense as the hydrocarbon chain is extended whereas the converse occurs in the a,cu series. This is illustrated in a different way in fig. 2 where we have plotted In y: = { 2A + (4B/3)m* + Dm)m. (4) 0.1 0.2 .-I -. 0.3 8 & M A 1 - .. I + 1 0.4 d I 0.5 0.6 I 2 3 4 5 number of C atoms in hydrocarbon chain FIG.2.-Pairwise interaction coefficient for (a) a- and (b) a,o-amino acids as a function of the number of carbon atoms in the hydrocarbon chains. the pairwise interaction coefficients for the two series. The values obtained for the a-acids appear to be constant after a-alanine whereas the values for the a,o-acids become increasingly more negative as this series is ascended. A qualitative explana- tion of these features would be that, since the interaction between the ions of the salt and the amino acids would intuitively be expected to occur primarily at the ionic head groups, then for the a-acids the side chain would not be “noticed” by the salt ions after some relatively short extension of the hydrocarbon chain, whereas for the a,w-acids, the interaction between a particular ion and the amino acid charged group of opposite charge would become more pronounced as the hydrocarbon chain is extended.2784 AQUEOUS SOLUTIONS OF AMINO ACIDS We attempted to quantify this by transposing our results from the Lewis-Randall (LR) to the McMillan-Mayer (MM) scales,’-11 since the latter is more closely related to the potential of mean force between solute molecules.The coefficients on the two scales are related by (5) where the terms have their previously defined meanings. The transposition from the LR to the MM scale was performed using appropriate volumetric data 2 * 4 9 l2 and the MM coefficients are given in table 4. L(B&+,i+B&-,i) = 2(9,,+,, +gcl-,i)v:M;l + v~,cl+2v:-2RTK TABLE 4.-MM PARAMETERS FOR THE NaCl+Q,U)-AMINO ACID SYSTEMS amino acid(i) L(B;.+, i+B;l-,)/cm3 mol-1 experimental excluded volume glycine - 394+ 14 388 p-alanine - 41 5 22 464 y-aminobu t yric acid - 612+ 80 529 8-aminocaproic acid - 866+ 82 657 chemical 782 879 1141 1523 0.6 0.8 r( * I 2 3 1.0 8 g 1.2 +, a \ E a I + * z ld 3 I 1.4 I.6 I 2 3 4 5 number of C atoms in hydrocarbon chain FIG. 3.-“ Chemical ” contribution to the MM second virial coefficients for (a) a- and (b) a,w-amino acids as a function of the number of carbon atoms in the hydrocarbon chains. These MM coefficients may be considered to consist of two principal contribu- tions lo which may be designated as an “ excluded volume ” term and a “ chemical ” term. The former contribution arises from the fact that when two molecules interact,B .P. KELLEY AND T . H . LILLEY 2785 the closed electronic shells of the molecules induce a repulsion at short intermolecular separations. We have estimated the excluded volume terms using the same procedure as that used earlier,l by assuming the amino acids .could be represented as hard ellipsoids and the ions may be represented as hard spheres. (The precise shape assumed for the amino acids has only a small effect on the value obtained for the excluded volume term. This is consistent with earlier lo* l3 conclusions). The difference between the experimental MM term and the calculated excluded volume term we call the " chemical " term. Table 4 includes the values obtained for this term. In fig. 3 we compare the " chemical " contributions obtained for the upacids with those obtained for the a-acids.The gross feature of this figure is that whereas the interaction between the a-amino acids and the salt ions remain roughly constant, i.e. independent of the hydrocarbon chain length, the corresponding interactions with the up-acids increases markedly as the hydrocarbon chain is extended. This is broadly the feature observed and discussed above from a consideration of the LR coefficients. We investigated the possibility of quantifying the electrostatic contributions to the " chemical " term by using the procedures developed by Kirkwood.14* l5 The most suitable of the models investigated by him which could be applied to the present systems would be that in which the amino acids are approximated by prolate ellipsoids with opposite charges at the foci.We spent some time investigating models such as these and were rather disappointed to find that relatively small changes in the geometry and charge disposition of the amino acids lead to rather marked changes in the electrostatic contributions to the interaction coefficients. We concluded that whilst the general features observed experimentally for the free energy coefficients are reproduced, any application of such an approach in a quantitative sense is not worthwhile, particularly in view of the fact that the electrostatic approach fails badly for the corresponding enthalpy measurements. 6-1 We acknowledge financial support from the S.R.C. to B. P. K. B. P. Kelley and T. H. Lilley, Canad. J. Chem., accepted for publication. B. P. Kelley and T. H. Lilley, J.C.S. Faraday I, 1978,742771. R. M. Roberts and J. G. Kirkwood, J. Amer. Chem. SOC., 1942,64,513. T. H. Lilley and R. P. Scott, J.C.S. Faraduy I, 1976,72, 184. E. E. Schrier and R. A. Robinson, J. Biol. Chem., 1971,246,2870. A. M. Squires, Thesis (University of Cornell, 1947). W. G. McMillan and J. E. Mayer, J. Chem. Phys., 1945,13,276. H. L. Friedman, J. Solution Chem., 1972, 1, 387. R. H. Wood, T. H. Lilley and P. T. Thompson, J.C.S. Faraday I, 1978,74, 1301. lo J. J. Kozak, W. S. Knight and W. Kaumann, J. Chem. Phys., 1968,48,675. l 1 J. E. Garrod and T. M. Herrington, J. Phys. Chem., 1969, 73, 1877. l2 J. J. Kozak, Thesis (Princeton, 1965). l 3 A. Isahara, J. Chem. Phys., 1950, 18, 1446; 1951, 19, 397. l4 J. G. Kirkwood, Chem. Rev., 1939,24,233. l5 J. G. Kirkwood, inproteins, Amino-acidsandpeptides, ed. E. J. Cohn and J. T. Edsall (Reinhold, l6 B. P. Kelley and T. H. Lilley, J. Chem. Thermodynamics, 1978, 10, 703. l7 J. W. Larson and D. G. Morrison, J. Phys. Chem., 1976,80,1449. l9 J . W. Larson, W. J. Plymale and A. F. Joseph, J. Phys. Chem., 1977, 81,2074. New York, 1943), chap. 12. B. P. Kelley, T. H. Lilley, E. M. Moses and I. R. Taker, to be published. (PAPER 8/610)