274 Acta Chim. Slov. 2006, 53, 274–283 Scientific Paper Apparent Molar Volume and Apparent Molar Expansibility of Sodium Saccharin, Potassium Acesulfame and Aspartame† Cveto Klofutar, Jaka Horvat and Darja Rudan-Tasič Biotechnical Faculty, University of Ljubljana, Jamnikarjeva 101, 1000 Ljubljana, Slovenia E-mail:darja.rudan.tasic@bf.uni-lj.si Received 17-05-2006 Dedicated to the memory of Prof. Dr. Davorin Dolar Abstract The apparent molar volume of sodium saccharin, potassium acesulfame and aspartame was determined from the density data of their aqueous solutions at 293.15, 298.15, 303.15, 313.15, 323.15 and 333.15 K. Solutions of sodium saccharin and potassium acesulfame were treated as 1:1 strong electrolyte, while aspartame was considered as a non-electrolyte. From the apparent molar volume, determinated at various temperatures, the limiting apparent molar expansibility was calculated. The limiting apparent molar volume and expansibility of ionic solutes were divided into their ionic components and discussed in terms of the various effects of the ion in solution on the structure of water. The limiting apparent molar volume of aspartame was discussed in terms of the scaled particle theory. The density of the investigated aqueous solutions can be adequately represented by an equation derived by Redlich. The coefficients of thermal expansion of the investigated solutions at 298.15 K were calculated and are presented graphically. The thermal expansion coefficient, d defined as a = 1/ V2°4 (dV^ I dT) and their temperature dependence was estimated. It was shown that d of electrolyte solutes is greater than that of aspartame and that d of ionic solutes decreases linearly with increasing temperature, while d of aspartame shows a slight increase with temperature. The limiting apparent molar volume and expansibility were correlated with the relative sweetness of the sweeteners investigated and some other alternatives. Key words: density data, expansibility, sweeteners, aqueous solutions 1. Introduction The volumetric behaviour of electrolyte and non-electrolyte solutions can provide useful information regarding solute-solvent and solute-solute interactions. Of particular relevance is the nature of the interactions of water with solute species, especially with ions possessing non-polar groups which effect the structural properties of water. Therefore the apparent and partial molar volumes and expansibilities of solute have proven to be very useful tools in elucidating the structural interactions occurring in solution, e. g. 1, 2 Among many sweeteners currently approved as food additives, sodium saccharin, saccharin-Na (2,3-dihydroxo-3-oxobenzisosulfonazole-Na salt), potassium acesulfame, acesulfame-K (6-methyl-1,2,3-oxathiazine-4-(3H)-one-2,2-dioxide-K salt) and aspartame (N-L-a-asparyl-L-phenylalaline-1-methyl ester) have received wide commercial use in the food industry.3 The alkali salts of saccharin are of special interest because of their pronounced solubility in water in comparison with saccharin. From the structural point of view, the saccharin nitranion has attracted appreciable scientific attention. Both nitranions of saccharin and acesulfame feature the sulfocarboximide moiety and thus three different groups, imino, sulfonyl and carbonyl, connected to each other. Aspartame, as dipeptide, contains structural elements such as a peptide bond, a charged zwitterionic group, a phenyl and an acetyl group which interact with water in different fashions. Therefore, the interactions of nitranions of saccharin and acesulfame and the molecule of aspartame with water molecules proceed as a subtle balance between the hydrophobic and hydrophilic characteristics of the mentioned groups. The partial molar and apparent specific volumes of various solutes have been used in assessing drug potency and in sweet taste chemoreception. In the past volumetric parameters were measured especially as a parameter to describe solute-water interactions in sweet-taste chemoreception. These results are limited to two temperatures, namely at 293.15 and 298.15 K and at a definite concentration.4-10 In this paper we report results of the experimental determination of Klofutar et al. Volume and Expansibility of Saccharine, Acesulfame and Aspartame Acta Chim. Slov. 2006, 53, 274–283 275 the apparent molar volumes and expansibilities of saccharin-Na, acesulfame-K and aspartame over a broad range of concentration and in the temperature range from 293.15 to 333.15 K. Aqueous solutions of saccharin-Na and acesulfame-K were treated as 1:1 electrolyte solutions, while aqueous solution of aspartame as a non-electrolyte solution, despite the fact that aspartame exists as a dipolar ion.11-13 2. Results and Discussion The values of density, d(g-cm-3), measured at various temperatures as a function of molality, m(molkg-1), are given in Table 1. The apparent molar volume, F24(cm3mol-1), of a solute with molar mass, M2(g-mol-1), is given by14 2, of acesulfame-K can be adequately represented without parameter Dv. In calculation of the parameters of Eq. (3), the coefficient Av, taken from ref.16, was divided by the square root of The calculated density, using the relations (5) and (6), are within 2.1x10-5, 1.2x10-5 and 0.5x10-5 g-cm-3 equal to the experimental values given in Table 1 for saccharin-Na, acesulfame-K and aspartame, respectively. The apparent molar volume or the apparent specific volume of the investigated compounds have also been measured previously, e. g.4-10 However, these results are confined to only two temperatures, namely 293.15 and 298.15 K, and at infinite dilution or at a specific concentration. Comparison of the apparent molar volumes at 293.15 and 298.15 K obtained in this work with those reported in the literature is shown in Table 3. Our values were calculated using relation (3) or (4) and the appropriate parameters from Table 2. The difference between the literature values of Vllb for acesulfame-K and ours is reasonable; and the differences for aspartame are more or less satisfactory, occasionally exceeding 2-3 cm3-mol-1. There are also great differences within the literature data for aspartame, e. g. between 206.044 and 212.46 cm3mol-1.6 The published data for V2SS> of saccharin-Na are higher than ours, except for the value of 106.7 cm3mol-1.4 Such differences may be ascribed to the substances used, especially those containing crystalline water. Klofutar et al. Volume and Expansibility of Saccharine, Acesulfame and Aspartame 276 Acta Chim. Slov. 2006, 53, 274–283 Table 1. Density of aqueous solutions of saccharin-Na, acesulfame-K and aspartame from 293.15 to 333.15 K. m (mol?kg-1) d (g?cm-3) at T (K) 293.15 298.15 303.15 313.15 323.15 333.15 Saccharin-Na 0.05255 1.00305 1.00184 1.00039 0.99687 8.99262 0.10505 1.00786 1.00658 1.00507 1.00146 0.99713 0.10514 1.00787 1.00660 1.00510 1.00149 0.99716 0.12605 1.00977 1.00847 1.00695 1.00331 0.99895 0.17413 1.01408 1.01273 1.01116 1.00743 1.00301 0.20229 1.01658 1.01520 1.01361 1.00984 1.00538 0.21499 1.01771 1.01631 1.01469 1.01089 1.00640 0.22767 1.01884 1.01743 1.01581 1.01199 1.00750 0.25514 1.02124 1.01981 1.01816 1.01430 1.00976 0.30220 1.02536 1.02387 1.02218 1.01824 1.01364 0.35697 1.03007 1.02852 1.02677 1.02274 1.01807 0.40485 1.03410 1.03250 1.03072 1.02661 1.02187 0.41338 1.03487 1.03326 1.03147 1.02736 1.02261 0.45701 1.03856 1.03691 1.03508 1.03089 1.02604 0.50658 1.04264 1.04094 1.03906 1.03479 1.02992 0.50878 1.04284 1.04115 1.03928 1.03501 1.03014 0.61330 1.05129 1.04949 1.04752 1.04310 1.03810 0.70799 1.05882 1.05694 1.05489 1.05033 1.04521 0.79997 1.06588 1.06392 1.06180 1.05712 1.05190 0.93037 1.07569 1.07363 1.07142 1.06657 1.06120 0.99524 1.08040 1.07830 1.07604 1.07112 1.06569 1.15241 1.09150 1.08928 1.08691 1.08180 1.07621 1.29500 1.10108 1.09875 1.09630 1.09103 1.08531 m (mol?kg-1) d (g?cm-3) at T (K) 293.15 298.15 303.15 313.15 323.15 333.15 Acesulfame-K 0.98772 0.05017 0.99216 0.10426 0.99219 0.20672 0.99396 0.30185 0.99796 0.40251 1.00030 0.50031 1.00131 0.60021 1.00239 0.69808 1.00462 0.79783 1.00845 0.89698 1.01283 1.01657 0.01043 1.01729 0.01474 1.02072 0.01982 1.02450 0.02532 1.02472 0.03137 1.03257 0.03546 1.03959 0.04097 1.04619 0.04597 1.05537 0.05042 1.05980 0.05505 1.07018 0.06140 1.07917 0.06764 1.00291 1.00170 1.00026 0.99674 0.99250 0.98761 1.00790 1.00665 1.00514 1.00155 0.99723 0.99228 1.01718 1.01582 1.01424 1.01049 1.00604 1.00098 1.02556 1.02410 1.02244 1.01855 1.01399 1.00883 1.03425 1.03271 1.03097 1.02693 1.02225 1.01699 1.04246 1.04083 1.03901 1.03484 1.03005 1.02470 1.05068 1.04897 1.04707 1.04278 1.03788 1.03243 1.05852 1.05673 1.05477 1.05036 1.04535 1.03982 1.06635 1.06450 1.06247 1.05793 1.05282 1.04720 1.07395 1.07203 1.06993 1.06528 1.06008 1.05437 Aspartame 0.99903 0.99786 0.99646 0.99301 0.98882 0.98396 0.99937 0.99820 0.99679 0.99334 0.98914 0.98428 0.99977 0.99859 0.99718 0.99372 0.98952 0.98465 1.00021 0.99903 0.99761 0.99414 0.98993 0.98505 1.00068 0.99950 0.99808 0.99460 0.99038 0.98549 1.00100 0.99981 0.99839 0.99490 0.99067 0.98579 1.00144 1.00024 0.99880 0.99530 0.99107 0.98618 1.00182 1.00062 0.99919 0.99569 0.99145 0.98654 1.00214 1.00097 0.99953 0.99603 0.99178 0.98686 1.00255 1.00133 0.99989 0.99636 0.99211 0.98720 1.00306 1.00183 1.00038 0.99684 0.99258 0.98765 1.00355 1.00231 1.00085 0.99730 0.99303 0.98809 Table 2. Limiting apparent molar volume, V,0«, Debye-Hückel limiting law slope, A, deviation constants Bv and Dv, and standard error of estimate, S, of saccharin-Na (Sac-Na), acesulfame-K (Acs-K) and aspartame (Asp) in aqueous solution at the indicated temperature. Solute T (K) 293.15 298.15 303.15 313.15 323.15 333.15 Sac -Na V2

is negative due to the shrinking of cavities caused by intramolecular attraction forces in the liquid. Thus the cavity volume was calculated by30 PTRT y ! 3yz (l + z ) | 9y2z2 , n=a0+a1(T-To) + a2(T-To (17) where a0, a1 and a2 are empirical constants depending on solute and solvent, and To=298.15 K. Eq. (17) is quadratic and consistent with the volumes going through a maximum; the latter behaviour is characteristic of most salts that have been studied in aqueous solution, as shown by Helgeson and Kirkham.32 The values of the constants of relation (17) are given in Table 5 together with the standard error of the estimate. From relation (17) it follows that within our rather limited temperature range &°E is a linear function of temperature and that 0°E=at at 298.15 K. The limiting apparent molar expansibility at other temperatures studied are given in Table 6. From these results it is apparent that &°E for both electrolytic solutes decreases with increasing temperature, while for aspartame the reverse was observed. The partial molar expansibility of aspartame at 298.15 K is greater than that of diglycine which amounts to (0.115+0.015) cm3mol-1K-1. The &°E values of diglycine also decrease with increasing temperature.33 The fact that &° is a linear function of temperature with a negative coefficient for the temperature term (-0.0027 and -0.0028 for saccharin-Na and acesulfame-K) means that the second derivative of V^ with respect to temperature is also negative. As Hepler34 has pointed out, d2V° dT2 JP dAC° _________P dP (18) Jt and a positive value of dAC° I dT is evidence that the investigated ionic solutes behave as structure breaking solutes in water over the experimental temperature range studied. On the other hand, aspartame with a small but negative value of d^C° / dT may be regarded as a structure making solute in water. Table 5. Values of the constants ai of relation (17) and standard error of estimate, s. Solute 0 *\ 2 Saccharin- 113.16±0.03 0.2092±0.04 -0.00133±0.0001 0.026 Na Acesulfame- K Aspartame 216.31±0.05 0.1742±0.009 0.00019±0.0001 0.084 107.60±0.02 0.1948±0.003 -0.00139±0.0001 0.036 As for the limiting apparent molar volume, the limiting apparent molar expansibility of ionic solutes permits us to calculate the limiting partial molar expansibility of the individual ions by dividing the ° o 2,E E2 = nhEh - Ei (21) whereEh=ldVh/dT\ and E° =ldV°/dT\ are the partial molar expansibilities of water in the^hydration shell of the solute (Eh) and the bulk state (Ei). Thus, from relation (21) it is possible to calculate the difference in the expansibility of water in the hydration shell and in the bulk state from the known hydration number. The hydration number of aspartame, nh= 17.68, was estimated at 293.15 K.6 From Eq. (21) it follows that the difference (Eh-Ei) is 0.0097 cm3mol-1-K-1. The expansibility of bulk water at 293.15 K, E\ =a0V\, was calculated from the density and expansibility of water,17 and amounts to 0.003732 cm3mol-1K-1. So, the expansibility of water in the hydration shell of aspartame is 0.0135 cm3mol-1K-1 which is considerably greater than that in pure water. From this it follows that water molecules in the hydration shell are less tightly bound than in the bulk state, since water molecules are under the influence of the strong electrostatic field in the vicinity of charged groups.37 The coefficient of thermal expansion of solutions, (K1), is defined by the relation dd ' (22) a =- 1- dT For the investigated electrolyte solutions oc (K1) can be calculated from relation (23) as a function of concentration in the following form14 a = a„ ¦ay: 1000 -a0A 1000 a0Bv 1000 a0Dv 1000 (23) where a0 (K1) is the coefficient of thermal expansion of pure water and AE = {dAJdT)p. The coefficient of the c3/2 term according to the theory of Debye-Hückel is common to all strong electrolytes of the same valence type in a given solvent at definite temperature. At 298.15 K its value for a 1:1 electrolyte amounts to 1.710x10-5 cm3-L1/2-K-1. On the other hand, the coefficients of the c, c2 and c5/2 terms are characteristic of a given solute. In the calculation of a we used a0 value given by Kell,17 Klofutar et al. Volume and Expansibility of Saccharine, Acesulfame and Aspartame Acta Chim. Slov. 2006, 53, 274–283 281 and for AE a value of (0.01757±0.00005) cm3?L1/2?mol-3/2?K-1 obtained from the temperature dependence of Av values.16 The last term of relation (23) was omitted in calculation of ? for acesulfame-K. Fig. 1 shows the dependence of the coefficient of thermal expansion on the square root of concentration, c1/2 (mol?L-1)1/2 at 298.15 K for aqueous solutions of some sweeteners, such as saccharin-Na acesulfame-K and cyclohexylsulfamate-Na.36 From Fig.1 it can be seen that the coefficient of thermal expansion increases with increasing concentration and that ? of an aqueous solution of saccharin-Na at definite concentration is higher than that of acesulfame-K and that the latter is higher than that of cyclohexylsulfamate-Na. 4 .0 3 .8 3 .6 3.2 0 2 .8 2 .6 Figure 1. Coefficient of thermal expansion of aqueous solutions of saccharin-Na, acesulfame-K and cyclohexylsulfamate-Na at 298.15 K. The density of an aqueous solution of aspartame at a given temperature can be fitted to an equation of the type d = d A1c (24) where d0 is the density of pure water17 and A1 is a coefficient which depends on solute, solvent and temperature. The least-squares values of the coefficient A1 are listed in Table 7 together with the standard error of estimate, s. Table 7. Coefficient A1 of relation (24) and standard error of the estimate, s, at the indicated temperatures. T(K) A^ (g-L mol" cm" ) sxlO 293.15 0.07978 3 298.15 0.07890 2 303.15 0.07825 2 313.15 0.07692 2 323.15 0.07595 2 333.15 0.07476 0.9 The coefficient of thermal expansion of an aqueous solution of aspartame was obtained by differentiating the expression for density (24) with respect to temperature at constant pressure and molality, and by dividing the obtained derivative with d. The following relation results a = a0-bc (25) where b1=(dAl/dT)-(\/do). The dependence of the coefficient A 1 of Eq.(24) on temperature was expressed by a relation identical to (17) and for dAx IdT a value of -(1.444+0.087)x10-4 gLmol1cm-3K-1 at 298.15 K was estimated. The value of b1 amounts to -(1.448±0.087)x10-4 L-mol-1- K-1. Owing to the low solubility of aspartame in water, the coefficient of thermal expansion of its aqueous solution at the highest concentration studied is only 2.668x10-4 K1, which is about four percent higher than that of pure water.17 The thermal expansion coefficient, «'(K1), defined as38 a 1 Vo dV° (26) JP was calculated for the investigated solutes and sodium cyclohexylsulfamate.36 The results are collected in Table 8. Analysis of these data shows that values of d of electrolyte solutes are greater than that of aspartame, which behaves as a non-electrolyte. Furthermore, the d values of ionic solutes decrese linearly with increasing temperature with dd/dT= -2.52x10-5, -2.73x10-5 and -1.50x10-6 K2 for saccharin-Na, acesulfame-K and Na-cyclohexylsulfamate, respectively, while d of aspartame shows a slight linear increase with temperature with dd/dT= 1.01x10-6 K2. The values of a*of the investigated ionic compounds are comparable with d values of inorganic salts such as ammonium chloride, ammonium acetate or ammonium propionate, which decrease with increasing temperature.38 On the contrary, d of aspartame is lower than that of diglycine and triglycine; this dipeptide and tripeptide also show a negative value of dd I dT.38 The complexity of the d functions highlights the strong dependence of the expansibility upon structure features, such as electrical charge, size, type of ion, as well as the relative proportions of the hydrophilic or hydrophobic parts of the molecule. Table 8. Thermal expansion coefficient, a" (rel. 26) of saccharin-Na, acesulfame-K, aspartame and Na-cyclohexylsulfamate10 at the indicated temperatures. Compound OC xlO3 at T(K) 293.15 298.15 303.15 313.15 323.15 333.15 Saccharin-Na 1.99 1.85 1.72 Acesulfame-K 1.96 1.81 1.67 Aspartame 0.80 0.81 0.81 Cyclohexyl-sulfamate-Na 1.46 1.22 0.98 1.39 1.12 0.86 0.82 0.83 0.84 1.24 1.24 1.23 1.21 1.20 3 A 0 .1 3 .2 0 .3 0.4 0 .5 3 .6 3 .7 3 .8 3 .9 c1 /2 (m o l.L -1)1 /2 Klofutar et al. Volume and Expansibility of Saccharine, Acesulfame and Aspartame 282 Acta Chim. Slov. 2006, 53, 274–283 Because apparent molar volumes and apparent molar expansibilities provide an important insight into the interactions of sweet solutes with water and perturbation effects on the structure of water, we correlated these parameters with the relative sweetness, RS, of the sweeteners investigated and some other alternatives (Table 9). The following equation, which relates log RS to V^ and <&lE, was derived : logRS = (l.47 + 0.6l)xl0-3V2°o+(l.8 + 0.5)