Scientific paper
Osmotic Coefficient of Aqueous Solutions of Cyclohexylsulfamic Acid at the Freezing Point
of Solutions
Marija Bester-Rogac,1 Cveto Klofutar2 and Darja Rudan-Tasic2'3'*
1 Faculty of Chemistry and Chemical Technology,University of Ljubljana, SI-1000 Ljubljana, Slovenia.
2 Biotechnical Faculty, University of Ljubljana, SI-1000 Ljubljana, Slovenia.
3 Krog-MIT d. o. o., Trzaska 43, SI-1000 Ljubljana, Slovenia.
* Corresponding author: E-mail: darja.rudan.tasic@bf.uni-lj.si darja.rudan.tasic@krog-mit.com
Received: 18-03-2010
Abstract
The osmotic coefficient of aqueous solutions of cyclohexylsulfamic acid was determined by freezing point measurements up to the molality 0.65 mol kg-1. The osmotic coefficients were fitted to the Pitzer equation, and ion interaction parameters av P(0) and p(1) were evaluated. The mean ion activity coefficient of the solute was calculated, and the nonideal behaviour of the system investigated was characterized by calculation of the excess Gibbs energy of solution, as well as the respective partial molar functions of solute and solvent. The partial molar excess Gibbs energy of the solute is negative, like the excess Gibbs energy of its solution, while the partial molar excess Gibbs energy of the solvent is positive and increases with increasing concentration of the solute. The solvation ability of water was calculated from the difference between the Gibbs energy of solution of water in solution and that of pure water, and found to be positive and small for the solute investigated, throughout the concentration range studied.
Keywords: Osmotic coefficient, mean ion activity coefficient, cyclohexylsulfamic acid, aqueous solution
1. Introduction
The use of artificial sweeteners, which show greatly enhanced sweetness compared with sucrose and have very low caloric value, is steadily increasing.1 Non-nutritive sweeteners represent a large commercial market in the field of pharmaceutical compounds and bulk chemicals. Among them cyclohexylsulfamic acid and its sodium or calcium salts are one of the most widely used artificial sweetening agents in foods, beverages and pharmaceuticals.
Although no plausible explanation of the molecular mechanism of taste chemoreceptor has been found, several models were proposed to describe the sweetener-receptor interaction, e. g.2-4. The exceptional role of water in the sweetness mechanism which takes into account the solute-solvent interaction in aqueous solutions of sweete-
ners, as well as the effect of sweet molecules on water structure was first recognized by Mathlouthi et al.5 In the past many of solution properties of artificial sweeteners were used in interpreting the ease of accession of sweet molecules or ions to the receptor side. The hydrophilic and hydrophobic balance as well as steric factors in the molecules of sweeteners is thought to affect the mobility of water in the vicinity of the solute. From this point of view it is surprisingly enough, that the data about ther-mophysical and thermochemical properties of cyclohexyl-sulfamic acid (on the contrary of its sodium salt) are very scarce in the literature.6, 7 8 9 10 Therefore, we focused a part of our recent studies on cyclohexylsulfamic acid it-self.11, 12, 13, 14
A number of ionic interaction models provide the simples and most coherent procedure for calculating the properties of electrolyte compounds, e. g. Pitzer model,15
the Bromley model,16' 17 the NRTL model,18 and the SIT model.19 The Pitzer model yields an extended Debye-HUckel formula using a virial expansion to account for the ionic strength dependence of the short-range forces in binary and ternary ion interactions.
The purpose of this work was to obtain the Pitzer ion interaction parameters from osmotic coefficient data of aqueous solution of cyclohexylsulfamic acid at high concentration. The obtained parameters enable us to characterize the non-ideal behaviour of aqueous solutions of cyclohexylsulfamic acid by calculation of the excess Gibbs energy of the solution, as well as the difference in the Gibbs energy of solvation of water in the solution relative to pure water. In addition, this study represents a continuation of our previous work on this matter.11
2. Experimental
2. 1. Materials
Commercially available cyclohexylsulfamic acid (HCy) was purchased from Sigma. The compound was used as delivered without further purification and stored in a desiccator over P2O5. The purity of the acid was checked by titration with sodium tetraborate and also by analysis of the elements C, H and N (Perkin Elmer, 2400 Series II CHNS/O Analyser); it was found to be at least 99.9 % purity.
2. 2. Preparation of Solutions
The solutions investigated were prepared on a molal concentration scale (mol kg-1) by precise weighing with double distilled water, on a digital balance (Mettler Toledo, model AT201, Switzerland) that was accurate to within ±1 x 10-5 g. Before use, the solutions were degassed by ultrasound (ultrasonic bath, Bandelin Sonorex, type TK 52, Berlin, Germany).
2. 3. Freezing Point Measurements
The freezing point depression was measured with a Knauer cryoscopic unit (model 7312400000, equipped with a strip chart recorder, Knauer Model 733.41). The solvent and the solutions were supercooled and the formation of ice crystals was initiated by internal vibrations. The freezing-point depression was recorded as the difference in resistance of the thermistor, Ar (arbitrary scale) between solvent and solution. The reproducibility of these Ar measurements was better than 0.5 % of the measuring scale. The instrument was calibrated with sodium chloride solutions20 of accurately known molality over the same freezing-point range as for the solutions investigated, and the calibration was checked before and after each run. The freezing-point data of the sodium chloride solution were smoothed using the Lagrange interpolation method. The
following relationship was obtained: 6 = k • Ar, where 6 is the freezing point depression and k is the calibration constant. The overall accuracy of the freezing-point depression of sodium chloride solution was ±0.005 K.
3. Results and Discussion
The freezing-point depression data, 6 (K), given in Table 1, were used to calculate the osmotic coefficient on molality basis, <m, through the relation (1) where the higher terms were omitted due to the uncertainty of the osmotic coefficient:21
(1)
where MH20RT2m/AfusH6m = 1.8598 K kg mol-1, the ideal freezing point depression constant, v is the number of ions into which the electrolyte dissociates, and m (mol kg1) are the molalities of the aqueous solutions investigated. The osmotic coefficients <j)m are given in Table 1 and shown in Fig. 1 where <m is plotted against square root of the molality. The uncertainties of the osmotic coefficient, 8<m, were evaluated according to Eq. (2), and found to be smaller than 0.003.
(2)
Table 1. The freezing point data, osmotic coefficients and mean ion activity coefficients of aqueous solutions of cyclohexylsulfamic acid at the freezing point of the solution.
m (mol kg 1)	e(K)	( Tm	-ln Y±
G.G466	G.126	G.728	G.749
G.G999	G.247	G.665	1.G47
G.154G	G.37G	G.646	1.219
G.2G17	G.472	G.629	1.327
G.2649	G.6G6	G.615	1.437
G.3G43	G.688	G.6G8	1.495
G.3563	G.795	G.6GG	1.564
G.4G9G	G.9G1	G.592	1.629
G.459G	1.GG2	G.587	1.686
G.51G2	1.G94	G.576	1.743
G.568G	1.196	G.566	1.8G5
G.622G	1.3G6	G.565	1.861
From Table 1 and Fig. 1, it can be seen that the osmotic coefficients <m decrease with increasing molality. The cyclohexylsulfamic acid is a moderately strong acid with the dissociation constant of Ka = 0.0154 ± 0.0005 at 298.15 K and as such it was treated as 1:1 electrolyte.12 The adjustable parameters of the Pitzer equation,15 which for dilute aqueous solutions of 1:1 electrolyte takes the
Fig. 1: Osmotic coefficients (•) and mean ion activity coefficient (A) of aqueous solutions of cyclohexylsulfamic acid at the freezing point of the solution
form shown in Eq. (3), were fitted to experimentally obtained osmotic coefficients:


where:
y (A) _
(Ai)
m
1 + bm
and:

a),
(3)
(4)
(5)
In Eq. (4), A(^m) is the Debye-HUckel constant, and b is a parameter of 1.2 (kg mol-1)1/2 for aqueous solutions. The B(^m) term in Eq. (5) is a slowly varying function of molality that takes into account short-range ion-ion interactions. The parameter has an especially simple form having the desired general properties, namely it has a finite value at zero molality, a rapid change linear in m1/2 at low ionic strength and slow approach to an asymptotic value at high molality. The constant /5(0) in Eq. (5) is often correlated with structure-making and structure-breaking effects. The parameters /3(0\ /5(1) and a1 are obtained from experimental data.
In fitting procedures of osmotic coefficients with Eq. (3), we used a value of A^ = 0.37642 (kg mol-1)1/2 for the Debye-HUckel constant,22 and for a temperature independent parameter, b = 1.2 (kg mol-1)1/2, which was proposed by Pitzer15 for aqueous 1:1 electrolyte solutions. The following values were received for the parameters: £(0)= - (0.387±0.009) kg mol-1, £(1) = - (16.32±0.10) kg mol-1, and a1 = (6.484±0.005) (kg mol-1)1/2. The value of parameter a1 is substantially higher than 2.0, which
was the value used for simple 1:1 electrolyte solutions.23 As was pointed out by Pitzer,23 the value of parameter a1 may be adjusted for each substance, if desired.
It has been noted previously on the bases of our viscosity studies that cyclohexylsulfamic acid is a weak structure-maker14 and the results here agree. The negative value of /5(0) cyclohexylsulfamic acid (between the values of sodium saccharin and potassium acesulfame, both with evident structure-breaking effects24) merely confirms that it is necessary to assume incomplete dissociationof the acid14, 25 and that important structure differences exist among these large organic ions. In zwitterion form of cyclohexylsulfamic acid the balance between hydrophili-city, hydrophobicity, anionic and cationic characteristics ensures only weak net interactions to surrounding water. The dissociation process results in the disappearance of the zwitterion structure and formation of hydrogen and cyclohexylsulfamate ions; the latter was already found as positive-solvating ion (structure-making ion) from the volumetric properties,24, 26 opposite to the nitranions of saccharin (sodium salt) and acesulfame (potassium salt) which were classified previously as negative-solvating ions or structure-breaking ions.27 However, the observed difference in parameters /5(0) and ^(1) relative to other 1:1 electrolytes can be attributed by the incomplete dissociation of cyclohexylsulfamic acid in aqueous solution and by hydrophobic hydration. Very large values of parameter ^(1) were also found for some higher carboxylate salts such as sodium octanoate (-7.73638 kg mol-1), manoate (-10.3798 kg mol-1), and decanoate (-7.40138 kg mol-1).28 The high values observed were described to the well known tendency of these salts to form micellar aggregates, especially at higher concentrations. The overall quality of the fit was expressed as the corresponding standard deviation shown in Eq. (6):
(6)
s = ±	n ^ \ (^m /iexn't fimJtc&X) / i=1	2	1/2
	n		
where 0m,i(exp) and 0m,i(cal) denote the experimental and calculated osmotic coefficients, and n is the number of experimental data. The standard deviation of the fit amounts to ±0.008. It was shown by Marshall et al.28 that for a small molality range the experimental data by the Pitzer relation provides the best fit although the parameters obtained for small molality ranges do not necessarily result in good prediction at higher molality. They concluded that the Pitzer model does not appear to have good extrapolative capacity. Furthermore, the Pitzer model assumes the solution consists only of solvent, anions and cations. Incomplete dissociation, micellar aggregation or hydrolysis of electrolyte solutes are left out of account.
The mean ion activity coefficient of the solute, y±, was calculated from Eq. (7):15
\nr± = f(j) + mB(j) where:
yO) _
m1'2 2 - +
1 + bm112 b
-ln(l + W/2)
(7)
(8)
and:
B(r) = 2/?(0) +
(9)
The calculated values of ln/± are given in Table 1 and shown as y± in Fig. 1.
The non-ideal behaviour of the aqueous solutions of cyclohexylsulfamic acid was further characterized by the excess Gibbs energy of solution, GE. From the mean ion activity coefficient and osmotic coefficient, the excess Gibbs energy of solution per kilogram of solvent is given by Eq. (10):15' 23 29
GE =2mRT (I-<j>m+\ny±) =
(10)
where:
and:

a~m L	'
(l + a,mV2)
(11)
(12)
The calculated values of GE are given in Table 2. The values of GE are negative and show the same tendency for non-ideal behaviour as the osmotic and mean ion activity coefficient. The negative sign of the excess Gibbs energy may come from non-structural interactions, through hydrophobic interactions which are largely responsible for this behaviour.
The excess Gibbs energy of solution can also be given by Eq. (13):29

(13)
where n1 represents the number of moles of solvent per kilogram of solvent, Gf (J mol-1) is the partial specific excess Gibbs energy of the solvent, and Gf (J mol1) is the partial molar excess Gibbs energy of the solute. Gf can be calculated according to Eq.(14):29, 30
Table 2. Excess Gibbs energies of solution, partial specific excess Gibbs energies of the solvent and the solute, and the differences in the Gibbs energy of solvation of water molecules at the freezing point of the solution.
m (mol kg-1)	-Ge (J kg-1)	"iGE (J kg-1)	-mGE (J kg-1)	AAG* (J mol-1)
0.04655	101	55.5	158	5
0.09987	323	150	474	17
0.15403	602	250	852	30
0.20173	878	339	1214	41
0.26492	1274	461	1725	56
0.30426	1535	538	2061	65
0.35631	1895	644	2627	77
0.40904	2276	755	3122	90
0.45895	2649	860	3503	101
0.51019	3046	977	4023	113
0.56796	3508	1116	4635	127
0.62201	3954	1221	5232	139
(14)
and GE according to Eq. (15):
Gf = 2MxmRT (l - <f)m ) = -2MxmRT [ /

+ mB

(15)
where M1(g mol1) is the molar mass of the solvent. The values of the products n1Gf and mGf are given in Table 2. As can be seen the Gf values are negative, like GE, i.e. they decrease with increasing concentration of the solute; in contrast, the n1Gf values are positive, and increase with increasing concentration of the solute. Cyclohexylsulfa-mic acid can exist in aqueous solution as a neutral molecule or in the zwitterionic form.12' 31 The positive value of the product n1Gf can be ascribed to the hydrophobic sol-vation of solute molecules. The negative sign of the product mGf comes from non-structural interaction and hydrophobic interaction of zwitterionic structure with solvent molecules.
Some information about the solvation ability of water can be obtained by the approach of Ben-Naim.32 According to this theory, the difference in the Gibbs energy of solvation of water molecules in solution relative to pure water, AAG! (J mol-1), is given by Eq. (16):
(16)
where AG^1 and AG^ are the Gibbs energy of solution l relative to that of pure water p, px is the number density of water in a pure solvent (molecules/cm3), pl1 is the number density of water, and ax is the activity of water in solution. The term pp/p1was obtained through the respective densities and expansibility of water33 and aqueous solution of
cyclohexylsulfamic acid.13 The values of ln ax were calculated from Eq. (17):
lnöj = -vmMx(f)m	(17)
where v = 2. The calculated values of AAG* (J mol-1) are given in Table 2. From Table 2 and Fig. 2, it follows that the AAG1 values are positive and small, and increase with increasing concentrations of the solute. It is interesting to note that AAG1 values of some strong acids, e. g. hydrochloric acid are small and negative.30 Contrary, values of AAG1 of aqueous solutions of sucrose and glucose are positive and high.30
According to Ben-Naim,32 it is not possible to state categorically whether the observed effects on AAG1 are due to direct solute-solvent interactions or to indirect changes in the structure of the solvent environment that are induced by the addition of the solute. Since the AGlP of water as a pure liquid at 0 °C is negative, AG^ = — 27.792 kJ mol-1,32 we can conclude that the addition of cyclohexylsulfamic acid makes the Gibbs energy of solvation of water in solution, AG^1, less negative than in pure water. The major reason for this appears to be the overall weakening of the average binding energy of water molecules to their surroundings when cyclohexylsulfamic acid is added to the solvent.
	160
	140
	120
o	100
a	
—-	80
	
ef	
<	60
<	
	40
	20
0.0	0.2	0.4	0.6	0.8
m 12 / (mol-kg"1)1'2
Fig. 2: Concentration dependence of the Gibbs energy of solvation of water molecules in solution relative to pure water, AAG^, for aqueous solution of cyclohexylsulfamic acid at the freezing point of solution
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Povzetek
Na osnovi znižanja zmrzišča smo določili osmozni koeficient vodnih raztopin cikloheksilsulfaminske kisline. Koncentracijsko odvisnost osmoznega koeficienta smo izrazili s Pitzerjevo enačbo in ovrednotili interakcijske koeficiente a^, j8<0) and j8(1). Neidealno obnašanje vodnih raztopin cikloheksilsulfaminske kisline smo okarakterizirali s presežno Gibb-sovo energijo raztopine, topljenca in topila ter pojasnili z nepopolno disociacijo in hidrofobno hidratacijo topljenca.