J. Phys. Chem. B 2000, 104, 9505-9512
9505
Ionic Interactions in Aqueous Mixtures of NaCl with Guanidinium Chloride: Osmotic Coefficients, Densities, Speeds of Sound, Surface Tensions, Viscosities, and the Derived Properties Anil Kumar† Physical Chemistry DiVision, National Chemical Laboratory, Pune 411 008, India ReceiVed: May 23, 2000; In Final Form: July 25, 2000
The isopiestic osmotic coefficients, densities, and speeds of sound of aqueous mixtures of NaCl with guanidinium chloride (GnCl) have been measured at different ionic strengths with varying compositions at 298.15 K with a view to determine the ionic interactions. The excess free energy, ∆mGE, volume, ∆mVE, and compressibility of mixing, ∆mKE, of the NaCl-GnCl mixtures at constant ionic strength show interesting features with changing ionic strength fractions of the electrolytes. These excess properties of mixing with both negative and positive signs can be attributed to the mixing of hydrophilic and hydrophobic ions. It is shown that the binary and ternary interaction terms play an important role in the accurate representation of the osmotic coefficients, activity coefficients, volumes, and compressibilities of the mixtures. Measurements on the surface tension and viscosity of the NaCl-GnCl mixtures have also been reported. A simple equation incorporating like charge interactions has been employed to correlate the surface tension of the mixtures. The mixture viscosities have also been estimated from the parameters of pure NaCl and GnCl with an empirical mixing rule.
Introduction Guanidinium hydrochloride (abbreviated as GnCl) is one of the most effective denaturants of the biological macromolecules, such as proteins and nucleic acids, while NaCl is known to stabilize their structures.1 It has been shown that the stabilizing effect of GnCl on the protein structure can be reverted by adding NaCl to the system.2 Similarly NaCl and GnCl can accelerate or retard the reaction profiles of the Diels-Alder reactions.3 The rate-retarding tendency of GnCl can be weakened substantially on the addition of NaCl.3f We were intrigued to note the combined role of Na+ and Gn+ on the stability of the proteins and the reaction kinetics of the Diels-Alder reactions. A competition between Na+ and Gn+ is perhaps responsible for such behavior. To obtain a deeper understanding of how these cations influence the behavior of biomolecules and reactivities in organic reactions, it is essential to study the ion-water and ion-ion interactions in the aqueous mixtures of NaCl and GnCl at different concentrations. Unfortunately, thermodynamic and other physicochemical studies on the aqueous mixtures of NaCl and GnCl are not available in the literature despite their applications in the above-mentioned areas. It is with this view we set out to investigate the isopiestic osmotic coefficients, densities, and ultrasonic sound speeds, surface tension, and viscosities of aqueous NaCl-GnCl solutions. The osmotic coefficients, derived activity coefficients therefrom, and volumetric properties are chosen in this study, as they offer direct information on the ionic interactions. Our experimental data on the isopiestic osmotic coefficients, surface tension, and viscosities are collected up to a maximum ionic strength, I, of mixtures of 4 mol kg-1 of water, whereas the densities and speeds of sound are collected up to I ) 2 mol kg-1 of water, all at 298.15 K. The experimental data and the †
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derived properties are analyzed to give information on the ionic interactions in the systems. This paper appears to be first complete investigation of the thermodynamic, volumetric, surface, and transport properties of the NaCl-GnCl system. Experimental Section NaCl (AR grade from Aldrich Chemical Co.) was used after being dried in an oven. GnCl from the same source was recrystallized from water several times and dried over P2O5. The concentration of NaCl was measured by its titration against AgNO3. The purity and concentration of GnCl were determined by the method of Nozaki.4 The isopiestic measurements were made in an apparatus similar to that described by Rard et al.5 Aqueous KCl was taken as a reference electrolyte, the osmotic coefficients of which were taken from a data source and the corrections described elsewhere.6 All the solutions were prepared by weight in deionized water and converted into mass. The molar masses used in the calculations were 74.551, 58.443, and 95.530 g mol-1 for KCl, NaCl, and GnCl, respectively. To handle both the dilute and concentrated solutions, two different stock solutions of KCl were prepared following the procedure of Rard et al.5 and Rard and Spedding.7 The molalities of aqueous KCl were determined by dehydrating duplicate samples. A period of 5 days was required for attaining the isopiestic equilibrium for the mixtures with ionic strength of 1 mol kg-1 and above. In the case of mixtures with ionic strength 0.5 mol kg-1, 8 days were noted to be sufficient for reaching the equilibrium. An average of two samples was considered as a final isopiestic molality. The agreement between two molaities was recorded as 0.08%. The comments of Rard and Platford8 were considered while the errors in the experimental data were analyzed. The densities of the solutions were measured with a pycnometer having a volume of 50 × 10-3 m3 with a precision of
10.1021/jp001893k CCC: $19.00 © 2000 American Chemical Society Published on Web 09/15/2000
9506 J. Phys. Chem. B, Vol. 104, No. 40, 2000
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TABLE 1: Osmotic Coefficients, φ, of Aqueous NaCl-GnCl Mixtures as a Function of the Ionic Fraction of NaCl, y1, at Different Ionic Strengths and at 298.15 K I/(mol kg-1)
y1
φ
I/(mol kg-1)
y1
φ
4.0152 4.0085 3.9925 4.0050 3.9885 4.0008 2.9957 3.0111 3.0085 3.0501 2.9986 3.0054 2.0101 1.9978 1.9902 2.0054 1.9992
0 0.1489 0.3506 0.5511 0.8008 1 0 0.1958 0.4018 0.5959 0.7845 1 0 0.2482 0.5017 0.7448 1
0.688 0.748 0.834 0.924 1.030 1.116 0.707 0.768 0.836 0.904 0.981 1.045 0.743 0.801 0.858 0.924 0.983
0.9958 0.9980 1.0101 1.0088 0.9970 0.5057 0.4985 0.4905 0.5099 0.4949 0.5027
0 0.2892 0.6060 0.8994 1 0 0.1985 0.3972 0.5953 0.7941 1
0.801 0.836 0.878 0.922 0.936 0.849 0.858 0.876 0.892 0.906 0.920
(0.005%. The pycnometer was calibrated9 against the densities of aqueous NaCl with an accuracy of 0.01%. Ultrasonic sound speeds in the solutions were measured using a microprocessor-controlled single-crystal interferometer at a constant 4 MHz frequency. The interferometer was calibrated10 with aqueous NaCl solutions with an accuracy of 0.1%. An average of 10 readings was recorded as the final experimental value. Periodic checks on the calibration were made throughout the time of the measurements. The experimental sound speeds were precise to 0.02%. The surface tension values of the solutions were measured using a Traube stalagmometer as described by Vazquez et al.11 The stalagmometer was calibrated with carbon tetrachloride and water12 with an accuracy of 0.02 × 10-3 N m-1. The estimated precision based on triplicate measurements was better than 0.5%. The viscosities were measured with an Ubbelhode suspendedlevel viscometer as described by Pal and Singh.13 The viscometer was calibrated with aqueous KCl solutions at 298.15 K. The viscosities were accurate to within 1%. The precision of the viscosity measured in triplicate was 0.25%. A constant-temperature bath (Julabo) with an accuracy of 0.005 K was used for maintaining the temperature. Mole fractions were accurate to 2 × 10-4. Throughout the paper, the subscripts 1 and 2 refer to NaCl and GnCl, respectively. Results and Discussion First we discuss the results on the osmotic coefficients of the mixtures. In Table 1 are given the osmotic coefficients, φ, of the aqueous NaCl-GnCl mixtures as a function of the ionic strength fraction of NaCl, y1 (y1 ) m1/(m1 + m2); y2 ) 1 - y1) at different ionic strengths. The ionic strength, I, is given by 0.5∑mizi2, zi being the ionic charge. In this case, I ) m1 + m2 ) mT, the total molality. The φ values for pure NaCl and GnCl solutions are in excellent agreement (root-mean-square deviation, rmsd, 0.004 and 0.006 for NaCl and GnCl, respectively) with those reported in the literature.14-17 Makhatadze et al.18 have calculated the activity coefficients from their measurements on partial molal enthalpies of aqueous GnCl solutions. The osmotic coefficients for pure GnCl obtained by us, Bonner,15 Shrier and Shrier,16 and Macaskill et al.,17 however, do not agree with those calculated from activity coefficients by Makhatadze et al.18 It is noted that the φ values of pure NaCl increase with the increase in concentration, while in the case of pure GnCl, a monotonic decrease in the φ values with concentration is seen.
Figure 1. Osmotic coefficients, φ, as a function of the ionic strength fraction, y1, for the aqueous NaCl-GnCl system at 298.15 K: (2) I ) 4 mol kg-1; (0) I ) 3 mol kg-1; (O) I ) 2 mol kg-1; (9) I ) 0.5 mol kg-1. The solid lines are calculated by the Pitzer equations.
For the pure electrolytes, the φ-m curves are located in two different directions. It is thus interesting to examine the φ-y1 plots at constant ionic strengths of the mixture. This is shown in Figure 1, where these plots at different ionic strengths cross each other. First, we analyze the mixture φ values by the specific interaction theory of Pitzer19 and Pitzer and Kim20 with an objective to extract information on the ionic interactions. The relevant Pitzer equations simplified for the mixture of 1:1 electrolytes with a common anion are listed in Table 2 for convenience. The Pitzer equations are essentially comprised of the long-range interaction forces described by the DebyeHuckel term, f φ, and the short-range interactions in the form of virial coefficients, β(0), β(1), and Cφ. The interactions between Na+ and Gn+ are characterized by a binary interaction term denoted by θNaGn. Similarly, ternary interactions involving Na+, Gn+, and Cl- are denoted by ψNaGnCl. We calculated the φ of mixtures by using eqs 1-3 given in Table 2 and the Pitzer coefficients for pure NaCl and GnCl from a compilation of Kim and Frederick.21 The values for NaCl are β(0) ) 0.077 22, β(1) ) 0.251 83, and Cφ ) 0.001 06 with an rmsd of 0.001 in φ for the pure NaCl fit. In the case of GnCl, these values are β(0) ) - 0.028 55, β(1) ) -0.109 97, and Cφ ) 0.001 77 with an rmsd of 0.005 in φ. It is important to point out the importance of mixing terms in the present case. The calculation of φ of the mixtures with pure electrolyte parameters shows large deviations from the experimental ones. The mixing terms θNaGn and ψNaGnCl were, therefore, evaluated from a common least-squares fitting program as suggested by Pitzer and Kim.20 The values of θNaGn and ψNaGnCl were noted as 0.019 and -0.005. The incorporation of θNaGn and ψNaGnCl terms in the calculations yields excellent agreement between the experimental and calculated φ of the mixtures. The average rmsd value with both mixing terms calculated from I ) 0.5 mol kg-1 to I ) 4 mol kg-1 of water is estimated as 0.008 in osmotic coefficients. The solid lines plotted in Figure 1 indicate the calculated φ of mixtures with the mixing terms. Remarkable improvement in the correlation of φ data with the use of the mixing term highlights the importance of the interactions of binary and ternary types. Very recently, Fox and Leifer22 have employed the Scatchard-Rush-Johnson (SRJ) equations23 to analyze the osmotic coefficient data of the LiCl-(n-Bu)4NCl-H2O system up to I ) 8 mol kg-1. These authors have successfully determined various interaction terms using the theories of Friedman24 and of Leifer and Wigent.25 In our work, we have preferred to use the Pitzer equations to analyze the osmotic coefficients, as three parameters each for both the pure NaCl and GnCl solutions are required in addition to two mixing terms. On the other hand,
Ionic Interactions in Mixtures of NaCl and GnCl
J. Phys. Chem. B, Vol. 104, No. 40, 2000 9507
TABLE 2: Pitzer Equations Used for the Analysis of Osmotic Coefficients, Activity Coefficients, Volumes, and Compressibilities of the NaCl-GnCl Mixturesa Osmotic Coefficients
φ ) 1 + f + mT{(1 - y2)B φ
+ y2B
φ NaCl
φ GnCl
+ y2(1 - y2)θ} + mT2{(1 - y2)CφNaCl) + y2CφGnCl + y2(1 - y2)ψ}
(1)
f φ ) -AφI0.5/(1 + bI0.5)
(2)
Bφ ) β(0) + β(1) exp(-RI1/2)
(3)
θ and ψ ) binary and ternary interactions as θNaGn and ψNaGnCl, respectively Activity Coefficients
ln γ(NaCl ) f + mT{B γ
γ NaCl
+ y2(B
φ GnCl
-B
φ NaCl
+ θ)} + mT2{3CφNaCl/2) + y2(CφGnCl - CφNaCl + ψ/2) + y2(1 - y2)ψ/2}
(4)
Bγ ) 2β(0) + (2β(1)/R2I){1 - exp(-RI0.5)(1 + RI0.5 - R2I/2)}
(5)
f ) -Aφ{(I /(1 + bI )) + (2/b) ln(1 + bI )}
(6)
γ
1/2
1/2
1/2
Aφ ) Pitzer-Debye-Huckel limiting slope (0.391 45 kg1/2 mol-1/2); R ) 2 and b ) 1.2 Apparent Molal Ionic Volumes and Compressibilities (superscript v for volume or compressibility; subscript V for volume; subscript K for compressibility)
φvi ) φvi0 + f v(I) + RT
∑B
+ 0.5RT
v
ijmj
i
∑C
v
2
ijmj
+ RT
i
∑θ m v
k
+ RT
∑m ∑m ψ k
k
v
j
(7)
j
in eq 7 summations over j are over ions of opposite charge, i.e., accounting for cation-anion interactions; k refers to the ion of the same charge as that of i
fv ) (Av/2b) ln(1 + bI0.5)
(8)
φvi0 ) apparent or partial molal volume or compressibility of an ion at infinite dilution;
Av ) 1.8743 × 10-6 m3 kg1/2 mol-3/2; AK ) -3.7784 × 10-15 m3 kg1/2 mol-3/2 Pa-1 at 298.15 K Bvij ) βv(0) + βv(1)(2/R2I)[1 - (1 + RI0.5)] exp(-RI0.5)
(9)
Cvij ) 0.5Cvφij
(10)
Pertinent Definitions for the Pitzer Coefficients for volumes:
βV(0) ) (∂β(0)/∂P)T, βV(1) ) (∂β(1)/∂P)T, and CVij ) (∂Cφ/∂P)T for compressibility:
β
K(0)
) (∂ β /∂P )T, β 2 (0)
2
K(1)
) (∂2β(1)/∂P2)T, and CKij ) (∂2Cφ/∂P2)T
θ and ψ ) binary and ternary interactions as θNaGn and ψNaGnCl, respectively
θv ) ∆φvI/2RTm1m2
(11)
ψv ) ∆φv/4RTm1m2
(12)
in eq 11 ∆φv ) φvexptl - φvcalcd, φvcalcd with interactions between ions of opposite charges; in eq 12 ∆φv ) φvexptl - φvcalcd, φvcalcd with interactions between ions of opposite charges and like charges a
Definitions of the symbols are described in the text.
seven and eight pure salt terms for LiCl and (n-Bu)4NCl were required in the SRJ model together with a total of 10 terms to account for the pairs, triplets, and quadruplets. Further, the SRJ equations involve the use of a series of terms involving parameters determined pairwise for the ions, including fourth virial coefficients. The activity coefficients of NaCl in the mixture, ln γ(NaCl, were calculated from eq 4 involving the Debye-Huckel term, f γ, for the activity coefficient (eq 6) given in Table 2. For calculating ln γ(GnCl, an expression analogous to eq 4 is used by transposing subscripts and replacing y2 by y1. These values are recorded in Table 3 at I ) 0.5, 1, 2, 3, and 4 mol kg-1 at round y2 values. We also plot the ln γ(NaCl as a function of y2 and ln γ(GnCl values as a function of y1 in parts a and b,
respectively, of Figure 2. Except at I ) 0.5 mol kg-1 the variation of ln γ(NaCl is nonlinear with respect to y2. On the other hand, ln γ(GnCl when plotted against y1 (Figure 2 b) shows large deviations from linearity at all the ionic strengths. At I ) 3 and 4 mol kg-1, the ln γ(GnCl is greatly influenced in the NaCl-rich mixture. Na+ is a hydrophilic cation; the activity coefficients of its salt, i.e., NaCl, first decrease and then increase with an increase in concentration. On the other hand, Gn+, a hydrophobic cation, is characterized by the decrease in the activity coefficients of its chloride salt in a monotonic manner with concentration. Thus, the γ(-m plots of both these salts are pointed in different directions. Addition of GnCl decreases the ln γ(NaCl in the mixture, indicating a decrease in the hydrophilic character of Na+. The hydrophobic nature of Gn+
9508 J. Phys. Chem. B, Vol. 104, No. 40, 2000
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TABLE 3: Computed Values of ln γ(NaCl and ln γ(GnCl as a Function of Y2 in the Mixture NaCl-GnCl at 298.15 K ln γ(NaCl
ln γ(GnCl
y2
0.5
1
2
3
4
0.5
1
2
3
4
0.2 0.4 0.5 0.6 0.8
-0.405 -0.435 -0.455 -0.472 -0.520
-0.475 -0.527 -0.560 -0.590 -0.650
-0.477 -0.581 -0.638 -0.691 -0.808
-0.450 -0.575 -0.637 -0.710 -0.875
-0.397 -0.551 -0.640 -0.725 -0.933
-0.455 -0.501 -0.518 -0.533 -0.551
-0.550 -0.632 -0.660 -0.675 -0.701
-0.639 -0.743 -0.783 -0.818 -0.875
-0.639 -0.780 -0.841 -0.900 -0.984
-0.641 -0.807 -0.876 -0.951 -1.051
Figure 3. Trace activity coefficient, γ(tr, of NaCl (9) and GnCl (O) as a function of ionic strength.
Figure 2. (a) Variation of ln γ(NaCl with y2 in the NaCl-GnCl mixtures at constant ionic strengths. (b) Variation of ln γ(GnCl with y1 in the NaCl-GnCl mixtures at constant ionic strengths. (-‚‚-) I ) 0.5, (-‚-) I ) 1, (- - -) I ) 2, (- - -) I ) 3, (s) I ) 4 mol kg-1.
is reduced at higher NaCl as evident from the enhanced ln γ(GnCl in the NaCl-rich mixture (Figure 2b). The deviations from linearity enlarge with the increase in the ionic strengths. The mutual effect of these ions will be later examined in terms of the excess free energy of mixing. The Harned expression describes the variation of ln γ( of a salt in the mixture at constant ionic strength.26 These relations are conveniently expressed as
ln γ(NaCl ) ln γ0(NaCl - R12y2 - β12y22
(13)
ln γ(GnCl ) ln γ0(GnCl - R21y1 - β21y12
(14)
and
with R and β being the Harned coefficients. When β12 ) β21 ) 0, the salt is said to obey the Harned rule. In Table 4 are listed the values of the Harned coefficients at constant ionic strengths. The trace activity coefficients, ln γ(tr, of both NaCl and GnCl were calculated using equations described elsewhere.26 The ionic strength dependence of ln γ(trNaCl and ln γ(trGnCl is shown in Figure 3. The plots show that the activity coefficients of pure NaCl and GnCl are greatly influenced by the trace amounts of the corresponding opposite salt. The ionic strength dependence of ln γ(trNaCl is stronger than that of ln γ(trGnCl. The effect of ionic strength on ln γ(trGnCl is nearly linear. The addition of GnCl, however, gives rise to ln γ(trNaCl, which is nonlinear with
ionic strength. The slopes of ln γ(tr with ionic strength are different in the cases of NaCl and GnCl with opposing signs. The volumetric properties of the mixtures throw light on the pressure dependence of the excess free energy of mixing. These properties are given in Table S1 in the Supporting Information in the form of the differences in the densities, ∆F (∆F ) F F0, F0 being the density of pure water), and speeds of sound, ∆U (∆U ) U - U0; U0 ) speed of sound in pure water) of aqueous NaCl-GnCl mixtures as a function of y1 at I ) 0.5, 1, 1.5, and 2 mol kg-1 and at 298.15 K. Both the ∆F and ∆U values increase nonlinearly with an increase in y1 at a constant ionic strength. The experimental F and U data of pure NaCl solutions are in excellent agreement with earlier reports.9,10 In the case of aqueous GnCl solutions, the measured densities agree with those of Makhatadze et al.18 Large differences in densities are, however, noted when our data (also those of Makhatadze et al.18) are compared with those reported by Kawahara and Tanford.28 Hammes and Swann29 and later on Arakawa et al.30 reported the sound speeds of aqueous GnCl at different temperatures. Our U values collected in this work are in agreement with those of Hammes and Swann29 to within 0.4 ms-1, but differ from those of Arakawa et al.30 by about 20 ms-1. No mixture data are reported in the literature for the purpose of comparison. Like the analysis of osmotic coefficients, we have employed the Pitzer theory19 for analyzing the volumetric properties. The simplified expressions for apparent molal volume or compressibility of an ion φvi in a mixture of uni-univalent salts with a common anion are collected as eqs 7-12 in Table 2 with details given elsewhere.32 Application of eq 7 without the last two terms on the right-hand side is a typical example of Young’s rule of mixing.32 The Pitzer coefficients for pure NaCl and GnCl are obtained from the least-squares fitting of the experimental data of pure electrolyte solutions using the volumetric Pitzer equation for a single electrolyte.32 The superscript v is common for both volume and compressibility. The superscripts V and K indicate volume and compressibility. The Pitzer coefficients of NaCl for volumes and compressibility were taken from an earlier report,32 while in the case of
Ionic Interactions in Mixtures of NaCl and GnCl
J. Phys. Chem. B, Vol. 104, No. 40, 2000 9509
TABLE 4: Harned Coefficients for Calculating the ln γ( Values of NaCl and GnCl in the NaCl-GnCl Mixtures at 298.15 K ln γ(NaCl 0.1210 ( 0.0201 0.2629 ( 0.0016 0.4124 ( 0.0250 0.4666 ( 0.0231 0.6225 ( 0.0329
0.5 1 2 3 4
ln γ( GnCl 0.0521 ( 0.0021 0.0304 ( 0.0068 0.1217 ( 0.0238 0.2584 ( 0.0220 0.2985 ( 0.0314
0.0419 ( 0.0011 0.0863 ( 0.0134 -0.0109 ( 0.0021 -0.1256 ( 0.0096 -0.1769 ( 0.0110
-0.0206 ( 0.0022 -0.3663 ( 0.0122 -0.4774 ( 0.0089 -0.5643 ( 0.0123 -0.6876 ( 0.0121
TABLE 5: Pitzer Coefficients for Correlating OV and OK of Aqueous NaCl and GnCl with Molalities param φV0 × 106/(m3 mol-1) (∂β(0)/∂P)T × 1010 (∂β(1)/∂P)T × 1010 φK0 × 1015/(m3 mol-1 Pa-1) (∂2β(0)/∂P2)T × 1019 (∂2β(1)/∂P2)T × 1019
NaCl
GnCl
16.58 ( 0.14 1.14 ( 0.08 1.15 ( 0.09
69.98 ( 0.39 -2.01 ( 0.21 4.99 ( 0.12
-49.12 ( 0.08 8.30 ( 0.24 36.62 ( 0.19
-10.01 ( 0.06 4.10 ( 0.19 4.08 ( 0.17
param
NaCl
GnCl
For φV (∂ Cφ/∂P)T × 1011 rmsd(φV) × 106/(m3 mol-1)
-1.11 ( 0.11 0.005
8.38 ( 0.19 0.01
For φK (∂2Cφ/∂P2)T × 1020 rmsd(φK) × 1015/(m3 mol-1 Pa-1)
-6.41 ( 0.20 0.06
4.64 ( 0.16 0.09
Figure 4. δ(∆F) against y1: (9) I ) 0.5 mol kg-1, (4) I ) 2 mol kg-1. δ(∆U) against y1: (4) I ) 1 mol kg-1; (O) I ) 1.6 mol kg-1; The δ values are calculated with mixing terms θvNa+,Gn+ and ψNa+,Gn+,Cl-. Symbols are the same as in Figure 2.
GnCl, the density18 and sound velocitiy29 data were fitted with the Pitzer equations32 to obtain the required coefficients. In Table 5 are listed the Pitzer coefficients for φV and φK of aqueous NaCl and GnCl solutions at 298.15 K. In view of large deviations obtained between experimental and calculated quantities, it was necessary to introduce the binary, θvNa,Gn and ternary ψvNa,Gn,Cl interaction terms given by eqs 11 and 12, respectively, in Table 2. For volumes, θvNa,Gn and ψvNa,Gn,Cl obtained from a common least-squares program were recorded to be 1.07 × 10-8 and 1.76 × 10-11, respectively. Similarly, in the case of compressibility, the values of θvNa,Gn and ψvNa,Gn,Cl were estimated to be 1.07 × 10-17 and 1.71 × 10-20, respectively. Incorporation of the θvNa,Gn and ψvNa,Gn,Cl terms in eq 7 yields highly accurate calculations of F, U, φ*V and φ*k as shown in Figure 4, where the deviations, δ values, calculated from the experimental and calculated F and U data with the mixing terms are plotted as a function of y1 at several ionic strengths. Figure 4 shows that both the densities and sound speeds can be estimated by the specific ion interaction theory of Pitzer with random deviations. In the ionic strength range, the F and φ*V of these mixtures can be estimated by the Pitzer equations with average rmsd values of 0.075 kg m-3 and 0.16 × 10-6 m3 mol-1, respectively, while the U and φ*K have average rmsd values of 0.16 ms-1 and 0.31 × 10-15 m3 mol-1 Pa-1, respectively. A remarkable improvement in the results by the use of θvNa+,Gn+ and ψvNa,Gn,Cl brought about by a complete removal of systematic deviations shows that the mixing effects due to the interactions of binary and ternary interactions involving Na+, Gn+, and Cl- ions are important in describing the volumetric properties of such systems.
Figure 5. (a) ∆mGE as a function of y2 at different ionic strengths. (b) ∆mXE, i.e., ∆mVE (s) and ∆mKE (- - -), as a function of y2 at different ionic strengths. Multiplication factors for ∆mVE and ∆mKE are 10-6 (m3 kg-1 of H2O) and 10-15 (m3 Pa-1 kg-1 of H2O).
The φk of aqueous NaCl is much lower than that of aqueous GnCl throughout the concentration range. Higher compressibilities are usually noted for the salts containing hydrophobic ions. Further, the ∂φ*K/∂m slope for NaCl is steeper than for GnCl. The calculated ionic compressibility of Gn+, i.e., φK,Gn+ decreases very slowly with the addition of Na+, indicating very minor reduction in the hydrophobic nature of Gn+. On the other hand, an addition of Gn+ increases the values of φK,Na+. The effect of Gn+ on φK,Na+ is stronger than that of Na+ on φK,Gn+. This may be attributed to the larger size of the Gn+ species. Let us now examine the excess properties of mixing for this system. The excess Gibbs free energies of mixing, ∆mGE, in aqueous NaCl-GnCl calculated by using activity coefficients and osmotic coefficients are shown in Figure 5a as a function of y2 at constant ionic strengths. We note negative ∆mGE below y2 ≈ 0.5 at all the ionic strengths. The ∆mGE values decrease with ionic strength in the region y2 < 0.5. The negative ∆mGE indicates that the water molecules are ordered in this region. The lowest ∆mGE values are observed at y2 ≈ 0.2. Beyond y2 ≈ 0.2, the increasing concentration of GnCl causes the water molecules to be disturbed, thus increasing the ∆mGE values. In the region y2 > 0.5, ∆mGE increases. The positive magnitude of ∆mGE in the GnCl-rich mixtures reaches a maximum at y2 ≈ 0.75, pointing to a maximum water-disordering in the system.
9510 J. Phys. Chem. B, Vol. 104, No. 40, 2000
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TABLE 6: Friedman Interaction Parameters, g0 and g1 for ∆mGE, W0 and W1 for ∆mVE, and k0 and k1 for ∆mKE I/(mol kg-1)
g0/(kg mol-1)
g1/(kg mol-1)
I/(mol kg-1)
107V0/(m3 kg mol-2)
106V1/(m3 kg mol-2)
1016k0/(m3 kg mol-2 Pa-1)
1015k1/(m3 kg mol-2 Pa-1)
0.5 1 2 3 4
0.001 0.006 0.002 0.003 -0.002
-0.117 -0.1370 -0.1552 -0.1447 -0.1526
0.5094 1.0364 1.5825 2.1496
-8.654 5.769 -2.457 -1.502
30.112 8.751 7.639 5.391
-33.269 3.361 1.068 2.731
-19.583 -7.125 -4.167 -3.398
Figure 6. (a) Ionic strength dependence of the Friedman interaction parameters, g0 and g1. (b) Ionic strength dependence of the Friedman interaction parameters, V0, V1, k0, and k1.
Quite interestingly, we note ∆mGE to be ∼0 at y2 ≈ 0.5. This situation indicates a neutralization of water-ordering and -disordering effects. Fox and Leifer22 have noted this type of behavior in the (n-Bu)4NCl-rich mixture with LiCl. The y2 values at which the maxima in the ∆mGE can be located increase with decreasing ionic strengths. No such effect however is seen in the negative component of ∆mGE. NaCl and GnCl are known to be the structure-maker and -breaker salts, respectively. In the mixture rich in GnCl at constant ionic strength, the positive ∆mGE above y2 ≈ 0.5 indicates the repulsion between Na+ and Gn+ ions with opposing tendency toward water molecules around them. In other words, the negative ∆mGE indicates the presence of pairwise interactions reaching a maximum at y2 ≈ 0.2. The higher order terms such as triple interactions are likely in the GnCl-rich region as evidenced by the positive ∆mGE. The Friedman equation27 can be used to analyze the ∆mGE values of the system with a common ion as
∆mGE ) I2RTy1y2[g0 + g1(1 - 2y2)]
(15)
where g0 and g1 are the Friedman interaction parameters characterizing the pairwise and higher order interactions, respectively. The ionic strength dependence of both g0 and g1 (given in Table 6) is shown in Figure 6a. The g0 value is negligible, showing ∆mGE to be zero at y2 ) 0.5. We plot the excess volumes ∆mVE and compressibilities ∆mKE on mixing (the corresponding quantities to ∆mGE) as a function of y2 in Figure 5b. Like ∆mGE, ∆mGE and ∆mKE also show similar trends. At a constant ionic strength, the ∆mVE becomes more negative upon addition of GnCl and reaches minimum at y2 ≈ 0.2. This region, i.e., y2 < 0.5, is the water-ordering region. The pairwise interactions as observed from ∆mGE are also
confirmed by the negative ∆mVE. Similarly, the positive ∆mVE in the GnCl-rich region (i.e., y2 < 0.5) can be explained. The pressure dependence of ∆mVE, i.e., ∆mKE, shown in Figure 5b also confirms the nature of pairwise interactions and ternary interactions. The zero ∆mVE at each ionic strength may be the result of balancing the structure-making and -breaking properties of Na+ and Gn+ ions. In other words, at y2 ) 0.5, NaCl-GnCl shows ideal mixing. The ideal mixing at y2 ≈ 0.5 is also seen in the cases of ∆mKE and ∆mGE. Both ∆mVE and ∆mKE can be analyzed in terms of the Friedman equation, analogous to eq 15, with V0 and V1 being the Friedman interaction parameters for volumes with analogous definitions for k0 and k1. Table 6 lists the values of V0, V1, k0, and k1 obtained from the least-squares analysis of the ∆mVE and ∆mKE of the mixture. It is interesting to note that the nature of nonideality is supported by ∆mGE, ∆mVE, and ∆mKE. The ionic strength dependence of the Friedman interaction parameters for g0 and g1 is shown in Figure 6a, while the analogous plots for V0, V1, k0, and k1 are depicted in Figure 6b. In regard to g0, its magnitude is nearly zero and thus is invariant with ionic strength. The values of g1 decrease with ionic strength, indicating the importance of ternary interactions in this system. Again both V0 and k0 are nearly independent of ionic strength. On the other hand, a strong ionic strength dependence is noted for V1 and k1. A study of these parameters points to the interactions arising out of the triplet, i.e., Na+, Gn+, and Clions. The surface tension, σm, data of the aqueous NaCl-GnCl mixtures at I ) 0.5, 1, 2, and 4 mol kg-1 at 298.15 K are listed in Table S2. The values of surface tension for pure aqueous NaCl and GnCl solutions are in excellent agreement with those available in the literature.33,34 The mixture data show negative deviations from the ideal mixing of NaCl and GnCl solutions at constant ionic strengths. The σm values do not show any appreciable variations in the lower y1 range extending up to ∼0.2. A sharp change in σm, however, is noted in the high NaCl concentration region at high ionic strengths of the mixtures. The changes in the surface tension upon mixing of both the solutions at a constant ionic strength, ∆mσ (∆mσ ) σm - σ1y1 - σ2y2), are symmetrical with respect to y1 at all the ionic strengths except I ) 4 mol kg-1. The surface tension values of pure NaCl and GnCl solutions are denoted by σ1 and σ2, respectively. The symmetrical behavior of ∆mσ indicates the presence of pairwise interactions. The σm data of these mixtures can be analyzed in terms of a simple model of Li et al.35 derived from the fundamental Butler equation.36 According to this model,35 the molality of an electrolyte in the surface phase, ms, is proportional to that in bulk water, mb, by ms ) gmb, with g being a proportionality constant. The value of g specific to an electrolyte can be estimated from the experimental surface tension data of pure electrolyte solutions. For aqueous mixtures of uni-univalent types of electrolytes, the σm can be calculated by using
∑mJb) - φs∑gJmJs)]
σm ) σw + (2RT/(1000/M1)Aw)[φb
(16)
Ionic Interactions in Mixtures of NaCl and GnCl
Figure 7. Deviations, δ (experimental σm - calculated σm), as plotted against y1 at I ) 4 mol kg-1 without mixing terms (0) and with mixing terms (O) and I ) 1 mol kg-1 without mixing terms (4) and with mixing terms (2).
Figure 8. σm-y1 plots at I ) 4 mol kg-1 (9) and I ) 0.5 mol kg-1 (0). The lines are calculated by scaled particle theory; symbols are experimental.
where φb and φs are the osmotic coefficients in the bulk and surface phases, respectively. The surface tension of pure water is indicated by σw. Aw and M1 are the molar surface area and molar mass of water, respectively. The summation is over j electrolytes. We used the Pitzer equations to interpolate our φ values of mixtures, required in eq 16 with mixing terms θNa,Gn and ψNa,GnCl as discussed by us.37 The values of the g parameters for aqueous NaCl and GnCl were taken as 0.107 42 and 0.762 01, respectively. In Figure 7 are shown the deviations, δ (experimental σm - calculated σm), without and with θNa,Gn and ψNa,GnCl terms for I ) 1 and 4 mol kg-1. The impact of the mixing term is primarily on the calculations of the osmotic coefficients, which is reflected in the calculations of the surface tension of mixtures of aqueous NaCl and GnCl. The surface tension data of the NaCl-GnCl system from I ) 0.5 mol kg-1 to I ) 4 mol kg-1 can be correlated by using eq 16 with an average rmsd of 0.04 × 10-2 N m-1. In the past, the scaled particle theory38 has been applied to calculate the surface tension of organic ionic melt-organic liquid systems.39 We apply the scaled particle theory to NaClGnCl-H2O with the mixing rule suggested by Lebowitz et al.38d The input parameters for NaCl and GnCl were taken from Marcus,40 Sapse and Massa,41a and Sapse et al.41b The radii of Na+, Gn+, and Cl- ions were taken as 0.095, 0.133, and 0.181 nm, respectively, whereas a value of 0.234 nm was chosen for the diameter of the water molecule. For the purpose of illustration, in Figure 8 we have plotted the calculated σm in contrast to the experimental data as a function of y1 at I ) 0.5 and 4 mol kg-1. An inspection of Figure 8 suggests that the scaled particle theory describes the surface tension of mixtures in the low and high NaCl compositions. The scaled particle theory can correctly predict the (∂σm/∂y1)I in both the NaClpoor and -rich regions. There are, however, strong deviations
J. Phys. Chem. B, Vol. 104, No. 40, 2000 9511
Figure 9. η-y1 plots: (0) I ≈ 3.8 mol kg-1; (O) I ≈ 2.9 mol kg-1; (4); I ≈ 1.8 mol kg-1; (3) I ≈ 0.6 mol kg-1. Lines are calculated by the method of Tamamushi and Isono43 with an empirical mixing rule.
in the middle concentration region, suggesting the need for a more effective mixing rule for the components. The viscosity, η, of the NaCl-GnCl mixtures at 298.15 K at different compositions and ionic strengths are given in Table S3 and shown in Figure 9. There exists excellent agreement of the η data of pure NaCl and GnCl measured in this work with those reported in the literature.28,42 An examination of plots given in Figure 9 suggests that there is a linear variation of η with respect to y1 at all the ionic strengths studied. We analyzed the mixture viscosity data by the equation of Tamamushi and Isono,43 which is an extension of the method of Feakins et al.44 for dilute electrolyte solutions. The Gibbs energy of activation, ∆qGvis as a function of the mole fraction of an electrolyte, x, is
∆qGvis ) ∆qG0vis + γGx + γ′Gx2
(17)
∆qG0vis is the activation parameter (9.17 ( 0.01 kJ mol-1) of pure water at 298.15 K. The γG coefficient represents the initial effect of an electrolyte on the activation parameter, i.e., the electrolyte-water interactions at infinite dilution, while the γ′G coefficient is significant in concentrated solutions. To apply the above equations to the mixtures, an empirical mixing rule can be applied for calculating the γG and γ′G coefficients in mixtures. The selection of a simple linear mixing rule in this case is guided by the linear change in η with y1 as evident from Figure 9. Thus, we have γG,m ) ∑yJγG,J; γ′Gm ) ∑yJγ′G,J. The expression for calculating the Gibbs free energy of activation, ∆qGvis,m is
∆qGvis,m ) ∆qG0vis + γG,my1 + γ′G,my12
(18)
where in the case of mixtures of 1:1 electrolytes, xi ) yi with a standard definition to follow: ∑xi ) ∑yi ) 1. The η can then be calculated from ∆qGvis,m by using a standard expression.26 The values of γG and γ′G obtained from the least-squares fits of ∆qGvis ((0.03 kJ mol-1) calculated from viscosity data of the pure aqueous NaCl and GnCl solutions are
for NaCl: γG/(kJ mol-1) ) 33.75 ( 0.19 and γ′G/ (kJ mol-1) ) 486 ( 3 for GnCl: γG/(kJ mol-1) ) 40.39 ( 0.09 and γ′G/ (kJ mol-1) ) -81.30 ( 0.92 Application of eq 18 together with the numerical values of γG and γ′G yields accurate predictions of the mixture viscosities with an average rmsd of 0.035 × 10-3 Pa‚s throughout the ionic strength range. Agreement between the experimental data shown
9512 J. Phys. Chem. B, Vol. 104, No. 40, 2000 by symbols and the predicted values by solid lines (Figure 9) lends credence to the proposed mixing rule used for predicting the viscosities. To summarize, we have experimentally measured several properties of the NaCl-GnCl systems. From osmotic and activity coefficients and volumetric properties, the importance of the binary and ternary interactions has been established. The information collected above is expected to be of tremendous use to biophysical chemists who are examining the mixed ion effects on the behavior of the biomolecules. Supporting Information Available: Table S1 listing the experimental density and speeds of sound data and Tables S2 and S3 listing the surface tension and viscosity data, respectively. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Hagihara, Y.; Aimoto, S.; Fink, A. L. Goto, Y. J. Mol. Biol. 1993, 231, 180. (2) (a) Mayr, L. M.; Schmid, F. Biochemistry 1993, 32, 7994 (b) von Hippel, P. H.; Schleich, T. Acc. Chem. Res. 1969, 2, 257. (3) For a review see: (a) Breslow, R. Acc. Chem. Res. 1991, 24, 159 (b) Kumar, A. J. Org. Chem. 1994, 59, 230 (c) Kumar, A. J. Org. Chem. 1994, 59, 4612. (d) Kumar, A. Pure Appl. Chem. 1998, 70, 625. (e) Pawar, S. S.; Phalgune, U.; Kumar, A. J. Org. Chem. 1999, 64, 7055. (f) Kumar, A.; Phalgune, U.; Pawar, S. S. J. Am. Chem. Soc., submitted for publication. (4) Nozaki, Y. Methods Enzymol. 1986, 26, 43. (5) Rard, J. A.; Habenschuss, A.; Spedding, F. H. J. Chem. Eng. Data 1976, 21, 374. (6) Rard, J. A. Habenschuss, A.; Spedding, F. H. J. Chem. Eng. Data 1977, 22, 180. (7) Rard, J. A.; Spedding, F. H. J. Chem. Eng. Data 1977, 22, 56. (8) Rard, J. A.; Platford, R. F. In ActiVity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; Chapter 5. (9) Lo Surdo, A.; Alzola, E. M.; Millero, F. J. J. Chem. Thermodyn. 1982, 14, 649. (10) Millero, F. J.; Ricco, J.; Schrieber, D. R. J. Solution Chem. 1982, 11, 671. (11) Vazquez, G.; Alvarez, E.; Navaza, J. M. J. Chem. Eng. Data, 1995, 40, 611. (12) Timmermans, J. The Physicochemical Constants of Binary Systems in Concentrated Solutions; Interscience: New York, 1959. (13) Pal, A.; Singh, Y. P. J. Chem. Eng. Data 1996, 41, 425. (14) Hamer, W. J.; Wu, Y.-C. J. Phys. Chem. Ref. Data 1972, 1, 1047.
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