Vapor Pressure Osmometry Determination of the Osmotic and Activity

Article pubs.acs.org/jced

Vapor Pressure Osmometry Determination of the Osmotic and Activity Coefficients of Dilute Aqueous Solutions of Symmetrical Tetraalkyl Ammonium Halides at 308.15 K Roonak Golabiazar and Rahmat Sadeghi* Department of Chemistry, University of Kurdistan, Sanandaj, Iran ABSTRACT: Osmotic coefficients were measured by the vapor pressure osmometry technique for dilute aqueous solutions of Me4NBr, Et4NBr, Pr4NBr, Bu4NBr, Me4NCl, and Me4NI at 308.15 K. From the experimental osmotic coefficient data, the water activity, water activity coefficient and vapor pressure values were evaluated. The experimental osmotic coefficient data were fitted to the Pitzer equation from which the values of the mean molal activity coefficients were calculated. The values of the obtained osmotic and mean molal activity coefficient data for the bromides decreased with the size of the cation: Bu4N+ < Pr4N+ < Et4N+ < Me4N+. The results for the tetramethylammoniums show that the osmotic and mean molal activity coefficient varies in the following way: Me4NCl > Me4NBr > Me4NI. However the values of the water activity, vapor pressure depression, and the water activity coefficient data follow the order Me4NBr < Et4NBr < Pr4NBr < Bu4NBr and Me4NCl < Me4NBr < Me4NI, which implies that the smaller ions hydrate more water molecules than the ions with larger size.

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INTRODUCTION Experimental phase equilibrium data of aqueous electrolytes are of considerable importance in the prediction of the behavior of electrolyte solutions, the development of the electrolyte models, and the estimation of interactions occurring in these systems. Among all the phase equilibrium data, the solvent activity is an important and key thermodynamic property because it is closely related with the other thermodynamic properties and, in thermodynamic modeling for separation methods, it is the essential variable. Several experimental techniques that include freezing point depression, boiling point elevation, dynamic and static vapor pressure measurements, osmotic pressure measurements, hygrometry, vapor sorption, isopiestic method and vapor pressure osmometry (VPO) have been employed to measure the solvent activity of nonvolative solutions. The symmetrical tetraalkyl ammonium halides make it possible to develop new materials that may have different industrial uses. On the fundamental level, the tetraalkyl ammonium salts are interesting models for the study of the hydrophobic interactions occurring in electrolyte solutions due to their fairly high solubility in water and the possibility of working with series having variable alkyl chain lengths.1,2 Although osmotic and activity coefficients of aqueous solutions of tetraalkyl ammonium halides have been extensively investigated through the isopiestic method by the research groups of Lindenbaum et al.,3−5 Wen et al.,6,7 and Amado et al.,2,8−11 the subject is not clearly understood and there is no VPO determination of vapor−liquid equilibria properties of aqueous solutions of tetraalkyl ammonium halides in the literature. In fact the isopiestic method is a limited technique © XXXX American Chemical Society

for the dilute solutions and at lower concentrations some difficulties appear so that the molality m = 0.1 is considered to be the lower limit of applicability for binary electrolytes solutions. Therefore the published osmotic and activity coefficients of dilute aqueous solutions of tetraalkyl ammonium halides are limited, and because of the potential use of these organic salts, new measurements are needed to supplement these studies. The VPO method which has become one of the most frequent techniques for solvent activity determination of dilute solutions is based on a precise determination of the temperature difference between a drop of solution and a drop of solvent hanging on temperature-recording thermistors. Thermistors are placed in a chamber filled with a saturated vapor of solvent. Since the vapor pressure of the solution is less than that of the pure solvent, the solvent vapor condenses on the solution droplet and causes a change in its temperatures. Temperature differences between the two thermistors are represented as voltage difference measured by a digital voltmeter. The present work presents experimental data on the vapor−liquid equilibria of dilute aqueous solutions of Me4NBr, Et4NBr, Pr4NBr, Bu4NBr, Me4NCl, and Me4NI at 308.15 K obtained from the VPO method.

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EXPERIMENTAL SECTION Materials. Me4NBr (≥ 99.0 % w/w), Et4NBr (≥ 99.0 % w/ w), Pr4NBr (≥ 99.0 % w/w), Bu4NBr (≥ 99.0 % w/w), Me4NCl (≥ 98.0 % w/w), Me4NI (≥ 99.0 % w/w), and NaCl Received: September 10, 2013 Accepted: December 5, 2013

A

dx.doi.org/10.1021/je400821q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Osmotic Coefficients, Water Activities, Vapor Pressures, Water Activity Coefficients, and Mean Molal Activity Coefficients of Aqueous Solutions of R4NX at T = 308.15 Ka m/mol·kg−1

a

Φ

aw

p/kPa

0.01285 0.02557 0.03787 0.05490 0.06504 0.07726 0.09560 0.13257 0.16775 0.20297 0.23829 0.30826

0.9931 0.9742 0.9583 0.9480 0.9400 0.9311 0.9195 0.8936 0.8796 0.8696 0.8623 0.8489

0.00795 0.01468 0.03035 0.03901 0.04468 0.05680 0.07479 0.09397 0.13712 0.17223 0.21495 0.25307 0.29694

0.9890 0.9667 0.9379 0.9265 0.9201 0.9063 0.8896 0.8732 0.8524 0.8415 0.8321 0.8261 0.8201

Me4NBr + Water 0.9995 5.6237 0.9991 5.6213 0.9987 5.6190 0.9981 5.6158 0.9978 5.6139 0.9974 5.6117 0.9968 5.6085 0.9957 5.6023 0.9947 5.5964 0.9937 5.5906 0.9926 5.5847 0.9906 5.5734 Pr4NBr + Water 0.9890 5.6247 0.9667 5.6234 0.9379 5.6205 0.9265 5.6190 0.9201 5.6180 0.9063 5.6159 0.8896 5.6128 0.8732 5.6097 0.8524 5.6026 0.8415 5.5970 0.8321 5.5901 0.8261 5.5840 0.9890 5.5771

0.01861 0.03679 0.05507 0.07403 0.09359 0.11118 0.13967 0.18769 0.23516 0.28397 0.33300

0.9937 0.9747 0.9580 0.9487 0.9393 0.9297 0.9173 0.8997 0.8878 0.8757 0.8675

Me4NCl + Water 0.9993 5.6226 0.9987 5.6190 0.9981 5.6156 0.9975 5.6121 0.9968 5.6085 0.9963 5.6054 0.9954 5.6003 0.9939 5.5921 0.9925 5.5841 0.9911 5.5760 0.9896 5.5679

γw

m/mol·kg−1

γ±

Φ

1.0000 1.0000 1.0001 1.0001 1.0001 1.0002 1.0003 1.0005 1.0007 1.0009 1.0011 1.0016

0.9557 0.9270 0.9019 0.8782 0.8629 0.8456 0.8221 0.7769 0.7464 0.7217 0.7011 0.6662

0.00966 0.01943 0.03868 0.04910 0.05837 0.07077 0.09678 0.11969 0.15610 0.21460 0.27993 0.33984

0.9933 0.9737 0.9492 0.9327 0.9256 0.9160 0.8994 0.8851 0.8690 0.8500 0.8376 0.8275

1.0000 1.0000 1.0001 1.0001 1.0001 1.0002 1.0003 1.0004 1.0007 1.001 1.0013 1.0015 1.0019

0.9490 0.9151 0.8620 0.8384 0.8245 0.7961 0.7608 0.7282 0.6772 0.6472 0.6184 0.5977 0.5775

0.00627 0.01250 0.02562 0.03159 0.03774 0.04597 0.06502 0.07496 0.11296 0.14589 0.17754 0.21263 0.25577 0.33047

0.9763 0.9517 0.9279 0.9191 0.9126 0.9006 0.8805 0.8725 0.8403 0.8228 0.8131 0.8046 0.7941 0.7854

1.0000 1.0000 1.0001 1.0001 1.0002 1.0003 1.0004 1.0007 1.0009 1.0012 1.0015

0.9649 0.9371 0.9100 0.8895 0.8694 0.8512 0.8262 0.7905 0.7627 0.7368 0.7159

0.01012 0.02006 0.03010 0.04063 0.04966 0.05912 0.07116 0.10259 0.12857 0.15270 0.18020

0.9766 0.9573 0.9365 0.9245 0.9108 0.8995 0.8830 0.8569 0.8396 0.8277 0.8188

aw

p/kPa

Et4NBr + Water 0.9997 5.6244 0.9993 5.6225 0.9987 5.6189 0.9984 5.6170 0.9981 5.6154 0.9977 5.6132 0.9969 5.6087 0.9962 5.6048 0.9951 5.5988 0.9934 5.5894 0.9916 5.5789 0.9899 5.5695 Bu4NBr + Water 0.9998 5.6251 0.9996 5.6239 0.9991 5.6215 0.9990 5.6204 0.9988 5.6193 0.9985 5.6179 0.9979 5.6147 0.9976 5.6130 0.9966 5.6071 0.9957 5.6020 0.9948 5.5971 0.9939 5.5917 0.9927 5.5852 0.9907 5.5738 Me4NI + Water 0.9996 5.6243 0.9993 5.6224 0.9990 5.6206 0.9986 5.6187 0.9984 5.6171 0.9981 5.6155 0.9977 5.6136 0.9968 5.6085 0.9961 5.6044 0.9955 5.6007 0.9947 5.5964

γw

γ±

1.0000 1.0000 1.0001 1.0001 1.0002 1.0002 1.0003 1.0005 1.0007 1.0011 1.0016 1.002

0.9608 0.9314 0.8867 0.8603 0.8441 0.8233 0.7861 0.7571 0.7211 0.6771 0.6415 0.6145

1.0000 1.0000 1.0001 1.0001 1.0001 1.0002 1.0003 1.0003 1.0006 1.0009 1.0012 1.0015 1.0019 1.0025

0.9198 0.8748 0.8204 0.8006 0.7837 0.7601 0.7172 0.6988 0.6378 0.6006 0.5739 0.5497 0.5241 0.4923

1.0000 1.0000 1.0001 1.0001 1.0002 1.0002 1.0003 1.0005 1.0007 1.0009 1.0012

0.9269 0.8891 0.8530 0.8257 0.8009 0.7789 0.7508 0.6976 0.6626 0.6363 0.6125

u(Φ) = 0.0005 and u(T) = 0.001 K.

Then the pure water on one thermistor is replaced by the R4NX aqueous solution and condensation of water from the vapor phase into the R4NX solution at the thermistor takes place. Because of the heat of condensation, the thermistor containing R4NX solution will be warmed and vapor pressure rises. These processes continue until the vapor pressure of the R4NX solution equals the vapor pressure of the pure water. The change in temperature changes the resistance of the thermistors. A bridge circuit measures the resistance difference of both thermistors. As long as changes in temperature are small, the resistance is proportional to ΔT. Generally, a time of 4−8 min suffices to reach this steady state. First, the instrument was calibrated using aqueous NaCl solutions as reference with known osmotic coefficients in the proper concentration range, yielding a function that correlates the panel readings to the corresponding concentrations of the reference solutions and therefore their osmotic coefficients. Then in the same

(≥ 99.5 % w/w) were obtained from Merck. The salts were used without further purification. Double distilled and deionized water was used. Apparatus and Procedures. The aqueous solutions were prepared by mass, using an analytical balance (Sartorius CP225D) with a precision of ± 1·10−5 g. In this study, the VPO method was used to obtain the water activities of the investigated tetraalkyl ammonium halides (R4NX) solutions. The VPO was performed with the help of an Osmomat K-7000 (Knauer Inc.). The details of the VPO method are similarly to the one used previously.12 The measuring chamber of the osmometer contains a reservoir of water, paper wicks to provide a saturated water atmosphere, and two thermistors that are placed in an airtight cell which measure resistance changes caused by changes in temperature. First, a droplet of pure water is attached to each thermistor with the help of a microsyringe, and after 5 min of equilibration, the reading is adjusted to zero. B



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conditions, the panel readings were measured for the studied R4NX solutions. For each solution, at least five determinations (zero point adjustment and new solution) were performed, and the mean value is reported. Generally, the deviations from the mean value were less than 1 %. The cell temperature, which is electronically controlled, has a standard uncertainty of ± 1.10−3 K. For a certain R4NX solution with molality m which has a same instrument reading as a sodium chloride solution with molality mNaCl and osmotic coefficient ΦNaCl, the osmotic coefficient Φ was obtained according to Φ = (νNaClmNaCl ΦNaCl )/(νm)

(1)

where ν is the stoichiometric number. ΦNaCl is the osmotic coefficient for aqueous solutions of NaCl with molality mNaCl calculated from the correlation given in the literature.13 From the experimental osmotic coefficients, it is possible to calculate the water activities of the investigated solutions using the following relation: a w = exp[−M w νmΦ]

(2)

Figure 1. Plot of the osmotic coefficient Φ of R4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr; , calculated by Pitzer model.

where Mw is the molar mass of water. The uncertainty in the measurement of water activity was found to be better than ± 2· 10−4.

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RESULTS AND DISCUSSION Table 1 shows the experimental osmotic coefficient and water activity data of the investigated solutions at 308.15 K. From the solvent activity data, the vapor pressure data of solutions, p, were determined with the help of the following equation: ⎛ p⎞ (B − V w◦ )(p − p°) ln(a w ) = ln⎜ ⎟ + RT ⎝ p° ⎠

(3)

where B, Vw° , and p° are the second virial coefficient, molar volume, and vapor pressure of pure water, respectively. R is the gas constant and T is the absolute temperature. The second virial coefficients of water vapor were calculated using the equation provided by Rard and Platford.14 Molar volumes of liquid water were calculated using the density of water at different temperatures. The vapor pressures of pure water were calculated using the equation of state of Saul and Wagner.15 The calculated vapor pressure data of investigated R4NX solutions are also given in Table 1. In Figures 1, 2 and 3, respectively, comparison of the experimental osmotic coefficient, water activity, and vapor pressure depression data (p − p°) for the Me4NBr, Et4NBr, Pr4NBr, Bu4NBr, Me4NCl and Me4NI systems has been made at T = 308.15 K. As can be seen, the effects of the size of the cation and anion on the osmotic coefficient data of aqueous R4NBr solutions are larger than that on the water activity or vapor pressure data. Figure 1 shows that the osmotic coefficients decrease with both cation and anion size. In the same solute molality, water activity and vapor pressure depression of the investigated binary aqueous solutions increased with the size of cation and anion: Bu4N+ > Pr4N+ > Et4N+ > Me4N+ and I− > Br− > Cl−. The smaller cations (and anions), because of the larger valence/size ratio, hydrates more water molecules than the larger cations (and anions) and therefore we may expect that the vapor pressure depression for smaller cations (and anions) solutions be greater than those for the larger cations (and anions) solutions. Aqueous solutions of the smaller cations (and anions) because of the stronger ion−water interactions have smaller water activities than those of the larger cations (and anions). In fact,

Figure 2. Plot of the water actvity aw of R4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr; , calculated by Pitzer model.

the salt molality dependence of the water activity or vapor pressure depression follows the orders Me4NBr > Et4NBr > Pr4NBr > Bu4NBr and Me4NCl > Me4NBr > Me4NI, and implies that the anion (and cation)−water interactions for anions (and cations) with smaller size are stronger than the anion (and cation)−water interactions for anions (and cations) with larger size. As an example, in Figure 4 comparisons of the experimental osmotic coefficient data measured in this work at 308.15 K with those taken from the literature3 measured at 298.15 K have been made for Me4NBr, Et4NBr, Pr4NBr, and Me4NCl systems. As can be seen, there is a good agreement between our data and those taken from the literature. To more scrutinize the vapor− liquid equilibria behavior of the investigated systems, the values C



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Calculated water activity coefficients, γw, of the investigated aqueous solutions are also given in Table 1. The experimental osmotic coefficients are related to the mean molal activity coefficients, γ±, at molality m′ by the relation ln γ± = Φ′ − 1 +

∫0

m′

Φ−1 dm m

(4)

The osmotic coefficients were correlated by the extended Pitzer ion-interaction model of Archer16,17 which has the following form for 1:1 electrolytes: Φ−1=

−Aϕ I 1+b I

+ m(β (0) + β (1) exp[−α1 I ]

+ β (2) exp[ −α2 I ]) + m2(C(0) + C(1) exp[ −α3 I ])

(5)

where β , β , β , C , and C are ion interaction parameter of the Archer extension of the Pitzer model that are dependent on temperature and pressure and are given in Table 2. The Aϕ value at 308.15 K for water is 0.39849 kg0.5·mol−0.5. I is the ionic strength in molality. The other constants are b = 1.2 kg0.5· mol−0.5, α1 = 2 kg0.5·mol−0.5, α2 = 7 kg0.5·mol−0.5 and α3 = 1 kg0.5·mol−0.5. The calculated values of γ± (obtained from eq 4 by using the Pitzer’s model, eq 5, for Φ) are also given in Table 1. The variations of γw and γ± with the solute concentration are shown in Figures 5 and 6, respectively. For all systems, γ± < 1 (0)

Figure 3. Plot of the vapor pressure depression p − p° of R4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◊, Bu4NBr; , calculated by Pitzer model.

Figure 4. Comparisons of the experimental osmotic coefficient data measured in this work at 308.15 (solid line) K with those taken from the literature3 measured at 298.15 K (dotted line): ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr.

(1)

(2)

(0)

(1)

Figure 5. Plot of the water activity coefficient, γw, of R4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr.

of the water activity coefficients, γw, and the mean molal activity coefficients, γ±, were also calculated. The water activities were used to obtain the solvent activity coefficients, γw = (aw/xw).

Table 2. Pitzer’s Model Parameters and the Corresponding Absolute Relative Deviation, ARDa, for Osmotic Coefficients of Aqueous Solutions of R4NX at T = 308.15 K

a

system

β(0)

β(1)

β(2)

C(0)

C(1)

ARD %

Me4NBr + water Et4NBr + water Pr4NBr + water Bu4NBr + water Me4NCl + water Me4NI + water

19.6395 35.8906 39.6283 5.62202 27.1021 29.4307

−33.3431 −59.9589 −65.8031 −10.9507 −45.6170 −48.7494

21.7340 33.5551 33.9423 6.2338 24.5210 29.3256

17.6976 32.0109 37.8985 3.0918 29.7811 27.1250

−82.6035 −151.5629 −172.2730 −18.9576 −123.8269 −126.1831

0.247 0.218 0.211 0.193 0.107 0.115

ARD = 1/(NP) Σ[(|Φexpt − Φcalc|)/Φexpt]. D



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by the following relations, and the values are shown in Figures 7 and 8. g ex = RT[x w ln γw + (xc + xa)ln γ±x]

(7)

Δg mix = RT[x w ln(x wγw ) + (xc + xa) ln γ±x(xc + xa)]

(8)

Figure 6. Plot of the mean molal activity coefficient, γ±, of R4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr.

(negative deviations from ideal-solution behavior) and decreased along with an increase in the solute concentration. The calculated water activity coefficients are very slightly larger than unity (positive deviations from ideal-solution behavior) and increase as solute concentration increases. Similar to the water activity and vapor pressure depression, in the same solute molality, water activity coefficients of the investigated binary aqueous solutions increased with the size of cation and anion: Bu4N+ > Pr4N+ > Et4N+ > Me4N+ and I− > Br− > Cl− which implies that the anion (and cation)−water interactions for anions (and cations) with smaller size are stronger than the anion (and cation)−water interactions for anions (and cations) with larger size. On the other hand, the observed trend for the calculated γ± of investigated solutions is similar to those obtained for Φ, so that the values of the mean molal activity coefficients decreased along with an increase in the cation and anion size. The change of the osmotic coefficient or mean molal activity coefficient with the size of cation or anion can be interpreted in terms of the hydrophobic hydrations and ion pair formations. The larger are the cations or anions, the more hydrophobic these ions will be, the more the water structure will be enforced, and the greater the free energy of the ion.3 Therefore, the larger activity coefficients can be expected in the case of the larger ions. As can be seen the observed order of the investigated salts is the opposite, therefore, the ion pairing effect must predominate. The large hydrophobic cations and anions will tend to combine with each other (ion association) to minimize their interaction with the surrounding water as well as to decrease the electrostatic free energy of the system and these lead to a drastic lowering of the their activity coefficients. The mole fraction mean ionic activity coefficients, γ(x) ± were obtained from the molal mean ionic activity coefficients γ± by using the following relation: ⎛ M υm ⎞ ln γ±(x) = ln γ± + ln⎜1 + w ⎟ ⎝ 1000 ⎠

Figure 7. Plot of the molar excess Gibbs energy, gex, of R4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◊, Bu4NBr.

Figure 8. Plot of the molar Gibbs free energy of mixing, Δgmix, of R4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr.

The values of the molar Gibbs free energy change due to mixing are negative and decrease with an increase in concentration of the solute and become more negative (very slightly) when the size of cation or anion increases. However the calculated values of the molar excess Gibbs free energy are positive and increase with increase in concentration of the solute and decrease in the size of cation or anion.

(6)

The obtained mole fraction mean ionic activity coefficients were used to calculate the molar excess Gibbs free energy (gex) and the molar Gibbs free energy of mixing (Δgmix) of solutions E



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calorimetric measurement below 154 °C. J. Phys. Chem. Ref. Data 1985, 14 (2), 489−610. (14) Rard, J. A.; Platford, R. F. In Activity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, 1991. (15) Saul, A.; Wagner, W. J. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data 1987, 16, 893−901. (16) Archer, D. G. Thermodynamic properties of the NaBr+H2O System. J. Phys. Chem. Ref. Data 1991, 20, 509−555. (17) Archer, D. G. Thermodynamic Properties of the NaCl+H2O System. II. Thermodynamic Properties of NaCl(aq), NaCl·2H2(cr), and Phase Equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829.

CONCLUSIONS In this work, the accurate vapor−liquid equilibrium data (water activity, vapor pressure, osmotic coefficient, and activity coefficients) for binary aqueous solutions of Me4NBr, Et4NBr, Pr4NBr, Bu4NBr, Me4NCl, and Me4NI were determined through the VPO method at T = 308.15 K. The results show that the values of the water activity, water activity coefficient, and vapor pressure depression follow the order Me4NBr < Et4NBr < Pr4NBr < Bu4NBr and Me4NCl < Me4NBr < Me4NI implies that the smaller ions hydrate more water molecule than the ions with larger size. The values of the osmotic and mean molal activity coefficients decreased along with an increase in the cation and anion size, which indicate that water structureenforced ion pairing overshadows the structure making ability of the ions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Tel./Fax: +98-871-6624133. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Lowe, B.; Rendall, H. Dilute aqueous solutions of unsymmetrical quarternary ammonium iodides. Part 1. Viscosity and density measurements. Trans. Faraday Soc. 1971, 2318−2327. (2) Amado, E.; Blanco, L. H. Osmotic and activity coefficients of dilute aqueous solutions of unsymmetrical tetraalkylammonium iodides at 298.15 K. J. Chem. Eng. Data 2012, 57, 1044−1049. (3) Lindenbaum, S.; Boyd, G. E. Osmotic and activity coefficients for the symmetrical tetraalkyl ammonium halides in aqueous solution at 25C. J. Phys. Chem. 1964, 68, 911−917. (4) Lindenbaum, S.; Liefer, L.; Boyd, G.; Chase, J. Variation of osmotic coefficients of aqueous solutions of tetraalkylammonium halides with temperature. Thermal and solute effects on solvent hydrogen bonding. J. Phys. Chem. 1970, 74, 761−764. (5) Boyd, G. E.; Schwarz, A.; Lindenbaum, S. Structural effects on the osmotic and activity coefficients of the quaternary ammonium halides in aqueous solutions at 25°. J. Phys. Chem. 1966, 70, 821−825. (6) Wen, W. Y.; Saito, S. Activity coefficients and molal volumes of two tetraethanolammonium halides in aqueous solutions at 25°. J. Phys. Chem. 1965, 69, 3569−3574. (7) Wen, W. Y.; Saito, S.; Lee, C.-M. Activity and osmotic coefficients of four symmetrical tetraalkylammonium fluorides in aqueous solutions at 25 C. J. Phys. Chem. 1966, 70, 1244−1248. (8) Amado, E.; Blanco, L. H. Isopiestic determination of the osmotic and activity coefficients of dilute aqueous solutions of symmetrical and unsymmetrical quaternary ammonium bromides with a new isopiestic cell at 298.15 K. Fluid Phase Equilib. 2005, 233, 230−233. (9) Amado, E.; Blanco, L. H. Osmotic and activity coefficients of dilute aqueous solutions of symmetrical and unsymmetrical quaternary ammonium bromides at 293.15 K. Fluid Phase Equilib. 2006, 243, 166−170. (10) Blanco, L. H.; Amado, E.; Calvo, J. C. Osmotic and activity coefficients of dilute aqueous solutions of the series Me4NI to MeBu3NI at 298.15 K. Fluid Phase Equilib. 2008, 268, 90−94. (11) Amado, E.; Blanco, L. H. Isopiestic determination of the osmotic and activity coefficients of aqueous solutions of symmetrical and unsymmetrical quaternary ammonium bromides at T = (283.15 and 288.15) K. J. Chem. Eng. Data 2009, 54, 2696−2700. (12) Sadeghi, R.; Shahebrahimi, Y. Vapor−liquid equilibria of aqueous polymer solutions from vapor pressure osmometry and isopiestic measurements. J. Chem. Eng. Data 2011, 56, 789−799. (13) Clarke, E. C. W.; Glew, D. N. Evaluation of the thermodynamic functions for aqueous sodium chloride from equilibrium and F


Vapor Pressure Osmometry Determination of the Osmotic and Activity

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