Vapor Pressure Osmometry Determination of the Osmotic andActivity Coefficients of Dilute Aqueous Solutions of SymmetricalTetraalkyl Ammonium Halides at 308.15 KRoonak Golabiazar and Rahmat Sadeghi*
Department of Chemistry, University of Kurdistan, Sanandaj, Iran
ABSTRACT: Osmotic coefficients were measured by the vaporpressure osmometry technique for dilute aqueous solutions ofMe4NBr, Et4NBr, Pr4NBr, Bu4NBr, Me4NCl, and Me4NI at 308.15K. 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 Pitzerequation from which the values of the mean molal activitycoefficients were calculated. The values of the obtained osmoticand mean molal activity coefficient data for the bromides decreasedwith 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 wateractivity, vapor pressure depression, and the water activity coefficient data follow the order Me4NBr < Et4NBr < Pr4NBr < Bu4NBrand Me4NCl < Me4NBr < Me4NI, which implies that the smaller ions hydrate more water molecules than the ions with largersize.
■ INTRODUCTION
Experimental phase equilibrium data of aqueous electrolytes areof considerable importance in the prediction of the behavior ofelectrolyte solutions, the development of the electrolytemodels, and the estimation of interactions occurring in thesesystems. Among all the phase equilibrium data, the solventactivity is an important and key thermodynamic propertybecause it is closely related with the other thermodynamicproperties and, in thermodynamic modeling for separationmethods, it is the essential variable. Several experimentaltechniques that include freezing point depression, boiling pointelevation, dynamic and static vapor pressure measurements,osmotic pressure measurements, hygrometry, vapor sorption,isopiestic method and vapor pressure osmometry (VPO) havebeen employed to measure the solvent activity of nonvolativesolutions.The symmetrical tetraalkyl ammonium halides make it
possible to develop new materials that may have differentindustrial uses. On the fundamental level, the tetraalkylammonium salts are interesting models for the study of thehydrophobic interactions occurring in electrolyte solutions dueto their fairly high solubility in water and the possibility ofworking with series having variable alkyl chain lengths.1,2
Although osmotic and activity coefficients of aqueous solutionsof tetraalkyl ammonium halides have been extensivelyinvestigated through the isopiestic method by the researchgroups of Lindenbaum et al.,3−5 Wen et al.,6,7 and Amado etal.,2,8−11 the subject is not clearly understood and there is noVPO determination of vapor−liquid equilibria properties ofaqueous solutions of tetraalkyl ammonium halides in theliterature. In fact the isopiestic method is a limited technique
for the dilute solutions and at lower concentrations somedifficulties appear so that the molality m = 0.1 is considered tobe the lower limit of applicability for binary electrolytessolutions. Therefore the published osmotic and activitycoefficients of dilute aqueous solutions of tetraalkyl ammoniumhalides are limited, and because of the potential use of theseorganic salts, new measurements are needed to supplementthese studies. The VPO method which has become one of themost frequent techniques for solvent activity determination ofdilute solutions is based on a precise determination of thetemperature difference between a drop of solution and a dropof solvent hanging on temperature-recording thermistors.Thermistors are placed in a chamber filled with a saturatedvapor of solvent. Since the vapor pressure of the solution is lessthan that of the pure solvent, the solvent vapor condenses onthe solution droplet and causes a change in its temperatures.Temperature differences between the two thermistors arerepresented as voltage difference measured by a digitalvoltmeter. The present work presents experimental data onthe vapor−liquid equilibria of dilute aqueous solutions ofMe4NBr, Et4NBr, Pr4NBr, Bu4NBr, Me4NCl, and Me4NI at308.15 K obtained from the VPO method.
(≥ 99.5 % w/w) were obtained from Merck. The salts wereused without further purification. Double distilled anddeionized water was used.Apparatus and Procedures. The aqueous solutions were
prepared by mass, using an analytical balance (SartoriusCP225D) with a precision of ± 1·10−5 g. In this study, theVPO method was used to obtain the water activities of theinvestigated 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 tothe one used previously.12 The measuring chamber of theosmometer contains a reservoir of water, paper wicks toprovide a saturated water atmosphere, and two thermistors thatare placed in an airtight cell which measure resistance changescaused by changes in temperature. First, a droplet of pure wateris attached to each thermistor with the help of a microsyringe,and after 5 min of equilibration, the reading is adjusted to zero.
Then the pure water on one thermistor is replaced by theR4NX aqueous solution and condensation of water from thevapor phase into the R4NX solution at the thermistor takesplace. Because of the heat of condensation, the thermistorcontaining R4NX solution will be warmed and vapor pressurerises. These processes continue until the vapor pressure of theR4NX solution equals the vapor pressure of the pure water. Thechange in temperature changes the resistance of thethermistors. A bridge circuit measures the resistance differenceof both thermistors. As long as changes in temperature aresmall, the resistance is proportional to ΔT. Generally, a time of4−8 min suffices to reach this steady state. First, the instrumentwas calibrated using aqueous NaCl solutions as reference withknown osmotic coefficients in the proper concentration range,yielding a function that correlates the panel readings to thecorresponding concentrations of the reference solutions andtherefore their osmotic coefficients. Then in the same
Table 1. Osmotic Coefficients, Water Activities, Vapor Pressures, Water Activity Coefficients, and Mean Molal ActivityCoefficients of Aqueous Solutions of R4NX at T = 308.15 Ka
m/mol·kg−1 Φ aw p/kPa γw γ± m/mol·kg−1 Φ aw p/kPa γw γ±
dx.doi.org/10.1021/je400821q | J. Chem. Eng. Data XXXX, XXX, XXX−XXXB
conditions, the panel readings were measured for the studiedR4NX solutions. For each solution, at least five determinations(zero point adjustment and new solution) were performed, andthe mean value is reported. Generally, the deviations from themean value were less than 1 %. The cell temperature, which iselectronically controlled, has a standard uncertainty of ± 1.10−3
K. For a certain R4NX solution with molality m which has asame instrument reading as a sodium chloride solution withmolality mNaCl and osmotic coefficient ΦNaCl, the osmoticcoefficient Φ was obtained according to
ν νΦ = Φm m( )/( )NaCl NaCl NaCl (1)
where ν is the stoichiometric number. ΦNaCl is the osmoticcoefficient for aqueous solutions of NaCl with molality mNaClcalculated from the correlation given in the literature.13 Fromthe experimental osmotic coefficients, it is possible to calculatethe water activities of the investigated solutions using thefollowing relation:
ν= − Φa M mexp[ ]w w (2)
where Mw is the molar mass of water. The uncertainty in themeasurement of water activity was found to be better than ± 2·10−4.
■ RESULTS AND DISCUSSIONTable 1 shows the experimental osmotic coefficient and wateractivity data of the investigated solutions at 308.15 K. From thesolvent activity data, the vapor pressure data of solutions, p,were determined with the help of the following equation:
=°
+− − °◦⎛
⎝⎜⎞⎠⎟a
pp
B V p pRT
ln( ) ln( )( )
ww
(3)
where B, Vw°, and p° are the second virial coefficient, molarvolume, and vapor pressure of pure water, respectively. R is thegas constant and T is the absolute temperature. The secondvirial coefficients of water vapor were calculated using theequation provided by Rard and Platford.14 Molar volumes ofliquid water were calculated using the density of water atdifferent temperatures. The vapor pressures of pure water werecalculated using the equation of state of Saul and Wagner.15
The calculated vapor pressure data of investigated R4NXsolutions are also given in Table 1. In Figures 1, 2 and 3,respectively, comparison of the experimental osmotic coef-ficient, water activity, and vapor pressure depression data (p −p°) for the Me4NBr, Et4NBr, Pr4NBr, Bu4NBr, Me4NCl andMe4NI 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 osmoticcoefficient data of aqueous R4NBr solutions are larger than thaton the water activity or vapor pressure data. Figure 1 shows thatthe osmotic coefficients decrease with both cation and anionsize. In the same solute molality, water activity and vaporpressure depression of the investigated binary aqueoussolutions 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 (andanions) and therefore we may expect that the vapor pressuredepression for smaller cations (and anions) solutions be greaterthan those for the larger cations (and anions) solutions.Aqueous solutions of the smaller cations (and anions) becauseof the stronger ion−water interactions have smaller wateractivities than those of the larger cations (and anions). In fact,
the salt molality dependence of the water activity or vaporpressure depression follows the orders Me4NBr > Et4NBr >Pr4NBr > Bu4NBr and Me4NCl > Me4NBr > Me4NI, andimplies that the anion (and cation)−water interactions foranions (and cations) with smaller size are stronger than theanion (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 withthose taken from the literature3 measured at 298.15 K havebeen made for Me4NBr, Et4NBr, Pr4NBr, and Me4NCl systems.As can be seen, there is a good agreement between our data andthose taken from the literature. To more scrutinize the vapor−liquid equilibria behavior of the investigated systems, the values
Figure 1. Plot of the osmotic coefficient Φ of R4NX aqueous solutionsagainst molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○,Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr; ,calculated by Pitzer model.
Figure 2. Plot of the water actvity aw of R4NX aqueous solutionsagainst molality of R4NX, m, at T = 308.15 K: ●, Me4NCl; ○,Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr; ,calculated by Pitzer model.
Journal of Chemical & Engineering Data Article
dx.doi.org/10.1021/je400821q | J. Chem. Eng. Data XXXX, XXX, XXX−XXXC
of the water activity coefficients, γw, and the mean molal activitycoefficients, γ±, were also calculated. The water activities wereused to obtain the solvent activity coefficients, γw = (aw/xw).
Calculated water activity coefficients, γw, of the investigatedaqueous solutions are also given in Table 1. The experimentalosmotic coefficients are related to the mean molal activitycoefficients, γ±, at molality m′ by the relation
∫γ = Φ′ − + Φ −±
′
mmln 1
1d
m
0 (4)
The osmotic coefficients were correlated by the extended Pitzerion-interaction model of Archer16,17 which has the followingform for 1:1 electrolytes:
β β α
β α
α
Φ − =−
++ + −
+ − +
+ −
ϕA I
b Im I
I m C
C I
11
( exp[ ]
exp[ ]) (
exp[ ])
(0) (1)1
(2)2
2 (0)
(1)3 (5)
where β(0), β(1), β(2), C(0), and C(1) are ion interaction parameterof the Archer extension of the Pitzer model that are dependenton 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 theionic 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 = 1kg0.5·mol−0.5. The calculated values of γ± (obtained from eq 4by using the Pitzer’s model, eq 5, for Φ) are also given in Table1. The variations of γw and γ± with the solute concentration areshown in Figures 5 and 6, respectively. For all systems, γ± < 1
Figure 3. Plot of the vapor pressure depression p − p° of R4NXaqueous 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 datameasured in this work at 308.15 (solid line) K with those taken fromthe literature3 measured at 298.15 K (dotted line): ●, Me4NCl; ○,Me4NBr; △, Et4NBr; ×, Pr4NBr.
Table 2. Pitzer’s Model Parameters and the Corresponding Absolute Relative Deviation, ARDa, for Osmotic Coefficients ofAqueous Solutions of R4NX at T = 308.15 K
system β(0) β(1) β(2) C(0) C(1) ARD %
Me4NBr + water 19.6395 −33.3431 21.7340 17.6976 −82.6035 0.247Et4NBr + water 35.8906 −59.9589 33.5551 32.0109 −151.5629 0.218Pr4NBr + water 39.6283 −65.8031 33.9423 37.8985 −172.2730 0.211Bu4NBr + water 5.62202 −10.9507 6.2338 3.0918 −18.9576 0.193Me4NCl + water 27.1021 −45.6170 24.5210 29.7811 −123.8269 0.107Me4NI + water 29.4307 −48.7494 29.3256 27.1250 −126.1831 0.115
aARD = 1/(NP) Σ[(|Φexpt − Φcalc|)/Φexpt].
Figure 5. Plot of the water activity coefficient, γw, of R4NX aqueoussolutions against molality of R4NX, m, at T = 308.15 K: ●, Me4NCl;○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr.
Journal of Chemical & Engineering Data Article
dx.doi.org/10.1021/je400821q | J. Chem. Eng. Data XXXX, XXX, XXX−XXXD
(negative deviations from ideal-solution behavior) anddecreased along with an increase in the solute concentration.The calculated water activity coefficients are very slightly largerthan unity (positive deviations from ideal-solution behavior)and increase as solute concentration increases. Similar to thewater activity and vapor pressure depression, in the same solutemolality, water activity coefficients of the investigated binaryaqueous 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 foranions (and cations) with smaller size are stronger than theanion (and cation)−water interactions for anions (and cations)with larger size. On the other hand, the observed trend for thecalculated γ± of investigated solutions is similar to thoseobtained for Φ, so that the values of the mean molal activitycoefficients decreased along with an increase in the cation andanion size. The change of the osmotic coefficient or mean molalactivity coefficient with the size of cation or anion can beinterpreted in terms of the hydrophobic hydrations and ion pairformations. The larger are the cations or anions, the morehydrophobic these ions will be, the more the water structurewill be enforced, and the greater the free energy of the ion.3
Therefore, the larger activity coefficients can be expected in thecase of the larger ions. As can be seen the observed order of theinvestigated salts is the opposite, therefore, the ion pairingeffect must predominate. The large hydrophobic cations andanions will tend to combine with each other (ion association)to minimize their interaction with the surrounding water as wellas to decrease the electrostatic free energy of the system andthese lead to a drastic lowering of the their activity coefficients.The mole fraction mean ionic activity coefficients, γ±
(x) wereobtained from the molal mean ionic activity coefficients γ± byusing the following relation:
γ γυ
= + +± ±⎜ ⎟⎛⎝
⎞⎠
M mln ln ln 1
1000x( ) w
(6)
The obtained mole fraction mean ionic activity coefficientswere used to calculate the molar excess Gibbs free energy (gex)and the molar Gibbs free energy of mixing (Δgmix) of solutions
by the following relations, and the values are shown in Figures7 and 8.
γ γ= + + ±g RT x x x[ ln ( )ln ]xexw w c a (7)
γ γΔ = + + +±g RT x x x x x x[ ln( ) ( ) ln ( )]xmixw w w c a c a (8)
The values of the molar Gibbs free energy change due tomixing are negative and decrease with an increase inconcentration of the solute and become more negative (veryslightly) when the size of cation or anion increases. Howeverthe calculated values of the molar excess Gibbs free energy arepositive and increase with increase in concentration of thesolute and decrease in the size of cation or anion.
Figure 6. Plot of the mean molal activity coefficient, γ±, of R4NXaqueous solutions against molality of R4NX, m, at T = 308.15 K: ●,Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇, Bu4NBr.
Figure 7. Plot of the molar excess Gibbs energy, gex, of R4NX aqueoussolutions 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, ofR4NX aqueous solutions against molality of R4NX, m, at T = 308.15 K:●, Me4NCl; ○, Me4NBr; △, Et4NBr; ×, Pr4NBr; ▲, Me4NI; ◇,Bu4NBr.
Journal of Chemical & Engineering Data Article
dx.doi.org/10.1021/je400821q | J. Chem. Eng. Data XXXX, XXX, XXX−XXXE
■ CONCLUSIONSIn this work, the accurate vapor−liquid equilibrium data (wateractivity, vapor pressure, osmotic coefficient, and activitycoefficients) for binary aqueous solutions of Me4NBr, Et4NBr,Pr4NBr, Bu4NBr, Me4NCl, and Me4NI were determinedthrough the VPO method at T = 308.15 K. The results showthat the values of the water activity, water activity coefficient,and vapor pressure depression follow the order Me4NBr <Et4NBr < Pr4NBr < Bu4NBr and Me4NCl < Me4NBr < Me4NIimplies that the smaller ions hydrate more water molecule thanthe ions with larger size. The values of the osmotic and meanmolal activity coefficients decreased along with an increase inthe cation and anion size, which indicate that water structure-enforced ion pairing overshadows the structure making abilityof the ions.
■ REFERENCES(1) Lowe, B.; Rendall, H. Dilute aqueous solutions of unsymmetricalquarternary ammonium iodides. Part 1. Viscosity and densitymeasurements. Trans. Faraday Soc. 1971, 2318−2327.(2) Amado, E.; Blanco, L. H. Osmotic and activity coefficients ofdilute aqueous solutions of unsymmetrical tetraalkylammoniumiodides at 298.15 K. J. Chem. Eng. Data 2012, 57, 1044−1049.(3) Lindenbaum, S.; Boyd, G. E. Osmotic and activity coefficients forthe symmetrical tetraalkyl ammonium halides in aqueous solution at25C. J. Phys. Chem. 1964, 68, 911−917.(4) Lindenbaum, S.; Liefer, L.; Boyd, G.; Chase, J. Variation ofosmotic coefficients of aqueous solutions of tetraalkylammoniumhalides with temperature. Thermal and solute effects on solventhydrogen bonding. J. Phys. Chem. 1970, 74, 761−764.(5) Boyd, G. E.; Schwarz, A.; Lindenbaum, S. Structural effects on theosmotic and activity coefficients of the quaternary ammonium halidesin aqueous solutions at 25°. J. Phys. Chem. 1966, 70, 821−825.(6) Wen, W. Y.; Saito, S. Activity coefficients and molal volumes oftwo 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 coefficientsof four symmetrical tetraalkylammonium fluorides in aqueoussolutions at 25 C. J. Phys. Chem. 1966, 70, 1244−1248.(8) Amado, E.; Blanco, L. H. Isopiestic determination of the osmoticand activity coefficients of dilute aqueous solutions of symmetrical andunsymmetrical quaternary ammonium bromides with a new isopiesticcell at 298.15 K. Fluid Phase Equilib. 2005, 233, 230−233.(9) Amado, E.; Blanco, L. H. Osmotic and activity coefficients ofdilute aqueous solutions of symmetrical and unsymmetrical quaternaryammonium bromides at 293.15 K. Fluid Phase Equilib. 2006, 243,166−170.(10) Blanco, L. H.; Amado, E.; Calvo, J. C. Osmotic and activitycoefficients of dilute aqueous solutions of the series Me4NI toMeBu3NI at 298.15 K. Fluid Phase Equilib. 2008, 268, 90−94.(11) Amado, E.; Blanco, L. H. Isopiestic determination of theosmotic and activity coefficients of aqueous solutions of symmetricaland unsymmetrical quaternary ammonium bromides at T = (283.15and 288.15) K. J. Chem. Eng. Data 2009, 54, 2696−2700.(12) Sadeghi, R.; Shahebrahimi, Y. Vapor−liquid equilibria ofaqueous polymer solutions from vapor pressure osmometry andisopiestic measurements. J. Chem. Eng. Data 2011, 56, 789−799.(13) Clarke, E. C. W.; Glew, D. N. Evaluation of the thermodynamicfunctions for aqueous sodium chloride from equilibrium and
calorimetric measurement below 154 °C. J. Phys. Chem. Ref. Data1985, 14 (2), 489−610.(14) Rard, J. A.; Platford, R. F. In Activity Coefficients in ElectrolyteSolutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, 1991.(15) Saul, A.; Wagner, W. J. International equations for the saturationproperties of ordinary water substance. J. Phys. Chem. Ref. Data 1987,16, 893−901.(16) Archer, D. G. Thermodynamic properties of the NaBr+H2OSystem. J. Phys. Chem. Ref. Data 1991, 20, 509−555.(17) Archer, D. G. Thermodynamic Properties of the NaCl+H2OSystem. II. Thermodynamic Properties of NaCl(aq), NaCl·2H2(cr),and Phase Equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829.
Journal of Chemical & Engineering Data Article
dx.doi.org/10.1021/je400821q | J. Chem. Eng. Data XXXX, XXX, XXX−XXXF
