Effect of Temperature and Concentration on Density, Apparent Molar

Article pubs.acs.org/jced

Effect of Temperature and Concentration on Density, Apparent Molar Volume, Ultrasound Velocity, Isoentropic Compressibility, Viscosity, and Conductivity of Hexadecyldimethylethylammonium Bromide Fayaz Ahmad Sheikh† and Parvaiz Ahmad Bhat*,‡ †

Department of Chemistry, Sri Pratap (S. P.) College, Srinagar-190006, J&K, India Department of Chemistry, Government Degree College Boys, Anantnag-192102, J&K, India

‡

ABSTRACT: Physicochemical properties like density, apparent molar volume, ultrasound velocity, isoentropic compressibility, viscosity, and conductivity of aqueous solutions of hexadecyldimethylethylammonoum bromide as a function of concentration at different temperatures ranging from (298.15 to 323.15) K have been determined. Critical micellar concentration values depend upon the technique used. Density data have been used to calculate the apparent molar volume of the surfactant. Viscosity data have been employed to compute degrees of hydration based on the Vand and Einstien equation. Conductivity measurements have been used to evaluate the degree of counterion binding and various thermodynamic paramaters.

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INTRODUCTION The study of surfactant systems has been a subject of research interest because of their technological, fundamental, pharmaceutical, and biological considerations.1−3 The size and shape of micelles can be controlled by varying surfactant structure and by changing solution conditions such as ionic strength, pH, overall surfactant concentration, and temperature. In this regard, extensive studies4−8 have been carried out to investigate the aqueous solutions of alkyl (octyl, nonyl, decyl, dodecyl, tetradecyl, and hexadecyl) trimethylammonium bromide as a function of concentration and temperature. The temperature dependence of critical micellar concentration (cmc) can be used to determine various thermodynamic properties like free energy, enthalpy, and entropy of micellization. The application of surfactant systems in industrial, technological, and pharmaceutical companies requires detailed understanding of their various physicochemical properties such as density, viscosity, critical micelle concentration (cmc), geometry, size, ultrasound velocity, conductivity, degree of counterion binding, and so forth. The study of aqueous solutions of ionic surfactants has emerging applications in industries and pharmaceutical companies.9,10 One important class of ionic surfactants, known as trialkylammonium halides, has been a subject of increasing interest and has been extensively exploited in the treatment of pollutants and other compounds in many biological, pharmaceutical, and environmental systems.11−13 Though the studies on micellization behavior of these quaternium nitrogen-based surfactants4−6,8,13 like hexadecyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, dodecyltrimethylammonium bromide, and so forth, © XXXX American Chemical Society

are frequently available, to our knowledge, there is no report of physicochemical studies of hexadecyldimethylethylammonium bromide (C16Me2EAB) yet. The surfactant is an effective surface active compound and can conveniently interact with neutral and anionic surfactants/polymers forming solutions of different consistencies. It has antifungal properties and a low cost of production. The present work aims at the detailed investigation of micellization behavior of C16Me2EAB with a special focus on density, apparent molar volume, ultrasound velocity, isoentropic compressibility, viscosity, conductivity, cmc, degree of counterion binding, and thermodynamics of micellization as a function of surfactant concentration at different temperatures.

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EXPERIMENTAL SECTION Materials. The surfactant C16Me2EAB with a purity of 99 % from Sigma was used without further purification. Doubledistilled water was used in all of the experiments. Methods. The densities of aqueous solutions of C16Me2EAB were measured using a calibrated dilatometer. The dilaltometer was filled up to a level slightly below the first calibrated mark, and after weighing, it was immersed in the constant temperature bath. The constancy of temperature was assured (with an accuracy of ± 0.02 °C) when the meniscus coincided and remained stationary at the mark for 15 min. A similar procedure was followed for all of the subsequent marks Received: March 15, 2012 Accepted: November 5, 2012

A

dx.doi.org/10.1021/je3003404 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Density and Molar Apparent Volumes of Aqueous Solutions of Hexadecyldimethylethylammonium Bromide as a Function of Concentration and Temperature (Pressure p = 0.1 MPa)a 104 [C16Me2EAB] (mol·kg−1)

2

5

8

a

16

20

10 density ρ kg·m

T/K 298.15 303.15 308.15 313.15 318.15 323.15

12 3

0.99643 0.99449 0.99255 0.99061 0.98867 0.98671

0.99647 0.99452 0.99258 0.99063 0.98868 0.98672

0.99651 0.99456 0.99261 0.99067 0.98870 0.98674

0.99654 0.99459 0.99263 0.99068 0.98873 0.98676

25

0.99656 0.99461 0.99265 0.99069 0.98874 0.98678

Vs

30

−3

0.99658 0.99462 0.99266 0.99070 0.98875 0.98679

0.99660 0.99464 0.99267 0.99072 0.98876 0.98680

0.99662 0.99466 0.99269 0.99073 0.98878 0.98681

ΔVm

Vm −1

−1

cm ·mol

cm ·mol

247.6 266.0 282.9 317.7 324.1 335.4

336.8 344.7 353.1 355.5 359.4 365.6

3

3

cm3·mol−1 89.2 78.7 70.2 37.8 35.3 30.3

Error limits in the measurements of T, ρ, Vs, and Vm are ± 0.01 %, ± 0.01 %, ± 4 %, and ± 4, respectively.

on the stem. The densities obtained corresponding to each mark were least-squares fitted to the recorded temperatures (ρ = a + bT). The best-fitted values of the parameters a and b were utilized to compute the densities of solutions at the required temperatures. The accuracy in the density measurement was ± 0.00001 g·cm−3. The viscosity measurements of the surfactant solutions were done using a Cannon Ubbelhold type suspended viscometer between (20 to 50) °C at five intervals. The constancy of temperature was achieved (within 0.02 °C) by circulating water from a HAAKE GH thermostat. The accuracy of viscosity measurements was within ± 10−6 Pa·s. The velocity of ultrasound waves in various surfactant solutions was measured by an ultrasonic interferometer (MittalM81). The measuring cell of the instruement is double-walled and is especially designed to maintain the temperature of solution constant. A fine micrometer screw provided at the top of the cell can raise or lower a disk shaped reflector plate by a known distance through the solution in the cell. If the distance traversed by the waves before reflection in the solution is equal to an integral multiple of half wavelengths, the current registered by the instruement is maximum. The displacement of the reflector plate as recorded by the micrometer for 20 such maxima was measured, and the average displacement (L) per maximum was calculated. This gives half wavelength of sound waves traveling in solution, and the wavelength of ultrasonic waves given by λ = L/10 was used to calculate ultrasound velocity (U = λv). Measurements were made at a frequency of 4 MHz in the given temperature range at 5° intervals with the precision of 0.01 m·s−1. The conductivity measurements of surfactant solutions were done using dip-type conductivity cell (Elico, EC-03) connected to a digital RLC meter (GR. 1695, USA) with an accuracy of ± 0.2 %. The temperature of the surfactant solutions was kept constant within ± 0.05 °C. The specific conductivities were computed from the corresponding measured resistances of surfactant solutions.

Figure 1. (a) Density of aqueous solutions of hexadecyldimethylethylammonium bromide as a function of concentration and temperature. (b) Apparent molar volume of surfactant and micelles as a function of temperature.

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RESULTS AND DISCUSSION Density and Apparent MolarVolumes. The experimentally determined density values of C16Me2EAB solutions at different concentrations and temperatures are given in Table 1. The representative plot of variation of density versus surfactant concentration at 298.15 K is plotted in Figure 1a. The plot shows a breakpoint at a particular concentration. This phenomenon is due to the formation of micelles in solution, and the breakpoint corresponds to the cmc at that temperature.14 However, no second inflection point was observed, indicating that the shape and size of micelle remains constant in

the investigated range of surfactant concentration and temperature.15−18 The estimated cmc values at different temperatures are given in Table 2. The concentration dependence of density can be expressed19 as ρ = ρ0 + (1 − vsρ0 )Cs + (1 − vmρ0 )Cm

(1)

where ρ and ρ0 are the densities of surfactant solution and water, respectively, vs and vm are the apparent specific volumes B



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Table 2. 104 cmc mol·kg−1 of Aqueous Solutions of Hexadecyldimethylethylammonium Bromide at Different Temperatures Using Different Methods T/K

density

viscosity

sound velocity

isoentropic compressibility

conductivity

298.15 303.15 308.15 313.15 318.15 323.15

9.25 10.25 10.24 11.89 12.00 12.11

9.52 10.87 11.05 12.00 12.75 12.35

8.96 9.85 10.31 12.00 12.25 12.48

9.11 9.97 10.00 11.93 12.11 12.31

8.93 10.12 10.22 9.25 9.56 9.89

1b), which may be due to lower contribution of less structured icebergs. However it has been reported19 that the increase in temperature increases the degree of ionization, which shall increase ΔVm. Therefore it may be argued that the effect of water molecules on ΔVm of the surfactant compensates the increase in ΔVm due to increase in degree of ionization around 310 K. Ultrasound Velocity and Isoentropic Compressibility. Ultrasound velocity in micellar solutions has been found to depend on surfactant concentration and temperature.25,26 The values of ultrasound velocity in micellar solutions are usually smaller than those containing monomeric surfactants only. Figure 2 shows the dependence of ultrasonic velocity (U) measured for aqueous solutions of C16Me2EAB as a function of concentration at different temperatures. The corresponding dependence of isoentropic compressibilities (k), calculated from the relation27 k = 1/(U2ρ) where U is expressed in m·s−1 and ρ in kg·m−3, is given in Table 3. The plots show a sharp break at each temperatures, corresponding to cmc. The ultrasound values of aqueous solutions of C16Me2EAB as a function of concentration and temperature are given in Table 3. The trend obtained is in tune with the literature for other surfactants.19,28 The dependence of isoentropic compressibility of aqueous solutions of surfactants on premicellar and postmicellar concentration regions can be expressed by two corresponding equations given below. They may be treated as approximations of the exact equations used by Zielinski et al.28

of monomers and micelles, respectively, and Cs and Cm are their corresponding concentrations in g·cm−3. If these apparent specific volumes were negligibly concentration-dependent, then for premicellar region (Cm = 0) and ρ = ρ0 + (1 − vsρ0)Cs and for postmicellar region (Cm = C − cmc) and ρ = ρ′ + (1 − vmρ0)(C − cmc) where ρ′ = ρ0 + (1 − vsρ0)Cs and (C − cmc) is the micellar concentration. The apparent molar volume may be taken as a tool to understand the behavior of surfactant solution with the change in concentration and temperature.19 The apparent molar volume of surfactant (Vs = vsM) and micelle (Vm = vmM) have been calculated from the slopes of density versus surfacatant/micelle concentration plots at different temperatures; M is the molecular weight of the surfactant. The values given in Table 1 are observed to increase with the increase in temperature (Figure 1b). This effect is related to the relaxation of structured water engaged in solvation of the hydrocarbon chain, the headgroup, and the counterions upon increase in temperature. A similar behavior has been observed for other surfactants.19,20 The change in apparent molar volume upon micellization (ΔVm = Vm − Vs) at different temperatures have been calculated and given in Table 1. The values of ΔVm found for C16Me2EAB are positive, consistent with the earlier reported values for other surfactants.21−24 This effect may primarily be due to the breaking of structured icebergs around the hydrophobic part of monomeric surfactants during micellization. A decrease of ΔVm values with the temperature increase was observed. However, at higher temperatures (above 310 K), the contribution to ΔVm was found to be lower (Figure

k = k 0 + (ks − k 0)VsCs

Cs < cmc

k = k′ + (k m − k 0)Vm(C − cmc)

(2)

C > cmc

(3)

where k′ = k0 + (ks − k0)vsCs; k0 is the isoentropic compressibility of water, and ks and km are the apparent isoentropic compressibilities of monomeric surfactant and micellar solutions, respectively. The apparent isoentropic compressibility in monomeric and micellar forms as a function of concentration is plotted in Figure 2 at different temperatures. The apparent molar isoentropic compressibility values for ionic compounds have been found to be large and negative, while for

Figure 2. Variation of ultrasound velocity of aqueous solutions of hexadecyldimethylethylammonium bromide with concentration and temperature. C



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Table 3. Ultrasound Velocity (U), Isoentropic Compressibility (k), Apparent Molar Isoentropic Compressibility of Monomoeric (ks) and Micellar Forms (km), Change in Apparent Molar Isoentropic Comressibility (Δkm) of Aqueous Solutions of Hexadecyldimethylethylammonium Bromide as a Function of Concentration and Temperature (Pressure p = 0.1 MPa)a Ultrasound Velocity (m·s−1) 4

T/K

10 [C16Me2EAB] mol·kg

−1

2 5 8 12 16 20 25 30 2 5 8 12 16 20 25 30 1011 ks (Pa−1) 1011 km (Pa−1) 1011 km (Pa−1) a

298.15

303.15

1498.50 1499.32 1499.96 1500.27 1500.08 1499.91 1499.89 1499.72

1510.35 1511.02 1511.84 1512.34 1512.15 1511.97 1511.78 1511.59

4.478 4.473 4.469 4.467 4.468 4.469 4.469 4.470 −5.61 0.87 6.48

4.408 4.404 4.399 4.396 4.397 4.398 4.399 4.400 −5.26 0.90 6.16

308.15

313.15

1518.56 1528.82 1519.24 1529.87 1519.91 1530.37 1520.41 1531.25 1520.23 1531.06 1520.04 1530.88 1519.95 1530.68 1519.50 1530.50 1012 Isoentropic Compressibility, k (Pa−1) 4.369 4.319 4.363 4.313 4.361 4.310 4.358 4.305 4.359 4.306 4.360 4.307 4.360 4.308 4.361 4.309 −4.89 −4.40 0.93 0.96 5.82 5.35

318.15

323.15

1537.09 1538.17 1538.51 1539.39 1539.20 1539.01 1538.83 1538.63

1541.69 1542.76 1543.47 1544.55 1544.35 1544.07 1543.97 1543.78

4.281 4.275 4.273 4.268 4.269 4.270 4.271 4.272 −4.02 0.98 5.00

4.264 4.258 4.254 4.248 4.249 4.250 4.251 4.252 −3.65 1.01 4.66

Error limits in the measurements of U, k, ks, km, and T are ± 0.04 %, ± 6 %, ± 5 %, ± 5 %, and ± 0.01 %, respectively.

Table 4. Viscosity (η), Intrinsic Viscosity (ηm), Vand’s (hv), and Einsteins’s (he) Degrees of Hydration, Interaction Coefficient (Q′), Partial Molar Volume of Hydrated Micelles (A3) of Aqueous Solutions of Hexadecyldimethylethylammonium Bromide at Different Temperatures (Pressure p = 0.1 MPa)a 104 Viscosity η/Pa·s −4

10

a

T/K

[C16Me2EAB] mol·kg−1

298.15

303.15

308.15

313.15

318.15

323.15

2 5 8 12 16 20 25 30 A3 (dm3·mol−1) Q′ ηm (dm3·mol−1) he (cm3·g−1) hv (cm3·g−1)

8.803 8.841 8.870 8.904 8.929 8.952 8.979 9.007 2.875 −3.300 6.620 6.270 6.270

7.889 7.920 7.945 7.978 8.001 8.021 8.047 8.070 2.793 −3.230 6.440 6.040 6.030

7.097 7.125 7.157 7.190 7.209 7.228 7.250 7.271 2.745 −3.130 6.320 5.860 5.870

6.410 6.432 6.469 6.502 6.520 6.539 6.558 6.576 2.723 −3.100 6.270 5.720 5.720

5.820 5.832 5.870 5.903 5.922 5.935 5.954 5.971 2.600 −2.980 5.990 5.410 5.410

5.274 5.298 5.334 5.357 5.384 5.398 5.413 5.426 2.476 −2.840 5.700 5.080 5.080

Error limits in the measurements of T, η, ηm, he, and hv are ± 0.01 %, ± 4 %, ± 5 %, ± 4, and ± 4, respectively.

hydrophobic solutes the values have been found to be positive.29,30 The values of apparent molar isoentropic compressibility above cmc (km) at all temperatures are positive, and those below cmc (ks) are negative, which reveal that monomers trapped in the micellar hydrophobic environment are more compressible than aqueous free monomer in solution. If the intrinsic compressibility of solute is considered as zero, the observed compressibilities are ascribed to the compressibility of the hydration sheath and an increase of compressibility characterizes the progressive hydrophobic hydration loss that

accompanies the micellization process, as has been observed previously for other surfactants.31 The ks values are negative at premicellar concentrations at all investigated temperatures, which correspond to ionic compounds in water. As can be observed from Table 3, the apparent molar isoentropic compressibilities of monomer and micelle increase with increase of temperature, which may be attributed to the decrease in less compressible structured water (than bulk) in the surfactant viscinity. The changes in apparent molar isoentropic compressibility upon micellization, Δkm = (km − k1), calculated are given in Table 2. D



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Figure 3. Viscosity of aqueous solutions of hexadecyldimethylethylammonium bromide as a function of concentration and temperature.

Viscosity. Table 4 shows the experimentally observed values of viscosity of C16Me2EAB at various temperatures and corresponding changes of viscosity with surfactant concentration are plotted in Figure 3. The observed viscosity values decrease with increasing temperature and increase with the increasing surfactant concentration. The increase in viscosity with the concentration increase may be due to increased cohesion forces, and the decrease with increase in temperature may be attributed to the kinetic energy increase of various constituents in solution. The plots show an inflection point corresponding to the cmc showing fair agreement with those determined by density and ultrasound measurements (Table 2). No second inflection was observed in the studied surfactant concentration range, indicating no structural transition in micelles. The concentration dependence of viscosity can be explained in terms of reduced and intrinsic viscosity. The reduced viscosity of a solution is given by ηred = {(η − η0) − 1}/C, where η is viscosity of solution, η0 is viscosity of water, and C is the concentration of solution. In postmicellar region ηred = {(η − ηm) − 1}/(C − cmc), where (C − cmc) represents the micellar concentration and ηm is viscosity of solution at cmc. The values of η are least-squares fitted to the equation in postmicellar region to determine the intrinsic viscosity ηm which corresponds to the intercept of ηred versus micellar concentration plots. The values of reduced viscosity were observed to be more or less constant in the investigated concentration range, indicating that the size and shape of micelle remain constant.32,33 The intrinsic viscosity values of surfactant solutions are given in Table 4. The intrinsic viscosity values were observed to decrease with increase in temperature, which may be due to the dehydration of head groups and consequent decrease in size of micelles. It may also be due to increase in kinetic energy of various constituents in solution. The hydration of micelles can be studied using the Vand equation34 given as log ηr = (A3 × C)/(1 − Q ′C)

micelles, shape factor a = 2.5. In the postmicellar region, the modified equation is {1/(C − cmc)}log(η /ηm) = A3 + Q ′ log(η /ηm)

(5)

Table 4 shows the values of A3 and Q′ obtained from the plots of left side of eq 5 versus log(η/ηm). All of the Q′ values were observed to be negative and A3 values as positive. The degree of hydration hv (cm3·g−1) of the micelle is calculated using hv = Vsh − Vs where Vsh = (921.2/M)/A3; Vsh is partial specific volume of hydrated micelle in cm3·g−1, and Vs is the partial specific volume of anhydrous micelle and is taken as apparent specific volume from density data. The hv values given in Table 4 show that degree of hydration of micelle is lowered with the increase in temperature as expected. Alternatively the degree of hydrophilic hydration in micelles was calculated using the Einstein equation35 ηm = a′(Vs + he), where a′ is the Einstein coefficient equal to 2.5 for spherical micelle and he is the hydration of the micelle. The degree of hydration of C16Me2EAB micelle calculated using both the Vand equation and Einstein equation are in excellent agreement (Table 4). Conductivity and Thermodynamics of Micellization. The specific conductivity, k̅, versus surfactant concentration plots at various temperatures are shown in Figure 4, and the corresponding values are given in Table 5. The intersection point of two linear lines in these plots corresponds to the cmc. It has been suggested19 that the degree of ionization (α) and hence the degree of counterion binding (β) can be estimated from the ratio of the slopes of linear lines in premicellar and postmicellar regions. The cmc values obtained at different temperatures (Table 2) are slightly different from those determined by viscosity and other methods. This infers that cmc determination depends upon the technique used. The lower cmc value of C16Me2EAB compared to that of C16Me3AB (hexadecyltrimethylammonium bromide: cmc = 0.93·10−3 mol·kg−1)36 at 298 K may be attributed to the presence of ethyl group present in the former. The free energy of micellization per mole of monomer unit, ΔGom, can be calculated by the equation37

(4)

where ηr is relative viscosity, Q′ represents the interaction coefficient, and A3 is related to partial molar volume of hydrated micelle (Vh) as A3 = (aVh)/2.303; for spherical

ΔGmo = (1 + β)RT ln cmc E

(6)



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positive. The positive ΔSmo values are attributed to the randomness resulting from the melting of “icebergs” around the nonpolar moiety39 of the monomeric surfactant during micellization and location of hydrophobic part in the like environment of the micelle core. The process of micellization is found to be entropy driven for the studied surfactant at the experimental temperatures since TΔSom > ΔHom.

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CONCLUSION All physicochemical properties (densities and its derived properties, ultrasonic velocities and its derived property, viscosities, and conductivities) were analyzed for understanding the micellization behavior of the C16Me2EAB solution. The determination of cmc depends upon the technique used. Viscosity data has been employed to evaluate degrees of hydration based on the Vand equation and Einstein equation. The parameters evaluated using the two equations were identical. The degree of ionization calculated using conductivity was observed to increase with the increase in temperature. The free energy of micellization and enthalpy of micellization values were found to be negative at all temperatures, though the entropy of micellization was positive.

Figure 4. Variation of the conductivity of aqueous solutions of hexadecyldimethylethylethylammonium bromide with concentration and temperature.

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Complete thermodynamic estimation requires ΔHom along with ΔGom. The temperature effect on the cmc is used to estimate ΔHom assuming counterion binding and aggregation number to be temperature-independent. The values of ΔGom can be obtained from the equation

Corresponding Author

*Email: [email protected]. Notes

The authors declare no competing financial interest.

(7)

ΔG = −RT ln cmc

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where R is the universal gas constant and T is the absolute temperature. ΔHmo = −RT 2

d ln cmc dT

REFERENCES

(1) Evans, D. F.; Wennestrom, H. The Colloidal Domain, Where Physics, Chemistry, and Biology Meet, 2nd ed.; Wiley-VCH: New York, 1999. (2) Goddard, E. D.; Ananthapadmanabhan, K. P. Interaction of Surfactant with Polymers and Protiens; CRC Press: Boca Raton, FL, 1993. (3) Zana, R.; Rubingh, D. N.; Holland, P. M. Cationic Surfactants, Physical Chemistry; Decker: New York, 1991. (4) Nikam, P. S.; Sawanta, A. B. Volumetric behaviour of R4N+ and Br− ions in acetonitrile + water at 303.15 K. J. Mol. Liq. 1998, 75 (3), 199−209. (5) Sardar, N.; Kamil, M.; Kabir-ud-din. Interaction between Nonionic Polymer Hydroxypropyl Methyl Cellulose (HPMC) and Cationic Gemini/Conventional Surfactants. Ind. Eng. Chem. Res. 2012, 51, 1227−1235. (6) Aswal, V. K.; Goyal, P. S. Dependence of the Size of Micelles on the Salt Effect in Micellar Solutions. Chem. Phys. Lett. 2002, 364, 44− 50.

(8)

where (d ln cmc)/(dT) at each temperature can be calculated using the plot of ln cmc vs T and represents change in logrithm of cmc as a result of a small increment in temperature. Therefore, the entropy of micellization, ΔSom, follows from the Gibb’s relationship ΔGmo = ΔHmo − T ΔSmo

AUTHOR INFORMATION

(9)

The evaluated thermodynamic parameters at various temperatures are contained in Table 5. The ΔGom and ΔHom values are negative, and ΔSom values are positive at all temperatures. The change of ΔGom with temperature, being common to aqueous surfactant solutions is due to the enthalpy−entropy compensation effect.38 The ΔSom values for surfactant systems are fairly

Table 5. Conductivity, Degree of ionization (α), Free Energy (ΔGom), Enthalpy (ΔHom), and Entropy (ΔSom) of Micellization of Aqueous Solutions of Hexadecyldimethylethylammonium Bromide at Different Temperaturesa 10−4 Conductivity k̅ (S·cm−1)

Thermodynamics

−1

4

10 [C16Me2EAB] (mol·kg )

a

ΔGom

ΔHom

ΔSom

T/K

2

5

8

12

16

20

25

30

α

KJ·mol−1

KJ·mol−1

KJ·mol−1

298.15 303.15 308.15 313.15 318.15 323.15

0.270 0.301 0.338 0.364 0.396 0.426

0.707 0.808 0.879 0.952 1.070 1.14

1.046 1.270 1.396 1.530 1.710 1.843

1.187 1.440 1.610 1.830 2.102 2.221

1.270 1.530 1.701 1.872 2.301 2.47

1.375 1.670 1.845 2.088 2.502 2.803

1.523 1.783 1.950 2.242 2.650 2.987

1.610 1.938 2.172 2.430 2.802 3.121

0.167 0.172 0.174 0.180 0.185 0.1888

−50.63 −51.06 −51.71 −52.12 −52.43 −52.98

−21.64 −22.29 −22.99 −23.66 −24.32 −24.99

97.24 94.90 93.19 90.88 88.36 86.38

Error limits in the measurements of conductivity and temperature are ± 4 % and ± 0.01 %, respectively. F



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Effect of Temperature and Concentration on Density, Apparent Molar

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