Acoustical and excess thermodynamic studies of

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Acoustical and excess thermodynamic studies of mixtures of 2-pyrrolidone with 1,3-propanediol and water as well as 1,3-propanediol with water at 308.15 K Balwinder Saini, Anjana Gupta, Renu Sharma & Rajinder K. Bamezai To cite this article: Balwinder Saini, Anjana Gupta, Renu Sharma & Rajinder K. Bamezai (2014) Acoustical and excess thermodynamic studies of mixtures of 2-pyrrolidone with 1,3-propanediol and water as well as 1,3-propanediol with water at 308.15 K, Physics and Chemistry of Liquids, 52:2, 262-271, DOI: 10.1080/00319104.2013.812020 To link to this article: http://dx.doi.org/10.1080/00319104.2013.812020

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Date: 05 September 2016, At: 21:28

Physics and Chemistry of Liquids, 2014 Vol. 52, No. 2, 262–271, http://dx.doi.org/10.1080/00319104.2013.812020

Acoustical and excess thermodynamic studies of mixtures of 2-pyrrolidone with 1,3-propanediol and water as well as 1,3-propanediol with water at 308.15 K Balwinder Saini, Anjana Gupta, Renu Sharma and Rajinder K. Bamezai* Department of Chemistry, University of Jammu, Jammu 180006, India (Received 5 March 2013; final version received 2 June 2013) The density (ρ), viscosity (η) and ultrasonic velocity (u) of three mixtures consisting of 2pyrrolidone with 1,3-propanediol (PD) and water and also of PD and water have been measured as a function of mole fraction at 308.15 K. The experimentally collected data has been used to calculate the excess molar volume (VE), deviation in viscosity (Δη), deviation in ultrasonic velocity (Δu), isentropic compressibility (κs), deviation in isentropic compressibility (Δκs) and excess Gibbs free energy of activation (ΔG*E). The Redlich–Kister polynomial equation has been used to fit the derived parameters. The variation in excessive thermodynamic properties as a consequence of possible molecular interactions is discussed. Keywords: 2-pyrrolidone; 1,3-propanediol; excess molar volume; isentropic compressibility; excess Gibbs free energy of activation

1. Introduction The ultrasonic behaviour [1], coupled with the measurement of density and viscosity of liquids, facilitates the understanding of the physical properties of liquid state. These physical properties form the basis for calculating the excess thermodynamic functions. These properties have been interpreted in terms of the strength of specific and nonspecific interactions [2–7], amongst the components of selected mixtures. Polyhydroxy compounds have a wide range of applications in biochemical research [8], cosmetics and household goods [9]. 1,3-Propanediol (abbreviated herein as PD) is relatively uncommon. It is used as a heat transfer fluid, solvent and provides improved heat stability compared to ethylene glycol. Still, due to its infrequent use, PD has found application as an internal standard for quantisation of ethylene glycol and other glycols [10]. 2-Pyrrolidone (PY), a five-member cyclic lactam, used as a non-aqueous medium, possesses high dipole moment due to the presence of acidic (–NH) and basic (C=O) groups. Such cyclic amides have proved useful in solving the problems of molecular biology [11,12]. Besides, compound PY is used as a high boiling and non-corrosive solvent in industries and also acts as an intermediate during the manufacture of polymers, such as polyvinyl and polypyrrolidone [13]. H

O N

Structure of PY. *Corresponding author. Email: [email protected] © 2013 Taylor & Francis

Physics and Chemistry of Liquids

263

The aim of the present study was to calculate the density, viscosity and ultrasonic velocity of three binary systems, namely PD + water, PY + water and PY + PD, and to derive the thermodynamic properties from the experimental data at 308.15 K, which is the optimum temperature at which biochemical processes usually occur. 2. Experimental 2.1. Materials The chemicals were obtained from E. Merck Limited, India. The mass fraction purity of chemicals was better than 0.99. In order to remove traces of water, if any, PY and PD were kept over the molecular sieves, for 20 h. Subsequently, their densities were measured and compared with the literature values. The results of the density along with the experimentally determined viscosity and ultrasonic velocity are given in Table 1. 2.2. Procedure and solution preparation Known volumes of pure liquids were taken in an airtight stopper bottles which were thoroughly homogenised. Each solution prepared, in this way, was divided into three parts for measuring density, viscosity and ultrasonic velocity. The extra precaution was taken during measurements, to prevent losses due to evaporation. The densities of solutions were measured using bicapillary pycnometer (Jain Scientific Glass Works, Ambala, India), which was calibrated using triply distilled water. Each reported density data was an average of at least five measurements. The accuracy during the measurement was 1 × 10−4 g·cm−3. The kinematic viscosities, υ (= η/ρ), of the experimental solutions were measured at 308.15 K and at atmospheric pressure using suspended level Ubbelohde viscometer (Jain Scientific Glass Works). The viscometer was calibrated so as to determine the two constants A and B in the equation, η/ρ = At – B/t, obtained by measuring the flow time (t) with triply distilled water, distilled benzene and cyclohexane. The constants A and B have been found to be 0.0117 and –2.2467 corresponding to the time of flow for water as 74.80 s, benzene 56.6 s and cyclohexane as 95.2 s at 298.15 K. The viscometer was filled with experimental solutions and the flow time measurements were made using an electronic stopwatch with an accuracy of ±0.01 s. The measured values of kinematic viscosities were converted into dynamic viscosities after multiplication with the density.

Table 1. Experimental and literature values of densities (ρ), viscosities (η) and ultrasonic velocities (u) for PY, PD and water at 308.15 K. Components

ρexp (g·cm−3)

ρref (g·cm−3)

ηexp (mPa·s)

ηref (mPa·s)

uExp (m·s−1)

uRef (m·s−1)

PY PD

1.09690 1.04387

1.09710 [11] 1.0441 [14] 1.04356 [15] 0.9940 [16]

8.920 27.240

8.922 [11] 27.240 [18]

1600.10 1616.20

1599.97 [11] 1616 [18]

–

0.719 [17]

1520.0

1519 [18]

Water

–

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B. Saini et al.

The reported value was an average of at least three measurements. The accuracy in the measurement of viscosity was ±0.001 mPa·s. The ultrasonic velocity in solutions was measured with the help of multifrequency ultrasonic interferometer (M-82, Mittal Enterprises, India) at 4 MHz having an accuracy of ±1 m·s−1 in velocity. A thermostatically controlled well-stirred water bath whose temperature was controlled to ±0.1 K was used for all the measurements. 3. Results and discussion The experimentally determined values for density (ρ), viscosity (η) and ultrasonic velocity (u) for various binary constituents at 308.15 K is presented in Table 2. The experimental data was used for calculating various thermodynamic parameters, namely, excess molar volume (VE), deviation in viscosity (Δη), excess Gibbs free energy of activation (ΔG*E), isentropic compressibility (κs), deviation in ultrasonic velocity (Δu) and deviation in Table 2. Mole fractions (x1), experimental densities (ρ), viscosities (η), ultrasonic velocities (u), excess molar volumes (VE), viscosity deviations (Δη), excess Gibbs free energy of activation of viscous flow (ΔG*E), isentropic compressibilities (κs), deviation in ultrasonic velocities (Δu) and deviation in isentropic compressibilities (Δκs) for the binary mixtures at 308.15 K. x1

Δη ΔG*E κs Δu Δκs ρ η u VE −3 −1 3 −3 (g·cm ) (mPa·s) (m·s ) (cm ·mol ) (mPa·s) (J·mol−1) (T·Pa−1) (m·s−1) (TPa−1)

(x1) PD + (1 – x1) 0.0950 1.01530 0.1968 1.02568 0.3019 1.03318 0.4108 1.03718 0.4950 1.03823 0.6009 1.03978 0.6920 1.04052 0.7938 1.04172 0.9232 1.04312 (x1) PY + (1 – x1) 0.0921 1.02692 0.1915 1.04879 0.3150 1.06495 0.4027 1.07326 0.5190 1.08125 0.5927 1.08497 0.6947 1.08918 0.7877 1.09234 0.9207 1.09594 (x1) PY + (1 – x1) 0.0970 1.04898 0.1929 1.05398 0.2929 1.05848 0.3918 1.06368 0.4915 1.06881 0.5918 1.07397 0.6929 1.07945 0.7945 1.08482 0.8970 1.09083

water 1.650 4.202 6.937 9.362 11.660 14.630 17.498 20.409 24.427 water 1.572 2.467 3.573 4.339 5.430 6.176 6.828 7.493 8.425 PD 25.010 22.604 20.224 17.828 15.949 14.514 12.895 11.571 10.062

1639.8 1689.8 1707.5 1693.7 1674.5 1668.5 1650.3 1637.3 1619.5

−0.148 −0.195 −0.240 −0.251 −0.193 −0.146 −0.082 −0.051 −0.017

−1.588 −1.736 −2.001 −2.252 −2.187 −2.025 −1.573 −1.362 −0.776

2339 4438 5079 5072 4872 4350 3736 2786 1250

366.29 341.44 331.97 336.10 343.51 345.46 352.87 358.09 365.51

110.74 150.88 157.74 134.26 106.94 90.73 63.80 40.94 10.68

−62.61 −80.47 −82.17 −71.11 −57.92 −48.69 −35.02 −22.81 −6.50

1658.5 1689.0 1704.4 1695.9 1668.4 1660.0 1656.5 1649.0 1632.4

−0.044 −0.083 −0.093 −0.110 −0.120 −0.112 −0.101 −0.091 −0.071

0.098 0.178 0.271 0.318 0.455 0.596 0.412 0.314 0.156

2526 3703 4310 4385 4213 3971 3314 2580 1207

354.02 334.23 323.24 323.96 332.25 334.47 334.59 336.66 342.42

131.18 153.73 159.23 143.77 106.89 92.62 80.95 66.05 38.74

−74.10 −86.00 −87.19 −79.51 −61.99 −53.92 −45.71 −36.26 −19.94

1620.8 1621.5 1624.0 1624.7 1620.3 1615.8 1612.4 1607.9 1604.3

0.023 0.045 0.113 0.123 0.137 0.146 0.131 0.121 0.064

−0.452 −1.102 −1.651 −2.234 −2.287 −1.884 −1.651 −1.114 −0.745

876 1332 1629 1755 1816 1818 1651 1385 866

362.88 360.85 358.21 356.37 356.64 356.33 356.55 356.18 356.07

6.00 8.39 12.59 14.79 11.99 9.00 7.00 4.00 2.00

−2.82 −3.83 −5.40 −6.41 −5.12 −3.78 −3.02 −1.71 −0.99


265

isentropic compressibility (Δκs) of binary mixtures, at 308.15 K. These results are also shown in Table 2. The deviation from ideal behaviour of the excess functions, which depends upon the sign and magnitude of the functions, has a bearing on the intermolecular interaction between the components of each mixture. The numeric value of the aforementioned excess functions was calculated using Equations (1)–(5) shown below. VE ¼

ðM1 x1 þ M2 x2 Þ M 1 x1 M 2 x2 þ ρ1 ρ2 ρm

(1)

Δη ¼ ηm ðη1 x1 þ η2 x2 Þ

(2)

ΔGE ¼ RT lnðηm V Þ x1 lnðη1 V1 Þ x2 lnðη2 V2Þ

(3)

Δu ¼ um ðx1 u1 þ x2 u2 Þ

(4)

ðx1 κs1 þ x2 κs2 Þ Δκs ¼ κmix s

(5)

The terms ρm, ηm, um, κsmix and V represent density, viscosity, ultrasonic velocity, isentropic compressibility and molar volume of the mixtures, respectively. The subscripts i (i = 1 and i = 2) used in ρ, η, u, κs, V and M (molecular weight) denote the respective parameters of ith component. Newton–Laplace equation (Equation (6)) was employed to calculate isentropic compressibility. 1 ks ¼ u2 ρ

(6)

3.1. Excess molar volume The excess molar volume (VE) for various mole fractions of each of the two-component liquid mixtures, under present investigation, was calculated from their experimentally determined density values, using Equation (1). It is known [19] that the opposing effects which contribute to excess molar volume may be broadly categorised into physical, chemical and structural ones. The physical effects, being non-specific interactions between the real species present in the mixture, contribute a positive term to VE. The chemical or specific intermolecular interactions contribute negative values to VE, resulting from the decrease in volume. Similar to the chemical contributions, the structural contributions are mostly negative which usually come from interstitial accommodation and changes of free volume [20]. The VE values for the mixture of PD + water, PY + water and PY + PD systems are summarised in Table 2 and illustrated in Figure 1. The liquid mixtures comprising PD + water and PY + water show a negative trend of VE over entire composition range. This may be inferred due to the formation of hydrogen bonding between unlike molecules, which results in the decrease in volume of mixture. The negative values further indicate that the degree of packing is enhanced in these mixtures with respect to the pure species suggesting that specific or chemical intermolecular interactions, such as, hydrogen bonding, between the component liquids is more effective [21,22]. Another negative factor to VE may be from structural fittings of unlike molecules into each other’s structure due to difference in size and shape of molecules [23]. On the other hand, the mixture of PY + PD showed a positive trend in VE over the whole range of mole fraction, indicating

266

B. Saini et al. 0.15 0.10

V E/(cm3·mol–3)

0.05 0.00 –0.05 –0.10 –0.15 –0.20 –0.25 0.0

0.2

0.4

0.6

0.8

1.0

X1 PD + water PY + water PY + PD Redlich–Kister Equation

Figure 1.

Excess molar volumes of binary mixtures vs. mole fraction x1 at 308.15 K.

weakening of the above effects, which result in the expansion of mixture compared with that of pure components. 3.2. Viscosity deviation The experimentally determined values of viscosity (η) for binary liquid mixtures of different compositions are presented in Table 2. The deviation in viscosity (Δη) (Table 2), calculated by using Equation (2), and its dependence on the mole fraction for various systems, is graphically illustrated in Figure 2. Δη has been found to be negative over the entire composition range for PD + water and PY + PD systems, but positive for PY + water systems. These effects may also be explained on the basis of the shape of components of the mixture and their intermolecular interaction [24]. 3.3. Excess Gibbs free energy of activation The calculated values of excess Gibbs free energy of activation (ΔG*E) for the twocomponent mixtures as binary constituents, calculated using Equation (3), are presented in Table 2 and the results are displayed in Figure 3. The values of ΔG*E have been found to be positive over the entire range of mole fractions. An increasing behaviour in the positive ΔG*E with increasing mole fraction of a component of the mixture up to a specific point is observed. At higher mole fractions, ΔG*E shows a decreasing trend. The specific


267

0.5

Δη/(mPa·s)

0.0

–0.5

–1.0

–1.5

–2.0

–2.5 0.0

0.2

0.4

0.6

0.8

1.0


Figure 2.

Viscosity deviation of the binary mixtures vs. mole fraction x1 at 308.15 K.

interactions like hydrogen bonding [25] and charge transfer between dissimilar molecules in comparison to the like molecules may be the contributing factors to the positive values of ΔG*E. The presence of dispersion forces, if any, is likely to give rise to the negative values. 3.4. Deviation in ultrasonic velocity and isentropic compressibility The deviation in velocity, Δu, calculated, using Equation (4), is presented in Table 2 and shown in Figure 4. The Δu values are positive over the entire mole fraction range for all the three binary mixtures. The deviation in velocity follows the order: PY + water > PD + water > PY + PD, the maximum being in the range from about 0.1 to 0.4 mole fractions for PY + H2O and PD + H2O systems. In aqueous medium, PY is expected to undergo hydrogen bonding between the carbonyl oxygen and hydrogen. PD + H2O also shows hydrogen bonding but the extent of hydrogen bonding in the former system is more. This seems to be the main contributing interaction in currently studied binary mixture, which is evident from the Δu changes in PY + H2O and PD + H2O mixtures than for the Δu changes in PD + PY mixture. The isentropic compressibility, κs, for the binary system was obtained using Equation (6), while its deviation was calculated using Equation (5). The results are shown in Table 2. The Δκs (Figure 5) values are negative over the entire range of mole fractions in all the three systems under study. These results can be explained in terms of molecular interactions

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B. Saini et al.

5000

ΔG*E/(J·mol–1)

4000

3000

2000

1000

0 0.0

0.2

0.4

0.6

0.8

1.0


Figure 3. Excess Gibbs free energy of activation of the binary mixtures vs. mole fraction x1 at 308.15 K.

[26,27]. The negative values of Δκs imply lesser compressibility of the binary liquid mixtures than the corresponding ideal mixtures. The excess properties, YE (VE, Δη, ΔG*E, Δu and Δκs), for the binary mixtures were fitted to Redlich–Kister polynomial equation [28]. Y E ¼ x1 x2

k X

Ai ðx1 x2 Þi

(7)

i¼0

where x1 and x2 are mole fractions of components 1 and 2, respectively. Making use of non- linear least square regression method and fitting of Equation (7) to the experimental results, the coefficients Ai were obtained. Using an approximation of variation in the standard deviation, the optimum numbers of coefficients were ascertained. Table 3 displays the estimated values and their standard deviations (using Equation (8)) for all the mixtures.


269

180 160 140

Δu/(m·s–1)

120 100 80 60 40 20 0 –20 0.0

0.2

0.4

0.6

0.8

1.0


Figure 4.

Deviation in ultrasonic velocity of binary mixtures vs. mole fraction at 308.15 K.

0

Δκs/(T·Pa–1)

–20

–40

–60

–80

–100 0.0

0.2

0.4

0.6

0.8

1.0


Figure 5.

Deviation in isentropic compressibility for binary mixtures vs. mole fraction at 308.15 K.

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B. Saini et al.

Table 3. Redlich–Kister parameters (Ai) and standard deviations (σ) of excess molar volume (VE), viscosity deviations (Δη), excess Gibbs free energy of activation of viscous flow (ΔG*E), deviations in ultrasonic velocity (Δu) and deviations in isentropic compressibility (Δκs) for the binary mixtures at 308.15 K. A0 PD + water –0.8154 VE (cm3·mol−3) Δη (mPa·s) −9.4759 ΔG*E (J·mol−1) 17,973.66 443.06 Δu (m·s−1) −236.80 Δκs (T·Pa−1) PY + water −0.5754 VE (cm3·mol−3) Δη (mPa·s) 1.5432 ΔG*E (J·mol−1) 16,854.96 464.42 Δu (m·s−1) −262.57 Δκs (T·Pa−1) PY + PD 0.3339 VE (cm3·mol−3) Δη (mPa·s) −5.3082 7296.55 ΔG*E (J·mol−1) Δu (m·s−1) 45.86 −20.54 Δκs (T·Pa−1)

A1

A2

A3

0.9998 0.3207 3.3331 6.5455 −7961.59 12,253.88 −500.04 499.75 240.04 −221.60 −0.0652 −2.6488 −4742.82 −450.30 222.81 −0.6998 6.7052 2159.96 −71.12 29.36

"

E E 2 ðYexp Ycald Þ σ¼ ðn mÞ

σ

–0.2609 –0.8298 0.0194 1.4136 −21.4789 0.3385 7423.05 −16,780.37 227.51 −276.77 −121.52 5.9751 206.51 −52.24 2.8461

−0.2602 −0.0685 0.3278 4.3792 605.42 −10,222.88 512.89 −208.29 −231.54 190.74 0.5424 −16.3901 553.86 −20.66 13.08

A4

0.3602 3.2866 −2224.88 99.19 −44.04

0.3347 0.0225 −2.0133 0.1021 20,406.24 309.62 468.59 10.7665 −314.62 5.0730 0.1014 0.0288 10.4940 0.1372 3495.51 169.69 −34.71 0.9419 13.11 0.3795

#1=2 (8)

Here, n and m represent the number of data points and number of coefficients, respectively. Acknowledgements The authors are thankful to Prof. Tej K Razdan, Department of Chemistry, University of Jammu, Jammu, for his critical remarks and support during the course of this study.

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