Journal of Thermodynamics & Catalysis

Journal of Thermodynamics & Catalysis
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Research Article - (2014) Volume 5, Issue 1

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Estimation of Some Important Thermodynamic Properties of Organic Liquid Mixtures from Ultrasonic Velocity and Density Data

Rama Shankar Saroj1*, Pavan Kumar Gautam1, A Mahan1, Sunil2 and Shailendra Badal3
1Department of Chemistry, University of Allahabad, Allahabad, 211002, U.P., India, E-mail: pavankumar@gmail.com
2Department of Chemistry, M. G. C. G. V., Chitrakoot, M.P., India, E-mail: pavankumar@gmail.com
3Hindustan College of Science and Technology, Agra-Delhi Highway, NH-2, Farah, Mathura, UP, India, E-mail: pavankumar@gmail.com
*Corresponding Author: Rama Shankar Saroj, Department of Chemistry, University of Allahabad, Allahabad 211002, U.P., India, Tel: +91-8574157842 Email:

Abstract

Using the recently proposed equations for calculating thermal expansion coefficient (α) and isothermal compressibility (βT) from density (ρ) and ultrasonic velocity (u) values, six binary organic liquid mixtures have been considered. These are: n-heptane+toluene (I); n-heptane+n-hexane (II); toluene+n-hexane (III); cyclohexane+nheptane (IV); cyclohexane+n-hexane (V), and n-decane+n-hexane (VI) at 298.15 K. Literature data for ρ and u of these mixtures are employed to compute α, βT, as well as γ, Pint and Γ. Calculated values of βT are compared with the earlier ones, and the agreement is found to be good.

Keywords: Isothermal compressibility; Thermodynamic properties; Ultrasonic velocity; Organic liquid mixtures

Introduction

Estimation of thermodynamic properties through empirical modeling have immense applications in industry, pollution control, oil recovery and separation processes. The measurements of ultrasonic velocity and density data of liquid and liquid mixtures provide very simple method for estimating a number of useful and important thermodynamic properties e.g. adiabatic compressibility, intermolecular free length, free volume, acoustic impedence, relative association, relaxation time etc. Such studies have been carried out by several workers [1-13]. On the other hand, various statistical mechanical theories [14-17] (Flory theory, hole theory, hard sphere equations of state etc.) have been employed to compute theoretically the ultrasonic velocity, density, excess volume, excess adiabatic compressibility, internal pressure, solubility parameter, non-linearity parameter, guineisen parameter etc. of liquid mixtures. However, thermal expansivity and isothermal compressibility and their related properties (heat capacities ratio, internal pressure etc.) have not been calculated from ultrasonic velocity (u) and density (ρ) values. Recently [16,18,19], two empirical relations based on dimensional analysis were obtained showing the direct relations between thermal expansion coefficients (α) and isothermal compressibility (βT) with ultrasonic velocity (u) and density (ρ). In the present communication we have applied these relations for the estimation of thermal expansivity (α), isothermal compressibility (βT), internal pressure (Pint), heat capacity ratio (γ) and pseudo guineisen parameter (Г) of binary organic liquid mixtures. The experimental data of ρ and u for these binary mixtures have been taken from literature (20).

Formula Used

α and βT of a liquid system is related to ρ and u by the following expressions:

(1)

(2)

where all the symbols have their usual meanings. The internal pressure, Pint, of liquid is given by

(3)

where P is the external pressure when P = 0, he above equations becomes

(4)

Substituting the values of α, βT from eqs (1) and (2) into above equation, we get

(5)

The heat capacity ratio (6)

Where Cp and Cv are respectively the heat capacities at constant pressure and at constant volume, βs is the isentropic compressibility, defined by

(7)

Combining eqs (2), (6) and (7), we gets

(8)

The value of pseudo-guineisen parameter, Г is given by

(9)

Obtaining the values α, from eq. (1) and γ from eq. (8), we have computed the value of Γ from eq. (9).

Results and Discussion

The method utilized in the present paper is easy to implement on variety of simple and complex fluid systems comparatively recently proposed methods based on various version of SAFT (Statistical associating fluid theory for variable range interactions (SAFT-VR) of the generic Mie form, SAFT+cubic and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). For the calculations of α, βT and other thermodynamic properties from equestions (1) to (9) we, have considered the following binary organic liquid mixtures:

(I) n-heptane(x1)+toluene(x2)

(II) n-heptane(x1)+n-hexane(x2)

(III) n-hexane(x2)+toluene(x1)

(IV) n-heptane(x2)+cyclohexane (x1)

(V) n-hexane(x2)+cyclohexane(x1)

(VI) n-hexane(x2)+n-decane(x1)Ultrasonic and density measurement of these systems were carried out by Pandey et al. [16-19] at 298.15 K. These data have been taken for the present calculation Table 1. Calculated values of α, βT, Pint,

298.15 K [Experimental]
Component V α  х 103 (deg-1) βT х 1012 (cm2 dyne-1)
Toluene 106.87 1.086 142.40
n-Heptane 147.47 1.258 112.40
Cyclohexane 108.76 1.215 112.77
n-Hexane 131.56 1.381 166.90
n-Decane 195.94 1.050 116.30
γ and Г of all the pure components are recorded in Table 1
298.15 K [Calculated]
Component  α х 103 (deg-1) βT х 1012 (cm2 dyne-1) Pint х 10-9 (dyne cm-2) γ Г  
Toluene              1.167 9729.2 3.322 1.427 1.226
Cyclohexane 1.235 122.0 3.021 1.480 1.302
n-Hexane 1.409 206.5 2.034 1.565 1.344
n-Heptane 1.357 178.0 2.273 1.546 1.348
n-Decane 1.331 164.5 2.411 1.512 1.289

Table 1: Experimental and calculated values of α, βT, Pint, γ and Г for pure components at 298.15 K

Similarly computed values of these properties for the systems (I) to (VI) are presented respectively in Tables 2-7. For each binary mixture, the percentage and average percentage deviation for the βT values are given. Since the experimental values of βT are known, only deviation in βT values was calculated. Calculations of βT for the afro said organic liquid mixture [20, 21] and also other mixtures have been carried out on the basis of various hard sphere models and Flory’s statistical theory.

(x1) α  х 103 (deg-1) βT х 1012 (cm2 dyne-1) Pint х 10-9 (dyne cm-2) γ Г %D βT
0.2979 1.190 105.2 3.371 1.424 1.195 6.32
0.3162 1.194 106.4 3.343 1.425 1.193 6.31
0.3325 1.196 107.3 3.322 1.427 1.197 6.41
0.3519 1.200 108.5 3.295 1.429 1.199 6.54
0.3709 1.203 109.7 3.267 1.431 1.201 6.68
0.3902 1.206 111.0 3.240 1.432 1.201 6.86
0.4029 1.199 111.9 3.220 1.434 1.214 6.90
0.4282 1.212 113.2 3.192 1.436 1.206 7.03
0.4484 1.206 114.6 3.163 1.438 1.218 7.18
0.4684 1.210 116.0 3.133 1.440 1.219 7.32
0.4874 1.222 117.0 3.135 1.442 1.213 7.42
0.5023 1.231 120.2 3.051 1.450 1.226 7.73
0.5227 1.225 121.8 3.020 1.452 1.237 6.47
0.5442 1.238 123.1 2.997 1.457 1.238 8.00
0.5446 1.242 124.7 2.968 1.456 1.231 8.15

Average percent deviation =7.04
List of abbreviations used in Table
х: Mole fraction
ρ: Density
u: Ultrasonic velocity
α: Thermal expansion coefficient
βT: Isothermal compressibility
Pint: Internal pressure
γ: heat capacity ratio
Г: Pseudo gruneisen parameter

Table 2: Calculated values of α, βT, Pint, γ and Г of binary system— n-heptane(x1) + toluene at 298.15 K.

(x1) α  х 103 (deg-1) βT х 1012 (cm2 dyne-1) Pint х 10-9 (dyne cm-2) γ Г %D βT
0.3388 1.394 198.1 2.098 1.559 1.344 13.31
0.3598 1.393 197.1 2.106 1.558 1.343 13.26
0.3782 1.393 197.4 2.104 1.560 1.348 13.27
0.4001 1.390 195.9 2.116 1.557 1.344 12.35
0.4193 1.390 195.7 2.117 1.558 1.346 13.18
0.4394 1.389 194.9 2.124 1.557 1.344 13.13
0.4604 1.388 194.3 2.129 1.556 1.343 13.10
0.4782 1.386 193.5 2.135 1.556 1.345 13.05
0.4986 1.385 192.7 2.141 1.555 1.344 13.02
0.5191 1.383 191.6 2.151 1.554 1.343 12.95
0.5395 1.381 190.8 2.157 1.553 1.304 12.90
0.5594 1.378 189.1 2.173 1.550 1.338 12.81
0.5795 1.378 189.2 2.171 1.551 1.341 12.82
0.6025 1.377 188.5 2.178 1.550 1.339 12.77
0.6185 1.376 188.1 2.181 1.550 1.340 12.75

Average percent deviation =12.97
List of abbreviations used in Tables:
х: Mole fraction
ρ: Density
u: Ultrasonic velocity
α: Thermal expansion coefficient
βT: Isothermal compressibility
Pint: Internal pressure
γ: heat capacity ratio
Г: Pseudo gruneisen parameter

Table 3: Calculated values of α, βT, Pint, γ and Г of binary system— n-heptane(x1) + n-hexane at 298.15 K.

(x1) α х 103 (deg-1) βT х 1012 (cm2 dyne-1) Pint х 10-9 (dyne cm-2) γ Г %D βT
0.4074 1.278 139.9 2.723 1.467 1.225 9.46
0.4299 1.274 137.9 2.752 1.465 1.224 9.30
0.4486 1.268 135.7 2.787 1.459 1.214 9.11
0.4704 1.264 133.9 2.814 1.460 1.220 8.97
0.4919 1.259 131.9 2.846 1.457 1.217 8.80
0.5114 1.254 129.8 2.881 1.454 1.214 8.60
0.5290 1.251 128.2 2.907 1.452 1.211 8.47
0.5491 1.243 125.2 2.960 1.446 1.203 6.78
0.5584 1.232 124.9 2.965 1.447 1.207 7.98
0.5880 1.242 123.0 3.000 1.444 1.202 6.53
0.6088 1.238 120.8 3.039 1.442 1.203 6.18
0.6275 1.232 119.2 3.070 1.440 1.197 6.85
0.6453 1.211 116.2 3.129 1.434 1.196 4.97
0.6637 1.217 115.1 3.152 1.433 1.193 6.30
0.6829 1.204 114.0 3.175 1.436 1.203 7.12

Average percent deviation =7.69
List of abbreviations used in Tables:
х: Mole fraction
ρ: Density
u: Ultrasonic velocity
α: Thermal expansion coefficient
βT: Isothermal compressibility
Pint: Internal pressure
γ: heat capacity ratio
Г: Pseudo gruneisen parameter

Table 4: Calculated values of α, βT, Pint, γ and Г of binary system— toluene(x1) + n-hexane at 298.15 K.

(x1) α х 103 (deg-1) βT  х 1012 (cm2 dyne-) Pint х 10-9 (dyne cm-2) γ Г %D βT
0.2227 1.318 158.0 2.485 1.517 1.315 10.83
0.2689 1.312 155.5 2.515 1.522 1.334 10.65
0.3158 1.623 153.4 2.542 1.513 1.060 10.50
0.3588 1.308 153.6 2.539 1.516 1.323 10.51
0.4016 1.305 150.7 2.575 1.513 1.318 10.30
0.4433 1.296 147.8 2.614 1.508 1.314 10.08
0.4861 1.291 145.6 2.643 1.507 1.317 9.94
0.5270 1.287 143.9 2.666 1.505 1.316 9.78
0.5642 1.284 142.3 2.688 1.503 1.313 9.65
0.6019 1.279 140.4 2.716 1.501 1.313 9.50
0.6414 1.275 138.7 2.741 1.500 1.315 9.36
0.6795 1.271 136.9 2.767 1.498 1.314 9.22
0.7164 1.268 135.3 2.792 1.497 1.314 9.08
0.7521 1.263 133.5 2.820 1.494 1.317 8.93
0.7877 1.260 132.0 2.845 1.491 1.307 8.80

Average percent deviation = 9.80
List of abbreviations used in Tables:
х: Mole fraction
ρ: Density
u: Ultrasonic velocity
α: Thermal expansion coefficient
βT: Isothermal compressibility
Pint: Internal pressure
γ: heat capacity ratio
Г: Pseudo gruneisen parameter

Table 5: Calculated values of α, βT, Pint, γ and Г of binary system- cyclohexane(x1) + n-heptane at 298.15 K.

(x1) α х 103 (deg-1) βT х 1012 (cm2 dyne-1) Pint х 10-9 (dyne cm-2) γ Г %D βT
0.2189 1.368 183.7 2.220 1.543 1.331 12.51
0.2541 1.354 179.4 2.260 1.541 1.340 12.23
0.2981 1.347 172.5 2.364 1.536 1.334 11.80
0.3150 1.346 171.9 2.333 1.535 1.333 11.77
0.3647 1.338 167.9 2.375 1.531 1.331 11.50
0.3897 1.331 164.7 2.410 1.529 1.333 11.28
0.4258 1.325 161.7 2.442 1.525 1.328 11.09
0.4777 1.317 157.7 2.489 1.521 1.326 10.81
0.5029 1.311 155.0 2.522 1.519 1.327 10.65
0.5675 1.301 150.2 2.581 1.514 1.325 10.26
0.5799 1.299 149.1 2.596 1.512 1.321 10.18
0.6012 1.294 146.9 2.625 1.511 1.324 10.01
0.6695 1.283 142.1 2.692 1.505 1.320 9.51
0.7187 1.274 138.1 2.749 1.501 1.318 9.32
0.7888 1.264 133.6 2.819 1.495 1.313 8.94

Average percent deviation = 10.79
List of abbreviations used in Tables:
х: Mole fraction
ρ: Density
u: Ultrasonic velocity
α: Thermal expansion coefficient
βT: Isothermal compressibility
Pint: Internal pressure
γ: heat capacity ratio
Г: Pseudo gruneisen parameter

Table 6: Calculated values of α, βT, Pint, γ and Г of binary system-cyclohexane(x1) + n-hexane at 298.15 K.

(x1) α х 103
(deg-1)		 βT х 1012
(cm2 dyne-1)		 Pint х10-9
(dyne cm-2)		 γ Г %D βT
0.0187 1.401 201.8 2.068 1.556 1.331 13.52
0.0588 1.396 198.8 2.092 1.553 1.328 13.35
0.1008 1.388 194.7 2.126 1.550 1.329 13.13
0.1436 1.381 190.6 2.169 1.547 1.328 12.90
0.1896 1.377 188.6 2.176 1.547 1.332 12.78
0.2348 1.367 183.2 2.225 1.541 1.327 12.46
0.2886 1.359 178.6 2.267 1.539 1.330 12.18
0.3350 1.351 174.7 2.305 1.536 1.330 11.99
0.3872 1.345 171.4 2.338 1.534 1.325 11.73
0.4449 1.338 167.8 2.376 1.531 1.331 11.50
0.5009 1.333 164.3 2.414 1.529 1.333 11.26
0.5627 1.321 159.8 2.465 1.525 1.332 10.95
0.6248 1.313 155.7 2.513 1.523 1.335 10.66
0.6944 1.306 152.6  2.551 1.522 1.340 10.43
0.7655 1.298 149.7 2.600 1.520 1.343 9.65

Average percent deviation = 11.89
List of abbreviations used in Tables:
х: Mole fraction
ρ: Density
u: Ultrasonic velocity
α: Thermal expansion coefficient
βT: Isothermal compressibility
Pint: Internal pressure
γ: heat capacity ratio
Г: Pseudo gruneisen parameter

Table 7: Calculated values of α, βT, Pint, γ and Г of binary system- n-decane(x1) + n-hexane at 298.15 K.

Unfortunately, in both the papers there is controversy about the experimental values of βT which have been used to compare the theoretical results. In one case authors [21] considered the βT values obtained from Flory theory as the experimental ones which is not justified. In the second case, authors [20] employed purely empirical relation (combination of Auerbach and Mc Gowan) for the experimental βT values which is absurd. A perusal of Tables 2-7 shows that the average percentage deviations of the calculated βT values for mixtures (I) to (VI) are respectively 7.04 and 12.97, 7.69, 9.80, 10.79 and 11.89. Keeping in view the uncertainties in the experimental βT values employed, our agreement is quite good, and far better than the earlier results.

The values of internal pressures are increasing with increasing mole fraction for the systems II, III, IV, V and VI. This decrease in Pint values may be attributed to the existence of columbic forces in the mixture [22]. In case of system I, the behavior is opposite due to lack of columbic forces. βT values are also increasing for all the systems except system- I. In system-I, intermolecular forces are strong due to the presence of π electrons. Similar observation was observed in case of thermal expansion coefficients [23,24] For system –I, α values are increasing with the mole fraction of component I which may be interpreted in terms of closure approach of unlike molecules [25]. γ values are found to follow the general trend.

Acknowledgement

The support and encouragement of Prof. J.D. Pandey, Deptt. of Chemistry, University of Allahabad is highly appreciated.

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Citation: Saroj RS, Gautam PK, Mahan A, Sunil, Badal S (2014) Estimation of Some Important Thermodynamic Properties of Organic Liquid Mixtures from Ultrasonic Velocity and Density Data. J Thermodyn Catal 5: 126.

Copyright: © 2014 Saroj RS, This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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