An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties

The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes. In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances. This equation is a function of normal boiling temperature, critical temperature, and critical pressure. The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range. The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3–722 K).

Journal of Advanced Research (2014) 5, 261–269 Cairo University Journal of Advanced Research ORIGINAL ARTICLE An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties Babak Mehmandoust, Ehsan Sanjari *, Mostafa Vatani Mechanical Engineering Department, Khomeinishahr Branch, Islamic Azad University, P.O Box 119-84175, Isfahan, Iran A R T I C L E I N F O Article history: Received 24 December 2012 Received in revised form 21 March 2013 Accepted 26 March 2013 Available online 31 March 2013 Keywords: Enthalpy Vaporization Correlation Pure substances Normal boiling temperature A B S T R A C T The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances This equation is a function of normal boiling temperature, critical temperature, and critical pressure The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3–722 K) ª 2013 Cairo University Production and hosting by Elsevier B.V All rights reserved Introduction Vaporization enthalpies are used frequently in adjusting enthalpies of formation of liquids to the standard state and in evaluating environmental transport properties Accurate thermodynamic correlations are required to enhance the reli* Corresponding author Tel.: +98 311 366 00 11 E-mail addresses: sanjary@gmail.com, sanjari@iaukhsh.ac.ir (E Sanjari) Peer review under responsibility of Cairo University Production and hosting by Elsevier ability of such simulations Of the thermodynamic properties, heat of vaporization is one of the most important parameters for a multi-component multistage vapor–liquid equilibrium process as it is the one which controls the temperature as well as liquid and vapor profiles in a column [1] Moreover, this property is sometimes used in the prediction or correlation of other thermodynamic properties There is thus engineering and theoretical interest in the measurement and correlation of values of this property [2–12] The normal boiling enthalpy can be calculated using either equations of state applied to the liquid and vapor phases or more simply by means of empirical correlations that allow calculating the enthalpy of vaporization of pure fluids [6–22] Some of them are general analytical expressions that only require as input parameters certain properties of the fluid, such 2090-1232 ª 2013 Cairo University Production and hosting by Elsevier B.V All rights reserved http://dx.doi.org/10.1016/j.jare.2013.03.007 262 B Mehmandoust et al as the critical temperature, critical pressure, normal boiling point temperature, and molecular weight [6,23] In this study, an accurate empirical correlation was presented by incorporating the normal boiling temperature and critical points of the pure substances This equation can predict the heat of vaporizations for pure substances over the entire range of normal boiling point temperatures of practical interest Table Tuned coefficients of new proposed model Methodology In this research, we considered some of well known analytical models that not require specific adjustable coefficients for each substance, but rather are based on a knowledge of some properties of the liquid–vapor equilibrium (critical properties mainly) or on molecular properties In particular, we selected seven specific expressions that are valid only for the calculation of the vaporization enthalpy These are including the correlation of Riedel [13], Chen [15], and Zhao et al (ZNY) [17], the simplest method defined as Trouton rule [19], two models presented by Vetere [20,21] and a more recent proposal of Liu [22] Riedel model [13] DHmb ¼ 1:093 RTb lnPc À 1:013 0:93 À Tb =Tc Coefficients Values A b1 b2 b3 c1 c2 c3 d1 d2 d3 0.01290 0.00086 À0.00206 0.01150 À0.01983 0.00632 À0.04279 0.02086 À0.00459 0.03544  DHmb ¼ RTb  0:0627 Tb 220 ð1 À Tb =Tc Þ0:38 lnðPc =Pa Þ Tb =Tc ỵ 0:38Tb =Tc ịlnTb =Tc ị 8ị where Pa is atmospheric pressure in bar ð1Þ New proposed vaporization enthalpy correlation À1 where DHvb is vaporization enthalpy (J mol ), R is universal gas constant (8.3145 J molÀ1 KÀ1), Tb is normal boiling point (K), Tc is critical temperature (K), and Pc is critical pressure (bar) Chen model [15] DHmb ẳ RTb 3:978Tb =Tc ị 3:958 ỵ 1:555lnPc 1:07 À Tb =Tc ð2Þ Trouton rule [19] DHmb ¼ 88 Tb J molÀ1 ð3Þ Zhao et al model (ZNY) [17] DHmb ẳ Tb 36:6 ỵ 8:314lnTb ị 4ị Vetere model (V-79) [21] DHmb ẳ RTb A ỵ BTbr ỵ CT2br ỵ DT3br ị DHmb ẳ RTb In this study, we tried to find a more accurate and rapid model to calculate vaporization enthalpies of pure substances based on experimental data [14,24–26] Thermophysical properties of compounds are obtained from the literatures [6,23] By investigation of more than 452 data points vaporization enthalpy of pure substances and using 352 points of them in multiple regression analysis, a new empirical correlation is suggested to accurately prediction of vaporization enthalpy with the wide ranges of normal boiling temperatures (20.3– 722 K) The new presented model has three dependent variables (Pc, Tc, and Tb) and 10 independent variables as follows: ð1 À Tb =Tc ị0:38 ẵlnPc 0:513 ỵ 0:5066T2c =Pc T2b ị 9ị B ẳ b1 ỵ b2 Pc ỵ b3 lnPc ị 10ị Tb =Tc ỵ ẵ1 ð1 À Tb =Tc Þ0:38 ŠlnðTb =Tc Þ ð5Þ 90 Vetere model (V-95) [20] – For hydrocarbons:   0:0068Tb 0:0009T2b DHmb ẳ 4:1868Tb 9:08 ỵ 4:36log10 Tb ỵ ỵ M M 6ị For alcohols:  6:37Tb DHmb ẳ4:1868Tb 18:82 ỵ 3:34log10 Tb M  0:036T2b 5:2 105 T3b ỵ M M where M is molecular weight (kg/kmol) Liu [22] Calculated Enthalpy (kJ/mol) 80 70 60 50 40 30 20 10 ð7Þ 10 20 30 40 50 60 70 80 90 Measured Enthalpy (kJ/mol) Fig Accuracy of presented model versus experimental data points from the literatures Estimation of the boiling vaporization enthalpy of pure substances Table models 263 Average absolute relative deviation of the values obtained by presented correlation in comparison with other empirical Hydrocarbon type C10H12 C10H14 C10H18 C10H20O2 C10H22 C10H22O C10H7Br C10H7Cl C10H8 C11H10 C11H24 C12H10O C12H26 C12H27N C13H28 C14H12O2 C15H32 C2H2Br4 C2H2Cl2 C2H2Cl4 C2H3Br C2H3Cl C2H3Cl2F C2H3Cl3 C2H3F3 C2H3N C2H4 C2H4Br2 C2H4Cl2 C2H4F2 C2H4O C2H4O2 C2H5Br C2H5Cl C2H5ClO C2H5I C2H5NO2 C2H6 C2H6O C2H6O2 C2H6OS C2H6S C2H6S2 C2H7N C2H7NO C2H8N2 C2HBrClF3 C2HCl3 C2HCl5 C2HF3O2 C2N2 C3Cl2F6 C3H3N C3H4O C3H5Br C3H5Cl C3H5Cl3 C3H5ClO2 C3H5N Number of isomers 2 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 AARD% Liu [22] V-95 [20] V-79 [21] Riedel [13] Chen [15] ZNY [17] Trouton [19] This study 2.29 1.79 1.34 6.28 1.10 7.35 2.74 7.88 1.70 2.38 2.69 0.12 4.12 3.18 3.74 3.12 2.86 7.86 3.86 2.49 11.40 3.60 0.82 1.71 2.19 8.11 2.22 2.21 0.33 2.33 1.04 6.18 2.74 1.19 2.40 3.76 5.03 1.92 3.39 7.87 0.99 0.84 0.36 5.01 0.56 1.83 1.50 0.04 0.25 3.73 3.50 4.78 3.50 3.11 0.78 8.62 2.47 3.37 3.22 2.58 8.68 6.09 4.00 5.36 15.77 5.40 3.54 7.24 7.87 4.43 3.70 2.69 3.87 2.16 0.24 1.29 3.99 1.98 0.25 6.14 7.80 1.22 1.33 0.85 14.94 3.57 3.55 0.63 1.74 1.65 29.70 0.25 1.59 9.51 2.51 5.32 5.32 6.98 6.41 4.16 2.87 3.09 5.14 12.00 2.35 1.12 1.56 5.24 8.09 6.45 0.54 0.39 4.96 0.05 2.54 5.40 6.29 9.99 3.87 1.88 3.04 5.07 0.69 7.45 0.49 9.64 0.34 0.38 1.98 1.20 – – – – – 10.73 4.20 3.74 12.69 4.58 0.48 2.35 0.09 8.41 1.02 0.77 0.32 0.52 2.28 31.86 3.31 0.49 0.82 3.47 5.00 0.74 1.21 8.47 2.59 0.61 1.47 3.46 3.34 2.62 1.20 0.53 1.50 1.40 1.39 3.89 3.17 3.75 0.81 8.92 1.29 3.06 3.06 1.95 2.62 1.96 5.06 2.21 9.52 3.06 7.47 1.39 2.56 1.94 1.88 – – – – – 10.41 4.28 2.51 14.66 4.53 0.23 1.39 0.73 11.06 0.19 1.62 1.92 0.58 4.21 34.98 4.90 0.22 5.24 4.69 2.10 0.21 2.63 4.69 0.56 0.18 0.33 1.28 13.01 7.34 0.07 0.52 0.91 3.56 0.69 3.42 0.90 5.94 2.47 8.96 3.03 0.64 5.08 2.86 2.26 2.61 4.60 0.63 8.06 1.85 8.56 0.65 1.51 1.62 0.22 – – – – – 10.61 4.26 3.07 14.45 4.50 0.11 1.80 0.32 10.11 0.17 1.41 1.45 0.15 3.84 33.48 4.61 0.01 2.38 4.46 3.11 0.24 0.96 5.95 1.11 0.04 0.52 1.95 8.03 5.69 0.61 0.17 1.31 0.82 0.19 3.92 1.78 5.22 1.96 9.08 2.24 0.94 4.24 3.69 2.89 0.33 8.10 0.96 10.86 0.18 9.31 0.16 0.79 1.04 2.18 2.20 8.03 2.67 5.40 3.39 6.07 4.66 3.21 3.37 3.47 1.45 2.58 2.86 1.87 0.76 0.71 3.75 5.09 5.87 25.19 2.80 3.18 16.11 0.03 12.24 0.48 13.51 18.24 6.05 3.06 3.25 11.48 22.20 11.45 2.53 1.82 2.16 11.42 10.79 1.54 8.29 2.50 3.36 7.26 0.89 11.25 0.16 3.63 4.75 3.53 1.36 0.72 2.20 7.81 5.59 1.60 1.57 11.73 1.23 1.08 1.23 10.12 0.96 0.03 1.19 0.16 0.75 1.18 1.10 3.03 2.93 2.31 1.21 8.13 3.34 3.12 1.49 7.23 6.58 4.44 1.76 6.64 10.44 2.49 4.25 1.89 4.00 8.66 10.66 9.94 3.59 3.04 0.28 2.27 2.49 4.68 0.91 4.95 6.42 10.17 1.46 2.44 0.07 1.34 0.78 1.31 0.90 1.21 0.85 24.56 2.73 1.42 1.81 1.91 1.08 14.60 1.46 3.32 2.13 10.34 7.23 10.55 1.61 10.70 0.85 18.02 10.75 5.64 4.05 1.22 1.45 1.48 2.46 6.66 5.03 21.56 3.22 9.60 0.18 1.33 1.21 0.99 1.09 3.25 0.56 8.52 5.81 4.93 2.86 2.88 0.73 5.40 4.83 1.29 2.17 0.11 0.34 3.43 8.42 2.03 0.56 9.68 6.39 2.44 1.82 (continued on next page) 264 Table B Mehmandoust et al (continued) Hydrocarbon type Number of isomers AARD% Liu [22] V-95 [20] V-79 [21] Riedel [13] Chen [15] ZNY [17] Trouton [19] This study 1.03 6.55 2.63 1.96 3.44 2.52 2.14 0.41 1.04 4.86 3.71 2.14 3.22 0.82 1.56 0.72 3.32 1.95 2.58 4.43 2.08 1.56 3.48 0.03 0.96 0.36 1.93 0.49 C3H6 C3H6Br2 C3H6Cl2 C3H6O C3H6O2 C3H6S C3H7Br C3H7Cl C3H7I C3H7NO2 C3H8 C4H10 C5H12 C5H12S C5H13N C6H10 C6H10O C6H10O2 C6H10O3 C6H10O4 C6H12 C6H12O C6H12O2 C6H12S C6H13Cl C6H13N C6H14 C6H14O 1 2 2 2 1 1 21 7 1 10 1.22 9.48 1.12 3.09 2.53 0.49 3.29 0.57 2.36 2.29 1.34 0.67 1.08 1.17 0.73 0.35 2.34 6.51 1.76 11.47 4.29 1.21 3.55 1.61 0.69 2.00 0.23 6.30 4.47 3.25 1.57 5.03 2.19 4.67 2.17 3.96 3.50 2.16 4.40 6.46 7.44 5.56 1.91 5.86 2.67 0.49 2.11 0.65 5.32 3.21 1.07 7.59 4.10 3.73 7.28 9.85 0.35 9.14 1.80 2.66 1.95 1.36 3.33 0.52 1.54 2.29 3.55 0.27 1.51 1.71 0.77 1.03 2.85 9.14 3.17 15.69 3.59 1.21 3.75 0.07 0.99 1.55 0.17 5.15 0.18 12.64 0.15 2.21 1.01 0.61 4.91 1.30 2.45 0.75 4.39 0.46 2.20 1.85 2.00 0.44 1.06 16.55 9.27 27.19 3.50 1.93 4.31 1.20 0.95 4.09 0.48 4.11 0.13 11.46 0.84 2.32 0.89 0.75 4.49 0.96 2.14 0.51 3.99 0.42 1.84 1.69 1.17 0.75 1.97 12.16 5.78 19.52 3.63 1.45 3.86 0.66 0.15 3.03 0.17 4.23 0.78 0.54 3.35 8.46 7.44 2.35 1.04 0.81 0.89 8.48 0.50 1.55 2.59 0.90 3.59 0.10 3.42 4.70 7.26 4.35 2.74 2.31 4.25 1.49 0.93 2.48 2.29 12.37 6.60 2.07 1.43 5.01 3.92 0.24 2.43 3.42 3.55 6.77 6.97 7.60 7.54 2.48 1.54 2.89 1.73 3.15 6.48 3.86 4.33 1.20 2.22 2.59 0.69 0.86 6.04 12.19 C6H14O2 C6H14O3 C6H14S C6H15N C6H4Cl2 C6H4F2 C6H5Cl C6H5F C6H6 C6H6ClN C6H6O C6H6S C6H7N C7H12 C7H14 C7H14O C7H14O2 C7H16 C7H16O C7H5F3 C7H5N C7H6O C7H6O2 C7H7Cl C7H7F C7H8 C7H8O C7H9N C8H10 4 3 1 1 1 17 6 1 1 2 8.26 11.75 1.99 1.62 1.71 1.79 0.95 2.49 0.16 3.02 1.53 3.83 0.96 7.96 3.07 4.59 3.08 0.53 2.43 2.01 2.35 1.13 6.25 1.03 2.38 0.60 3.34 1.49 11.85 2.21 10.20 3.68 3.49 5.45 1.72 4.93 3.00 5.09 2.00 5.42 3.13 3.26 6.31 9.37 7.05 1.06 7.15 4.49 2.02 4.21 0.13 15.36 4.62 2.18 5.75 4.83 3.03 17.47 8.79 13.29 2.76 2.28 1.34 1.98 0.24 2.55 0.39 2.05 1.90 3.16 0.86 9.77 1.93 3.99 3.65 0.43 4.19 2.36 3.77 2.04 27.39 1.02 2.86 0.19 3.92 1.39 11.22 7.81 19.22 4.00 4.99 2.11 3.17 0.96 4.67 0.44 5.73 2.26 6.49 2.29 11.53 2.04 1.81 5.78 0.41 9.48 1.21 11.00 0.85 35.79 1.45 2.57 1.02 3.43 3.67 12.76 8.45 15.70 2.94 3.46 1.79 2.71 0.50 3.87 0.14 4.21 0.84 5.20 1.47 11.47 1.94 3.06 4.28 0.27 6.28 1.89 7.11 0.28 31.69 1.00 2.51 0.48 3.07 2.30 11.85 6.67 4.80 1.72 1.81 0.55 2.34 0.46 1.91 1.05 4.52 12.88 3.37 3.92 1.00 3.85 8.81 3.55 2.19 3.83 1.23 11.35 6.98 8.01 1.14 3.47 0.34 11.07 3.85 10.92 4.78 7.60 5.87 8.81 1.19 1.41 1.94 1.15 1.22 1.09 0.43 1.00 1.25 0.72 0.97 1.08 1.99 0.75 4.48 1.18 12.36 2.13 2.53 0.39 2.68 1.64 3.73 5.34 6.49 1.66 8.17 2.14 2.08 2.42 5.11 1.64 3.42 1.84 1.20 1.63 10.99 3.81 6.38 4.40 8.31 2.15 1.19 1.10 2.08 3.27 1.89 0.41 10.69 3.04 3.13 1.52 12.45 0.82 (continued on next page) Estimation of the boiling vaporization enthalpy of pure substances (continued) Hydrocarbon type C8H10O C8H11N C8H14 C8H14O3 C8H16 C8H16O C8H16O2 C8H17F C8H18 C8H18O C8H18S C8H19N C8H8 C8H8O C8H8O3 C9H10 C9H10O2 C9H18 C9H20 C9H7N CH2Br2 CH2Cl2 CH2I2 CH2O2 CH3Br CH3Cl CH3I CH3NO2 CH4 CH4O CH5N CHBr3 CHCl3 Number of isomers 11 1 19 1 1 1 1 1 1 1 1 1 AARD% Liu [22] V-95 [20] V-79 [21] Riedel [13] Chen [15] ZNY [17] Trouton [19] This study 3.95 0.75 5.31 9.31 1.79 10.84 4.07 10.27 1.47 3.83 4.73 3.96 5.39 0.70 5.88 1.21 9.63 2.51 1.76 3.36 1.85 2.08 7.26 7.60 2.52 0.51 3.08 3.72 1.71 0.15 3.56 6.31 0.18 2.55 3.07 1.42 12.69 8.29 3.86 0.11 6.64 6.89 4.59 15.05 2.56 0.26 1.64 0.78 5.95 8.39 8.98 8.05 1.43 1.13 1.76 4.15 59.43 0.83 0.71 0.29 3.33 7.08 6.09 4.94 5.62 0.27 4.19 1.46 5.90 7.23 1.62 12.90 4.00 9.42 0.64 4.82 7.70 6.10 6.43 1.84 6.45 0.24 10.05 2.02 1.73 5.34 1.28 1.77 9.51 51.90 3.73 1.04 3.46 3.81 3.65 2.55 1.57 7.96 0.11 10.20 0.98 4.70 0.47 1.84 14.67 1.65 6.49 1.02 7.13 10.80 12.52 5.07 0.98 13.06 1.53 6.71 3.94 2.30 3.07 2.73 0.68 9.30 55.57 4.93 1.68 4.77 6.79 1.39 8.59 0.95 7.35 1.25 7.40 0.28 5.45 4.86 1.85 14.45 3.06 8.34 0.61 5.27 10.39 8.43 5.71 0.27 9.59 0.75 8.50 2.77 1.93 3.85 2.62 0.87 9.38 54.58 4.99 1.67 4.72 6.02 1.31 6.51 0.54 7.43 0.96 9.14 2.84 3.93 16.91 2.91 0.82 4.11 10.86 1.95 3.60 10.28 2.75 6.23 5.09 6.31 0.50 13.36 3.41 3.17 7.95 3.56 5.83 6.31 41.58 3.56 4.01 2.49 5.44 3.36 18.46 13.44 7.52 2.90 9.14 2.04 2.29 16.73 4.84 0.80 2.84 9.55 4.13 4.12 11.72 1.81 4.92 4.93 6.53 0.17 13.40 4.59 4.85 8.45 1.05 1.79 5.76 45.11 1.82 2.42 1.62 3.08 19.99 15.59 8.28 6.31 0.62 1.18 2.70 4.87 0.96 0.77 6.54 3.69 9.17 1.62 2.91 1.62 1.72 6.78 4.08 0.38 1.08 0.65 2.80 2.72 7.05 0.81 3.12 10.09 1.87 0.20 1.25 0.98 2.05 6.06 1.80 2.87 9.29 0.85 C ẳ c1 ỵ c2 Pc ỵ c3 lnPc ị 11ị D ẳ d1 ỵ d2 Pc ỵ d3 lnPc ị 12ị In this equation, DHvb is vaporization enthalpy (kJ mol ), R is universal gas constant and equals to 8.3145 J molÀ1 KÀ1, Tb (K) is normal boiling temperature, Tc (K) is critical temperature, Tbr is reduced temperature defined as Tb/Tc, and Pc (bar) is critical pressure Also, tuned coefficients that have been determined by minimizing the sum of square errors of the model are presented in Table Table Statistical parameters of this study compared with other methods Liu [22] V-95 [20] V-79 [21] Riedel [13] Chen [15] ZNY [17] Trouton [19] This Study AARD% ARD% RMSD 3.05 5.44 3.28 3.95 3.47 4.49 4.91 2.28 0.090 À3.091 0.046 À2.121 À0.982 2.298 0.033 À0.025 4.28 7.79 7.21 8.63 7.87 7.56 7.67 3.61 Results and discussions We carried out regression analysis for 352 pure substances and also for 100 other substances which are not participate in 0.9 Cumulative frequency % Table 265 0.8 0.7 0.6 0.5 0.4 Liu [22] V-95 [20] 0.3 V-79 [21] Riedel [13] 0.2 Chen [15] ZNY [17] 0.1 Trouton [19] This study 0 10 12 14 AARD% Fig AARD% of various methods in calculating vaporization enthalpies as function of cumulative frequency 266 B Mehmandoust et al Table Average absolute relative deviation of the values obtained by presented correlation in comparison with other empirical models for 100 new data Hydrocarbon type CH6N2 C2Br2ClF3 C2Cl2F4 C2Cl3F3 C2Cl4 C2ClF5 C2F6 C4F10 C4F8 C4H10O C4H10O2 C4H10S C4H11N C4H4N2 C4H4O C4H4S C4H5N C4H6 C4H6O2 C4H6O3 C4H7N C4H8 C4H8O C4H8O2 C4H9Br C4H9Cl C4H9N C4H9NO C5H10 C5H12 C5H5N C5H6S C5H8O C5H9N C6H12 C16H34 C17H36 C18H34O2 C18H38 C19H40 C20H42 C21H44 C22H46 C23H48 C24H50 C25H52 C26H54 C27H56 C28H58 C29H60 C30H62 CCl2F2 CCl3F CCl4 CClF3 CO CS2 H2O Number of isomers 1 1 1 1 1 1 3 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AARD% This study Liu [22] V-95 [20] V-79 [21] Riedel [13] Chen [15] ZNY [17] Trouton [19] 0.56 0.43 0.44 0.55 1.63 3.05 1.60 2.69 0.69 4.77 3.05 3.17 2.92 1.80 2.81 2.51 5.09 1.21 7.93 2.28 1.90 1.64 4.30 5.21 2.50 1.51 3.36 0.85 1.54 3.32 0.95 1.77 2.69 1.41 0.43 1.92 2.01 8.19 2.24 1.96 1.99 3.14 2.57 2.14 1.54 0.05 0.46 0.16 0.73 1.36 1.85 1.35 4.05 5.10 0.65 7.46 2.33 2.37 0.23 0.76 2.37 0.91 0.02 0.57 4.30 1.80 3.82 5.14 1.84 2.38 2.55 19.16 2.34 0.87 3.00 1.15 9.37 1.06 3.55 2.77 6.96 6.50 4.00 2.16 1.86 1.63 1.09 0.48 1.15 0.27 0.71 3.76 0.10 – – – – – – 15.67 16.20 16.70 17.09 – 17.92 18.06 18.52 18.64 19.03 – – – – 5.56 3.19 1.28 4.59 1.82 0.25 1.91 1.24 0.21 0.00 0.00 3.58 11.46 0.45 3.41 0.68 11.78 0.37 2.62 1.36 3.60 8.44 0.44 8.53 4.86 4.77 4.54 3.68 3.93 0.10 0.16 5.20 8.22 2.50 3.56 3.32 7.63 6.52 0.98 0.56 11.16 0.20 0.49 0.90 10.22 10.74 11.26 11.75 12.21 12.69 13.09 13.57 13.97 14.38 1.07 1.32 2.65 1.62 0.10 6.09 5.26 0.75 1.43 1.28 0.69 1.02 1.80 1.12 0.85 1.57 3.16 1.56 2.16 2.19 30.98 1.89 1.50 3.60 0.95 9.45 1.44 3.45 2.51 7.76 7.02 3.88 2.47 2.05 1.43 1.11 0.01 0.51 1.19 1.55 3.63 0.51 – – – – – – 9.71 9.54 9.40 8.98 – 8.22 7.45 6.95 6.00 5.48 – – – – 1.49 3.13 0.26 4.91 0.83 0.82 0.08 0.19 2.65 0.98 2.70 0.08 3.80 0.69 1.81 0.99 0.00 0.85 0.64 1.28 1.64 7.07 5.47 5.84 3.02 11.31 9.09 6.01 2.78 0.27 4.55 1.15 0.47 2.45 0.30 0.23 6.68 0.02 – – – – – – 0.08 1.23 2.34 4.07 – 7.58 10.24 12.67 16.10 18.78 – – – – 0.99 3.47 3.48 3.92 1.24 1.23 0.53 0.23 2.07 1.32 1.49 0.93 2.14 0.30 1.97 1.27 37.12 1.11 0.83 1.81 1.25 7.99 3.58 4.76 3.05 9.47 7.91 5.15 2.74 0.74 3.53 1.06 0.61 2.02 0.43 0.43 5.20 0.35 – – – – – – 8.66 8.58 8.52 8.21 – 7.73 7.11 6.82 6.10 5.81 – – – – 0.91 3.63 4.07 14.58 0.64 0.92 0.36 1.85 0.64 2.85 1.47 4.32 13.75 5.55 4.78 5.06 20.86 5.40 3.03 10.08 2.01 14.42 6.37 0.03 0.86 5.21 6.72 1.22 0.69 6.80 6.54 1.48 3.84 4.63 2.10 3.94 0.43 1.06 3.63 3.97 15.24 4.26 4.85 5.19 14.06 14.50 14.95 15.37 15.76 16.17 16.51 16.92 17.26 17.60 0.38 0.69 0.05 2.55 1.04 0.90 21.21 (continued 12.13 3.37 4.60 4.42 0.09 6.63 6.28 4.24 1.37 13.48 2.78 3.37 1.62 20.81 1.07 0.16 8.49 3.41 12.53 4.94 2.27 5.06 3.79 5.20 2.83 2.78 4.11 4.85 4.43 9.40 2.60 0.12 2.26 1.06 4.40 4.94 5.51 17.33 6.02 6.78 7.30 16.14 16.72 17.29 17.82 18.33 18.83 19.27 19.76 20.19 20.61 6.55 4.12 3.22 6.80 18.96 5.03 19.22 on next page) Estimation of the boiling vaporization enthalpy of pure substances Table (continued) Hydrocarbon type H3N Kr N2 N2O N2O4 Ne NO O2 O2S Xe Average 267 Number of isomers AARD% This study Liu [22] V-95 [20] V-79 [21] Riedel [13] Chen [15] ZNY [17] Trouton [19] 1 1 1 1 1 2.41 1.28 6.73 4.04 4.96 2.46 9.85 3.29 2.93 0.37 2.86 2.59 30.65 4.81 11.05 5.88 14.28 4.15 3.26 0.45 2.77 1.24 1.91 7.91 33.05 1.85 31.50 1.14 8.87 4.14 0.07 2.50 27.41 1.34 6.37 7.34 5.93 2.64 1.34 2.78 2.41 0.69 38.31 0.42 2.24 1.77 0.37 0.86 0.84 1.13 2.54 0.61 37.71 0.41 1.60 1.94 2.33 0.80 0.61 1.08 15.54 0.91 1.04 10.64 35.26 1.35 32.84 2.09 12.51 3.79 9.54 16.23 22.22 1.69 32.06 39.31 22.75 16.39 7.17 15.54 100 2.74 5.17 5.49 3.93 3.87 3.97 6.52 8.15 fitting procedure It showed that presented model can be used for many types of pure substances The values of the critical pressure, critical temperature, normal boiling temperature, and molecular weight (for comparison with other models) were taken from the literatures [14,24–26] To compare the accuracy of presented empirical model, calculated enthalpies of vaporizations for 352 pure substances versus experimental measured enthalpies have been presented in Fig In Table 2, the AARD% of enthalpies calculated from proposed and other models for each substance include one or more isomers with respect to the values given by experimental measurements were presented It showed that presented model was more accurate than other empirical correlations for all types of compounds considered in this study Data points with AARD of more than 40% were not participated in statistical parameters calculations These data were marked with dash Table presents the statistical parameters including average absolute relative deviation percentage (AARD%), average relative deviation, (ARD%), and root mean square deviation (RMSD) of the considered models and new proposed correlation Fig shows the cumulative frequency of different empirical correlations versus average absolute relative deviations Fig also shows the accuracy of different empirical methods in prediction of vaporization enthalpies of 352 pure substances As shown in Fig 2, the new proposed model is more accurate than the seven commonly used correlations The new method has successfully predicted 75% of the all measurements with AARD less than 3% and 84% of the data with AARD less than 4% Only 2% of the enthalpy measurements were predicted with AARD of more than 10% by the new method Liu model, that is the second accurate empirical method, predicted 65% of the enthalpies measurements with AARD less than 3% and 75% of the measurements with AARD less than 4% For real comparison and estimate the applicability of presented method to calculate vaporization enthalpy of pure substances, some independent data for more than 100 pure substances which are not employed in regression analysis of new proposed correlation were studied [24–26] Finally, AARD of the new method and other mentioned models for these substances are presented in Table Table presents the statistical parameters including average absolute percentage relative deviation percentage (AARD%), average relative deviation, (ARD%), and root mean square deviation (RMSD) of the considered models and new proposed correlation for 100 new data points Consequently, Fig shows calculated enthalpies of vaporizations versus experimental measured enthalpies and Fig indicates cumulative frequency of different empirical correlations versus average absolute relative deviations for new 100 substances As shown in Fig 4, the new presented model estimated 85% of all 100 measurements with AARD less than 4, while Riedel model, that is the second accurate empirical method in this comparison, predicts 77% of 100 measurements with AARD less than 4% Hence, the superiority of this new empirical method over the other empirical methods has been verified for all experimental data All considered models were obtained by using some experimental data points for vaporization enthalpies But our presented correlation was fitted with more experimental data for more constant parameters than other models which can helps to generalize the equation to calculate fitting data and other independent data which are not employed in regression analysis with lower deviations The new correlation has a potential validation for calculation of vaporization enthalpy for acetates, alcohols, aldehyds, alkans, alkenes, alkyl and multi-alkyl benzene, alkynes, amines, anhydrides, anilines, carboxylic acids, cetones, cyclo alkanes, dimethyl alkanes, esters, halo alkanes, halo alkenes, halo benzene, methyl alkans, naphthalenes, nitriles, nitro alkanes, pyridynes, sulfid and sulfoxids, xylene, and some other hydrocarbons Table Statistical parameters of this study compared with other methods for 100 new substances Liu [22] V-95 [20] V-79 [21] Riedel [13] Chen [15] ZNY [17] Trouton [19] This Study AARD% ARD% RMSD 5.17 5.49 3.93 3.87 3.97 6.52 8.15 2.74 0.14 À3.95 0.85 À1.14 0.59 3.01 0.98 0.07 3.76 8.06 8.04 6.43 6.93 7.31 9.88 11.25 268 B Mehmandoust et al 90 Acknowledgements Calculated Enthalpy (kJ/mol) 80 70 The supports of Khomeinishahr branch of Islamic Azad University for supporting this work are gratefully acknowledged 60 References 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 Measured Enthalpy (kJ/mol) Fig Accuracy of presented model versus experimental data points for 100 new substances Cumulative frequency % 0.9 0.8 0.7 0.6 0.5 0.4 Liu [22] V-95 [20] 0.3 V-79 [21] Riedel [13] 0.2 Chen [15] ZNY [17] 0.1 Trouton [19] This study 0 10 12 14 AARD% Fig AARD% of various methods in calculating vaporization enthalpies as function of cumulative frequency for 100 new substances Conclusions In this study, the new empirical method was presented to estimate the vaporization enthalpy of pure substances at their normal boiling temperature To estimate accuracy of this correlation, the comparisons were done for presented model and seven commonly used empirical methods include Vetere (V-95), Vetere (V-79), Riedel, Chen, Zhao et al (ZNY), Liu, and Tourton rule Results indicate the superiority of the new presented correlation over all other methods used to calculate vaporization enthalpies with average absolute relative deviation percent (AARD%) of 2.28 Also to estimate the applicability of the new method, some data for more than 100 pure substances which are not participate in regression analysis are examined, and the results showed again the superiority of presented correlation with lower deviation Conflict of interest The authors have declared no conflict of interest [1] Gopinathan N, Saraf DN Predict heat of vaporization of crudes and pure components: revised II Fluid Phase Equilib 2001;179:277–84 [2] Viswanath DS, Kuloor NR On a generalized 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Thermophysical properties of chemicals and hydrocarbons Norwich: William Andrew; 2008 [24] Majer V, Svoboda V Enthalpies of vaporization of organic compounds Oxford: Blackwell Scientific Publications; 1985 269 [25] Chase MW, Davies CA, Downey JR, Frurip DJ, McDonald RA, Syverud AN JANAF thermochemical tables J Phys Chem Ref Data 1985;14(Suppl 1) [3rd ed.] [26] Daubert TE, Danner RP, Sibul HM, Stebbins CC Physical and thermodynamic properties of pure compounds: data compilation Bristol, PA: Taylor & Francis; 1994  ... incorporating the normal boiling temperature and critical points of the pure substances This equation can predict the heat of vaporizations for pure substances over the entire range of normal boiling. .. this study, the new empirical method was presented to estimate the vaporization enthalpy of pure substances at their normal boiling temperature To estimate accuracy of this correlation, the comparisons... presented model can be used for many types of pure substances The values of the critical pressure, critical temperature, normal boiling temperature, and molecular weight (for comparison with other models)