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

doi:10.1016/j.jare.2013.03.007

. 2013 Mar 31;5(2):261–269. doi: 10.1016/j.jare.2013.03.007

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

Babak Mehmandoust ¹, Ehsan Sanjari ^1,^⁎, Mostafa Vatani ¹

PMCID: PMC4294737 PMID: 25685493

Abstract

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).

Keywords: Enthalpy, Vaporization, Correlation, Pure substances, Normal boiling temperature

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 reliability 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 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.

Methodology

In this research, we considered some of well known analytical models that do 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]

Δ H_{ν b} = 1.093 {RT}_{b} \frac{ln P_{c} - 1.013}{0.93 - T_{b} / T_{c}}

(1)

where ΔH_vb is vaporization enthalpy (J mol⁻¹), R is universal gas constant (8.3145 J mol⁻¹ K⁻¹), T_b is normal boiling point (K), T_c is critical temperature (K), and P_c is critical pressure (bar).

Chen model [15]

Δ H_{ν b} = {RT}_{b} \frac{3.978 (T_{b} / T_{c}) - 3.958 + 1.555 ln P_{c}}{1.07 - T_{b} / T_{c}}

(2)

Trouton rule [19]

Δ H_{ν b} = 88 T_{b} J {mol}^{- 1}

(3)

Zhao et al. model (ZNY) [17]

Δ H_{ν b} = T_{b} (36.6 + 8.314 ln T_{b})

(4)

Vetere model (V-79) [21]

Δ H_{ν b} = {RT}_{b} \frac{{(1 - T_{b} / T_{c})}^{0.38} [ln (P_{c} - 0.513 + 0.5066 T_{c}^{2} / (P_{c} T_{b}^{2})]}{1 - T_{b} / T_{c} + [1 - {(1 - T_{b} / T_{c})}^{0.38}] ln (T_{b} / T_{c})}

(5)

Vetere model (V-95) [20]

–
For hydrocarbons:

Δ H_{ν b} = 4.1868 T_{b} (9.08 + 4.36 \log_{10} T_{b} + \frac{0.0068 T_{b}}{M} + \frac{0.0009 T_{b}^{2}}{M})

(6)

–
For alcohols:

Δ H_{ν b} = 4.1868 T_{b} (18.82 + 3.34 \log_{10} T_{b} - \frac{6.37 T_{b}}{M} + \frac{0.036 T_{b}^{2}}{M} - \frac{5.2 \times 10^{- 5} T_{b}^{3}}{M})

(7)

where M is molecular weight (kg/kmol).

Liu [22]

Δ H_{ν b} = {RT}_{b} {(\frac{T_{b}}{220})}^{0.0627} \times \frac{{(1 - T_{b} / T_{c})}^{0.38} ln (P_{c} / P_{a})}{1 - T_{b} / T_{c} + 0.38 (T_{b} / T_{c}) ln (T_{b} / T_{c})}

(8)

where P_a is atmospheric pressure in bar.

New proposed vaporization enthalpy correlation

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 (P_c, T_c, and T_b) and 10 independent variables as follows:

Δ H_{ν b} = {RT}_{b} (A + {BT}_{br} + {CT}_{br}^{2} + {DT}_{br}^{3})

(9)

B = b_{1} + b_{2} P_{c} + b_{3} ln (P_{c})

(10)

C = c_{1} + c_{2} P_{c} + c_{3} ln (P_{c})

(11)

D = d_{1} + d_{2} P_{c} + d_{3} ln (P_{c})

(12)

In this equation, ΔH_vb is vaporization enthalpy (kJ mol⁻¹), R is universal gas constant and equals to 8.3145 J mol⁻¹ K⁻¹, T_b (K) is normal boiling temperature, T_c (K) is critical temperature, T_br is reduced temperature defined as T_b/T_c, and P_c (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 1.

Table 1.

Tuned coefficients of new proposed model.

Coefficients	Values
A	0.01290
b₁	0.00086
b₂	−0.00206
b₃	0.01150
c₁	−0.01983
c₂	0.00632
c₃	−0.04279
d₁	0.02086
d₂	−0.00459
d₃	0.03544

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Results and discussions

We carried out regression analysis for 352 pure substances and also for 100 other substances which are not participate in 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. 1.

Fig. 1 — Accuracy of presented model versus experimental data points from the literatures.

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.

Table 2.

Average absolute relative deviation of the values obtained by presented correlation in comparison with other empirical models.

Hydrocarbon type	Number of isomers	AARD%
Hydrocarbon type	Number of isomers	Liu [22]	V-95 [20]	V-79 [21]	Riedel [13]	Chen [15]	ZNY [17]	Trouton [19]	This study
C10H12	1	2.29	2.58	3.87	1.95	2.86	3.69	3.63	4.75
C10H14	2	1.79	8.68	1.88	2.62	2.26	2.89	3.53	1.36
C10H18	2	1.34	6.09	3.04	1.96	2.61	0.33	0.72	2.20
C10H20O2	2	6.28	4.00	5.07	5.06	4.60	8.10	7.81	5.59
C10H22	5	1.10	5.36	0.69	2.21	0.63	0.96	1.60	1.57
C10H22O	1	7.35	15.77	7.45	9.52	8.06	10.86	11.73	1.23
C10H7Br	1	2.74	5.40	0.49	3.06	1.85	0.18	1.08	1.23
C10H7Cl	1	7.88	3.54	9.64	7.47	8.56	9.31	10.12	0.96
C10H8	1	1.70	7.24	0.34	1.39	0.65	0.16	0.03	1.19
C11H10	1	2.38	7.87	0.38	2.56	1.51	0.79	0.16	0.75
C11H24	8	2.69	4.43	1.98	1.94	1.62	1.04	1.18	1.10
C12H10O	1	0.12	3.70	1.20	1.88	0.22	2.18	3.03	2.93
C12H26	2	4.12	2.69	–	–	–	2.20	2.31	1.21
C12H27N	1	3.18	3.87	–	–	–	8.03	8.13	3.34
C13H28	1	3.74	2.16	–	–	–	2.67	3.12	1.49
C14H12O2	1	3.12	0.24	–	–	–	5.40	7.23	6.58
C15H32	1	2.86	1.29	–	–	–	3.39	4.44	1.76
C2H2Br4	1	7.86	3.99	10.73	10.41	10.61	6.07	6.64	10.44
C2H2Cl2	3	3.86	1.98	4.20	4.28	4.26	4.66	2.49	4.25
C2H2Cl4	1	2.49	0.25	3.74	2.51	3.07	3.21	1.89	4.00
C2H3Br	1	11.40	6.14	12.69	14.66	14.45	3.37	8.66	10.66
C2H3Cl	1	3.60	7.80	4.58	4.53	4.50	3.47	9.94	3.59
C2H3Cl2F	1	0.82	1.22	0.48	0.23	0.11	1.45	3.04	0.28
C2H3Cl3	2	1.71	1.33	2.35	1.39	1.80	2.58	2.27	2.49
C2H3F3	1	2.19	0.85	0.09	0.73	0.32	2.86	4.68	0.91
C2H3N	1	8.11	14.94	8.41	11.06	10.11	1.87	4.95	6.42
C2H4	1	2.22	3.57	1.02	0.19	0.17	0.76	10.17	1.46
C2H4Br2	1	2.21	3.55	0.77	1.62	1.41	0.71	2.44	0.07
C2H4Cl2	2	0.33	0.63	0.32	1.92	1.45	3.75	1.34	0.78
C2H4F2	1	2.33	1.74	0.52	0.58	0.15	5.09	1.31	0.90
C2H4O	2	1.04	1.65	2.28	4.21	3.84	5.87	1.21	0.85
C2H4O2	2	6.18	29.70	31.86	34.98	33.48	25.19	24.56	2.73
C2H5Br	1	2.74	0.25	3.31	4.90	4.61	2.80	1.42	1.81
C2H5Cl	1	1.19	1.59	0.49	0.22	0.01	3.18	1.91	1.08
C2H5ClO	1	2.40	9.51	0.82	5.24	2.38	16.11	14.60	1.46
C2H5I	1	3.76	2.51	3.47	4.69	4.46	0.03	3.32	2.13
C2H5NO2	1	5.03	5.32	5.00	2.10	3.11	12.24	10.34	7.23
C2H6	1	1.92	5.32	0.74	0.21	0.24	0.48	10.55	1.61
C2H6O	2	3.39	6.98	1.21	2.63	0.96	13.51	10.70	0.85
C2H6O2	1	7.87	6.41	8.47	4.69	5.95	18.24	18.02	10.75
C2H6OS	1	0.99	4.16	2.59	0.56	1.11	6.05	5.64	4.05
C2H6S	2	0.84	2.87	0.61	0.18	0.04	3.06	1.22	1.45
C2H6S2	2	0.36	3.09	1.47	0.33	0.52	3.25	1.48	2.46
C2H7N	1	5.01	5.14	3.46	1.28	1.95	11.48	6.66	5.03
C2H7NO	1	0.56	12.00	3.34	13.01	8.03	22.20	21.56	3.22
C2H8N2	1	1.83	2.35	2.62	7.34	5.69	11.45	9.60	0.18
C2HBrClF3	1	1.50	1.12	1.20	0.07	0.61	2.53	1.33	1.21
C2HCl3	1	0.04	1.56	0.53	0.52	0.17	1.82	0.99	1.09
C2HCl5	1	0.25	5.24	1.50	0.91	1.31	2.16	3.25	0.56
C2HF3O2	1	3.73	8.09	1.40	3.56	0.82	11.42	8.52	5.81
C2N2	1	3.50	6.45	1.39	0.69	0.19	10.79	4.93	2.86
C3Cl2F6	1	4.78	0.54	3.89	3.42	3.92	1.54	2.88	0.73
C3H3N	1	3.50	0.39	3.17	0.90	1.78	8.29	5.40	4.83
C3H4O	1	3.11	4.96	3.75	5.94	5.22	2.50	1.29	2.17
C3H5Br	1	0.78	0.05	0.81	2.47	1.96	3.36	0.11	0.34
C3H5Cl	1	8.62	2.54	8.92	8.96	9.08	7.26	3.43	8.42
C3H5Cl3	1	2.47	5.40	1.29	3.03	2.24	0.89	2.03	0.56
C3H5ClO2	1	3.37	6.29	3.06	0.64	0.94	11.25	9.68	6.39
C3H5N	1	3.22	9.99	3.06	5.08	4.24	0.16	2.44	1.82
C3H6	2	1.22	4.47	0.35	0.18	0.13	0.78	6.60	1.03
C3H6Br2	1	9.48	3.25	9.14	12.64	11.46	0.54	2.07	6.55
C3H6Cl2	1	1.12	1.57	1.80	0.15	0.84	3.35	1.43	2.63
C3H6O	4	3.09	5.03	2.66	2.21	2.32	8.46	5.01	1.96
C3H6O2	2	2.53	2.19	1.95	1.01	0.89	7.44	3.92	3.44
C3H6S	1	0.49	4.67	1.36	0.61	0.75	2.35	0.24	2.52
C3H7Br	2	3.29	2.17	3.33	4.91	4.49	1.04	2.43	2.14
C3H7Cl	2	0.57	3.96	0.52	1.30	0.96	0.81	3.42	0.41
C3H7I	2	2.36	3.50	1.54	2.45	2.14	0.89	3.55	1.04
C3H7NO2	2	2.29	2.16	2.29	0.75	0.51	8.48	6.77	4.86
C3H8	1	1.34	4.40	3.55	4.39	3.99	0.50	6.97	3.71
C4H10	2	0.67	6.46	0.27	0.46	0.42	1.55	7.60	2.14
C5H12	3	1.08	7.44	1.51	2.20	1.84	2.59	7.54	3.22
C5H12S	6	1.17	5.56	1.71	1.85	1.69	0.90	2.48	0.82
C5H13N	2	0.73	1.91	0.77	2.00	1.17	3.59	1.54	1.56
C6H10	1	0.35	5.86	1.03	0.44	0.75	0.10	2.89	0.72
C6H10O	1	2.34	2.67	2.85	1.06	1.97	3.42	1.73	3.32
C6H10O2	1	6.51	0.49	9.14	16.55	12.16	4.70	3.15	1.95
C6H10O3	1	1.76	2.11	3.17	9.27	5.78	7.26	6.48	2.58
C6H10O4	1	11.47	0.65	15.69	27.19	19.52	4.35	3.86	4.43
C6H12	21	4.29	5.32	3.59	3.50	3.63	2.74	4.33	2.08
C6H12O	7	1.21	3.21	1.21	1.93	1.45	2.31	1.20	1.56
C6H12O2	7	3.55	1.07	3.75	4.31	3.86	4.25	2.22	3.48
C6H12S	1	1.61	7.59	0.07	1.20	0.66	1.49	2.59	0.03
C6H13Cl	1	0.69	4.10	0.99	0.95	0.15	0.93	0.69	0.96
C6H13N	1	2.00	3.73	1.55	4.09	3.03	2.48	0.86	0.36
C6H14	5	0.23	7.28	0.17	0.48	0.17	2.29	6.04	1.93
C6H14O	10	6.30	9.85	5.15	4.11	4.23	12.37	12.19	0.49
C6H14O2	4	8.26	2.21	8.79	7.81	8.45	6.67	4.78	7.60
C6H14O3	3	11.75	10.20	13.29	19.22	15.70	4.80	5.87	8.81
C6H14S	4	1.99	3.68	2.76	4.00	2.94	1.72	1.19	1.41
C6H15N	6	1.62	3.49	2.28	4.99	3.46	1.81	1.94	1.15
C6H4Cl2	3	1.71	5.45	1.34	2.11	1.79	0.55	1.22	1.09
C6H4F2	3	1.79	1.72	1.98	3.17	2.71	2.34	0.43	1.00
C6H5Cl	1	0.95	4.93	0.24	0.96	0.50	0.46	1.25	0.72
C6H5F	1	2.49	3.00	2.55	4.67	3.87	1.91	0.97	1.08
C6H6	1	0.16	5.09	0.39	0.44	0.14	1.05	1.99	0.75
C6H6ClN	1	3.02	2.00	2.05	5.73	4.21	4.52	4.48	1.18
C6H6O	1	1.53	5.42	1.90	2.26	0.84	12.88	12.36	2.13
C6H6S	1	3.83	3.13	3.16	6.49	5.20	3.37	2.53	0.39
C6H7N	4	0.96	3.26	0.86	2.29	1.47	3.92	2.68	1.64
C7H12	1	7.96	6.31	9.77	11.53	11.47	1.00	3.73	5.34
C7H14	17	3.07	9.37	1.93	2.04	1.94	3.85	6.49	1.66
C7H14O	6	4.59	7.05	3.99	1.81	3.06	8.81	8.17	2.14
C7H14O2	6	3.08	1.06	3.65	5.78	4.28	3.55	2.08	2.42
C7H16	9	0.53	7.15	0.43	0.41	0.27	2.19	5.11	1.64
C7H16O	5	2.43	4.49	4.19	9.48	6.28	3.83	3.42	1.84
C7H5F3	1	2.01	2.02	2.36	1.21	1.89	1.23	1.20	1.63
C7H5N	1	2.35	4.21	3.77	11.00	7.11	11.35	10.99	3.81
C7H6O	1	1.13	0.13	2.04	0.85	0.28	6.98	6.38	4.40
C7H6O2	1	6.25	15.36	27.39	35.79	31.69	8.01	8.31	2.15
C7H7Cl	2	1.03	4.62	1.02	1.45	1.00	1.14	1.19	1.10
C7H7F	2	2.38	2.18	2.86	2.57	2.51	3.47	2.08	3.27
C7H8	1	0.60	5.75	0.19	1.02	0.48	0.34	1.89	0.41
C7H8O	5	3.34	4.83	3.92	3.43	3.07	11.07	10.69	3.04
C7H9N	9	1.49	3.03	1.39	3.67	2.30	3.85	3.13	1.52
C8H10	4	11.85	17.47	11.22	12.76	11.85	10.92	12.45	0.82
C8H10O	1	3.95	2.55	4.19	10.20	7.40	9.14	9.14	1.18
C8H11N	2	0.75	3.07	1.46	0.98	0.28	2.84	2.04	2.70
C8H14	4	5.31	1.42	5.90	4.70	5.45	3.93	2.29	4.87
C8H14O3	1	9.31	12.69	7.23	0.47	4.86	16.91	16.73	0.96
C8H16	11	1.79	8.29	1.62	1.84	1.85	2.91	4.84	0.77
C8H16O	1	10.84	3.86	12.90	14.67	14.45	0.82	0.80	6.54
C8H16O2	1	4.07	0.11	4.00	1.65	3.06	4.11	2.84	3.69
C8H17F	1	10.27	6.64	9.42	6.49	8.34	10.86	9.55	9.17
C8H18	19	1.47	6.89	0.64	1.02	0.61	1.95	4.13	1.62
C8H18O	4	3.83	4.59	4.82	7.13	5.27	3.60	4.12	2.91
C8H18S	1	4.73	15.05	7.70	10.80	10.39	10.28	11.72	1.62
C8H19N	2	3.96	2.56	6.10	12.52	8.43	2.75	1.81	1.72
C8H8	1	5.39	0.26	6.43	5.07	5.71	6.23	4.92	6.78
C8H8O	1	0.70	1.64	1.84	0.98	0.27	5.09	4.93	4.08
C8H8O3	1	5.88	0.78	6.45	13.06	9.59	6.31	6.53	0.38
C9H10	1	1.21	5.95	0.24	1.53	0.75	0.50	0.17	1.08
C9H10O2	1	9.63	8.39	10.05	6.71	8.50	13.36	13.40	0.65
C9H18	1	2.51	8.98	2.02	3.94	2.77	3.41	4.59	2.80
C9H20	5	1.76	8.05	1.73	2.30	1.93	3.17	4.85	2.72
C9H7N	2	3.36	1.43	5.34	3.07	3.85	7.95	8.45	7.05
CH2Br2	1	1.85	1.13	1.28	2.73	2.62	3.56	1.05	0.81
CH2Cl2	1	2.08	1.76	1.77	0.68	0.87	5.83	1.79	3.12
CH2I2	1	7.26	4.15	9.51	9.30	9.38	6.31	5.76	10.09
CH2O2	1	7.60	59.43	51.90	55.57	54.58	41.58	45.11	1.87
CH3Br	1	2.52	0.83	3.73	4.93	4.99	3.56	1.82	0.20
CH3Cl	1	0.51	0.71	1.04	1.68	1.67	4.01	2.42	1.25
CH3I	1	3.08	0.29	3.46	4.77	4.72	2.49	1.62	0.98
CH3NO2	1	3.72	3.33	3.81	6.79	6.02	5.44	3.08	2.05
CH4	1	1.71	7.08	3.65	1.39	1.31	3.36	19.99	6.06
CH4O	1	0.15	6.09	2.55	8.59	6.51	18.46	15.59	1.80
CH5N	1	3.56	4.94	1.57	0.95	0.54	13.44	8.28	2.87
CHBr3	1	6.31	5.62	7.96	7.35	7.43	7.52	6.31	9.29
CHCl3	1	0.18	0.27	0.11	1.25	0.96	2.90	0.62	0.85

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Data points with AARD of more than 40% were not participated in statistical parameters calculations. These data were marked with dash.

Table 3 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.

Table 3.

Statistical parameters of this study compared with other methods.

	AARD%	ARD%	RMSD
Liu [22]	3.05	0.090	4.28
V-95 [20]	5.44	−3.091	7.79
V-79 [21]	3.28	0.046	7.21
Riedel [13]	3.95	−2.121	8.63
Chen [15]	3.47	−0.982	7.87
ZNY [17]	4.49	2.298	7.56
Trouton [19]	4.91	0.033	7.67
This Study	2.28	−0.025	3.61

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Fig. 2 shows the cumulative frequency of different empirical correlations versus average absolute relative deviations. Fig. 2 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 4.

Table 4.

Average absolute relative deviation of the values obtained by presented correlation in comparison with other empirical models for 100 new data.

Hydrocarbon type	Number of isomers	AARD%
Hydrocarbon type	Number of isomers	This study	Liu [22]	V-95 [20]	V-79 [21]	Riedel [13]	Chen [15]	ZNY [17]	Trouton [19]
CH6N2	1	0.56	0.23	4.59	0.75	4.91	3.92	14.58	12.13
C2Br2ClF3	1	0.43	0.76	1.82	1.43	0.83	1.24	0.64	3.37
C2Cl2F4	1	0.44	2.37	0.25	1.28	0.82	1.23	0.92	4.60
C2Cl3F3	1	0.55	0.91	1.91	0.69	0.08	0.53	0.36	4.42
C2Cl4	1	1.63	0.02	1.24	1.02	0.19	0.23	1.85	0.09
C2ClF5	1	3.05	0.57	0.21	1.80	2.65	2.07	0.64	6.63
C2F6	1	1.60	4.30	0.00	1.12	0.98	1.32	2.85	6.28
C4F10	1	2.69	1.80	0.00	0.85	2.70	1.49	1.47	4.24
C4F8	1	0.69	3.82	3.58	1.57	0.08	0.93	4.32	1.37
C4H10O	4	4.77	5.14	11.46	3.16	3.80	2.14	13.75	13.48
C4H10O2	1	3.05	1.84	0.45	1.56	0.69	0.30	5.55	2.78
C4H10S	2	3.17	2.38	3.41	2.16	1.81	1.97	4.78	3.37
C4H11N	5	2.92	2.55	0.68	2.19	0.99	1.27	5.06	1.62
C4H4N2	1	1.80	19.16	11.78	30.98	0.00	37.12	20.86	20.81
C4H4O	1	2.81	2.34	0.37	1.89	0.85	1.11	5.40	1.07
C4H4S	1	2.51	0.87	2.62	1.50	0.64	0.83	3.03	0.16
C4H5N	1	5.09	3.00	1.36	3.60	1.28	1.81	10.08	8.49
C4H6	3	1.21	1.15	3.60	0.95	1.64	1.25	2.01	3.41
C4H6O2	3	7.93	9.37	8.44	9.45	7.07	7.99	14.42	12.53
C4H6O3	1	2.28	1.06	0.44	1.44	5.47	3.58	6.37	4.94
C4H7N	2	1.90	3.55	8.53	3.45	5.84	4.76	0.03	2.27
C4H8	5	1.64	2.77	4.86	2.51	3.02	3.05	0.86	5.06
C4H8O	2	4.30	6.96	4.77	7.76	11.31	9.47	5.21	3.79
C4H8O2	5	5.21	6.50	4.54	7.02	9.09	7.91	6.72	5.20
C4H9Br	2	2.50	4.00	3.68	3.88	6.01	5.15	1.22	2.83
C4H9Cl	3	1.51	2.16	3.93	2.47	2.78	2.74	0.69	2.78
C4H9N	1	3.36	1.86	0.10	2.05	0.27	0.74	6.80	4.11
C4H9NO	1	0.85	1.63	0.16	1.43	4.55	3.53	6.54	4.85
C5H10	7	1.54	1.09	5.20	1.11	1.15	1.06	1.48	4.43
C5H12	1	3.32	0.48	8.22	0.01	0.47	0.61	3.84	9.40
C5H5N	1	0.95	1.15	2.50	0.51	2.45	2.02	4.63	2.60
C5H6S	2	1.77	0.27	3.56	1.19	0.30	0.43	2.10	0.12
C5H8O	1	2.69	0.71	3.32	1.55	0.23	0.43	3.94	2.26
C5H9N	1	1.41	3.76	7.63	3.63	6.68	5.20	0.43	1.06
C6H12	1	0.43	0.10	6.52	0.51	0.02	0.35	1.06	4.40
C16H34	1	1.92	–	0.98	–	–	–	3.63	4.94
C17H36	1	2.01	–	0.56	–	–	–	3.97	5.51
C18H34O2	1	8.19	–	11.16	–	–	–	15.24	17.33
C18H38	1	2.24	–	0.20	–	–	–	4.26	6.02
C19H40	1	1.96	–	0.49	–	–	–	4.85	6.78
C20H42	1	1.99	–	0.90	–	–	–	5.19	7.30
C21H44	1	3.14	15.67	10.22	9.71	0.08	8.66	14.06	16.14
C22H46	1	2.57	16.20	10.74	9.54	1.23	8.58	14.50	16.72
C23H48	1	2.14	16.70	11.26	9.40	2.34	8.52	14.95	17.29
C24H50	1	1.54	17.09	11.75	8.98	4.07	8.21	15.37	17.82
C25H52	1	0.05	–	12.21	–	–	–	15.76	18.33
C26H54	1	0.46	17.92	12.69	8.22	7.58	7.73	16.17	18.83
C27H56	1	0.16	18.06	13.09	7.45	10.24	7.11	16.51	19.27
C28H58	1	0.73	18.52	13.57	6.95	12.67	6.82	16.92	19.76
C29H60	1	1.36	18.64	13.97	6.00	16.10	6.10	17.26	20.19
C30H62	1	1.85	19.03	14.38	5.48	18.78	5.81	17.60	20.61
CCl2F2	1	1.35	–	1.07	–	–	–	0.38	6.55
CCl3F	1	4.05	–	1.32	–	–	–	0.69	4.12
CCl4	1	5.10	–	2.65	–	–	–	0.05	3.22
CClF3	1	0.65	–	1.62	–	–	–	2.55	6.80
CO	1	7.46	5.56	0.10	1.49	0.99	0.91	1.04	18.96
CS2	1	2.33	3.19	6.09	3.13	3.47	3.63	0.90	5.03
H2O	1	2.37	1.28	5.26	0.26	3.48	4.07	21.21	19.22
H3N	1	2.41	2.86	2.77	0.07	2.41	2.54	15.54	9.54
Kr	1	1.28	2.59	1.24	2.50	0.69	0.61	0.91	16.23
N2	1	6.73	30.65	1.91	27.41	38.31	37.71	1.04	22.22
N2O	1	4.04	4.81	7.91	1.34	0.42	0.41	10.64	1.69
N2O4	1	4.96	11.05	33.05	6.37	2.24	1.60	35.26	32.06
Ne	1	2.46	5.88	1.85	7.34	1.77	1.94	1.35	39.31
NO	1	9.85	14.28	31.50	5.93	0.37	2.33	32.84	22.75
O2	1	3.29	4.15	1.14	2.64	0.86	0.80	2.09	16.39
O2S	1	2.93	3.26	8.87	1.34	0.84	0.61	12.51	7.17
Xe	1	0.37	0.45	4.14	2.78	1.13	1.08	3.79	15.54

Average	100	2.74	5.17	5.49	3.93	3.87	3.97	6.52	8.15

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Table 5 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.

Table 5.

Statistical parameters of this study compared with other methods for 100 new substances.

	AARD%	ARD%	RMSD
Liu [22]	5.17	0.14	3.76
V-95 [20]	5.49	−3.95	8.06
V-79 [21]	3.93	0.85	8.04
Riedel [13]	3.87	−1.14	6.43
Chen [15]	3.97	0.59	6.93
ZNY [17]	6.52	3.01	7.31
Trouton [19]	8.15	0.98	9.88
This Study	2.74	0.07	11.25

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Consequently, Fig. 3 shows calculated enthalpies of vaporizations versus experimental measured enthalpies and Fig. 4 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.

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.

Acknowledgements

The supports of Khomeinishahr branch of Islamic Azad University for supporting this work are gratefully acknowledged.

Footnotes

Peer review under responsibility of Cairo University.

References

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[b0005] 1.Gopinathan N., Saraf D.N. Predict heat of vaporization of crudes and pure components: revised II. Fluid Phase Equilib. 2001;179:277–284. [Google Scholar]

[b0010] 2.Viswanath D.S., Kuloor N.R. On a generalized Watson’s relation for latent heat of vaporization. Can J Chem Eng. 1967;45:29–31. [Google Scholar]

[b0015] 3.Fish L.W., Lielmezs J. On a generalized Watson’s relation for latent heat of vaporization. Ind Eng Chem Fundam. 1975;14:248–256. [Google Scholar]

[b0020] 4.Chickos J.S., Hanshaw W. Vapor pressures and vaporization enthalpies of the n-alkanes from C21 to C30 at T = 298.15 K by correlation gas chromatography. J Chem Eng Data. 2004;49:77–85. [Google Scholar]

[b0025] 5.Verevkin S.P. Determination of vapor pressures and enthalpies of vaporization of 1,2-alkanediols. Fluid Phase Equilib. 2004;224:23–29. [Google Scholar]

[b0030] 6.Poling B.E., Thomson G.H., Friend D.G., Rowley R.L., Wilding W.V. 8th ed. McGraw-Hill Companies; United States of America: 2008. Perrys chemical engineers handbook. [Google Scholar]

[b0035] 7.Kikic I., Vetere A. Evaluation of several literature equations to predict the vaporization enthalpies at the normal boiling point. Fluid Phase Equilib. 2011;309:151–154. [Google Scholar]

[b0040] 8.Cachadĩna I., Mulero A. New corresponding states model for the estimation of the vaporization enthalpy of fluids. Fluid Phase Equilib. 2009;287:33–38. [Google Scholar]

[b0045] 9.Cachadina I., Mulero A. Evaluation of correlations for prediction of the normal boiling enthalpy. Fluid Phase Equilib. 2006;240:173–178. [Google Scholar]

[b0050] 10.Sanjari E., Honarmand M., Afshar N., Esfahani R.S. A new general correlation for the prediction of the boiling vaporization enthalpy of hydrocarbons. Thermochim Acta. 2013;556:30–33. [Google Scholar]

[b0055] 11.Reid R.C., Prausnitz J.M., Poling B.E. 4th ed. McGraw-Hill; 1987. The properties of gases and liquids. [Google Scholar]

[b0060] 12.Majer V., Svoboda V., Pick J. Elsevier; Amsterdam: 1989. Heats of vaporization of fluids. [Google Scholar]

[b0065] 13.Riedel L. Kritischer Koeffizient, Dichte des gesättigten Dampfes und Verdampfungswärme. Untersuchungen über eine Erweiterung des Theorems der übereinstimmenden Zustände. Teil III. Chem Ing Tech. 1954;26:679–683. [Google Scholar]

[b0070] 14.Poling B.E., Prausnitz J.M., OíConnell J.P. McGraw-Hill; New York: 2001. The properties of gases and liquids. [Google Scholar]

[b0075] 15.Chen N.H. Generalized correlation for latent heat of vaporization. J Chem Eng Data. 1965;10:207–210. [Google Scholar]

[b0080] 16.Carruth G.F., Kobayashi R. Extension to low reduced temperatures of three-parameter corresponding states: vapor pressures, enthalpies and entropies of vaporization, and liquid fugacity coefficients. Ind Eng Chem Fundam. 1972;11:509–516. [Google Scholar]

[b0085] 17.Zhao L., Ni N., Yalkowsky S. A modification of Trouton’s rule by simple molecular parameters for hydrocarbon compounds. Ind Eng Chem Res. 1999;38:324–327. [Google Scholar]

[b0090] 18.Morgan D.L. Use of transformed correlations to help screen and populate properties within databanks. Fluid Phase Equilib. 2007;256:54–61. [Google Scholar]

[b0095] 19.Nash L.K. Trouton and T–H–E rule. J Chem Educ. 1984;61:981–984. [Google Scholar]

[b0100] 20.Vetere A. Methods to predict the vaporization enthalpies at the normal boiling temperature of pure compounds revisited. Fluid Phase Equilib. 1995;106:1–10. [Google Scholar]

[b0105] 21.Vetere A. New correlations for predicting vaporization enthalpies of pure compounds. Chem Eng J. 1979;17:157–162. [Google Scholar]

[b0110] 22.Liu Z.Y. Estimation of heat of vaporization of pure liquid at its normal boiling temperature. Chem Eng Commun. 2001;184:221–228. [Google Scholar]

[b0115] 23.Yaws C.L. William Andrew; Norwich: 2008. Thermophysical properties of chemicals and hydrocarbons. [Google Scholar]

[b0120] 24.Majer V., Svoboda V. Blackwell Scientific Publications; Oxford: 1985. Enthalpies of vaporization of organic compounds. [Google Scholar]

[b0125] 25.Chase M.W., Davies C.A., Downey J.R., Frurip D.J., McDonald R.A., Syverud A.N. JANAF thermochemical tables. J Phys Chem Ref Data. 1985;14(Suppl. 1) [3rd ed.] [Google Scholar]

[b0130] 26.Daubert T.E., Danner R.P., Sibul H.M., Stebbins C.C. Taylor & Francis; Bristol, PA: 1994. Physical and thermodynamic properties of pure compounds: data compilation. [Google Scholar]

PERMALINK

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

Abstract

Introduction

Methodology