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 .
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 [ 212 ] .
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 [ 622 ] .
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 . 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 .
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 .
( zny ) , the simplest method defined as trouton rule , two models presented by vetere   and a more recent proposal of liu .
riedel model 
 ( 1)hb=1.093rtblnpc-1.0130.93-tb / tcwhere hvb is vaporization enthalpy ( j  mol ) , r is universal gas constant ( 8.3145  j  mol  k ) , tb is normal boiling point ( k ) , tc is critical temperature ( k ) , and pc is critical pressure ( bar ) .
chen model 
 ( 2)hb = rtb3.978(tb / tc)-3.958 + 1.555lnpc1.07-tb / tc trouton rule 

( 3)hb=88tbjmol-1 zhao et al . model ( zny ) 
 ( 4)hb = tb(36.6 + 8.314lntb ) vetere model ( v-79 ) 
 ( 5)hb = rtb(1-tb / tc)0.38[ln(pc-0.513 + 0.5066tc2/(pctb2)]1-tb / tc+[1-(1-tb / tc)0.38]ln(tb / tc ) vetere model ( v-95 ) 
 for hydrocarbons:(6)hb=4.1868tb9.08 + 4.36log10tb+0.0068tbm+0.0009tb2 m for alcohols:(7)hb=4.1868tb18.82 + 3.34log10tb-6.37tbm+0.036tb2m-5.210 - 5tb3mwhere m is molecular weight ( kg / kmol ) .
liu 
 ( 8)hb = rtbtb2200.0627(1-tb / tc)0.38ln(pc / pa)1-tb / tc+0.38(tb / tc)ln(tb / tc ) where pa is atmospheric pressure in bar . in this study , we tried to find a more accurate and rapid model to calculate vaporization enthalpies of pure substances based on experimental data [ 14,2426 ] .
thermophysical properties of compounds are obtained from the literatures . 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 ( 20.3722  k ) .
the new presented model has three dependent variables ( pc , tc , and tb ) and 10 independent variables as follows:(9)hb = rtb(a+btbr+ctbr2+dtbr3)(10)b = b1+b2pc+b3ln(pc)(11)c = c1+c2pc+c3ln(pc)(12)d = d1+d2pc+d3ln(pc)in this equation , hvb is vaporization enthalpy ( kj  mol ) , r is universal gas constant and equals to 8.3145  j  mol  k , 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 1
in this study , we tried to find a more accurate and rapid model to calculate vaporization enthalpies of pure substances based on experimental data [ 14,2426 ] .
thermophysical properties of compounds are obtained from the literatures . 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 ( 20.3722  k ) .
the new presented model has three dependent variables ( pc , tc , and tb ) and 10 independent variables as follows:(9)hb = rtb(a+btbr+ctbr2+dtbr3)(10)b = b1+b2pc+b3ln(pc)(11)c = c1+c2pc+c3ln(pc)(12)d = d1+d2pc+d3ln(pc)in this equation , hvb is vaporization enthalpy ( kj  mol ) , r is universal gas constant and equals to 8.3145  j  mol  k , 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 1
we carried out regression analysis for 352 pure substances and also for 100 other substances which are not participate in fitting procedure .
the values of the critical pressure , critical temperature , normal boiling temperature , and molecular weight ( for comparison with other models ) were taken from the literatures [ 14,2426 ] . to compare the accuracy of presented empirical model , calculated enthalpies of vaporizations for 352 pure substances versus experimental measured enthalpies
1 . 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 .
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 .
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 [ 2426 ] .
finally , aard of the new method and other mentioned models for these substances are presented in table 4 .
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 .
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 .
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 .
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 .
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 .
 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 ( 20.3722  k ) . 
Introduction
Methodology
New proposed vaporization enthalpy correlation
Results and discussions
Conclusions
Conflict of interest