ESTIMATION OF STANDARD ENTHALPY OF FORMATION OF ALKANES IN GASEOUS STATE BY CALCULATING SIZE , STRUCTURAL AND ELECTRONIC PARAMETERS IN THE MOLECULES

A quantitative analysis is made on the correlation ship of thermodynamic property, i.e., standard enthalpy of formation (ΔH fo) with Kier's molecular connectivity index(1Xv),vander waal's volume (Vw) electrotopological state index (E) and refractotopological state index (R) in gaseous state of alkanes. The regression analysis reveals a significant linear correlation of standard enthalpy of formation (ΔH fo) with 1Xv, Vw, E and R. The equations obtained by regression analysis may be used to estimate standard enthalpy of formation (ΔH fo) of alkanes in gaseous state.


I. INTRODUCTION
Standard enthalpy of formation is a basic thermodynamic property.It is used in chemical engineering calculations.Experimental measurements of standard enthalpy of formation (ΔH f 0 ) involve experimental diffi culties and they are not always feasible and the corresponding methods possess real drawbacks.Consequently, it is necessary to resort to a theoretical calculation of these parameters.This option is now accessible because an important, fruitful and current fi eld of research.
The additive approach applied to the estimation of thermo physical properties was systematically developed by S.W.Benson and coworkers 1-3 .Many topological distances based indices as molecular descriptors for QSAR 4, 5 and additive scheme 6 have been developed for the es-timation of enthalpy of formation of organic compounds.
One of the most important points in such research is the selection of adequate descriptors containing the information stored in the molecular structure.The quite satisfactory results of applying regression analysis may be used to calculate heats of formation seems to indicate this way is a suitable one to compute the enthalpy content of molecules.Since results are good enough and errors are nearly the same as experimental uncertainties, the equations show to be a suitable method to systematize data and to derive certain rules regarding the structural elements and group contribution to the molecular enthalpy of formation.
There are a wide variety of molecular descriptors to be used as independent variable and this large number of possibilities allows one to make quite different choices to perform the calculation

Educação Education
Educação Education and to interpret in a meaningful way the results.In view of the above, it is thought that heat enthalpies of formation which depend upon the size, structure, electronic environment and complexity of the molecules, may be quantitatively correlated with size, structure and electronic parameters, i.e. fi rst order valence connectivity ( 1 X v) , vander waal's volume (Vw), electrotopological state index (E) and refractotopological state (R) in alkanes.Previously we have established a signifi cant quantitative co-relationship of these parameters with diamagnetic susceptibility of many organic compounds 7,8 .The aim of this paper is to obtain the correlation equations of (ΔH f 0 ) with 1 X v , Vw, E and R parameters.

Calculation of Kier`s 9 molecular connectivity ( 1 X v ):
It is calculated by a hydrogen suppressed graph of the molecule 10 .The fi rst order valence connectivity ( 1 X v ) is given by eq.1: (1) Here the sum is the overall connections or edges in such a graph, δi v and δj v are numbers assigned to each atom refl ecting the numbers of atoms adjacent or connected to atom (i) and (j) which are formally bonded.The atom connectivity term (δi v) is defi ned as Zi v -hi Where Zi v = number of valence electron of atom (i), Z = atomic number of atom (i) and hi = number of hydrogen atoms attached to atom (i).
Table (1) shows the atom connectivity (δi v) values in different groups as calculated by eq.( 2) Another atomic parameter accounting for the size of a molecule, the vander waal`s volume (Vw) may be calculated as suggested by Bond 11 .The atoms are assumed to be spherical and necessary corrections for the overlap in the hydrogen chain are also incorporated 12 Vw = ∑ n i a i + [ ∑ corrections for bonds + ∑ corrections for no. of branching ] ( Where , Vw = vander waal's volume of the molecules ni = no. of atoms.a i = vander waal's volume of atom i.
Table 2 shows vander waal's volume of different atoms and table 3 shows correction values of vander waal's volume for sphere overlapping due to covalent bonding and for Branching.The value of vander waal's may be calculated as eq. 3.

Calculation of electrotopological state Index (E-State):
This index is developed from chemical graph theory and uses the chemical graph (hydrogen -suppressed skeleton) for generation of atom -level structure indices.This index recognizes that every atom in a molecule is unique, and this uniqueness arises from differences in the electronic and topological environment of each atom.This descriptor is formulated as an intrinsic value Ii plus a perturbation given by the electronic infl uence of the topological environment of the molecule [13][14][15] .Intrinsic state valence Ii of each atom is calculated as follow: Where N is the principal quantum number of the atom i, δv the number of valence electrons in the skeleton (Z v -hi) ; δ the number of σ electrons in the skeleton (σ -h).For a skeleton, Z v the total number of electrons on the atom .σ the number of electrons in the σ orbitals, h the number of bonded hydrogen atom.E-state for an atom i in molecule (Si) is given by Si = Ii + ∑ Δ Ii (5) Δ Ii = quantifi es the perturbation effect on the intrinsic atom value.This perturbation is assumed to be a function of the difference in the intrinsic values Ii and Ij: Where, r ij is the number of atoms in the shortest path between atoms i and j including both i and j.
The difference in intrinsic values Δ Ii , for a pair of skeletal atoms encode both electronic and topological attributes that arise from electro negativity differences and skeletal connectivity.Therefore, the total of sum of the differences in intrinsic values, ∑Δ Ii, due to perturbation for a whole molecule is zero i.e.. ∑ Δ Ii = 0 so, Si = Ii (7) Therefore, E-state for a molecule = ∑ni Si or ∑ni Ii (8) The R state index is also developed from the chemical graph theory.This index is based on the infl uence of dispersive forces of each atom on the other atom in the molecule, modifi ed by molecular topology.Crippen et al 16

II. RESULTS AND DISCUSSION:
The values of standard heat enthalpy of formation (ΔH f 0 ) of gases are taken from literature. 17-21Standard heat enthalpies (ΔH f 0 ) are taken in kilo calories per mole at atmospheric pressure at 298.15K in gas phase.The values of 1 χ v , V w , E and R are correlated with standard heat enthalpies (ΔH f 0 ) .
The regression analysis reveals that the correlations of standard heat enthalpies (ΔH f 0 ) with the molecular connectivity ( 1 χ v ) & van der waals volume (V w ) show very low level of signifi cance , but with the inclusion of indicator variable (I), i.e,I = 0 for straight chain and I = 1 for branched alkanes, shows high level of signifi cance and are shown by equations ( 10) & (11).The correlations of standard heat enthalpies (ΔH f 0 ) with electrotopological state index (E) and refractotopological state index (R) have been given by equations ( 12) & ( 13).Experimental and theoretical values of standard heat enthalpies of formation (ΔH f 0 ) of some alkanes calculated by equations ( 10), (11), (12) and (13) shows good agreement and are listed in tables 6. & 7.

Table 1 .
Atom connectivity (δi v) values in different groups

Table 2 .
vander waal's volume of different atoms

Table 3 .
Correction values of vander waal's volume for sphere overlapping due to covalent bonding and for Branching

Table 4 .
Intrinsic state valence Ii of atoms in some groups

Table 5 .
Atomic refractivity values as calculated by Ghose and Crippen used in the analysis

Table 6 .
Experimental and theoretical calculated values of ΔHf0 by 1Xv & Vw parameters in alkanes

Table 7 .
Experimental and theoretical calculated values of ΔHf0 by E and R parameters in alkanes