Estimation of standard enthalpy of formation of alkanes in gaseous state by calculating size, structural and electronic parameters in the molecules

Abstract

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.

Kier's molecular connectivity (1Xv); vander waal's volume (Vw); Electrotopological state index (E); Refractotopological state (R)

ARTICLE

Estimation of standard enthalpy of formation of alkanes in gaseous state by calculating size, structural and electronic parameters in the molecules

Verma,P.S.^I; Gorsi, B.L.^*; Kalwania,G.S.^II; Lovel^II

^IProf.& Head of Department of Chemistry, University of ajasthan, Jaipur (India)

^IIDept of Chemistry, S.K.Govt. P. G. College, Sikar (India)

ABSTRACT

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(¹X^v),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 ¹X^v, 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.

Keywords: Kier's molecular connectivity (1Xv); vander waal's volume (Vw); Electrotopological state index (E); Refractotopological state (R).

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 _fº) involve experimental difficulties 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 field 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 scheme⁶ have been developed for the estimation 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 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. first order valence connectivity (1Xv), vander waal's volume (Vw), electrotopological state index (E) and refractotopological state (R) in alkanes. Previously we have established a significant 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_fº) with ¹X^v, Vw, E and R parameters.

1. Calculation of Kier's⁹ molecular connectivity (¹X^v):

It is calculated by a hydrogen suppressed graph of the molecule¹⁰. The first order valence connectivity (¹X^v) is given by eq. 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 reflecting the numbers of atoms adjacent or connected to atom (i) and (j) which are formally bonded. The atom connectivity term (δi^v)is defined as

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 (δiv) values in different groups as calculated by eq.(2)

2. Calculation of vander waal's Volume (Vw):

Another atomic parameter accounting for the size of a molecule, the vander waal's volume (Vw) may be calculated as suggested by Bond¹¹. The atoms are assumed to be spherical and necessary corrections for the overlap in the hydrogen chain are also incorporated¹²

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.

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 uni queness 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 influence of the topological environment of the molecule^13-15. 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

Δ Ii = quantifies 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,

Therefore, E- state for a molecule = ∑ni Si or

Tabela 4

4. Calculation of refractotopological state Index (R- state):

The R state index is also developed from the chemical graph theory. This index is based on the influence of dispersive forces of each atom on the other atom in the molecule, modified by molecular topology. Crippen et al ¹⁶ reported the atomic refractivity values of the topological environment of each skeleton atom in the molecule. The evaluation of the individual atomic refractivity value (Calculated by Ghose and Crippen¹⁶) is based on the idea that the sum of the atomic values (αi) being related to the molecular value of the molar refractivity:

Where, ni = No. of atoms ; αi = Atomic refractivity value

Tabela 5

II. RESULTS AND DISCUSSION:

The values of standard heat enthalpy of formation (ΔH _fº₎ of gases are taken from literature.^17-21 Standard heat enthalpies (ΔH _fº₎ are taken in kilo calories per mole at atmospheric pressure at 298.15K in gas phase. The values of ¹χ^v , V_{w ,}E and R are correlated with standard heat enthalpies (ΔHºf )^.

The regression analysis reveals that the correlations of standard heat enthalpies (ΔH _fº) with the molecular connectivity (¹χ^{v )} & van der waals volume (V_w) show very low level of significance , 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 significance and are shown by equations (10) & (11).

N = 44 , r = 0.994 , s = 1.889 , F (2, 41) = 1776.123

N = 45 , r = 0.996 , s = 1.711 , F (2,42) = 2362.53

Both equations show almost 100 % correlation . It shows that branching in chains plays an important role in the correlations of the molecular connectivity (¹χ^v) & van der waals volume (V) with the standard heat enthalpies (ΔH_fº) of the the alkanes. In the equation (10) & (11), the F values are significant at 99% level [ F²₄₂ (0.01) = 5.18 ] and are accounting for 98.8% & 99.2% variance (r² = 0.988 & 0.992) respectively.

The correlations of standard heat enthalpies (ΔH _fº₎ with electrotopological state index (E) and refractotopological state index (R) have been given by equations (12) & (13).

N = 45 , r = 0.999 , s = 0.810 , F (1, 43) = 19512.99

N = 46 , r = 0.997 , s = 1.452 , F (1,44) = 6581.835

These equations show the high level of significance. Because, correlation coefficients and F value is again at 99% level [ F¹₄₄(0.01) = 7.31 ] ,99.8% & 99.4%

variance (r² = 0.998 & 0.994) high.Standard deviations have minimum variation about the line of regression. All these factors show perfect correlations.

Experimental and theoretical values of standard heat enthalpies of formation (ΔH _fº₎ of some alkanes calculated by equations (10),(11), (12) and (13) shows good agreement and are listed in tables 6. & ⁷.

III CONCLUSION:

Therefore, standard heat enthalpies of formation (ΔH _fº) of alkanes can be estimated by equations(10),(11), (12) and (13) simply by calculating molecular connectivity (¹χ^{v )} , van der waals volume (V_w), electrotopological state index (E) and refractotopological state index (R) parameters.

IV. REFERENCES:

[1] S. W. Benson and H. Buss , J. Chem. Phy., 29 (1958) 546 - 72

[2] S. W. Benson , R. R .Cruickshank , D. M. Golden , G. R. Haugen, H. E. O' Neal, A. S. Rodgers, R. J. Shaw and R. Walsh, Chem. Rev., 69 (1969) 279 -321.

[3] M. Luria and S. W. Benson , J. Chem. Eng. Data , 22 (1977) 90 -100.

[4] A.Mercader, E.A.Castro and A.A.Toropov,Int.J.Mol.Sci.2 (2001)121-132.

[5] P.Duchowicz and E.A.Castro.,J.of the Korean Chemical Society 44 (6) (2000).

[6] N.Cohen, J.Phys.Chem. Ref Data, 25 (6) (1995).

[7] B.L.Gorsi, G.S.Kalwania and M.Sharma, Indian J,Chem.,Sec.A , 32A(1993) 889.

[8] B.L.Gorsi,G.S.Kalwania and M.Sharma , J.Indian Chem. Soc., 75 (1998) 373.

[9] L.B.Kier and L.H.,Hall ("Molecular Connectivity in Chemistry and Drug Research" Academic Press, New York 1976.

[10] M. Randic, J. Am. Chem. Soc., 97 (1975) 6609.

[11] A. Bondi, J. Phy. Chem., 68 (1964) 441.

[12] A. Moriguchi, Chem. Pharm. Bull. (Jpn.), 23 (1975) 247.

[13] L. H. Hall , B. Mohnly and L. B. Kier , J. Chem. Inf. Compt. Sc., 1 (1991) 31.

[14] L.H. Hall, B. Mohnly and L.B. Kier,Quant. Struct- Net., Relat, 10(1991) 43 -51.

[15] L. B. Kier and L. H., Hall , Pharmae Res., 7, 8 (1990) 801-807.

[16] A. K. Ghose and G. M. Crippen , J.Chem. Inf. Comput. Sci. 27.1,(1987) 21 -35.

[17] F. D. Rossini, K. S. Pitzer, R. L. Arnett, R. M. Braum and G. C. Pimentel, "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons

[18] and Related Compounds",Carnegie Press Pittsburgh, Pa., 1953 .

[19] J.G. Aston, " Some Observations on the Thermodynamics of Hydrocarbons and Related Compounds", Chem.. Rev., 27(1940)59-73.

[20] K.S. Pitzer, " Chemical Equilibria, Free Energies and Heat Contents for gaseous Hydrocarbons", Chem. Rev., 27(1940)75-83.

[21] M. Sounders, Jr., C.S. Matthewa and C.O. Hurd,"Entropy and Heat of

[22] Formation of Hydrocarbon Vapors", Ind. Eng. Chem. ,41 (1949)1048-1056.

[23] F.D. Rossini, "Heats of Formation of Gaseous Hydrocarbons", Chem. Rev., 27 (1940)1-16.

Publication Dates

• Publication in this collection
  09 Dec 2010
• Date of issue
  Sept 2010