# Calculating of π-bonds, σ-bonds, single and double bonds in Straight Chain and Cycloalkene Systems

The molecular formula which defines a very large number of chemical structure, in this particular case, it is a Herculean task to calculate the nature and number of bonds. Earlier Badertscher et al. studied a novel formalism to characterize the degree of unsaturation of organic molecules.1 But no such work has not been taken till now to calculate the number and types of bonds in open chain olefinic system having complex molecular formulae like C176H250, C2000H2000. Keeping this in view, a rapid method has been proposed2,3,4 for the calculation of number of π-bonds, σ-bonds, single and double bonds with the help of following formulae for certain aliphatic unsaturated open chain and cyclic olefinic hydrocarbons.

## Open Chain Olefinic Hydrocarbons

Calculation of π-bonds and double bonds (P):

In the first case, we have to count the number of carbon atoms (X) and the number of hydrogen atoms (Y) in a given unsaturated hydrocarbon containing double bonds. The formula to calculate the number of π bonds or double bonds for an aliphatic straight chain olefin is

$P= \dfrac{2X-Y}{2} + 1 \tag{1}$

where, X = number of carbon atoms; Y = number of hydrogen atoms and P = number of π bonds/double bonds. E.g.: In C176H250, X = 176, Y = 250, therefore P = (2 x 176 – 250)/2 +1 = 51 + 1 = 52 number of π bonds or double bonds.

Calculation of σ-bonds (S):

In this case, first we have to count the number of carbon atoms (X) and the number of hydrogen atoms (Y) in the given unsaturated hydrocarbon containing double bonds. The formula to calculate the number of σ bonds for an aliphatic straight chain olefin is

$S = X + Y - 1 \tag{2}$

where, X = number of carbon atoms; Y = number of hydrogen atoms and S = number of sigma bonds (σ-bonds). E.g.: In C176H250, X = 176, Y = 250, therefore P = 176 + 250 -1 = 425 σ bonds.

Calculation of Single bonds (A):

The total number of single bond for an aliphatic straight chain olefin is

$A = \dfrac{3Y}{2}-2 \tag{3}$

where A = number of single bonds and Y is number of hydrogen atoms. E.g.: In C176H250, Y = 250, therefore A =[(3 x 250)/2] = 375 -2 = 373 single bonds. Examples have been illustrated in Table 1.

 Example (CxHy) Straight-chain Structure π bond/ bonds [(2X-Y)/2+1] σ bonds [X+Y-1] Single bonds [(3Y/2)-2] Double bond/bonds [(2X-Y)/2 + 1] C2H4 H2C=CH2 1 5 4 1 C3H6 H2C=CH-CH3 1 8 7 1 C3H4 H2C=C=CH2 2 6 4 2 C4H8 H2C=CH-CH2-CH3 or H3C-HC=CH-CH3 1 11 10 1 C4H6 H2C=C=CH-CH3 or H2C=CH-CH=CH2 2 9 7 2 C4H4 H2C=C=C=CH2 3 7 4 3 C176H250 - 52 425 373 52 C2000H2000 - 1001 3999 2998 1001 C99H4 - 98 102 4 98

## Cyclic Olefinic Hydrocarbons

Calculation of π-bonds and double bonds (Pc):

In the first case, we have to count the number of carbon atoms (X) and the number of hydrogen atoms (Y) in the given unsaturated cyclic olefinic hydrocarbons. The formula to calculate the number of π bonds or double bonds for an aliphatic cyclic olefin is

$P_c= \dfrac{2X-Y}{2} \tag{4}$

where, X = number of carbon atoms; Y = number of hydrogen atoms and Pc = number of π bonds or double bonds in the cyclic olefinic system. E.g.: In cyclooctatetraene (C8H8), X = Y = 8, therefore Pc = 16-8/2 = 4 number of π bonds or double bonds.

Calculation of σ-bonds (Sc):

In the first case, we have to count the number of carbon atoms (X) and the number of hydrogen atoms (Y) in the given unsaturated cyclic olefinic hydrocarbons. The formula to calculate the number of σ bonds for an aliphatic cyclic olefin is

$S_c = X + Y \tag{5}$

where, X = number of carbon atoms; Y = number of hydrogen atoms and Sc = number of sigma bonds (σ-bonds) in cyclic olefinic system. Eg: In cyclooctatetraene (C8H8), X = Y = 8, therefore Sc = 8+8 = 16 number of σ bonds.

Calculation of Single bonds (Ac):

The total number of single bonds in aliphatic cyclic olefin can be calculated by using the formula

$A_c = \dfrac{3Y}{2} \tag{6}$

where Ac = number of single bonds and y is number of hydrogen atoms in aliphatic cyclic olefin. E.g.: In cyclooctatetraene (C8H8), Y = 8, therefore Ac = 24/2 = 12 number of single bonds. Examples have been illustrated in Table 2.

 Example (CxHy) Cycloalkene π bond / bonds (Pc) = [(2X-Y)/2] σ bonds (Sc) [X+Y] Single bonds (Ac) [(3Y/2)] Double bond/bonds [(2X-Y)/2] C3H4 Cyclopropene 1 7 6 1 C4H4 Cyclobuta diene 2 8 6 2 C5H6 Cyclopentadiene 2 11 9 2 C6H8 Cyclohexadiene 2 14 12 2 C7H8 Cycloheptatriene 3 15 12 3 C8H8 Cyclooctatetraene 4 16 12 4

## References

1. Martin Badertscher, Kaspar Bischofberger, Morton E. Munk, and Erno Pretsch, ‘A Novel Formalism To Characterize the Degree of Unsaturation of Organic Molecules’, J.Chem.Inf. Comput. Sci. 2001, 41, 889-893.

2. Arijit Das, Debapriya Pal, Bijaya Paul, R. Sanjeev and V. Jagannadham, ‘Rapid calculation of the number of π-bonds, σ-bonds, single and double bonds in aliphatic unsaturated open chain and cyclic olefinic hydrocarbons’, Education in Chemical Science and Technology, Ind. Chem. Soc., Aug-2014, 2(1), 41- 46