Calculating of πbonds, σbonds, single and double bonds in Straight Chain and Cycloalkene Systems
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 35900
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 C_{176}H_{250}, C_{2000}H_{2000}. Keeping this in view, a rapid method has been proposed^{2,3,4} for the calculation of number of πbonds, σbonds, 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 πbonds 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
\[P= \dfrac{2XY}{2} + 1 \tag{1}\]
where, X = number of carbon atoms; Y = number of hydrogen atoms and P = number of π bonds/double bonds. E.g.: In C_{176}H_{250}, X = 176, Y = 250, therefore P = (2 x 176 – 250)/2 +1 = 51 + 1 = 52 number of π bonds or double bonds.
Calculation of σbonds (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 (σbonds). E.g.: In C_{176}H_{250}, 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 C_{176}H_{250}, Y = 250, therefore A =[(3 x 250)/2] = 375 2 = 373 single bonds. Examples have been illustrated in Table 1.
Example (C_{x}H_{y})  Straightchain Structure  π bond/ bonds [(2XY)/2+1]  σ bonds [X+Y1]  Single bonds [(3Y/2)2]  Double bond/bonds [(2XY)/2 + 1] 
C_{2}H_{4}  H_{2}C=CH_{2}  1  5  4  1 
C_{3}H_{6}  H_{2}C=CHCH_{3}  1  8  7  1 
C_{3}H_{4}  H_{2}C=C=CH_{2}  2  6  4  2 
C_{4}H_{8}  H_{2}C=CHCH_{2}CH_{3} or H_{3}CHC=CHCH_{3}  1  11  10  1 
C_{4}H_{6}  H_{2}C=C=CHCH_{3} or H_{2}C=CHCH=CH_{2}  2  9  7  2 
C_{4}H_{4}  H_{2}C=C=C=CH_{2}  3  7  4  3 
C_{176}H_{250}    52  425  373  52 
C_{2000}H_{2000}    1001  3999  2998  1001 
C_{99}H_{4}    98  102  4  98 
Cyclic Olefinic Hydrocarbons
Calculation of πbonds 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
\[P_c= \dfrac{2XY}{2} \tag{4}\]
where, X = number of carbon atoms; Y = number of hydrogen atoms and P_{c} = number of π bonds or double bonds in the cyclic olefinic system. E.g.: In cyclooctatetraene (C_{8}H_{8}), X = Y = 8, therefore P_{c} = 168/2 = 4 number of π bonds or double bonds.
Calculation of σbonds (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 S_{c} = number of sigma bonds (σbonds) in cyclic olefinic system. Eg: In cyclooctatetraene (C_{8}H_{8}), X = Y = 8, therefore S_{c} = 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 A_{c} = number of single bonds and y is number of hydrogen atoms in aliphatic cyclic olefin. E.g.: In cyclooctatetraene (C_{8}H_{8}), Y = 8, therefore A_{c} = 24/2 = 12 number of single bonds. Examples have been illustrated in Table 2.
Example (C_{x}H_{y})  Cycloalkene  π bond / bonds (P_{c}) = [(2XY)/2]  σ bonds (S_{c}) [X+Y]  Single bonds (A_{c}) [(3Y/2)]  Double bond/bonds [(2XY)/2] 
C_{3}H_{4}  Cyclopropene  1  7  6  1 
C_{4}H_{4}  Cyclobuta diene  2  8  6  2 
C_{5}H_{6}  Cyclopentadiene  2  11  9  2 
C_{6}H_{8}  Cyclohexadiene  2  14  12  2 
C_{7}H_{8}  Cycloheptatriene  3  15  12  3 
C_{8}H_{8}  Cyclooctatetraene  4  16  12  4 
References

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, 889893.

Arijit Das, Debapriya Pal, Bijaya Paul, R. Sanjeev and V. Jagannadham, ‘Rapid calculation of the number of πbonds, σbonds, single and double bonds in aliphatic unsaturated open chain and cyclic olefinic hydrocarbons’, Education in Chemical Science and Technology, Ind. Chem. Soc., Aug2014, 2(1), 41 46
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Contributor
 Dr. Arijit Das, Ph.D. (Inorganic Chemistry), MACS ( Invited,USA ), SFICS, MISC, MIAFS (India), Assistant Professor, Department of Chemistry, Ramthakur College, Agartala, Tripura(W), Tripura, India, Pin799003.