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 proposed^2,3,4 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.

Table 1: Calculation of π-bonds, σ-bonds, single and double bonds in open chain olefinic hydrocarbons

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 P_c = number of π bonds or double bonds in the cyclic olefinic system. E.g.: In cyclooctatetraene (C₈H₈), X = Y = 8, therefore P_c = 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 S_c = number of sigma bonds (σ-bonds) in cyclic olefinic system. Eg: In cyclooctatetraene (C₈H₈), 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 (C₈H₈), Y = 8, therefore A_c = 24/2 = 12 number of single bonds. Examples have been illustrated in Table 2.

Table 2: Calculation of π-bonds, σ-bonds, single and double bonds in Cyclo Alkene system

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

External Links

1. https://communities.acs.org/docs/DOC-46667
2. https://communities.acs.org/docs/DOC-45853

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, Pin-799003.