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Calculating of π-bonds, σ-bonds, 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 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.

    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 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.

                                          
    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

    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.