Question

How can I calculate the bond order of benzene?

Answer 1

Hint: In molecular orbital theory bond order is defined as half the difference between the number of bonding electrons and the number of antibonding electrons which can be shown as:
\[B.O = \dfrac{number\ of\ bonding\ electron-number\ of\ antibonding\ electron}{2}\]

Complete Step by step solution:
Bond order is directly proportional to the strength of the bond i.e. higher the bond order more the strength of bond is. The effective nuclear charge is defined as the positive charge experienced by an electron in an atom here the term effective is used because the shielding effect of negatively charged electrons prevents higher orbital electrons form experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons. The effective nuclear charge experienced by the electron is also known by the name core charge. It is possible to determine the strength of the nuclear charge by knowing the oxidation number of the atom.
We know that benzene has 6 molecular $\pi $ orbitals. Bond order is half of the difference between the number of bonding and antibonding molecular orbitals. In this case there are three bonding and three antibonding electrons. Now the six $\pi $ electrons will go into three bonding orbitals.
$\pi B.O.=\dfrac{1}{2}(B-A)=\dfrac{1}{2}(6-0)=3$
This is for the $\pi $ bond order for 6 $C-C$bonds. Now for one $C-C\pi $ bond, $BO=\dfrac{3}{6}=0.5$
Hence, For single $C-C$ bond in benzene the total $BO=\sigma +\pi $
i.e. 1 + 0.5 = 1.5
Hence the bond order of benzene is 1.5.
Note: The number of bonds that an atom can form as part of a compound is expressed by the valency of the element. Valency is different from the oxidation number. For example valency of nitrogen is 3 whereas it can have oxidation numbers from -3 to +5.