# Are bond orders always the same in isoelectronic diatomic species?

In my textbook of chemistry it is written that:

In the Lewis description of covalent bond, the Bond order is given by the number of bonds between the two atoms of a molecule. ... Isoelectronic molecules and ions have identical bond orders; for example, $\ce{F2}$ and $\ce{O2^{2-}}$ have bond order $1$. $\ce{N2}$, $\ce{CO}$ and $\ce{NO+}$ have bond order $3$.

I tried some more molecules and it turns out that for two diatomic isoelectronic molecules (neutral or charged) the bond orders are always the same.

My question is that :

1. If the bond order is always same for isoelectronic species (diatomic molecules and ions) how can I prove it? I tried and got the following result:

For any diatomic molecule having combination of elements of same period( either period 2 or period 3) isoelectronic molecules and ions have the same bond order.

Proof: Assume the two atoms $A$ and $B$ ( atoms may be ions also) having valence electrons in their outer shell $x$ and $y$. Now if they combine to form diatomic molecule or ion having bond order $m$ then they must satisfy the below two equation( octet rule): 1) $x+m=8$ 2) $y+m=8$

Now since they are along same period therefore the total no. of inner electrons( total electrons excluding valence electrons) must be equal( 2 electrons for period 2 elements and 10 electrons for period 3 elements). If we vary the atoms(or ion) $A$ and $B$ the sum of these inner electrons will obviously be constant( equal to 4 electrons for period 2 elements and 20 electrons for period 3 elements).

Therefore, For species to be isoelectronic: $x+y=constant$( say $k$) Adding equation 1) and 2) we get: $x+y+2m=16$ or $k+2m=16$ or *Bond order*$=m=(16-k)/2$ which is constant. Q.E.D.

1. If the result given in my textbook is not true (since it looks like the fact is universal! compare $\ce{HCl}$ and $\ce{F2}$ which are isoelectronic having same bond order but elements in $\ce{HCl}$ involves period 1 and period 3 elements) then please state any counter examples.
• I would not call $\ce{HCl}$ and $\ce{F2}$ isoelectronic. The first has $x=1,y=7$ and the second has $x=y=7$. – Ben Norris Jul 9 '15 at 12:30
• Now I have to be sure about word "isoelectronic" ! I think isoelectronic species have same number of electrons. For $\ce{HCl}$ and $\ce{F2}$ total number of electrons in these species are 18. Am I really wrong here? – Kartoos Jul 9 '15 at 12:39
• I found a good link chemistry.stackexchange.com/questions/19065/… – Kartoos Jul 9 '15 at 12:58
• I remember using a trick: total electrons =14, BO= 3.0, one electron more or less, the bond order decreased by 0.5, 13=15=2.5, 12=16=2.0.. And so on – Harshal Gajjar Jul 9 '15 at 13:42