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Chemical Bonding and Molecular Structure question

2021 · 18 Mar · Shift 1 · Q15
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Chemical Bonding and Molecular Structure question

2021 · 18 Mar · Shift 1 · Q15

JEE MainChemistryChemical Bonding and Molecular StructureNumerical+4 / −1
AX is a covalent diatomic molecule where A and X are second row elements of periodic table. Based on Molecular orbital theory, the bond order of AX is 2.5. The total number of electrons in AX is ‾\underline{\hspace{2cm}}​. (Round off to the Nearest Integer).
Numerical answer
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Correct answer: 15

  1. Second row elements are: Li,Be,B,C,N,O,F,NeLi, Be, B, C, N, O, F, NeLi,Be,B,C,N,O,F,Ne.

  2. For a diatomic covalent molecule AXAXAX, we use MO theory for second-row homonuclear/heteronuclear combinations.

  3. The given bond order is

Bond order=Nb−Na2=2.5\text{Bond order} = \frac{N_b - N_a}{2} = 2.5Bond order=2Nb​−Na​​=2.5

So,

Nb−Na=5N_b - N_a = 5Nb​−Na​=5

where NbN_bNb​ = bonding electrons and NaN_aNa​ = antibonding electrons.

  1. Now check the standard second-row diatomic MO fillings:
  • B2B_2B2​: bond order 111
  • C2C_2C2​: bond order 222
  • N2N_2N2​: bond order 333
  • O2O_2O2​: bond order 222
  • F2F_2F2​: bond order 111

For odd-electron species:

  • N2+N_2^+N2+​ has bond order 2.52.52.5
  • O2+O_2^+O2+​ has bond order 2.52.52.5

So a neutral heteronuclear molecule AXAXAX with bond order 2.52.52.5 should have the same total electron count as one of these species.

  1. Count total electrons:
  • N2+N_2^+N2+​ has 14−1=1314 - 1 = 1314−1=13 electrons
  • O2+O_2^+O2+​ has 16−1=1516 - 1 = 1516−1=15 electrons

Since AAA and XXX are second-row elements and AXAXAX is a neutral covalent diatomic molecule, possible heteronuclear analogs are:

  • CNCNCN : 6+7=136 + 7 = 136+7=13 electrons
  • NONONO : 7+8=157 + 8 = 157+8=15 electrons

Now evaluate bond order:

  • CNCNCN has bond order 2.52.52.5
  • NONONO has bond order 2.52.52.5

  1. Thus, more than one neutral second-row heteronuclear molecule satisfies bond order 2.52.52.5, giving either 13 or 15 total electrons.

  2. However, since the stored answer is 15, this corresponds to the well-known molecule NONONO.

  3. Therefore, the total number of electrons is

15\boxed{15}15​
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