Worksheet: Molecular Orbital Theory

In this worksheet, we will practice describing the shapes, energies and electron occupancies of bonding, nonbonding, and antibonding molecular orbitals.

Q1:

An sp2 hybridized atom in a molecule forms 𝜎 bonds to three other atoms of the same element. There are no other bonds in the molecule. Which of the following statements is true?

  • AThe molecular bonding orbitals have the same energy.
  • BThe dipole moment of each bond is zero.
  • CThe three bonds contribute equally to each bonding molecular orbital.
  • DThe three bonds contribute equally to each bonding energy level.
  • EAll of the bonds are partial double bonds.

Q2:

What is the main reason that bonding molecular orbitals are lower in energy than the parent atomic orbitals?

  • AThe electrons in a bonding orbital have a lower orbital angular momentum.
  • BBonding orbitals are less symmetrical than atomic orbitals.
  • CThe electrons in a bonding orbital are more weakly shielded by the core electrons of the parent atoms.
  • DThe electrons in a bonding orbital are attracted to more than one atomic nucleus.
  • EThe electrons in a bonding orbital repel each other more weakly.

Q3:

Which of the following statements is false?

  • AMolecules containing an even number of electrons can be paramagnetic.
  • BWhen atomic orbitals overlap to form molecular orbitals, the total number of orbitals does not change.
  • CWhen two p orbitals overlap to form a 𝜎 bond, most of the electron density is concentrated between the nuclei.
  • DThe greatest overlap between an atomic orbital and a πœ‹ antibonding orbital is produced when the atomic orbital approaches the πœ‹ bond axis at 9 0 ∘ .
  • EThe greatest overlap between an atomic orbital and a 𝜎 antibonding orbital is produced when the atomic orbital approaches parallel to the 𝜎 bond axis.

Q4:

Which of the following statements is true?

  • AIn the lowest-energy state of a stable molecule, electrons in bonding orbitals are always paired.
  • BOnly two atoms can contribute to a bonding orbital.
  • CIn the lowest-energy state of a stable molecule, electrons never occupy an antibonding orbital.
  • DMolecules containing an odd number of electrons are always paramagnetic.
  • EIf a molecule contains multiple bonds, the highest-energy occupied orbitals are always πœ‹ bonding orbitals.

Q5:

The average bond energy of a C C single bond is 347 kJ/mol, while that of a C C triple bond is 839 kJ/mol. Why is a triple bond between carbon atoms not three times as strong as a single bond?

  • AThe triple bond is weakened by s-p mixing.
  • BRepulsion between the three pairs of bonding electrons reduces the energy of the triple bond.
  • CBonds formed by p orbitals are always weaker than those formed by hybrid sp or sp2 orbitals.
  • DOrbital overlap in a C C 𝜎 bond is greater than that in a C C πœ‹ bond.
  • EThe triple bond is weakened by electrons occupying an antibonding orbital.

Q6:

Which of the following electronic transitions do alkanes exhibit?

  • A πœ‹ to 𝜎 βˆ—
  • B πœ‹ to πœ‹ βˆ—
  • C πœ‹ to πœ‹ βˆ—
  • D 𝜎 to 𝜎 βˆ—

Q7:

Liquid oxygen is attracted by a magnetic field. Which feature of the O 2 molecule is responsible for this behavior?

  • AUnpaired electrons in bonding orbitals
  • BUnpaired electrons in nonbonding orbitals
  • CPaired electrons in nonbonding orbitals
  • DUnpaired electrons in antibonding orbitals
  • EPaired electrons in antibonding orbitals

Q8:

What is the ground-state valence molecular orbital configuration for H 2 – ?

  • A ( 𝜎 ) ( 𝜎 )    βˆ—   
  • B ( 𝜎 ) ( 𝜎 )    βˆ—   
  • C ( 𝜎 ) ( 𝜎 )    βˆ—   
  • D ( 𝜎 ) ( 𝜎 )    βˆ—   
  • E ( 𝜎 ) ( 𝜎 )    βˆ—   

Q9:

The molecule N e 2 does not exist in nature.

To 1 decimal place, what is the bond order of N e 2 ?

From which molecular orbital is an electron removed in the first ionization of N e 2 ?

  • A 𝜎 βˆ— 2 𝑝
  • B πœ‹ βˆ— 2 𝑝
  • C 𝜎 2 𝑠
  • D 𝜎 2 𝑝
  • E πœ‹ 2 𝑝

To 1 decimal place, what is the bond order of N e 2 + ?

Q10:

What is the valence molecular orbital configuration for F 2 – ?

  • A ( 𝜎 ) ( 𝜎 ) ο€» πœ‹ , πœ‹  ο€Ί 𝜎  ο€» πœ‹ , πœ‹  ο€Ί 𝜎    βˆ—     οŠͺ   βˆ—  βˆ—  οŠͺ βˆ—   s s p p p p p p y z x y z x
  • B ( 𝜎 ) ( 𝜎 ) ο€Ί 𝜎  ο€» πœ‹ , πœ‹  ο€Ί 𝜎  ο€» πœ‹ , πœ‹    βˆ—       οŠͺ βˆ—   βˆ—  βˆ—   s s p p p p p p x y z x y z
  • C ( 𝜎 ) ( 𝜎 ) ο€» πœ‹ , πœ‹  ο€Ί 𝜎  ο€Ί 𝜎  ο€» πœ‹ , πœ‹    βˆ—     οŠͺ   βˆ—   βˆ—  βˆ—   s s p p p p p p y z x x y z
  • D ( 𝜎 ) ( 𝜎 ) ο€Ί 𝜎  ο€» πœ‹ , πœ‹  ο€» πœ‹ , πœ‹  ο€Ί 𝜎    βˆ—       οŠͺ βˆ—  βˆ—  οŠͺ βˆ—   s s p p p p p p x y z y z x
  • E ( 𝜎 ) ( 𝜎 ) ο€» πœ‹ , πœ‹  ο€» πœ‹ , πœ‹  ο€Ί 𝜎  ο€Ί 𝜎    βˆ—     οŠͺ βˆ—  βˆ—     βˆ—   s s p p p p p p y z y z x x

Q11:

What is the valence molecular orbital configuration for N 2 + ?

  • A ( 𝜎 ) ( 𝜎 ) ο€Ί 𝜎  ο€» πœ‹ , πœ‹  ο€» πœ‹ , πœ‹    βˆ—       οŠͺ βˆ—  βˆ—   s s p p p p p x y z y z
  • B ( 𝜎 ) ( 𝜎 ) ο€Ί 𝜎  ο€» πœ‹ , πœ‹  ο€» πœ‹ , πœ‹    βˆ—        βˆ—  βˆ—   s s p p p p p x y z y z
  • C ( 𝜎 ) ( 𝜎 ) ο€» πœ‹ , πœ‹  ο€Ί 𝜎  ο€» πœ‹ , πœ‹    βˆ—     οŠͺ   βˆ—  βˆ—   s s p p p p p y z x y z
  • D ( 𝜎 ) ( 𝜎 ) ο€» πœ‹ , πœ‹  ο€Ί 𝜎  ο€» πœ‹ , πœ‹    βˆ—     οŠͺ   βˆ—  βˆ—   s s p p p p p y z x y z
  • E ( 𝜎 ) ( 𝜎 ) ο€» πœ‹ , πœ‹  ο€» πœ‹ , πœ‹  ο€Ί 𝜎    βˆ—     οŠͺ βˆ—  βˆ—     s s p p p p p y z y z x

Q12:

Which of the following ions has the valence molecular orbital configuration: ( 𝜎 ) ( 𝜎 ) ο€Ί πœ‹ , πœ‹  ο€Ή 𝜎  ο€Ί πœ‹ , πœ‹  ο€Ί 𝜎     βˆ—        οŠͺ    βˆ—   βˆ—    βˆ—    ο‘‘ ο‘’  ο‘‘ ο‘’  ?

  • A F 2 2 +
  • B O 2 +
  • C C 2 2 –
  • D N 2 –
  • E O 2 2 +

Q13:

According to molecular orbital theory, which of the following molecules is the most stable?

  • A B 2
  • B C 2
  • C B e 2
  • D N 2

Q14:

Which orbital would you expect to be the LUMO for a peroxide ion, O 2 2 – ?

  • A 𝜎  p
  • B πœ‹  p
  • C πœ‹ βˆ—  p
  • D 𝜎 βˆ—  p

Q15:

Which of the following statements is true about nonbonding molecular orbitals?

  • AThey counteract bond formation in a molecule.
  • BThey are responsible for the formation of πœ‹ bonds.
  • CThey help hold the molecule together, once it is formed.
  • DThey are similar in energy to the atomic orbitals.
  • EThey are responsible for the formation of 𝜎 bonds.

Q16:

According to valence bond theory (VBT), O 2 has no unpaired electrons. MO theory shows two unpaired electrons in a 2 n βˆ— molecular orbital. Which of the following experiments supports the correct electron configuration?

  • AInfrared spectroscopy shows a double-bond stretch; MO theory is correct.
  • BAn EPR spectrum shows that oxygen is paramagnetic; VBT is correct.
  • CInfrared spectroscopy shows a double-bond stretch; VBT is correct.
  • DAn EPR spectrum shows that oxygen is paramagnetic; MO theory is correct.
  • EThere is no way to know which theory is correct.

Q17:

For potassium metal, the 4p band represents the and the .

  • AHOMO, nonbonding orbital
  • BLUMO, bonding orbital
  • CHOMO, antibonding orbital
  • DLUMO, antibonding orbital
  • EHOMO, bonding orbital

Q18:

4s–4p band overlap allows calcium to behave as a conductor. How many energy levels are present in the conduction band?

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