How is a sigma bond formed in valence bond theory?
End-to-end overlap along the internuclear axis
✓
Side-by-side overlap of parallel p orbitals
Complete transfer of an electron between atoms
Sharing of two lone pairs between atoms
Correct Answer
End-to-end overlap along the internuclear axis
A sigma bond forms when orbitals meet head on, concentrating electron density along the line between the nuclei. Side-by-side overlap of parallel p orbitals produces a pi bond instead. Complete transfer of an electron between atoms describes ionic bonding. Sharing of two lone pairs between atoms is not how a covalent bond forms; each bond pairs one electron from each half-filled orbital.
Category: Valence Bond Theory
Question 2
According to valence bond theory, which factor makes a covalent bond stronger?
Less overlap of the bonding orbitals
Greater overlap of the bonding orbitals
✓
More lone pairs on the bonded atoms
A larger distance between the nuclei
Correct Answer
Greater overlap of the bonding orbitals
The more two orbitals overlap, the more electron density lies between the nuclei and the stronger the bond. Less overlap of the bonding orbitals gives a weaker bond. More lone pairs on the bonded atoms does not strengthen the shared pair. A larger distance between the nuclei reduces overlap and weakens the bond.
Category: Valence Bond Theory
Question 3
Two hydrogen atoms approach each other. What happens to the energy of the system if they are pushed closer than the H-H bond length?
It keeps falling as overlap increases
It stays at its minimum value
It rises because nuclear repulsion dominates
✓
It falls because more electrons pair
Correct Answer
It rises because nuclear repulsion dominates
The bond length is the distance of lowest energy; closer than that, repulsion between the two nuclei and between the electrons outweighs the attraction, so energy rises steeply. It keeps falling as overlap increases is true only at larger distances. It stays at its minimum value is true only at the bond length itself. It falls because more electrons pair is wrong because H2 has only one pair to form.
Category: Valence Bond Theory
Question 4
Which combination of bonds makes up a triple bond?
Two sigma and one pi
Three sigma
Three pi
One sigma and two pi
✓
Correct Answer
One sigma and two pi
The first bond between two atoms is always a sigma bond, and each additional bond is a pi bond, so a triple bond is one sigma and two pi. Two sigma and one pi is impossible because only one head-on overlap fits along the axis. Three sigma fails for the same reason. Three pi leaves out the required sigma bond.
Category: Multiple Bonds
Question 5
Ammonia's nitrogen forms three N-H bonds and keeps one lone pair. Which hybrid orbital set describes this nitrogen?
The sp3 set
✓
The sp2 set
The sp set
The sp3d set
Correct Answer
The sp3 set
Nitrogen has four regions of electron density, three bonds plus a lone pair, so it uses four sp3 hybrid orbitals, one of which holds the lone pair. The sp2 set provides only three orbitals. The sp set provides only two. The sp3d set provides five orbitals and requires valence d orbitals, which nitrogen lacks.
Category: Hybrid Orbitals
Question 6
According to valence bond theory, what kind of hybrid orbitals does boron adopt in BF3, where it bonds to three fluorine atoms with no lone pairs?
The sp3 set
The sp2 set
✓
The sp set
The sp3d set
Correct Answer
The sp2 set
Three regions of electron density call for three hybrid orbitals, made from one s and two p orbitals, giving sp2 and a trigonal planar arrangement. The sp3 set would provide four orbitals for four regions. The sp set provides only two orbitals. The sp3d set provides five and is not available to a second-period atom.
Category: Hybrid Orbitals
Question 7
BeCl2 is a linear molecule with no lone pairs on beryllium. Which set of hybrid orbitals does beryllium use?
The sp2 set
The sp3 set
The sp set
✓
The sp3d2 set
Correct Answer
The sp set
Two regions of electron density require two hybrid orbitals, formed from one s and one p orbital, so beryllium is sp hybridized with a 180 degree angle. The sp2 set would give three orbitals at 120 degrees. The sp3 set would give four tetrahedral orbitals. The sp3d2 set gives six orbitals and needs d orbitals that beryllium does not have.
Category: Hybrid Orbitals
Question 8
What is the angle between any two sp3 hybrid orbitals on the same atom?
120°
180°
90°
109.5°
✓
Correct Answer
109.5°
The four sp3 orbitals point to the corners of a tetrahedron, so any two are separated by 109.5°. 120° is the angle between sp2 orbitals in a trigonal plane. 180° is the angle between the two sp orbitals of a linear atom. 90° is the angle between neighboring regions in an octahedral arrangement, not a tetrahedral one.
Category: Hybrid Orbitals
Question 9
How many hybrid orbitals are produced when one s orbital mixes with two p orbitals on the same atom?
3
✓
2
4
6
Correct Answer
3
The number of hybrid orbitals always equals the number of atomic orbitals combined, so one s plus two p gives three sp2 orbitals. 2 would come from one s and one p orbital. 4 would come from one s and three p orbitals. 6 would require an s, three p and two d orbitals.
Category: Hybrid Orbitals
Question 10
How many unhybridized p orbitals remain on an sp2 hybridized carbon atom?
1
✓
2
3
Correct Answer
1
Carbon has three 2p orbitals; sp2 hybridization uses two of them, leaving one p orbital that can form a pi bond. 0 is the case for an sp3 carbon. 2 is the case for an sp carbon. 3 would mean no p orbitals were hybridized at all.
Category: Hybrid Orbitals
Question 11
In ethyne, HCCH, the two carbon atoms share a triple bond. Which orbitals form its two pi bonds?
The sp hybrid orbitals on each carbon
The sp2 hybrid orbitals on each carbon
Unhybridized p orbitals on each carbon
✓
The 2s orbitals on each carbon
Correct Answer
Unhybridized p orbitals on each carbon
Each sp hybridized carbon keeps two unhybridized p orbitals, and side-by-side overlap of these with the matching pair on the other carbon forms two pi bonds. The sp hybrid orbitals on each carbon form the sigma bonds instead. The sp2 hybrid orbitals on each carbon are not present in ethyne. The 2s orbitals on each carbon have been mixed into the hybrids and do not form pi bonds.
Category: Multiple Bonds
Question 12
In ethene, C2H4, which orbitals overlap to form the carbon-carbon sigma bond?
Unhybridized p orbitals on each carbon
The sp3 hybrid orbitals on each carbon
The 1s orbitals on each carbon
The sp2 hybrid orbitals on each carbon
✓
Correct Answer
The sp2 hybrid orbitals on each carbon
Each carbon in ethene is sp2 hybridized, and one sp2 orbital from each carbon overlaps end to end to form the sigma bond. Unhybridized p orbitals on each carbon overlap side by side to form the pi bond. The sp3 hybrid orbitals on each carbon describe ethane, which has only single bonds. The 1s orbitals on each carbon are core orbitals and do not take part in bonding.
Category: Multiple Bonds
Question 13
How many sigma bonds and pi bonds are in a molecule of HCN, which has a C-N triple bond?
2 sigma and 2 pi
✓
3 sigma and 1 pi
1 sigma and 3 pi
4 sigma and 0 pi
Correct Answer
2 sigma and 2 pi
The H-C single bond is one sigma bond, and the C-N triple bond adds one more sigma bond plus two pi bonds, for 2 sigma and 2 pi. 3 sigma and 1 pi would describe a molecule with one double bond and two single bonds. 1 sigma and 3 pi ignores the sigma bond within the triple bond. 4 sigma and 0 pi treats every line as a sigma bond.
Category: Multiple Bonds
Question 14
Which set of hybrid orbitals does each carbon atom in benzene, C6H6, use?
The sp3 set
The sp2 set
✓
The sp set
The sp3d set
Correct Answer
The sp2 set
Each benzene carbon bonds to three atoms, two carbons and one hydrogen, in a planar ring, so it is sp2 hybridized regardless of which resonance form is drawn. The sp3 set would require four regions and a nonplanar arrangement. The sp set would require only two regions. The sp3d set is not available to carbon, a second-period element.
Category: Multiple Bonds
Question 15
An O2 molecule has 8 valence electrons in bonding molecular orbitals and 4 in antibonding molecular orbitals. What is its bond order?
4
6
2
✓
1
Correct Answer
2
Bond order equals bonding electrons minus antibonding electrons, divided by two: (8 - 4) / 2 = 2, matching a double bond. 4 forgets to divide by two. 6 adds the antibonding electrons instead of subtracting them. 1 is the bond order of F2, which has two more antibonding electrons.
Category: Bond Order and Magnetism
Question 16
Molecular orbital theory, including s-p mixing, predicts which of these diatomic molecules to be paramagnetic?
C2
N2
F2
B2
✓
Correct Answer
B2
In B2, s-p mixing places the pi 2p orbitals below the sigma 2p orbital, so its last two electrons occupy the two degenerate pi orbitals singly and remain unpaired. C2 fills both pi 2p orbitals with paired electrons. N2 has all its electrons paired. F2 also has all its electrons paired.
Category: Bond Order and Magnetism
Question 17
Which of these diatomic species is predicted by molecular orbital theory to have a bond order of zero?
He2
✓
H2
Li2
B2
Correct Answer
He2
He2 would place two electrons in the sigma 1s bonding orbital and two in the sigma 1s antibonding orbital, so (2 - 2) / 2 = 0 and no stable bond forms. H2 has a bond order of 1. Li2 has a bond order of 1 from its 2s electrons. B2 has a bond order of 1.
Category: Bond Order and Magnetism
Question 18
What feature distinguishes a sigma antibonding orbital from the sigma bonding orbital formed from the same atomic orbitals?
Greater electron density between the nuclei
A node between the two nuclei
✓
Lower energy than the atomic orbitals
Electron density only above and below the axis
Correct Answer
A node between the two nuclei
The out-of-phase combination cancels between the nuclei, creating a node there and raising the orbital's energy. Greater electron density between the nuclei is the mark of the bonding orbital. Lower energy than the atomic orbitals also describes the bonding orbital. Electron density only above and below the axis describes a pi orbital, not a sigma orbital.
Category: Molecular Orbitals
Question 19
When the six 2p atomic orbitals of two atoms combine in a diatomic molecule, how many molecular orbitals form?
3
4
6
✓
12
Correct Answer
6
The number of molecular orbitals always equals the number of atomic orbitals combined, so six 2p orbitals give six: one sigma, two pi, one sigma antibonding and two pi antibonding. 3 counts only the bonding orbitals. 4 leaves out the two pi antibonding orbitals. 12 double counts the orbitals.
Category: Molecular Orbitals
Question 20
For which of these diatomic molecules does the sigma 2p orbital lie higher in energy than the pi 2p orbitals?
O2
F2
Ne2
N2
✓
Correct Answer
N2
s-p mixing is significant for the elements lithium through nitrogen, so in N2 the sigma 2p orbital is pushed above the pi 2p set. O2 has negligible s-p mixing, so its sigma 2p is below the pi 2p orbitals. F2 follows the same unmixed order as O2. Ne2 would also follow the unmixed order.
Category: Molecular Orbitals