Question 1

Which of the following spin functions represents a valid spin wavefunction for two paired electrons?&#10;A) $\alpha$(1)$\alpha$(2)&#10;B) $\beta$(1)$\beta$(2)&#10;C) $\alpha$(1)$\beta$(2) +$\beta$(1)$\alpha$(2)&#10;D) $\alpha$(1)$\beta$(2) -$\beta$(1)$\alpha$(2)

Accepted Answer

The correct answer represents a valid spin wavefunction for two paired electrons because it is an antisymmetric combination of the spin states of the two electrons, which is a requirement for fermions (like electrons) due to the Pauli exclusion principle. This combination ensures that the overall wavefunction changes sign upon exchange of the two electrons, which is a characteristic of a singlet state where the spins are paired (one up, one down), resulting in a total spin of zero.

Question 2

Which of the following represents the best description of the bonding in an octahedral molecule such as sulfur hexafluoride, SF₆, using valence-bond theory. A) Six spd⁴ hybrid orbitals formed by the central sulfur atom, each making up a $\sigma$ bond. B) Six equivalent sp³d² hybrid orbitals formed by the central sulfur atom, each making up a $\sigma$ bond. C) Six p³d³ hybrid orbitals formed by the central sulfur atom, each making up a $\sigma$bond. D) Seven equivalent pd⁶ hybrid orbitals formed by the central sulfur atom, with six making up

Accepted Answer

The correct description of the bonding in an octahedral molecule like sulfur hexafluoride (SF6) using valence-bond theory involves six equivalent sp^3d^2 hybrid orbitals formed by the central sulfur atom. Each of these hybrid orbitals overlaps with an orbital from a fluorine atom to form a sigma (σ) bond, resulting in the octahedral geometry.

Question 3

The bonding within xenon tetrafluoride, XeF₄, is best described, using valence-bond and valence-shell electron-pair repulsion theory, as resulting from formation of sp³d² hybrid orbitals on the xenon atom, four of which form $\sigma$ bonds to fluorine atoms. Which of the following structures is consistent with this model?

A) Tetrahedral
B) Irregular tetrahedral
C) See-saw
D) Square planar

Square planar

Accepted Answer

The description of xenon tetrafluoride (XeF4) bonding involves sp3d2 hybridization on the xenon atom, leading to the formation of sigma bonds with four fluorine atoms. This hybridization and bonding arrangement result in a square planar molecular geometry, consistent with valence-shell electron-pair repulsion (VSEPR) theory, which accounts for the repulsion between electron pairs to determine the shape of the molecule.

Question 4

How many molecular orbitals can be built from the valence atomic orbitals of molecular bromine, Br₂? A) 4 B) 8 C) 9 D) 18

Accepted Answer

Molecular bromine (Br2) has a total of 14 valence electrons per bromine atom, with the valence orbitals being 4s, 4p_x, 4p_y, and 4p_z. Since there are two bromine atoms, the total number of atomic orbitals available for bonding is 4 orbitals per atom times 2 atoms, which equals 8 atomic orbitals. According to the principle of conservation of orbitals, the number of molecular orbitals formed must equal the number of atomic orbitals combined, which is 8 from one bromine atom plus 8 from the other, totaling 16 molecular orbitals, not 18. My initial response contained an error in calculation; the correct number of molecular orbitals formed is indeed 16, not 18 as previously stated.

Question 5

What is the symmetry of the bonding molecular orbital formed by a linear combination of the p_x or p_yatomic orbitals in a homonuclear diatomic molecule? A) $\sigma$_g B) $\sigma$_u C) $\pi$_g D) $\pi$_u

Accepted Answer

The answer of What is the symmetry of the bonding...

Question 6

Use molecular orbital theory to determine whether the Ne₂⁺ ion is likely to be bound, and if so, to predict its bond order. A) Not bound, bond order b = 0 B) Bound, bond order b = ½ C) Bound, bond order b = 1 D) Bound, bond order b = 2

Accepted Answer

The Ne2+ ion has 19 electrons. Using molecular orbital theory, the bond order is calculated as (number of bonding electrons - number of antibonding electrons)/2. For Ne2+, this results in a bond order of ½, indicating it is likely to be bound.

Question 7

Which of the following describes the electronic configuration of the electronic ground state of the F₂ molecule? A) 1$\sigma$_g²1$\sigma$_u²2$\sigma$_g²1 $\pi$_u⁴1 $\pi$_g⁴ B) 1$\sigma$_g²1$\sigma$_u²1 $\pi$_u⁴2$\sigma$_g²2$\sigma$_u²1 $\pi$_g² C) 1$\sigma$_g²1$\sigma$_u²1 $\pi$_u⁴2$\sigma$_g²1 $\pi$_g⁴ D) 1$\sigma$_g²1$\sigma$_u²1 $\pi$_u⁴2$\sigma$_g²1 $\pi$_g²2$\sigma$_u²

Accepted Answer

The correct electronic configuration of the electronic ground state of the F₂ molecule is 1F1F1F1S1F1F1F10_g²1F1F1F1S1F1F1F10_u²1F1F1F1S1F1F1F10_u⁴1F1F1F1S1F1F1F10_g⁴. This configuration corresponds to a bonding molecular orbital (1F1F1F1S1F1F1F10_g) and an antibonding molecular orbital (1F1F1F1S1F1F1F10_u) formed from the overlap of the 2p orbitals of the two fluorine atoms. The remaining four electrons occupy two degenerate bonding molecular orbitals (1F1F1F1S1F1F1F10_u and 1F1F1F1S1F1F1F10_g) formed from the overlap of the 2p orbitals of the two fluorine atoms.

Question 8

Using the Hückel method, the energies of the $\pi$ orbitals of the allyl radical, C₃H₄, are calculated to be
,α and α±√2 β
Calculate the energy of the delocalised $\pi$ system relative to the energy of electrons in isolated p orbitals.

A) -2√2α
B) -√2α
C) +√2α
D) +2√2α

Accepted Answer

The answer of Using the H&#252;ckel method, the energies of...

Question 9

What is the separation between the highest occupied and lowest unoccupied molecular orbitals of benzene?&#10;A) &#8730;2&#945;&#10;B) &#945;&#10;C) 2&#8730;2&#945;&#10;D) 2&#945;

Accepted Answer

The separation between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in benzene is 2α, where α is the Coulomb integral. This is derived from the Hückel molecular orbital theory for benzene.

Question 10

Hückel theory predicts that the energies of the $\pi$ orbitals of 1,3-butadiene, C₄H₆, are
E₁=α+1.62α
E₂=α+1.62α
E₃=α-1.62α
E₄=α-1.62α
Predict the wavelength of the lowest energy transition in the electronic spectrum of butadiene, given that $\beta$ = -3.8 eV.

A) 326 nm
B) 526 nm
C) 263 nm
D) 201 nm

Accepted Answer

The answer of H&#252;ckel theory predicts that the energies of...

Deck 9: The Chemical Bond