Shapes & Structures 2

Question 1

Name the 5 quantum numbers

Answer 1

• n, principal quantum number
• l, angular momentum quantum number
• m_l, magnetic quantum number
• s
• m_s

Question 2

What does each quantum number represent?

• n
• l
• m_l
• s
• m_s

Answer 2

n = shell/energy

l = type of orbital (magnitude of angular momentum), s = 0 for s-orbitals

m_l = number of degenerate orbitals (component of the orbital angular momentum on a particular axis / orientation of angular momentum). For a d-orbital, l = 2 → ml = 2, 1, 0 -1, -2 → 5 degenerate orbitals

s = magnitude of spin (intrinsic angular momentum), always = 1/2

m_s = orientation of spin (intrinsic angular momentum), = -1/2 or 1/2

Question 3

orbital energy equation

Answer 3

E_n = -R_HZ²/n²

Question 4

Give formulae for:

• Total #nodes
• # angular
• # radial

Answer 4

• Total #nodes = n - 1 = #angular + #radial
• # angular = l (so all s = 0, all p = 1, all d = 2)
• # radial = n - l - 1

Radial nodes: first appearance of each orbital type has none, then go up by 1 with each shell.

Question 5

When is it correct that energy of 4s energy of 3d?

Answer 5

Up to Ni

Question 6

Name the symmetry labels and what each represents

Answer 6

• σ: rotational symmetry about the internuclear axis, without a change in phase
• π: nodal plane (change in phase) in internuclear axis

If there is a centre of inversion (2 points equidistant but opposite directions from centre are equivalent):

• g: no change in sign on passing through centre of inversion
• u: change in sign on passing through centre of inversion

Question 7

Draw the MO diagram for O₂, and sketch each MO and assign its symmetry.

Answer 7

Question 8

For the first-period homonuclear diatomics up to & including __, sp mixing is strong enough to make the sigma-g orbital higher-energy than the pi-u orbital.

Answer 8

N

Question 9

describe the effect of sp mixing on the following MOs

• (2s)σg
• (2p)σg
• (2s)σu*
• (2p)σu*

Answer 9

• (2s)σg becomes more bonding (lowered)
• (2s)σg becomes less bonding (raised)
• (2p)σu* becomes less antibonding
• (2s)σu* becomes more antibonding

Question 10

To obtain linear geometry, which AOs contribute to the HAOs?

Answer 10

sp

s, pz (IN axis)

Question 11

To obtain trig planar geometry, which AOs contribute to the HAOs?

Answer 11

sp2

s, p_z, p_y

Question 12

To obtain tetrahedral geometry, which AOs contribute to the HAOs?

Answer 12

s, pz, py, px

Question 13

To obtain bent geometry, which AOs contribute to the HAOs?

Answer 13

sp3 but not equal

s, pz, py, px with greater p-character

Question 14

To obtain octahedral geometry, which AOs contribute to the HAOs?

Answer 14

sp3d2

s, px, py, pz, d_z^2, d_x^2-y^2

Question 15

To obtain square planar geometry, which AOs contribute to the HAOs?

Answer 15

sp2d: s, px, py, d_x^2-y^2

or p2d2: px, py, d_x^2-y^2, d_z^2

Question 16

To obtain trig bipyramidal geometry, which AOs contribute to the HAOs?

Answer 16

sp3d: d, px, py, pz, d??

spd3: s, p??,

Question 17

Why is BH₃ sp2 hybridised rather than sp3?

Answer 17

• Want to minimise energy of HOMO
• Sp2 arrangement has:
  
  • 3 x occupied sigma
  • A vacant boron p-orbital (non-bonding)
  • 3 x vacant sigma*
• So HOMO = sigma, made from sp2 HAOs
• Sp3 arrangement has:
  
  • 3 x occupied sigma
  • a vacant sp3 HAO (non-bonding)
  • 3 x vacant sigma*.
• So HOMO = sigma, made from sp3 HAOs
• HOMO of sp3 arrangement has more p-character than that of sp2 arrangement, so is higher in energy, so is less favourable

Another way of thinking about it: don’t want to waste s-character on an unoccupied orbital. Highest preference for using lowest-energy (s) orbitals when building HAOs

Question 18

Using diagrams, describe the conjugated system and bonding in the allyl cation, H₂C=CH-C⁺H₂, and draw the resonance structures.

Answer 18

Higher-energy MOs have more nodes, so shape of π MOs can be predicted with sine waves:

• Begin sine wave one bond-length away from end of molecule
• n AOs → n MOs, and first MO has no nodes, so highest-energy MO has (n - 1) nodes
• MOs are labelled in order of energy: 1π, 2π, etc
• Atoms drawn in a straight line for simplicity, but might be a simplification
• Nodes are where wave changes sign / crosses axis
• Height of wave predicts shape of MO (contribution each AO makes to it)
• NB: when combining p-orbitals of different elements, AOs are different energies → MOs aren’t symmetrical → e- density isn’t even (highest where AO energy was lowest)

Question 19

How would you compare the energies of orbitals of the same type?

Answer 19

Poorer size/energy match between constituent AOs → worse interaction → lower energy

Question 20

HOMO-LUMO interactions cause net reduction in energy of the highest-energy electrons. The best interaction is between the orbitals closest in energy, which are?

Answer 20

Whichever HOMO is highest-energy, & the LUMO of the other reactant.

Question 21

State the most favourable angle of approach for nucleophiles,

Answer 21

107⁰

Question 22

use diagrams to show that 107^o is the best angle of nucleophilic approach

Answer 22