SME
General Chemistry I
Bonding and molecular geometry
Use this for “XeF₄ has 36 valence electrons. Find the lone pairs on xenon, the shape, the smallest bond angle and the hybridization.”
Diagram
4 bonded atoms and 2 lone pairs: 6 electron domains in an octahedral arrangement, sp³d² hybrid orbitals.
The shape is square planar (for example XeF₄); the domains are 90° apart at the closest.
The two lone pairs sit trans, 180° apart, leaving a square plane.
This is an example. Type your own values to start a new problem.
l
=
(
V
−
2
×
b
−
o
)
÷
2
d
Electron domains on the center
calculated
θ
Smallest ideal angle between domains
calculated · °
Formulas
l
=
V
− 2 ×
b
−
o
2
2
=
36 − 2 × 4 − 24
2
d
=
b
+
l
6 = 4 + 2
θ
=
smallest
angle
between
d
domains
90 = smallest angle between 6 domains
Assumptions
•
V counts the valence electrons of every atom, plus one for each negative charge of an ion and less one for each positive charge.
•
Each outer atom first fills its octet with lone pairs (a halogen keeps three, so o = 6 for each); the central atom takes what is left.
•
Lone pairs take the roomiest places: equatorial in 5 domains, opposite each other in 6. The shape is named by the atoms only.
•
The hybrid orbitals on the center equal the domains: 2 sp, 3 sp², 4 sp³, 5 sp³d, 6 sp³d².
Step-by-step
WE KNOW
V = 36, b = 4, o = 24
FIND
lone pairs on the center (l), electron domains on the center (d), smallest ideal angle between domains (θ)
Step 1 · Find lone pairs on the center (l)
Use l = (V − 2 × b − o) ÷ 2
Take
two
electrons
for
each
bond
and
the
outer
atoms’
lone
electrons
from
V
.
What
is
left
sits
on
the
center,
two
to
a
lone
pair.
l
=
36 − 2 × 4 − 24
2
l
=
36 − 8 − 24
2
l
=
4
2
l
=
2
Step 2 · Find electron domains on the center (d)
Use d = b + l
Each bonded atom is one domain (a double bond counts once) and each lone pair is one more.
d
=
4
+
2
d
=
6
Step 3 · Find smallest ideal angle between domains (θ)
Use θ = smallest angle between d domains
Two domains sit 180° apart, three 120°, four 109.5°; with five or six the closest are 90° apart.
θ
=
smallest
angle
between
6
domains
θ
=
90°
Check
Put the numbers back in. Both sides should match.
2
=
36 − 2 × 4 − 24
2
✓
6 = 4 + 2 ✓
90 = smallest angle between 6 domains ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Formal charge
Use this for “In one resonance form of nitrate, NO₃⁻, nitrogen has one double bond, two single bonds and no lone pairs. Find its formal charge.”
Lattice energy from a Born–Haber cycle
Use this for “Find the lattice energy of NaCl from these values in kJ/mol: sublimation of Na 107, first ionization energy of Na 496, half the Cl–Cl bond energy 121, electron affinity of Cl −349 and ΔH°f of NaCl −411.”
Bond order and magnetism from an MO diagram
Use this for “Draw the MO diagram of O₂ from its 12 valence electrons. Find the bond order and the unpaired electrons: is O₂ paramagnetic?”