CHEM 2060 Lecture 10: Electrostatics L10-1
Electrostatics of Atoms & Molecules
We have considered how Coulombic attractions and repulsions help to organize
electrons in atoms and ions.
We now look at Coulombic attractions between atoms and molecules…
Coulomb’s Law has survived every experimental test…
…no exceptions have ever been found.
It holds deep within the atom, correctly describing the force between the (+)vely
charged nucleus and each (-)vely charged extra-nuclear electron.
It holds up where classical Newtonian
mechanics breaks down!
Coulomb’s Law:
€
F=C
q1q2
r2
€
€
CHEM 2060 Lecture 10: Electrostatics L10-2
A Closer Look at Coulomb’s Law:
F=
1 q1q2
4 πε0 r 2
1
= 8.99 ×10 9 N ⋅ m 2 /C 2
4 πε0
Written this way, Coulomb’s law defines a FORCE.
€
This isn’t very convenient because we are more interested in ENERGIES…
…ultimately, we’d like to talk about bond energies…
So a less familiar statement of Coulomb’s law of electrostatics is:
E=C
q1q2
r
where C is a constant
(C = 8.99 × 109 J⋅m/C2 to get energy in Joules)
This defines the energy of attraction (–ve value) or repulsion (+ve value)
between two point charges.
Note the dependence on reciprocal distance 1/r … not on 1/r2 !
CHEM 2060 Lecture 10: Electrostatics L10-3
Types Of Inter(atomic/molecular) Coulombic Interactions
a) Monopole – Monopole
b) Monopole – Dipole
c) Dipole – Dipole
(a) Monopole – Monopole
(anions and cations)
(ions and polar or polarizable species)
(between polar or polarizable species)
Coulombic interactions between point charges
• Non-directional
- only “directionality” is repulsive vs. attractive
• Strong over atomic distances
• Good model for ionic bonding (we’ll look at this more closely later)
e.g. LiF estimate 686 kJ mol-1
(measured 755 kJ mol-1)
LiF used in UV optics
(very large band gap)
CHEM 2060 Lecture 10: Electrostatics L10-4
Google: “lithium fluoride battery”
“molten salt reactor”
r
E=
€
q1q2
r
from now on, we’ll ignore the constant C and just
look at the form of the equation…
CHEM 2060 Lecture 10: Electrostatics L10-5
(b) Monopole – Dipole one ion and one polar species
Q+δ −
E =
r- R
2
attractive
€
+
Q+δ+
-Qµ
−Q+δR
(recall µ = δR)
=
=
2
R
2
2−R
r+
2 R
r
r
−
2

4
4
repulsive
net attraction: even though there is no net charge on the dipole…
Monopole orients the dipole in favourable direction!!
CHEM 2060 Lecture 10: Electrostatics L10-6
Example:
Solvated Ions
When NaCl dissolves in water, Na+ is surrounded by H2O because of dipolemonopole interaction.
In aqueous solution, Na+ is hydrated by an
octahedron of water molecules.
Note the negatively charged Cl- (from NaCl)
does not participate in the hydration shell.
QUESTION: What do you think the hydration sphere of the chloride ion looks
like?
CHEM 2060 Lecture 10: Electrostatics L10-7
Polar nature of water makes it an excellent solvent for ionic solids like NaCl.
• Energy needed to separate ions (monopole-monopole interactions) is provided
by formation of hydrated ions (monopole-dipole interactions).
• Non-polar solvents (e.g., vegetable oil)
cannot form such strong bonds. So, NaCl
and other salts are insoluble in vegetable
oil.
Strengths Of Bonds
Monopole – Monopole ~ 400 kJ mol-1
Monopole – Dipole ~ 40 kJ mol-1
smaller energy because of
distance dependence
…1/r2 !
CHEM 2060 Lecture 10: Electrostatics L10-8
Soaps and detergents … a relevant example…
Soaps (and detergents) work because their structures
have both…
• …a hydrocarbon chain which is hydrophobic
(rejects water) but lipophilic (attracts oily materials)
• and an end (or “head”) which is hydrophilic (attracts
water) and lipophobic (rejects oily materials).
Since you normally bathe or wash
your clothes in water…
• the polar (usually ionic) head
makes the detergent soluble in
water
• the long “fatty” chains solublize
other hydrocarbons (grease)
CHEM 2060 Lecture 10: Electrostatics L10-9
The detergent provides a "bridge" by dissolving its hydrocarbon chain in a
droplet of oil in such a way that the ionic, hydrophilic end sticks out into the
surrounding water.
This arrangement is called a micelle and permits soapy water to "wash away"
greasy materials.
The hydrophilic (polar) end of the
detergent binds strongly to water
and the non-polar part bonds to
the grease.
CHEM 2060 Lecture 10: Electrostatics L10-10
(c) Dipole – Dipole between polar species
r
R
µ = δR
-δ 2
δ2
δ2
δ2
E =
+
+
−
2 + R2
2 + R 2 
r
r

r
r


attractive
attractive
repulsive
€
δ 2 R2
E=
# 2&
rR (
r 3 + %%
(
2
$
'
for R << r
E=
−µ 2
r3
Magnitude ~ 5 kJ mol-1
€ RANGE INTERACTION (AND WEAK)
VERY SHORT
€
CHEM 2060 Lecture 10: Electrostatics L10-11
−µ 2
for dipole-dipole is a special case.
E=
3
r
If there is an angle θ between the dipoles then:
€
-µ1µ 2
2
(13cos
θ)
3
r
E =
IMPORTANCE: Polar Liquids, Dissolving of Molecular Solids (see Later)
_
_
_+ _+
+ +
€
+
_
_
+
+
_
+
+
_
_
_+
+
Energy
Required
+
_
+
Energy Released
_
SOLVATION
_
+
_
CHEM 2060 Lecture 10: Electrostatics L10-12
Induced Dipoles & Van der Waals Forces
• We have seen now that ionic type bonds can occur when a dipole moment
exists in a molecule.
• A dipole can be set up in a non-polar molecule by an electric field.
induced dipole
moment
For example:
_
+
_+
Electrons attracted to +
Holes attracted to
-
_
_ +
_
_+
+
_ +
voltage
off
+
_
_
_
_
_
_
_
+
+
+
+
+
+
+
+
voltage
on
_
CHEM 2060 Lecture 10: Electrostatics L10-13
Electric field can arise from neighboring atom or ion !
µ
_
_
_
_
_
_
q+
Monopole
+
+
+
+
+
• The magnitude of the induced dipole moment (µIND) is related to the
polarizability of the molecule.
µIND = α E
Polarizability
Strength of
Electric field.
CHEM 2060 Lecture 10: Electrostatics L10-14
Polarizability α is the ease of deformation of the electron “cloud”.
It is a measure of how “soft” the electron cloud is (on an atom or on a molecule).
NOTE:
The interaction of induced dipole with another charge can only be
an attraction since it is automatically created with the correct
geometry.
• If the species being polarized is atom … no orienting effect.
• If species is molecule, α may be anisotropic (i.e., not the same in all
directions.) The molecule will tend to orient itself to create the largest induced
dipole moment.
QUESTION: Why might the polarizability of a molecule be anisotropic?