electrostatics of atoms & molecules · chem 2060 lecture 10: electrostatics l10-1...

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 q1q2r2


A Closer Look at Coulomb’s Law:

€

F =14πε0

q1q2r2

€

14πε0

= 8.99×109 N ⋅m2 /C2

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 q1q2r 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 !


Types Of Inter(atomic/molecular) Coulombic Interactions a) Monopole – Monopole (anions and cations) b) Monopole – Dipole (ions and polar or polarizable species) c) Dipole – Dipole (between polar or polarizable species) (a) Monopole – Monopole 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)


Google: “lithium fluoride battery” “molten salt reactor”

€

E =q1q2r

from now on, we’ll ignore the constant C and just look at the form of the equation…

r


(b) Monopole – Dipole one ion and one polar species

€

E = Q+δ−

r - R2attractive

+ Q+δ+

r+ R2repulsive

= −Q+δR

r2 − R2

4

= -Qµ

r2 − R2

4

(recall µ = δR)

net attraction: even though there is no net charge on the dipole…

Monopole orients the dipole in favourable direction!!


Example: Solvated Ions When NaCl dissolves in water, Na+ is surrounded by H2O because of dipole-monopole 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?


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 !


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)


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.


(c) Dipole – Dipole between polar species µ = δR

€

E = -δ2

rattractive

+ δ2

r2 + R2 + δ2

r2 + R2

repulsive

− δ2

rattractive

€

E =δ2R2

r3 +rR2

2

#

$ % %

&

' ( (

for R << r

€

E =−µ2

r3 Magnitude ~ 5 kJ mol-1

VERY SHORT RANGE INTERACTION (AND WEAK)

rR


€

E =−µ2

r3 for dipole-dipole is a special case.

If there is an angle θ between the dipoles then:

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E = -µ1µ2r3 (1- 3cos2θ )

IMPORTANCE: Polar Liquids, Dissolving of Molecular Solids (see Later)

+__+ _+

+__+ _+

_+

_++_

+_

+

_

+

_ +_

+_

EnergyRequired

Energy Released

SOLVATION


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. For example: Electrons attracted to + Holes attracted to -

_+_ _

__

__

+

++

+

++

++++

++

+

__

____

_

+ _

induced dipole moment

voltage off

voltage on


Electric field can arise from neighboring atom or ion ! • The magnitude of the induced dipole moment (µIND) is related to the polarizability of the molecule.

µIND = α E

Polarizability Strength of

Electric field.

_+_

__

__

++

+

+q+

Monopole

µ


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?

electrostatics of atoms & molecules · chem 2060 lecture 10: electrostatics l10-1...

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