Atkins Physical Chemistry 9e Chapter 17 Molecular Interactions Chapter 17 Molecular Interactions ELECTRIC PROPERTIES OF MOLECULES 171 Electric dipole moments electric dipole two electric charges ID: 265739
Download Presentation The PPT/PDF document "Atkins & de Paula:" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Atkins & de Paula: Atkins’ Physical Chemistry 9e
Chapter 17: Molecular InteractionsSlide2
Chapter 17: Molecular InteractionsELECTRIC PROPERTIES OF MOLECULES
17.1 Electric dipole moments
electric dipole, two electric charges +q and –q separated by a distance R. electric dipole moment, μ, the vector that points from –q to + q with magnitude μ = qR.
1 D = 3.33564 × 10
-30
Cm Slide3
Chapter 17: Molecular Interactions
polar molecule,
a molecule with a permanent electric dipole moment.
nonpolar molecule, a molecule without a permanent electric dipole moment.Slide4
Chapter 17: Molecular Interactions
Resultant electric dipole moments, μres2 = μ12 + μ22 + 2μ1μ2 cos θ.Slide5
Chapter 17: Molecular Interactions
Calculation of electric dipole moments,
μ
2 = μx2 + μy2 + μz2 (μi =Σqjij)
μ
= 2.7 DSlide6
Chapter 17: Molecular Interactions
Self-test; calculation of the
μ
of formaldehyde Slide7
Chapter 17: Molecular Interactions17.2 Polarizabilities
induced dipole moment, μ*, the dipole moment induced by an applied electric field. polarizability, the constant of proportionality α in μ* = αE. (unit = C2 m2 J-1) polarizability volume, α
=
α
/4π
ε
0
. (
unit of
ε
0
:
C
2
m
-1
J
-1
)
polarizability,
perturbation expression.
α
≈
R
3
α increases as the molecular size increases
α increases as the HOMO-LUMO gap decreasesSlide8
Chapter 17: Molecular Interactions17.3 Polarization
polarization, P, the electric dipole moment density, P = μN. dielectric, a polarizable, nonconducting medium.μz = μ2E/3kT, where a weak electric field is applied
μ
=
0
, where no electric field is applied
μ
z
=
μ
, where a strong electric field is applied
Slide9
Chapter 17: Molecular Interactions
orientation polarization,
the polarization arising from the permanent dipole moments; is
lost at microwave frequency distortion polarization, the polarization arising from the distortion of the positions of the nuclei by the applied field; is lost at IR frequency electronic polarizability, the polarizability due to the distortion of the electron distribution; is still alive at Vis frequency frequency dependence of polarizabilities
ħ
ω
n0
= E
n
–
E
0Slide10
Chapter 17: Molecular Interactions17.4 Relative permittivities
permittivity, the quantity ε in the Coulomb potential energy, V = q1q2/4πεr. relative permittivity (dielectric constant), εr = ε/ε0. (
ε0
= vacuum permittivity)
Debye equation,
(
ε
r
– 1)/(
ε
r
+ 2) =
ρP
m
/
M
.
molar polarization,
P
m
= (
N
A
/3
ε
0
)(
α
+
μ2
/3kT
).
Clausius–Mossotti equation, (ε
r – 1)/(
εr
+ 2) = ρN
A
α
/3
Mε
0
.;
no contribution from permanent dipole,
μ
Nonpolar
molecules or high frequency of applied field
μ
α
ε
r
= C/C
0
P
m
Example 17.2
Debye eqn.
refractive index and relative permittivity,
n
r
= ε
r
1/2
.
refractive index,
n
r
= c/c. c: speed of light in vacuum, c: speed of light in medium Slide11
Chapter 17: Molecular InteractionsINTERACTIONS BETWEEN MOLECULES
van
der
Waals interaction, an interaction between closed-shell molecules that varies with separation as 1/r6.17.5 Interactions between dipoles multipole, an array of point charges. n-pole, an array of point charges with an n-pole moment but no lower moment.
monopole, a point charge.
quadrupole,
an array of point charges that has neither net charge nor dipole moment.
octupole,
an array of point charges that sum to zero and which has neither a dipole moment nor a quadrupole moment.Slide12
Chapter 17: Molecular Interactions
multipole–multipole
potential energy,
V 1/rn+m-1. Slide13
Chapter 17: Molecular Interactions17.5 (
a)
The potential energy of interaction
point dipole, a dipole in which the separation between the charges is much smaller than the distance at which the dipole is being observed; l << r point dipole-point charge interaction, Slide14
Chapter 17: Molecular Interactions,
Calculating the interaction energy of two dipoles
Self-test 17.4Slide15
Chapter 17: Molecular Interactions17.5 (b)
Dipole-dipole interactions
electric field
of point charge, E = q/4πε0r2. electric field of point dipole, E = μ/2πε0r3.,
potential energy
of two
parallel
point dipoles
[
f(θ)
= 1 – 3 cos
2
θ
]
See
Further information
17.1Slide16
Chapter 17: Molecular Interactions,
Keesom
interaction,
the interaction of two freely rotating point dipoles: first contribution to the vdW interaction<V> = μ1μ2<f>/ 4πε0
r
3
<f>
; weighting factor in the averaging;
probability that a particular orientation will be adopted by a dipole
p
e
-V/kT
,
V
=
μ
1
μ
2
f
/4
πε
0
r
3
p
1-
V/kT
+
∙∙∙,
when
V
‹‹
kTSlide17
Chapter 17: Molecular Interactions,
Keesom interaction,
the interaction of two rotating point dipoles:
first contribution to the vdW interactionNegative sign: the average interaction is attractive.V 1/r6 : a van der Waals interaction.
V
1
/
T
:
the greater thermal motion overcomes the dipole interactions at higher temperatures.
V
1
/
r
6
:
arises from
V
1
/
r
3
weighted by the energy in the Boltzmann term ( 1
/r
3)Slide18
Chapter 17: Molecular Interactions17.5 (c)
Dipole-induced-dipole interactions
,
Independent on the temperature; thermal motion has no effect on the averaging processSlide19
Chapter 17: Molecular Interactions17.5 (d)
Induced-dipole-induced-dipole interactions
dispersion interaction (London interaction) , London formula Slide20
Chapter 17: Molecular Interactions17.5 (
e)
Hydrogen bonding
hydrogen bond, an attractive interaction between two species that arises from a link of the form A–H∙∙∙B, where A and B are highly electronegative elements (N, O, or F) and B possesses a lone pair of electrons., = c1 A + c2 H + c3 B
bonding
nonbonding
anti-bonding
Net effect: lowering of energySlide21
Chapter 17: Molecular Interactions17.5 (
f)
The hydrophobic interaction
hydrophobic, water-repelling; possessing a positive Gibbs energy of transfer from a nonpolar to a polar solvent. ΔtransferG > 0, ΔtransferH < 0, ΔtransferS < 0hydrophobicity constant, π = log(S/S0
)
S
: ratio of the molar solubility of R-A in
octanol
to that in water
S
0
: ratio of the molar solubility of H-A in
octanol
to that in water
hydrophobic interaction,
an effective interaction that is due to the increase in entropy of the surrounding solvent.
,
A hydrocarbon molecule in a water cageSlide22
Chapter 17: Molecular Interactions17.5 (g
)
The total attractive interaction
total attractive interaction between rotating molecules; dipole-dipole, dipole-induced-dipole, and dispersion interactions. V = –C6/r6limitation of V = –C6/r6; consider only dipolar interactions, assume freely rotating molecules, and consider only the interactions of pairs of molecules Axilrod–Teller formula,
total dispersion energy of three closed-shell molecules
,
C
=
a
(
3 cos
θ
A
cos
θ
B
cos
θ
C
+ 1), where
a
≈
3
/
4
α
C
6
Slide23
Chapter 17: Molecular InteractionsInteractions between dipoles; impact on medicine (molecular recognition & drug design). See I17.1Slide24
Chapter 17: Molecular Interactions,
17.6 Repulsive and total interactions
hard-sphere potential, V = for r d; V = 0 for r > d. Mie potential, V = Cn/r
n –
C
m
/
r
m
.
Lennard-Jones potential,
V
= 4
ε
{(
r
0
/
r
)
12
– (
r
0
/
r
)
6
}.
ε:depth of the well, r
0
:seperation where V=0
exp–6 potential, V
= 4ε{e–
r/r0
– (r0/
r)
6}.; better than L-J(12,6) potentialSlide25
Chapter 17: Molecular InteractionsGASES AND LIQUIDS
17.7 Molecular interactions in gases
molecular beam,
a collimated, narrow stream of molecules travelling though an evacuated vessel. hydrodynamic flow, net flow arising from intermolecular collisions. molecular flow, collision-free flow.Slide26
Chapter 17: Molecular InteractionsSlide27
Chapter 17: Molecular Interactions
supersonic,
a stream of molecules in which the average speed of the molecules is much greater than the speed of sound for the molecules that are not part of the stream.
supersonic beam, a beam obtained when the region of hydrodynamic flow is skimmed from a supersonic jet and the excess gas pumped away. crossed beam technique, a technique in which two molecular beams are incident at right angles.Low translational T Slide28
Chapter 17: Molecular Interactions
differential scattering cross-section,
σ
, the constant of proportionality between the change in intensity (dI) and the intensity of the incident beam (I), the number density of target molecules (N), and the infinitesimal path length dx through the sample: dI = σIN dx. impact parameter, b, the initial perpendicular separation of the paths of the colliding molecules.Slide29
Chapter 17: Molecular Interactions
Scattering patterns depend on the impact parameter (b) for the impact of two hard spheres Slide30
Chapter 17: Molecular Interactions
for real molecules;
scattering patterns depend on the intermolecular potential, molecular shape, and relative speed of approach as well as the impact parameter.
repulsive corelong range attractive potentialSlide31
Chapter 17: Molecular Interactionsquantum oscillation,
the modification of the scattering in the forward direction by interference between the wavefunctions of a particle along two different paths.
rainbow scattering,
strongly enhanced scattering in a nonforward direction. rainbow angle, θr, the angle for which dθ/db = 0 and the scattering is strong. van der Waals molecules, complexes of the form AB in which A and B are held together by van der Waals forces or hydrogen bonds. Slide32
Chapter 17: Molecular Interactions17.8 The liquid–vapour interface17.8 (a) surface tension
surface tension,
γ
, the constant of proportionality between the increase in surface area of a liquid and the work needed to create the increase: dw = γdσ (=dA, where constant T). dA < 0 (dσ < 0); spontaneous process: surfaces have a natural tendency to contract.
Example17.4
d
w
=2
γlh
Slide33
Chapter 17: Molecular Interactions17.8 (b) curved surfaces
bubble, a region in which a vapour is trapped by a thin film. cavity, a vapour-filled hole in a liquid. droplet, a small volume of liquid Laplace equation, pin = pout + 2γ/r.outward force; pressure × area = 4πr2
pin
inward force; force from
p
out
& surface tension
force from
p
out
; pressure × area
= 4
πr
2
p
out
force from surface tension;
8
π
γ
r
d
σ
= 4
π(
r+dr
)
2
-
4
πr
2
=
8πrdr
dw
= 8
πγ
rd
r
4
πr
2
p
in
= 4
πr
2
p
out
+
8
π
γ
r
p
in
= p
out
+ 2γ/rSlide34
Chapter 17: Molecular Interactions17.8 (c) capillary action
capillary action, the tendency of liquids to rise up capillary tubes. capillary rise and surface tension, γ = (ρβ –ρα)ghr/2Same pressure at same height in a same phaseP1=P6, P2=P5, P2=P3
P
5
=P
3
Curved surface:
P
4
< P
5
=P
3
P
4
< P
3
;capillary rise
At equilibrium
P
1
=P
6
, P
2
=P
3
P
8
=P
5, P3
=P4
P8-P
3= P5-P4
P
8-P2
= P5
-P
4
P
8
-P
2
= (P
5
-P
7
)+(
P
7
-P
4
)
P
8
-P
2
=-
ρα
gh, P7
-P4 =-ρβ
gh, P5
-P7=2γ
/r
(θc=0)-ραgh
= 2
γ/r - ρβ
gh γ
= (ρβ –
ρα)ghr/2 Slide35
Chapter 17: Molecular Interactions
nonzero angle between the edge of meniscus and the wall
;
γsg = γsl+ γlg cos θc contact angle and interfacial tension, cos θc = (γsg – γsl
)/γ
lg
.
superficial work of adhesion,
w
ad
=
γ
sg
+
γ
lg
–
γ
sl
(work of adhesion/area of contact)
cos
θ
c
=
w
ad
/
γ
lg
– 1
criterion for surface wetting,
1<
wad /
γlg
< 2.
criterion for non-surface wetting, 0<
wad /γ
lg < 1.
Slide36
Chapter 17: Molecular Interactions17.9 Surface films; will be covered in Chap. 18
17.10 Condensation
Kelvin equation for the vapour pressure of droplets, p = p* e2γVm/rRT supersaturated phase, a phase that is thermodynamically unstable with respect to the liquid. spontaneous nucleation centre, a location at which a sufficiently large number of molecules congregate into a droplet. nucleate, provide surfaces to which molecules can attach and thereby induce condensation.
superheated,
a liquid that has not boiled but is above its boiling temperature.
supercooled
,
a liquid that has not frozen but is below its freezing temperature.
Slide37
Chapter 17: Molecular InteractionsImpact on nanotechnology
Spontaneous Assembly of a Monolayer of Charged Gold Nanocrystals at the Water/Oil Interface
Angew. Chem. Int. Ed. 2004, 43, 458.Angew. Chem. Int. Ed. 2004, 43, 5639. Directing Self-Assembly of Nanoparticles at Water/Oil Interfaces