Atkins & de Paula: Atkins’ Physical Chemistry 9e

Atkins & de Paula:

Atkins’ Physical Chemistry 9e

Chapter 17: Molecular Interactions


ELECTRIC PROPERTIES OF MOLECULES17.1 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


polar molecule, a molecule with a permanent electric dipole moment.

nonpolar molecule, a molecule without a permanent electric dipole moment.


Resultant electric dipole moments, μres2 = μ1

2 + μ22 + 2μ1μ2 cos θ.


Calculation of electric dipole moments, μ2 = μx2 + μy

2 + μz2 (μi =Σqjij)

μ = 2.7 D


Self-test; calculation of the μ of formaldehyde


17.2 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/4πε0. (unit of ε0: C2 m-1 J-1) polarizability, perturbation expression.

α ≈ R3

α increases as the molecular size increasesα increases as the HOMO-LUMO gap decreases

eR μEEE

nz,

n

0

0 gap) LUMO-HOMO( mean value

direction -z in the transition:where,2 0,0 0

2

0,

nzn n

nz

EE

ERe

22

2

ReE

0

2

4

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 μz = μ, where a strong electric field is applied

kTxxL

xeeeexLxL

xee

xeedyye

xeedye

dye

dyye

de

dedpdp

de

dedp

zxxxxe

xx

xx

z

xxxxxy

xxxy

xy

xy

zddyy

x

x

z

kTE

kTE

x

EkTx

3)(

functionLangevin ;1)()(

sin

sincoscoscos

n orientatio dipole ofy probabilit ; sin

sin

2

3111

2

1

1

1

1

1

1

1

1sin,cos

0

cos

0

cos

0

/)(

/)(

3612

21

dipole ofenergy ; cos)(,/

E

EE


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 polarizabilitiesħωn0 = En – E0

20 0

2

0,

n n

nz

EE

2)( 220

20,0

n n

nzn

0n

2)(2

0,02 n

nzn

as 02)(2

0,02n

nzn

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, (εr – 1)/(εr + 2) = ρPm/M. molar polarization, Pm = (NA/3ε0)(α + μ2/3kT). Clausius–Mossotti equation, (εr – 1)/(εr + 2) = ρNAα/3Mε0.; no contribution from permanent dipole, μ

Nonpolar molecules or high frequency of applied field

μ

αεr = C/C0 Pm

Example 17.2

Debye eqn.

refractive index and relative permittivity, nr = εr1/2.

refractive index, nr = c/c. c: speed of light in vacuum, c: speed of light in medium

kN A

0

2

9slope

03intercept

AN


INTERACTIONS BETWEEN MOLECULESvan 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.


multipole–multipole potential energy, V 1/rn+m-1.


17.5 (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

,

20

21

4 rqV

20

212

0

21

0

21

0

21

22

0

212/

2121

2121

0

4442)1()1(

4

11

111

11

11

11

441

11

rq

rlqq

rqxqxx

rqqV

xxx

xxx

xrl

xxrqq

lrqq

lrqqV

lq

rlx

Chapter 17: Molecular Interactions, Calculating the interaction energy of two dipoles

Self-test 17.4

30

21

2 rV

30

21

0

212

22

0

21/21212121

0

242

11

111

11

112

11

441

rrqqxV

xxx

xxx

xrl

xxrqq

lrqq

rqq

rqq

lrqqV rlx

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 cos2 θ ]

See Further information 17.1

30

21

4)(

rfV

Chapter 17: Molecular Interactions, Keesom interaction, the interaction of two freely rotating point dipoles:

first contribution to the vdW interaction

<V> = μ1μ2<f>/ 4πε0r3

<f>; weighting factor in the averaging; probability that a particular orientation will be adopted by a dipole

p e-V/kT, V=μ1μ2 f/4πε0r3

p 1- V/kT + ∙∙∙, when V ‹‹ kT

620

22

21

620

0

222

21

0

20

0

0

23

0

210

0

23

0

21

0

0

23

0

21

000

00

/

0

0

)4(32

)4(0sin)cos31(1

average spherical unweightedan denotes where,

41

41

411)/(11

)/1(11

32

02

kTrV

kTr

fVdf

fkTr

fdfkTr

fd

dfkTr

fddkTVffdf

dkTVfdfed

fpdf

f

kTV

kTC

rCV 2

0

22

21

6 )4(32

Chapter 17: Molecular Interactions,

Keesom interaction, the interaction of two rotating point dipoles: first contribution to the vdW interaction

Negative 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/r6 : arises from V 1/r3 weighted by the energy

in the Boltzmann term ( 1/r3)

kTC

rCV 2

0

22

21

6 )4(32


17.5 (c) Dipole-induced-dipole interactions,

Independent on the temperature; thermal motion has no effect on the averaging process

0

221

6

4

C

rCV


17.5 (d) Induced-dipole-induced-dipole interactions dispersion interaction (London interaction)

,

London formula

21

21212

3

6

IIIIC

rCV


17.5 (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 energy

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 < 0 hydrophobicity constant, π = log(S/S0) S: ratio of the molar solubility of R-A in octanol to that in water S0: 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 cage


17.5 (g) The total attractive interaction total attractive interaction between rotating molecules; dipole-dipole, dipole-induced-

dipole, and dispersion interactions. V = –C6/r6

limitation 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 θA cos θB cos θC + 1), where a ≈ 3/4αC6

6 6 6

6 6 6 3AB BC CA AB BC CA

C C C CVr r r r r r


Interactions between dipoles; impact on medicine (molecular recognition & drug design). See I17.1

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/rn – Cm/rm. Lennard-Jones potential, V = 4ε{(r0/r)12 – (r0/r)6}. ε:depth of the well, r0:seperation where V=0

exp–6 potential, V = 4ε{e–r/r0 – (r0/r)6}.; better than L-J(12,6) potential


GASES AND LIQUIDS17.7 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.



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

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.


Scattering patterns depend on the impact parameter (b) for the impact of two hard spheres


for real molecules; scattering patterns depend on the intermolecular potential, molecular shape, and relative speed of approach as well as the impact parameter.

repulsive core

long range attractive potential

Chapter 17: Molecular Interactions quantum 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.

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.

Example17.4dw =2γlh


17.8 (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 = 4πr2pin

inward force; force from pout & surface tensionforce from pout ; pressure × area = 4πr2pout

force from surface tension; 8πγrdσ = 4π(r+dr)2 - 4πr2 = 8πrdr dw = 8πγrdr

4πr2pin = 4πr2pout+ 8πγr

pin = pout + 2γ/r


17.8 (c) capillary action capillary action, the tendency of liquids to rise up capillary tubes. capillary rise and surface tension, γ = (ρβ –ρα)ghr/2

Same pressure at same height in a same phaseP1=P6, P2=P5, P2=P3 P5=P3

Curved surface: P4 < P5=P3 P4 < P3

;capillary rise

At equilibriumP1=P6, P2=P3

P8=P5, P3=P4 P8-P3= P5-P4 P8-P2= P5-P4

P8-P2= (P5-P7)+(P7-P4)P8-P2=-ραgh, P7-P4 =-ρβgh, P5-P7=2γ/r (θc=0)-ραgh = 2γ/r - ρβgh γ = (ρβ –ρα)ghr/2

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)/γlg. superficial work of adhesion, wad = γsg + γlg – γsl (work of adhesion/area of contact)

cos θc = wad/γlg – 1 criterion for surface wetting, 1< wad /γlg < 2. criterion for non-surface wetting, 0< wad /γlg < 1.


17.9 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.


Impact 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

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Atkins & de Paula: Atkins’ Physical Chemistry 9e