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Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins • Julio de Paula

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Page 1: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Atkins’ Physical ChemistryEighth Edition

Chapter 21 – Lecture 2

Molecules in Motion

Copyright © 2006 by Peter Atkins and Julio de Paula

Peter Atkins • Julio de Paula

Page 2: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Homework Set # 21Homework Set # 21

Atkins & de Paula, 8eAtkins & de Paula, 8e

Chap 21 (pp 748 - 764 only)Chap 21 (pp 748 - 764 only)

ExercisesExercises: all part (b) unless noted:: all part (b) unless noted:

2, 6, 7, 8, 11, 13, 15, 172, 6, 7, 8, 11, 13, 15, 17

Page 3: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Objectives:

• Describe the motion of all types of particles in all typesof fluids

• Concentrate of transportation properties:

• Diffusion ≡ migration of matter down a concentrationgradient

• Thermal conduction ≡ migration of energy down atemperature gradient

• Electrical conduction ≡ migration of charge along apotential gradient

• Viscosity ≡ migration of linear momentum down a velocitygradient

Page 4: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Fig 21.10 The flux of particles down a concentration gradient

Fick’s first law of diffusion:

If the concentration gradientvaries steeply with position,then diffusion will be fast

Page 5: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

The Phenomenological Equations

• Flux (J) ≡ the quantity of that property passing througha given area per unit time

• Matter flux – molecules m-2 s-1

• Energy flux – J m-2 s-1

• e.g., J(matter) ∝ dN/dz and J(energy) ∝ dT/dz

• Since matter flows from high to low concentration:

• where D ≡ diffusion coefficient in m-2 s-1

dz

dND)matter(J

Page 6: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

The Phenomenological Equations

• Since energy flows from high to low temperature:

• where κ ≡ coefficient of thermal conductivity in J K-1 m-1 s-1

dz

dT)energy(J κ

Page 7: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Laminar (smooth) flow:

• If the entering layer has highlinear momentum, it acceleratesthe layer

• If the entering layer has lowlinear momentum, it retardsthe layer

Fig 21.11 The viscosity of a fluid arises from the transportof linear momentum

Page 8: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

The Phenomenological Equations

dz

dv)momentumx(J xη

• where η ≡ coefficient of viscosity in kg m-1 s-

1

So the viscosity ofa gas increases with

temperature!

21

M

RT8c

π

Page 9: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Fig 21.13 The experimental temperature dependence of water

As the temperature is increased, more molecules are able to escape from the potential wells of theirneighbors; the liquid then becomes more fluid

RTaE

Molecular Motion in Liquids

Page 10: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio
Page 11: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio
Page 12: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Conductivities of electrolyte solutions

• Conductance, G, of a solution ≡ the inverse of its resistance:

G = 1/R in units of Ω-1

• Since G decreases with length, l, we can write:

where κ ≡ conductivity and A ≡ cross-sectional area

• Conductivity depends on number of ions, so

molar conductivity ≡ Λm = κ/c with c in molarity units

A

Page 13: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Fig 21.14 The concentration dependence of the molar conductivities of (a) a strong and (b) a weak electrolyte

Λm = κ/c

• Strong electrolyte – molar conductivitydepends only slightly on concentration

• Weak electrolyte – molar conductivity is normal at very low concentrations but fallssharply to low values at high concentrations

Page 14: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Weak electrolyte solutions

• Only slightly dissociated in solution

• The marked concentration dependence of their molar conductivities arises from displacement of the equilibrium

towards products a low concentrations

HA (aq) + H2O (l) ⇌ H3O+ (aq) + A− (aq)

where α ≡ degree of dissociation

α

α

1

c

]HA[

]A][OH[K

23

a

Page 15: Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio

Weak electrolyte solutions

• At infinite dilution, the weak acid is fully dissociated (α = 100%)

• ∴ Its molar conductivity is

• At higher concentrations α << 100% and molar conductivity is

omΛ

omm ΛΛ α