Peter Atkins • Julio de Paula
Atkins’ Physical Chemistry
Eighth Edition
Chapter 21 – Lecture 2
Molecules in Motion
Copyright © 2006 by Peter Atkins and Julio de Paula
Homework Set # 21
Atkins & de Paula, 8e
Chap 21 (pp 748 - 764 only)
Exercises: all part (b) unless noted:
2, 6, 7, 8, 11, 13, 15, 17
Objectives:
• Describe the motion of all types of particles in all types
of fluids
• Concentrate of transportation properties:
• Diffusion ≡ migration of matter down a concentration
gradient
• Thermal conduction ≡ migration of energy down a
temperature gradient
• Electrical conduction ≡ migration of charge along a
potential gradient
• Viscosity ≡ migration of linear momentum down a velocity
gradient
Fig 21.10 The flux of particles down a concentration gradient
Fick’s first law of diffusion:
If the concentration gradient
varies steeply with position,
then diffusion will be fast
The Phenomenological Equations
• Flux (J) ≡ the quantity of that property passing through
a 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:
J(matter )  D
dN
dz
• where D ≡ diffusion coefficient in m-2 s-1
The Phenomenological Equations
• Since energy flows from high to low temperature:
dT
J(energy)  κ
dz
• where κ ≡ coefficient of thermal conductivity
in J K-1 m-1 s-1
Fig 21.11 The viscosity of a fluid arises from the transport
of linear momentum
Laminar (smooth) flow:
• If the entering layer has high
linear momentum, it accelerates
the layer
• If the entering layer has low
linear momentum, it retards
the layer
The Phenomenological Equations
dv x
J(x  momentum)   η
dz
• where η ≡ coefficient of viscosity in kg m-1 s-1
 8RT 
c

 πM 
1
2
So the viscosity of
a gas increases with
temperature!
Molecular Motion in Liquids
Fig 21.13 The experimental temperature dependence of water
ηe
Ea
RT
As the temperature is
increased, more molecules
are able to escape from the
potential wells of their
neighbors; the liquid then
becomes more fluid
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:
κA
G

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
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 conductivity
depends only slightly on concentration
• Weak electrolyte – molar conductivity is
normal at very low concentrations but falls
sharply to low values at high concentrations
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)
[H3 O  ][ A  ] α 2 c
Ka 

[HA ]
1 α
where α ≡ degree of dissociation
Weak electrolyte solutions
• At infinite dilution, the weak acid is fully dissociated (α = 100%)
o
• ∴ Its molar conductivity is Λ m
• At higher concentrations α << 100% and molar conductivity is
Λm  αΛom