atkins’ physical chemistry eighth edition chapter 21 – lecture 2 molecules in motion copyright...
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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
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
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
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
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
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
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
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
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
eη
Molecular Motion in Liquids
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
Gκ
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
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
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