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

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