Chapter 21
Molecular motion in liquids
Summary of Midterm I
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Class average 78%;
Lowest 25%; highest 96%
A+ 12 students
A
17 students
A15 students
B+
6 students
B
4 students
B6 students
F
3 students
21.5 Experimental results
• Measuring techniques: NMR, ESR, inelastic neutron scattering, etc.
• Big molecules in viscous fluids typically rotate in a series of small (5o)
steps.
• Small molecules in nonviscous fluid typically jump through about 1
radian (57o).
• For a molecule to move in liquid, it must acquire at least a minimum
energy to escape from its neighbors.
• The change in density has pronounced influence on the viscosity.
• The probability that a molecule has at least an energy Ea is
proportional to e-Ea/RT.
• Viscosity, η, is inversely proportional to the mobility of the particles,
η ∞ eEa/RT
Temperature dependence of the
viscosity of water
This is opposite to the gases, where the viscosity increases with temperature
24.6 The conductivities of electrolyte
solutions
•
Conductance (G, siemens) of a solution sample decreases with its
length l and increases with its cross-sectional area A:
G
•
kA
l
k is the conductivity (Sm-1).
Molar conductivity, Λm, is defined as:
m 
k
c
c is the molar concentration
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Λm varies with the concentration due to two reasons:
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Based on the concentration dependence of molar conductivities,
electrolytes can be classified into two categories:
1. Strong electrolyte: its molar conductivity depends only
slightly on the molar concentration.
2. Weak electrolyte: its molar conductivity is normal at diluted
environment, but falls sharply as the concentration increases.
Strong electrolyte
•
Strong electrolyte is virtually fully ionized in solution, such as ionic solid,
strong acids and bases.
•
According to Kohlrausch’s law, the molar conductivity of strong
electrolyte varies linearly with the square root of the concentration:
 m  0m
•
 c1 / 2
Λ0m , the limiting molar conductivity, can be expressed as the sum of
contributions from its individual ions:
0m  v    v  
where v+ and v- are the numbers of cations and anions per formula
unit. (For example: HCl: v+ = 1 and v- = 1; MgCl2, v+ = 1 and v- = 2)
Weak electrolyte
• Weak electrolytes are not fully ionized in solution, such as weak
acids and bases.
• Degree of ionization (α): defined as the ratio of the amount of ions
being formed in the solution and the amount of electrolyte added to
the solution.
•
For the acid HA at a molar concentration c,
[H3O+] = αc,
[A-] = αc ,
[HA] = c –αc
K
a a
2c
1/ 2


4c 


  1
 1 
Ka 




• Since only fraction, α, of electrolyte is actually presents as ions, the
measured conductivity Λm, is given by:
Λm = αΛ0m
Ostwald’s dilution law
1
1
 0
m m

mc
K a 0m 
2
24.7 The mobility of ions
• Drift speed (s): the terminal speed reached when the accelerating
force is balanced by the viscous drag.
• Accelerating force induced by a uniform electric field (E = Δø/l):
F = z e E = z e Δø/l
• Friction force (Stokes formula) Ffric = (6πηa)s,
hydrodynamic radius
a is the
• Introducing a new quantity, the mobility of an ion:
u
• Then
ze
6 a
Mobility and conductivity
• λ = z u F ( λ is an ion’s molar conductivity)
• For the solution:
Λ0m = (z+u+v+ + z-u-v-) F
Transport numbers
•
Is defined as the fraction of total current carried by the ions of a
specified type.
I
t 
I
•
t 
I
I
The limiting transport number, t0±, is defined for the limit of zero
concentration of the electrolyte solution.
t 0 
z v  u
z v  u  zv  u
v 
t 
v   v 
0

The measurement of transport
numbers
• Moving boundary method
• Indicator solution
• Leading solution
z  clAF
t 
It
Conductivities and ion-ion
interactions
• To explain the c1/2 dependence in the
Kohlrausch law.