1. Chapter 21 Molecular motion in liquids

2. Summary of Midterm I Class average 78%; Lowest 25%; highest 96%
A students
A students
A students
B students
B students
B students
F students

3. 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

4. Temperature dependence of the viscosity of water
This is opposite to the gases, where the viscosity increases with temperature

5. 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:
k is the conductivity (Sm-1).
Molar conductivity, Λm, is defined as:
c is the molar concentration
Λm varies with the concentration due to two reasons:
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.

7. 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:
Λ0m , the limiting molar conductivity, can be expressed as the sum of contributions from its individual ions:
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)

8. 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
Since only fraction, α, of electrolyte is actually presents as ions, the measured conductivity Λm, is given by:
Λm = αΛ0m

9. Ostwald’s dilution law

10. 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, a is the hydrodynamic radius
Introducing a new quantity, the mobility of an ion:
Then

11. 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

12. Transport numbers
Is defined as the fraction of total current carried by the ions of a specified type.
The limiting transport number, t0±, is defined for the limit of zero concentration of the electrolyte solution.

13. The measurement of transport numbers
Moving boundary method
Indicator solution
Leading solution

14. Conductivities and ion-ion interactions
To explain the c1/2 dependence in the Kohlrausch law.