Chapter 21 Molecular motion in liquids

Summary of Midterm I Class average 78%; Lowest 25%; highest 96% A+ 12 students A 17 students A- 15 students B+ 6 students B 4 students B- 6 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: 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.

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)

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

Ostwald’s dilution law

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

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. The limiting transport number, t0±, is defined for the limit of zero concentration of the electrolyte solution.

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

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