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 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 measure conductivity Λm, is given by: Λm = αΛ0m

Ostwald’s dilution law

24.7 The mobility of ions Drift speed: 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 Ffric = (6πηa)s, a is the hydrodynamic radius Mobility of an ion: u is called the mobility of the ion

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 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.

Hückel-Onsager Theory