Conductance and ionic speeds

Since the conductivity of an electrolyte is a measure of the current it can carry, and therefore of the rate of charge transfer, it is also a function of the rate with which the constituent ions carry their charge through a solution. This rate depends upon the concentration and valency of the ions as well as upon their speeds. 

Movement of ions through a solution is induced by the imposition of an electric field - a consequence of the applied potential between the electrodes. The electric field force experienced by an ion causes it to accelerate. This acceleration, however, is opposed by the retarding forces of the asymmetry and electrophoretic effects as well as by the solvent viscosity, so that an ion ultimately moves with a uniform velocity determined by a balance of these opposing forceg. For a concentration c of a 1 1 strong electrolyte the concentration of cations, c+, is equal to that of anions, c. If the speeds of cations and anions are, respectively, u+ and u, the amount of charge crossing unit area of solution in unit time is 

the speeds with which ions move are linear functions of the field intensity F so that 

This may further be expressed in terms of the conductivity or molar conductivity Kc, Ac for a concentration c moles per cm, for since 

Equations (4.16) and (4.17) are valid for both strong and weak electrolytes at infinite dilution. Sometimes equivalent ion conductances are termed mobilities since they may be expressed as the product of an ion speed and the faraday. Equation (4.17) enables us to calculate the speeds with which ions move under the influence of an applied field when their conductivities are known. For instance, if X+° = 50 ohm cm equiv .  

---