PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 364

Note:The term molar conductivity is often used also for the conductivity related to unit

concentration of the fractions of molecules and ions containing one positive or negative

charge (e.g. 1/2 H 2 SO 4 , 1/3 Fe3+, 1/3 [Fe(CN) 6 ]^3 −), in older literature, referred to as the

equivalent conductivityΛeandequivalent conductivity of ions, defined by the

relations

Λe=

Λ

z+ν+

=

Λ

z−ν−

, Λ+e,∞=

Λ+∞

z+

, Λ−e,∞=

Λ−∞

z−

. (11.29)

Thus, e.g., Λe(1/3 Fe3+)= 1/3 Λ(Fe3+) and Λe = (1/2 H 2 SO 4 ) = (1/2) Λ(H 2 SO 4 ).

Kohlrausch’s law of the independent migration of ions then acquires the form

Λe,∞= Λ+e,∞+ Λ−e,∞. (11.30)

It has to be checked whether the tables we use give molar or equivalent conductivities.

11.3.5 Molar conductivity and the degree of dissociation

The following relation applies between the molar conductivity, the degree of dissociation and
the ionic mobility.
Λ =αF

(

ν+z+u++ν−z−u−

)

. (11.31)

If we use the same relation at an infinite dilution, whereα= 1, and neglect the concentra-
tion dependence of the ionic mobility, we obtain theArrhenius relationfor the degree of
dissociation

α=

Λ

Λ∞

. (11.32)

11.3.6 Molar conductivity and transport numbers

The following relations apply at infinite dilution

Λ+∞=Fz+u+, Λ−∞=Fz−u−. (11.33)

Their combination with equations (11.16) yields relations for transport numbers at infinite
dilution

t+∞=

ν+Λ+∞

Λ∞

, t−∞=

ν−Λ−∞

Λ∞

. (11.34)