Physical Chemistry Third Edition

480 10 Transport Processes

Some cations with a small radius, such as the lithium ion, have somewhat lower

mobilities and larger effective radii than might be expected. Small cations are more

strongly hydrated (more strongly bound to water molecules) than larger cations, because

water molecules can approach closely to the center of charge of the smaller ion. These

strongly bound water molecules are likely to be carried along with the ions, increasing

the apparent size of the ions.

Exercise 10.21

Calculate the effective radius of the lithium ion from its ion mobility.

Themolar conductivityof an electrolyte solute is denoted byΛand is defined by

Λ

σ

c

(10.5-25)

wherecis the stoichiometric concentration of the electrolyte in mol m−^3 or mol L−^1.

For complete dissociation Eq. (10.5-24) gives

Λ

σ

c

F(ν+z+u++ν−|z−|u−) (10.5-26)

At fairly small concentrations the molar conductivity of a strong electrolyte is found

to depend linearly on the square root of the concentration:

ΛΛ 0 −Ac^1 /^2 (10.5-27)

whereAis a parameter depending on the temperature and identities of all ions present.

This equation was discovered empirically by Kohlrausch in 1900. In the limit of

infinite dilution,Λapproaches a constant limit, just as do the mobility and friction

coefficient:

Λ 0 lim

c→ 0

Λ (10.5-28)

The value at infinite dilution,Λ 0 , is called thelimiting molar conductivity.

The conductivity contains a term for the cation and a term for the anion, so the molar

conductivity can be written as a sum. For a uni-univalent electrolyte

Λλ++λ− (10.5-29)

Λ 0 (λ+) 0 +(λ−) 0 (10.5-30)

where (λ+) 0 and (λ−) 0 are the limiting molar conductivities of the ions. Equation

(10.5-30) was established around 1875 by Kohlrausch. Equations (10.5-27) and

(10.5-30) are known asKohlrausch’s laws. The limiting molar conductivities for the

ions can be separately tabulated, making it possible to construct a shorter table than if

values for neutral electrolytes were tabulated. Table A.20 contains values of limiting

molar conductivities of several ions in water at 25◦C.

Kohlrausch’s laws are named for
Friedrich Wilhelm Georg Kohlrausch,
1840–1910, who was probably the
greatest experimental physicist of the
19th century. He studied many electric
and magnetic phenomena as well as
electrolyte conduction and the
autoionization of water.