Degree of Dissociation of Weak Electrolyte and its Dissociation Constant:

Conductivity values can be used for calculating degree of dissociation. Let's recapitulate equilibrium constants of weak acid and bases. When a weak acid or a weak base dissolved in water, partial dissociation occurs.

For a weak acid HA, equilibrium state can be represented as:

HA    ?      H⁺   + A^-

Initial concentrations                       c          0          0

Equilibrium concentrations           c (1- α)           cα        cα

while c is the concentration of the acid and α is the degree of dissociation or degree of ionization.

The thermodynamic equilibrium constant (that in this case in an acid dissociation constant, K_a) is written as

K_a= (a_H+ a_A-)/a_HA ≈ [H⁺][A^-]/[HA]

From Eq. 6.1, it clears that,

[HA] =  (1- α) c  and  [H⁺]  =  [A ^- ]  =  αc

Substitute these vales in Eq. (6.2)

K_a = α ² c/ (1 - α)

Eq. (6.3) is termed as Ostwal's dilution law.