The conductance of 0.1 M acetic acid at 298 K is 5.20 and that of 0.001 M acetic acid is 49.2. The ionic molar conductivity at infinite dilution of acetate and hydrogen ions are 349.8 and 40.9 S cm2 mol-1 resp. Calculate the degree of dissociation of acetic acid at these concentrations.

Sir, how to solve this.. and the conductances given in the first statement may be confused with conductivities because with dilution, it has decreased.. right sir?? or not??

The degree of dissociation of a weak electrolyte is given by the following relation

 α = Λ / Λ⁰

where α is the degree of dissociation of the electrolyte, Λ is the molar conductivity and Λ⁰ is the limiting molar conductivity. 

We are given that the ionic molar conductivity at infinite dilution of acetate and hydrogen ions are 349.8 and 40.9 S cm² mol^-1 respectively. Hence the limiting molar conductivity of acetic acid would be written as 

 Λ⁰ _{acetic acid}  = λ⁰(H⁺) + λ⁰(CH₃COO^- )

 = 40.9 + 349.8

 = 390.7 cm² mol^-1

The Λ for an electrolyte is given by 

 Λ = κ / c

where κ is the conductivity of the solution and c is the concentration of the solution containing the electrolyte. However in the given example, we have been given conductance, and not conductivity. The relation between conductance and conductivity is written as follows

 κ = G X (l / A)

 where G is the conductance and (l / A) is the cell constant. Hence in order to calculate the degree of dissociation, we need to know the cell constant of the reaction. By knowing the cell constant, we can calculate the conductivity κ and hence the molar conductivity.

Also note that while conductivity decreases with increase in dilution, molar conductivity increases with increase in dilution.