Electrochemistry | Variation of Conductivity and Molar Conductivity with Concentration#

Conductivity#

The conductivity of a solution at any given concentration is the conductance of one unit volume of solution kept between platinum electrodes with unit area of cross-section and at a distance of unit length.

\[G = { ΚA \over l} = Κ\]

Conductivity always decreases with decrease in concentration both for weak and strong electrolyte because the number of ions per unit volume that carry the current in a solution decreases on dilution.

Molar conductivity of a solution at a given concentration is the conductance of the volume V of solution containing one mole of electrolyte kept between two electrodes with area of cross section A and distance of unit length.
Molar conductivity is also defined as the conductivity of solution per unit its concentration.

\[ λ_m = {Κ \over C}\]

\[ λ_m = {Κ \over {n \over V}}\]

\[ ∴ λ_m = {Κ V \over n} \]

Molar conductivity increases with decrease in concentration because $λ_m ∝ {1 \over C}$.
It has been found that decrease in conductivity on dilution of a solution is more than compensated by increase in its volume. Physically, it means that at a given concentration, λ_m can be defined as the conductance of the electrolytic solution kept between the electrodes of a conductivity cell at a unit distance but having area of cross-section large enough to accommodate sufficient volume of solution that contains one mole of the electrolyte.
Limiting Molar Conductivity: When the concentration approaches zero, the molar conductivity is known as limiting molar conductivity and is represented by $λ^0_m$.
The variation of molar conductivity, λ_m with concentration is different for strong and weak electrolytes.

For strong electrolytes, λ_m increases slowly with dilution and can be represented by the equation:

\[ λ_m = λ^0_m - AC^{1/2} \]

Here, intercept = $λ^0_m$ and slope = A

The value of 'A' for a given solvent and temperature depends on the type of electrolyte, ie, charges on the cation and anion produced on the dissociation of the electrolyte in the solution.
NaCl, CaCl₂, MgSO₄ are 1-1, 2-1 and 2-2 electrolytes respectively. All electrolytes of particular type have the same value for 'A'.

It states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte.
In general, if an electrolyte on dissociation gives $ ν+ $ cations and $ ν- $ anions, then its limiting molar conductivity is given by:

\[ λ^0_m = ν_+ λ^0_+ + ν_- λ^0_- \]

Here, $λ^0_+$ = Limiting molar conductivity of cation and $λ^0_-$ = Limiting molar conductivity of anion

For weak electrolytes, molar conductivity (λ_m) increases steeply on dilution, especially near lower concentrations. Therefore, limiting molar conductivity (λ⁰_m) cannot be obtained by extrapolation of λ_m to zero concentration.
At infinite dilution (i.e, concentration → 0), electrolyte dissociates completely (α=1) but at such low concentration, the conductivity of the solution cannot be measured accurately.
Therefore, λ⁰_m for weak electrolytes is obtained by using Kohlrausch law of independent migration of ions.
At any concentration C, if α is the degree of dissociation, then it can be approximated to the ratio of molar conductivity λ_m at the concentration C to limiting molar conductivity λ⁰_m.

\[ α = {λ_m \over λ^0_m} \]

\[CH_3COOH ⇌ CH_3COO^- + H^+\]

At time t = 0, let concentration of CH₃COOH = c and concentration of CH₃COO^- and H⁺ = 0.

If α is the degree of dissociation, at time t = t, concentration of CH₃COOH = c-cα and concentration of CH₃COO^- and H⁺ = cα

Dissociation constant, K_a is given by:

\[K_a = {[CH_3COO^-] [H^+] \over [CH_3COOH]}\]

\[K_a = {cα \times cα \over c-cα}\]

\[K_a = {cα^2 \over (1-α)}\]

\[where, α = {λ_m \over λ^0_m}\]