Solution:

Given:
Concentration of weak base, [BoH] = 0.03 M
Specific conductance, κ = 1.5 × 10^-4 S cm^-1
Molar conductance at infinite dilution, λ° = 250 S cm^2 mol^-1

To find:
Ionization constant of weak base, Kb
pH of the solution

Calculation:

1. Calculation of molar conductance, λm
Molar conductance, λm = κ / [BoH]
λm = 1.5 × 10^-4 / 0.03
λm = 5 × 10^-3 S cm^2 mol^-1

2. Calculation of degree of dissociation, α
The degree of dissociation of a weak base is given by the formula:
α = λm / λ°

Substituting the given values, we get:
α = 5 × 10^-3 / 250
α = 2 × 10^-5

3. Calculation of concentration of OH- ions, [OH^-]
Since the weak base BoH dissociates in water as:
BoH + H2O ⇌ Bo^- + H3O^+

We can write the equilibrium constant, Kb as:
Kb = [Bo^-] [H3O^+] / [BoH]

At equilibrium, the concentration of [Bo^-] and [BoH] are approximately equal. Therefore, we can write:
Kb = [H3O^+] α^2 / (1 - α)

Substituting the given values, we get:
Kb = [H3O^+] (2 × 10^-5)^2 / (1 - 2 × 10^-5)

4. Calculation of pH
The concentration of [H3O^+] can be calculated using the formula:
pH = -log [H3O^+]

Substituting the value of [H3O^+] in the above equation, we get:
pH = -log (Kb (1 - α) / α^2)

Substituting the values, we get:
pH = -log [(Kb (1 - 2 × 10^-5) / (2 × 10^-5)^2]
pH = 10.27

Therefore, the ionization constant of the weak base BoH is 5.5 × 10^-8 and the pH of the solution is 10.27.

Explanation:

In this problem, we are given the specific conductance of a solution of weak base BoH and we are asked to find out the ionization constant of the weak base and the pH of the solution.

The specific conductance of a solution is the conductance of a solution of unit volume and unit concentration. It is a measure of the ability of the solution to conduct electricity. The molar conductance of a solution is the conductance of a solution of unit volume and molar concentration.

The molar conductance of a weak electrolyte increases as the dilution of the solution increases. At infinite dilution, the molar conductance of a weak electrolyte becomes equal to the sum of the molar conductances of its ions. Therefore, the molar conductance at infinite dilution, λ°, is a measure of the maximum conductivity of a